TSTP Solution File: SWW100+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW100+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 20:57:46 EDT 2022
% Result : Theorem 45.49s 29.59s
% Output : Proof 45.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SWW100+1 : TPTP v8.1.0. Released v5.2.0.
% 0.11/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Sep 4 11:29:10 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 45.49/29.59 % SZS status Theorem
% 45.49/29.59 % SZS output start Proof
% 45.49/29.59 tff(false_type, type, (
% 45.49/29.59 false: $i)).
% 45.49/29.59 tff(not1_type, type, (
% 45.49/29.59 not1: $i > $i)).
% 45.49/29.59 tff(phi_type, type, (
% 45.49/29.59 phi: $i > $i)).
% 45.49/29.59 tff(d_type, type, (
% 45.49/29.59 d: $i > $o)).
% 45.49/29.59 tff(err_type, type, (
% 45.49/29.59 err: $i)).
% 45.49/29.59 tff(true_type, type, (
% 45.49/29.59 true: $i)).
% 45.49/29.59 tff(lazy_impl_type, type, (
% 45.49/29.59 lazy_impl: ( $i * $i ) > $i)).
% 45.49/29.59 tff(impl_type, type, (
% 45.49/29.59 impl: ( $i * $i ) > $i)).
% 45.49/29.59 tff(prop_type, type, (
% 45.49/29.59 prop: $i > $i)).
% 45.49/29.59 tff(bool_type, type, (
% 45.49/29.59 bool: $i > $o)).
% 45.49/29.59 tff(f2_type, type, (
% 45.49/29.59 f2: ( $i * $i * $i ) > $i)).
% 45.49/29.59 tff(apply_type, type, (
% 45.49/29.59 apply: ( $i * $i ) > $i)).
% 45.49/29.59 tff(tptp_fun_X_4_type, type, (
% 45.49/29.59 tptp_fun_X_4: ( $i * $i ) > $i)).
% 45.49/29.59 tff(tptp_fun_P_7_type, type, (
% 45.49/29.59 tptp_fun_P_7: $i)).
% 45.49/29.59 tff(tptp_fun_X_3_type, type, (
% 45.49/29.59 tptp_fun_X_3: $i > $i)).
% 45.49/29.59 tff(exists2_type, type, (
% 45.49/29.59 exists2: $i > $i)).
% 45.49/29.59 tff(exists1_type, type, (
% 45.49/29.59 exists1: $i > $i)).
% 45.49/29.59 tff(forallprefers_type, type, (
% 45.49/29.59 forallprefers: ( $i * $i ) > $o)).
% 45.49/29.59 tff(f7_type, type, (
% 45.49/29.59 f7: $i > $i)).
% 45.49/29.59 tff(tptp_fun_P_6_type, type, (
% 45.49/29.59 tptp_fun_P_6: $i)).
% 45.49/29.59 tff(false2_type, type, (
% 45.49/29.59 false2: $i)).
% 45.49/29.59 tff(f4_type, type, (
% 45.49/29.59 f4: ( $i * $i * $i ) > $i)).
% 45.49/29.59 tff(tptp_fun_R_5_type, type, (
% 45.49/29.59 tptp_fun_R_5: $i > $i)).
% 45.49/29.59 tff(f5_type, type, (
% 45.49/29.59 f5: ( $i * $i ) > $i)).
% 45.49/29.59 tff(f6_type, type, (
% 45.49/29.59 f6: ( $i * $i ) > $i)).
% 45.49/29.59 tff(existsprefers_type, type, (
% 45.49/29.59 existsprefers: ( $i * $i ) > $o)).
% 45.49/29.59 tff(f1_type, type, (
% 45.49/29.59 f1: ( $i * $i * $i ) > $i)).
% 45.49/29.59 tff(1,plain,
% 45.49/29.59 (d(false) <=> d(false)),
% 45.49/29.59 inference(rewrite,[status(thm)],[])).
% 45.49/29.59 tff(2,axiom,((d(true) & d(false)) & d(err)), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','false_true_err_in_d')).
% 45.49/29.59 tff(3,plain,
% 45.49/29.59 (d(true) & d(false)),
% 45.49/29.59 inference(and_elim,[status(thm)],[2])).
% 45.49/29.59 tff(4,plain,
% 45.49/29.59 (d(false)),
% 45.49/29.59 inference(and_elim,[status(thm)],[3])).
% 45.49/29.59 tff(5,plain,
% 45.49/29.59 (d(false)),
% 45.49/29.59 inference(modus_ponens,[status(thm)],[4, 1])).
% 45.49/29.59 tff(6,plain,
% 45.49/29.59 ((d(false) | (~(phi(false) = err))) | (~d(false))),
% 45.49/29.59 inference(tautology,[status(thm)],[])).
% 45.49/29.59 tff(7,plain,
% 45.49/29.59 (d(false) | (~(phi(false) = err))),
% 45.49/29.59 inference(unit_resolution,[status(thm)],[6, 5])).
% 45.49/29.59 tff(8,plain,
% 45.49/29.59 (^[X: $i] : refl(((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err))))) <=> ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err))))))),
% 45.49/29.59 inference(bind,[status(th)],[])).
% 45.49/29.59 tff(9,plain,
% 45.49/29.59 (![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err))))) <=> ![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 45.49/29.59 inference(quant_intro,[status(thm)],[8])).
% 45.49/29.59 tff(10,plain,
% 45.49/29.59 (^[X: $i] : trans(monotonicity(rewrite((d(X) & (phi(X) = X)) <=> (~((~d(X)) | (~(phi(X) = X))))), rewrite(((~d(X)) & (phi(X) = err)) <=> (~(d(X) | (~(phi(X) = err))))), (((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err))) <=> ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err))))))), rewrite(((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err))))) <=> ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))), (((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err))) <=> ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))))),
% 45.49/29.59 inference(bind,[status(th)],[])).
% 45.49/29.59 tff(11,plain,
% 45.49/29.59 (![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err))) <=> ![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 45.49/29.59 inference(quant_intro,[status(thm)],[10])).
% 45.49/29.59 tff(12,plain,
% 45.49/29.59 (![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err))) <=> ![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err)))),
% 45.49/29.59 inference(rewrite,[status(thm)],[])).
% 45.49/29.59 tff(13,axiom,(![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','def_phi')).
% 45.49/29.59 tff(14,plain,
% 45.49/29.59 (![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err)))),
% 45.49/29.59 inference(modus_ponens,[status(thm)],[13, 12])).
% 45.49/29.59 tff(15,plain,(
% 45.49/29.59 ![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err)))),
% 45.49/29.59 inference(skolemize,[status(sab)],[14])).
% 45.49/29.59 tff(16,plain,
% 45.49/29.59 (![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 45.49/29.59 inference(modus_ponens,[status(thm)],[15, 11])).
% 45.49/29.60 tff(17,plain,
% 45.49/29.60 (![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[16, 9])).
% 45.49/29.60 tff(18,plain,
% 45.49/29.60 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(false)) | (~(phi(false) = false)))) | (~(d(false) | (~(phi(false) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(false)) | (~(phi(false) = false)))) | (~(d(false) | (~(phi(false) = err)))))),
% 45.49/29.60 inference(rewrite,[status(thm)],[])).
% 45.49/29.60 tff(19,plain,
% 45.49/29.60 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(false)) | (~(phi(false) = false)))) | (~(d(false) | (~(phi(false) = err)))))),
% 45.49/29.60 inference(quant_inst,[status(thm)],[])).
% 45.49/29.60 tff(20,plain,
% 45.49/29.60 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(false)) | (~(phi(false) = false)))) | (~(d(false) | (~(phi(false) = err))))),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[19, 18])).
% 45.49/29.60 tff(21,plain,
% 45.49/29.60 (~((~d(false)) | (~(phi(false) = false)))),
% 45.49/29.60 inference(unit_resolution,[status(thm)],[20, 17, 7])).
% 45.49/29.60 tff(22,plain,
% 45.49/29.60 (((~d(false)) | (~(phi(false) = false))) | (phi(false) = false)),
% 45.49/29.60 inference(tautology,[status(thm)],[])).
% 45.49/29.60 tff(23,plain,
% 45.49/29.60 (phi(false) = false),
% 45.49/29.60 inference(unit_resolution,[status(thm)],[22, 21])).
% 45.49/29.60 tff(24,plain,
% 45.49/29.60 (^[B: $i] : refl((lazy_impl(not1(false), B) = phi(B)) <=> (lazy_impl(not1(false), B) = phi(B)))),
% 45.49/29.60 inference(bind,[status(th)],[])).
% 45.49/29.60 tff(25,plain,
% 45.49/29.60 (![B: $i] : (lazy_impl(not1(false), B) = phi(B)) <=> ![B: $i] : (lazy_impl(not1(false), B) = phi(B))),
% 45.49/29.60 inference(quant_intro,[status(thm)],[24])).
% 45.49/29.60 tff(26,plain,
% 45.49/29.60 (^[B: $i] : rewrite((lazy_impl(true, B) = phi(B)) <=> (lazy_impl(not1(false), B) = phi(B)))),
% 45.49/29.60 inference(bind,[status(th)],[])).
% 45.49/29.60 tff(27,plain,
% 45.49/29.60 (![B: $i] : (lazy_impl(true, B) = phi(B)) <=> ![B: $i] : (lazy_impl(not1(false), B) = phi(B))),
% 45.49/29.60 inference(quant_intro,[status(thm)],[26])).
% 45.49/29.60 tff(28,plain,
% 45.49/29.60 (![B: $i] : (lazy_impl(true, B) = phi(B)) <=> ![B: $i] : (lazy_impl(true, B) = phi(B))),
% 45.49/29.60 inference(rewrite,[status(thm)],[])).
% 45.49/29.60 tff(29,axiom,(![B: $i] : (lazy_impl(true, B) = phi(B))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','lazy_impl_axiom3')).
% 45.49/29.60 tff(30,plain,
% 45.49/29.60 (![B: $i] : (lazy_impl(true, B) = phi(B))),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[29, 28])).
% 45.49/29.60 tff(31,plain,
% 45.49/29.60 (![B: $i] : (lazy_impl(not1(false), B) = phi(B))),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[30, 27])).
% 45.49/29.60 tff(32,plain,(
% 45.49/29.60 ![B: $i] : (lazy_impl(not1(false), B) = phi(B))),
% 45.49/29.60 inference(skolemize,[status(sab)],[31])).
% 45.49/29.60 tff(33,plain,
% 45.49/29.60 (![B: $i] : (lazy_impl(not1(false), B) = phi(B))),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[32, 25])).
% 45.49/29.60 tff(34,plain,
% 45.49/29.60 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), false) = phi(false))),
% 45.49/29.60 inference(quant_inst,[status(thm)],[])).
% 45.49/29.60 tff(35,plain,
% 45.49/29.60 (lazy_impl(not1(false), false) = phi(false)),
% 45.49/29.60 inference(unit_resolution,[status(thm)],[34, 33])).
% 45.49/29.60 tff(36,plain,
% 45.49/29.60 (d(true) <=> d(not1(false))),
% 45.49/29.60 inference(rewrite,[status(thm)],[])).
% 45.49/29.60 tff(37,plain,
% 45.49/29.60 (d(true) <=> d(true)),
% 45.49/29.60 inference(rewrite,[status(thm)],[])).
% 45.49/29.60 tff(38,plain,
% 45.49/29.60 (d(true)),
% 45.49/29.60 inference(and_elim,[status(thm)],[3])).
% 45.49/29.60 tff(39,plain,
% 45.49/29.60 (d(true)),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[38, 37])).
% 45.49/29.60 tff(40,plain,
% 45.49/29.60 (d(not1(false))),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[39, 36])).
% 45.49/29.60 tff(41,plain,
% 45.49/29.60 ((d(not1(false)) | (~(phi(not1(false)) = err))) | (~d(not1(false)))),
% 45.49/29.60 inference(tautology,[status(thm)],[])).
% 45.49/29.60 tff(42,plain,
% 45.49/29.60 (d(not1(false)) | (~(phi(not1(false)) = err))),
% 45.49/29.60 inference(unit_resolution,[status(thm)],[41, 40])).
% 45.49/29.60 tff(43,plain,
% 45.49/29.60 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(not1(false))) | (~(phi(not1(false)) = not1(false))))) | (~(d(not1(false)) | (~(phi(not1(false)) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(not1(false))) | (~(phi(not1(false)) = not1(false))))) | (~(d(not1(false)) | (~(phi(not1(false)) = err)))))),
% 45.49/29.60 inference(rewrite,[status(thm)],[])).
% 45.49/29.60 tff(44,plain,
% 45.49/29.60 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(not1(false))) | (~(phi(not1(false)) = not1(false))))) | (~(d(not1(false)) | (~(phi(not1(false)) = err)))))),
% 45.49/29.60 inference(quant_inst,[status(thm)],[])).
% 45.49/29.60 tff(45,plain,
% 45.49/29.60 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(not1(false))) | (~(phi(not1(false)) = not1(false))))) | (~(d(not1(false)) | (~(phi(not1(false)) = err))))),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[44, 43])).
% 45.49/29.60 tff(46,plain,
% 45.49/29.60 (~((~d(not1(false))) | (~(phi(not1(false)) = not1(false))))),
% 45.49/29.60 inference(unit_resolution,[status(thm)],[45, 17, 42])).
% 45.49/29.60 tff(47,plain,
% 45.49/29.60 (((~d(not1(false))) | (~(phi(not1(false)) = not1(false)))) | (phi(not1(false)) = not1(false))),
% 45.49/29.60 inference(tautology,[status(thm)],[])).
% 45.49/29.60 tff(48,plain,
% 45.49/29.60 (phi(not1(false)) = not1(false)),
% 45.49/29.60 inference(unit_resolution,[status(thm)],[47, 46])).
% 45.49/29.60 tff(49,plain,
% 45.49/29.60 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), not1(false)) = phi(not1(false)))),
% 45.49/29.60 inference(quant_inst,[status(thm)],[])).
% 45.49/29.60 tff(50,plain,
% 45.49/29.60 (lazy_impl(not1(false), not1(false)) = phi(not1(false))),
% 45.49/29.60 inference(unit_resolution,[status(thm)],[49, 33])).
% 45.49/29.60 tff(51,plain,
% 45.49/29.60 ((not1(false) = phi(false)) <=> (not1(false) = false)),
% 45.49/29.60 inference(monotonicity,[status(thm)],[23])).
% 45.49/29.60 tff(52,plain,
% 45.49/29.60 ((not1(false) = false) <=> (not1(false) = phi(false))),
% 45.49/29.60 inference(symmetry,[status(thm)],[51])).
% 45.49/29.60 tff(53,plain,
% 45.49/29.60 ((~(not1(false) = false)) <=> (~(not1(false) = phi(false)))),
% 45.49/29.60 inference(monotonicity,[status(thm)],[52])).
% 45.49/29.60 tff(54,plain,
% 45.49/29.60 ((~(true = false)) <=> (~(not1(false) = false))),
% 45.49/29.60 inference(rewrite,[status(thm)],[])).
% 45.49/29.60 tff(55,plain,
% 45.49/29.60 ((~(true = false)) <=> (~(true = false))),
% 45.49/29.60 inference(rewrite,[status(thm)],[])).
% 45.49/29.60 tff(56,axiom,(((~(true = false)) & (~(true = err))) & (~(false = err))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','distinct_false_true_err')).
% 45.49/29.60 tff(57,plain,
% 45.49/29.60 ((~(true = false)) & (~(true = err))),
% 45.49/29.60 inference(and_elim,[status(thm)],[56])).
% 45.49/29.60 tff(58,plain,
% 45.49/29.60 (~(true = false)),
% 45.49/29.60 inference(and_elim,[status(thm)],[57])).
% 45.49/29.60 tff(59,plain,
% 45.49/29.60 (~(true = false)),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[58, 55])).
% 45.49/29.60 tff(60,plain,
% 45.49/29.60 (~(not1(false) = false)),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[59, 54])).
% 45.49/29.60 tff(61,plain,
% 45.49/29.60 (~(not1(false) = phi(false))),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[60, 53])).
% 45.49/29.60 tff(62,plain,
% 45.49/29.60 (^[A: $i] : refl((bool(A) | (not1(A) = phi(A))) <=> (bool(A) | (not1(A) = phi(A))))),
% 45.49/29.60 inference(bind,[status(th)],[])).
% 45.49/29.60 tff(63,plain,
% 45.49/29.60 (![A: $i] : (bool(A) | (not1(A) = phi(A))) <=> ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 45.49/29.60 inference(quant_intro,[status(thm)],[62])).
% 45.49/29.60 tff(64,plain,
% 45.49/29.60 (![A: $i] : (bool(A) | (not1(A) = phi(A))) <=> ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 45.49/29.60 inference(rewrite,[status(thm)],[])).
% 45.49/29.60 tff(65,plain,
% 45.49/29.60 (^[A: $i] : rewrite(((~bool(A)) => (not1(A) = phi(A))) <=> (bool(A) | (not1(A) = phi(A))))),
% 45.49/29.60 inference(bind,[status(th)],[])).
% 45.49/29.60 tff(66,plain,
% 45.49/29.60 (![A: $i] : ((~bool(A)) => (not1(A) = phi(A))) <=> ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 45.49/29.60 inference(quant_intro,[status(thm)],[65])).
% 45.49/29.60 tff(67,axiom,(![A: $i] : ((~bool(A)) => (not1(A) = phi(A)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','not1_axiom1')).
% 45.49/29.60 tff(68,plain,
% 45.49/29.60 (![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[67, 66])).
% 45.49/29.60 tff(69,plain,
% 45.49/29.60 (![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[68, 64])).
% 45.49/29.60 tff(70,plain,(
% 45.49/29.60 ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 45.49/29.60 inference(skolemize,[status(sab)],[69])).
% 45.49/29.60 tff(71,plain,
% 45.49/29.60 (![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[70, 63])).
% 45.49/29.60 tff(72,plain,
% 45.49/29.60 (((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | (bool(false) | (not1(false) = phi(false)))) <=> ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | bool(false) | (not1(false) = phi(false)))),
% 45.49/29.60 inference(rewrite,[status(thm)],[])).
% 45.49/29.60 tff(73,plain,
% 45.49/29.60 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | (bool(false) | (not1(false) = phi(false)))),
% 45.49/29.60 inference(quant_inst,[status(thm)],[])).
% 45.49/29.60 tff(74,plain,
% 45.49/29.60 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | bool(false) | (not1(false) = phi(false))),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[73, 72])).
% 45.49/29.60 tff(75,plain,
% 45.49/29.60 (bool(false) | (not1(false) = phi(false))),
% 45.49/29.60 inference(unit_resolution,[status(thm)],[74, 71])).
% 45.49/29.60 tff(76,plain,
% 45.49/29.60 (bool(false)),
% 45.49/29.60 inference(unit_resolution,[status(thm)],[75, 61])).
% 45.49/29.60 tff(77,plain,
% 45.49/29.60 (^[B: $i] : refl(((~bool(B)) | (impl(false, B) = not1(false))) <=> ((~bool(B)) | (impl(false, B) = not1(false))))),
% 45.49/29.60 inference(bind,[status(th)],[])).
% 45.49/29.60 tff(78,plain,
% 45.49/29.60 (![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false))) <=> ![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))),
% 45.49/29.60 inference(quant_intro,[status(thm)],[77])).
% 45.49/29.60 tff(79,plain,
% 45.49/29.60 (^[B: $i] : rewrite(((~bool(B)) | (impl(false, B) = true)) <=> ((~bool(B)) | (impl(false, B) = not1(false))))),
% 45.49/29.60 inference(bind,[status(th)],[])).
% 45.49/29.60 tff(80,plain,
% 45.49/29.60 (![B: $i] : ((~bool(B)) | (impl(false, B) = true)) <=> ![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))),
% 45.49/29.60 inference(quant_intro,[status(thm)],[79])).
% 45.49/29.60 tff(81,plain,
% 45.49/29.60 (![B: $i] : ((~bool(B)) | (impl(false, B) = true)) <=> ![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 45.49/29.60 inference(rewrite,[status(thm)],[])).
% 45.49/29.60 tff(82,plain,
% 45.49/29.60 (^[B: $i] : rewrite((bool(B) => (impl(false, B) = true)) <=> ((~bool(B)) | (impl(false, B) = true)))),
% 45.49/29.60 inference(bind,[status(th)],[])).
% 45.49/29.60 tff(83,plain,
% 45.49/29.60 (![B: $i] : (bool(B) => (impl(false, B) = true)) <=> ![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 45.49/29.60 inference(quant_intro,[status(thm)],[82])).
% 45.49/29.60 tff(84,axiom,(![B: $i] : (bool(B) => (impl(false, B) = true))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','impl_axiom3')).
% 45.49/29.60 tff(85,plain,
% 45.49/29.60 (![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[84, 83])).
% 45.49/29.60 tff(86,plain,
% 45.49/29.60 (![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[85, 81])).
% 45.49/29.60 tff(87,plain,
% 45.49/29.60 (![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[86, 80])).
% 45.49/29.60 tff(88,plain,(
% 45.49/29.60 ![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))),
% 45.49/29.60 inference(skolemize,[status(sab)],[87])).
% 45.49/29.60 tff(89,plain,
% 45.49/29.60 (![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[88, 78])).
% 45.49/29.60 tff(90,plain,
% 45.49/29.60 (((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | ((~bool(false)) | (impl(false, false) = not1(false)))) <=> ((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | (~bool(false)) | (impl(false, false) = not1(false)))),
% 45.49/29.60 inference(rewrite,[status(thm)],[])).
% 45.49/29.60 tff(91,plain,
% 45.49/29.60 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | ((~bool(false)) | (impl(false, false) = not1(false)))),
% 45.49/29.60 inference(quant_inst,[status(thm)],[])).
% 45.49/29.60 tff(92,plain,
% 45.49/29.60 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | (~bool(false)) | (impl(false, false) = not1(false))),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[91, 90])).
% 45.49/29.60 tff(93,plain,
% 45.49/29.60 (impl(false, false) = not1(false)),
% 45.49/29.60 inference(unit_resolution,[status(thm)],[92, 89, 76])).
% 45.49/29.60 tff(94,plain,
% 45.49/29.60 (lazy_impl(not1(false), impl(false, false)) = lazy_impl(not1(false), not1(false))),
% 45.49/29.60 inference(monotonicity,[status(thm)],[93])).
% 45.49/29.60 tff(95,plain,
% 45.49/29.60 (lazy_impl(not1(false), impl(false, false)) = not1(false)),
% 45.49/29.60 inference(transitivity,[status(thm)],[94, 50, 48])).
% 45.49/29.60 tff(96,plain,
% 45.49/29.60 (impl(lazy_impl(not1(false), impl(false, false)), false) = impl(not1(false), false)),
% 45.49/29.60 inference(monotonicity,[status(thm)],[95])).
% 45.49/29.60 tff(97,plain,
% 45.49/29.60 (impl(not1(false), false) = impl(lazy_impl(not1(false), impl(false, false)), false)),
% 45.49/29.60 inference(symmetry,[status(thm)],[96])).
% 45.49/29.60 tff(98,plain,
% 45.49/29.60 (^[B: $i] : refl(((~bool(B)) | (impl(not1(false), B) = B)) <=> ((~bool(B)) | (impl(not1(false), B) = B)))),
% 45.49/29.60 inference(bind,[status(th)],[])).
% 45.49/29.60 tff(99,plain,
% 45.49/29.60 (![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B)) <=> ![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))),
% 45.49/29.60 inference(quant_intro,[status(thm)],[98])).
% 45.49/29.60 tff(100,plain,
% 45.49/29.60 (^[B: $i] : rewrite(((~bool(B)) | (impl(true, B) = B)) <=> ((~bool(B)) | (impl(not1(false), B) = B)))),
% 45.49/29.60 inference(bind,[status(th)],[])).
% 45.49/29.60 tff(101,plain,
% 45.49/29.60 (![B: $i] : ((~bool(B)) | (impl(true, B) = B)) <=> ![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))),
% 45.49/29.60 inference(quant_intro,[status(thm)],[100])).
% 45.49/29.60 tff(102,plain,
% 45.49/29.60 (![B: $i] : ((~bool(B)) | (impl(true, B) = B)) <=> ![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 45.49/29.60 inference(rewrite,[status(thm)],[])).
% 45.49/29.60 tff(103,plain,
% 45.49/29.60 (^[B: $i] : rewrite((bool(B) => (impl(true, B) = B)) <=> ((~bool(B)) | (impl(true, B) = B)))),
% 45.49/29.60 inference(bind,[status(th)],[])).
% 45.49/29.60 tff(104,plain,
% 45.49/29.60 (![B: $i] : (bool(B) => (impl(true, B) = B)) <=> ![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 45.49/29.60 inference(quant_intro,[status(thm)],[103])).
% 45.49/29.60 tff(105,axiom,(![B: $i] : (bool(B) => (impl(true, B) = B))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','impl_axiom4')).
% 45.49/29.60 tff(106,plain,
% 45.49/29.60 (![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[105, 104])).
% 45.49/29.60 tff(107,plain,
% 45.49/29.60 (![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[106, 102])).
% 45.49/29.60 tff(108,plain,
% 45.49/29.60 (![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[107, 101])).
% 45.49/29.60 tff(109,plain,(
% 45.49/29.60 ![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))),
% 45.49/29.60 inference(skolemize,[status(sab)],[108])).
% 45.49/29.60 tff(110,plain,
% 45.49/29.60 (![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[109, 99])).
% 45.49/29.60 tff(111,plain,
% 45.49/29.60 (((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | ((~bool(false)) | (impl(not1(false), false) = false))) <=> ((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | (~bool(false)) | (impl(not1(false), false) = false))),
% 45.49/29.60 inference(rewrite,[status(thm)],[])).
% 45.49/29.60 tff(112,plain,
% 45.49/29.60 ((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | ((~bool(false)) | (impl(not1(false), false) = false))),
% 45.49/29.60 inference(quant_inst,[status(thm)],[])).
% 45.49/29.60 tff(113,plain,
% 45.49/29.60 ((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | (~bool(false)) | (impl(not1(false), false) = false)),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[112, 111])).
% 45.49/29.60 tff(114,plain,
% 45.49/29.60 (impl(not1(false), false) = false),
% 45.49/29.60 inference(unit_resolution,[status(thm)],[113, 110, 76])).
% 45.49/29.60 tff(115,plain,
% 45.49/29.60 (false = impl(not1(false), false)),
% 45.49/29.60 inference(symmetry,[status(thm)],[114])).
% 45.49/29.60 tff(116,plain,
% 45.49/29.60 (false = impl(lazy_impl(not1(false), impl(false, false)), false)),
% 45.49/29.60 inference(transitivity,[status(thm)],[115, 97])).
% 45.49/29.60 tff(117,plain,
% 45.49/29.60 (^[X: $i] : refl(((prop(X) = not1(false)) <=> bool(X)) <=> ((prop(X) = not1(false)) <=> bool(X)))),
% 45.49/29.60 inference(bind,[status(th)],[])).
% 45.49/29.60 tff(118,plain,
% 45.49/29.60 (![X: $i] : ((prop(X) = not1(false)) <=> bool(X)) <=> ![X: $i] : ((prop(X) = not1(false)) <=> bool(X))),
% 45.49/29.60 inference(quant_intro,[status(thm)],[117])).
% 45.49/29.60 tff(119,plain,
% 45.49/29.60 (^[X: $i] : rewrite(((prop(X) = true) <=> bool(X)) <=> ((prop(X) = not1(false)) <=> bool(X)))),
% 45.49/29.60 inference(bind,[status(th)],[])).
% 45.49/29.60 tff(120,plain,
% 45.49/29.60 (![X: $i] : ((prop(X) = true) <=> bool(X)) <=> ![X: $i] : ((prop(X) = not1(false)) <=> bool(X))),
% 45.49/29.60 inference(quant_intro,[status(thm)],[119])).
% 45.49/29.60 tff(121,plain,
% 45.49/29.60 (![X: $i] : ((prop(X) = true) <=> bool(X)) <=> ![X: $i] : ((prop(X) = true) <=> bool(X))),
% 45.49/29.60 inference(rewrite,[status(thm)],[])).
% 45.49/29.60 tff(122,axiom,(![X: $i] : ((prop(X) = true) <=> bool(X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','prop_true')).
% 45.49/29.60 tff(123,plain,
% 45.49/29.60 (![X: $i] : ((prop(X) = true) <=> bool(X))),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[122, 121])).
% 45.49/29.60 tff(124,plain,
% 45.49/29.60 (![X: $i] : ((prop(X) = not1(false)) <=> bool(X))),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[123, 120])).
% 45.49/29.60 tff(125,plain,(
% 45.49/29.60 ![X: $i] : ((prop(X) = not1(false)) <=> bool(X))),
% 45.49/29.60 inference(skolemize,[status(sab)],[124])).
% 45.49/29.60 tff(126,plain,
% 45.49/29.60 (![X: $i] : ((prop(X) = not1(false)) <=> bool(X))),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[125, 118])).
% 45.49/29.60 tff(127,plain,
% 45.49/29.60 ((~![X: $i] : ((prop(X) = not1(false)) <=> bool(X))) | ((prop(false) = not1(false)) <=> bool(false))),
% 45.49/29.60 inference(quant_inst,[status(thm)],[])).
% 45.49/29.60 tff(128,plain,
% 45.49/29.60 ((prop(false) = not1(false)) <=> bool(false)),
% 45.49/29.60 inference(unit_resolution,[status(thm)],[127, 126])).
% 45.49/29.60 tff(129,plain,
% 45.49/29.60 ((~((prop(false) = not1(false)) <=> bool(false))) | (prop(false) = not1(false)) | (~bool(false))),
% 45.49/29.60 inference(tautology,[status(thm)],[])).
% 45.49/29.60 tff(130,plain,
% 45.49/29.60 ((~((prop(false) = not1(false)) <=> bool(false))) | (prop(false) = not1(false))),
% 45.49/29.60 inference(unit_resolution,[status(thm)],[129, 76])).
% 45.49/29.60 tff(131,plain,
% 45.49/29.60 (prop(false) = not1(false)),
% 45.49/29.60 inference(unit_resolution,[status(thm)],[130, 128])).
% 45.49/29.60 tff(132,plain,
% 45.49/29.60 (not1(false) = prop(false)),
% 45.49/29.60 inference(symmetry,[status(thm)],[131])).
% 45.49/29.60 tff(133,plain,
% 45.49/29.60 (lazy_impl(not1(false), false) = lazy_impl(prop(false), impl(lazy_impl(not1(false), impl(false, false)), false))),
% 45.49/29.60 inference(monotonicity,[status(thm)],[132, 116])).
% 45.49/29.60 tff(134,plain,
% 45.49/29.60 (lazy_impl(prop(false), impl(lazy_impl(not1(false), impl(false, false)), false)) = lazy_impl(not1(false), false)),
% 45.49/29.60 inference(symmetry,[status(thm)],[133])).
% 45.49/29.60 tff(135,plain,
% 45.49/29.60 (^[P: $i, Q: $i, R: $i] : refl((f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R))) <=> (f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R))))),
% 45.49/29.60 inference(bind,[status(th)],[])).
% 45.49/29.60 tff(136,plain,
% 45.49/29.60 (![P: $i, Q: $i, R: $i] : (f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R))) <=> ![P: $i, Q: $i, R: $i] : (f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R)))),
% 45.49/29.60 inference(quant_intro,[status(thm)],[135])).
% 45.49/29.60 tff(137,plain,
% 45.49/29.60 (![P: $i, Q: $i, R: $i] : (f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R))) <=> ![P: $i, Q: $i, R: $i] : (f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R)))),
% 45.49/29.60 inference(rewrite,[status(thm)],[])).
% 45.49/29.60 tff(138,axiom,(![P: $i, Q: $i, R: $i] : (f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','def_f2')).
% 45.49/29.60 tff(139,plain,
% 45.49/29.60 (![P: $i, Q: $i, R: $i] : (f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R)))),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[138, 137])).
% 45.49/29.60 tff(140,plain,(
% 45.49/29.60 ![P: $i, Q: $i, R: $i] : (f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R)))),
% 45.49/29.60 inference(skolemize,[status(sab)],[139])).
% 45.49/29.60 tff(141,plain,
% 45.49/29.60 (![P: $i, Q: $i, R: $i] : (f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R)))),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[140, 136])).
% 45.49/29.60 tff(142,plain,
% 45.49/29.60 ((~![P: $i, Q: $i, R: $i] : (f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R)))) | (f2(not1(false), false, false) = lazy_impl(prop(false), impl(lazy_impl(not1(false), impl(false, false)), false)))),
% 45.49/29.60 inference(quant_inst,[status(thm)],[])).
% 45.49/29.60 tff(143,plain,
% 45.49/29.60 (f2(not1(false), false, false) = lazy_impl(prop(false), impl(lazy_impl(not1(false), impl(false, false)), false))),
% 45.49/29.60 inference(unit_resolution,[status(thm)],[142, 141])).
% 45.49/29.60 tff(144,plain,
% 45.49/29.60 (^[X: $i, Y: $i] : refl((forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false))))))) <=> (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false))))))))),
% 45.49/29.60 inference(bind,[status(th)],[])).
% 45.49/29.60 tff(145,plain,
% 45.49/29.60 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false))))))) <=> ![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))),
% 45.49/29.60 inference(quant_intro,[status(thm)],[144])).
% 45.49/29.60 tff(146,plain,
% 45.49/29.60 (^[X: $i, Y: $i] : rewrite((forallprefers(X, Y) <=> (((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)) | ((X = false) & (Y = not1(false))))) <=> (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false))))))))),
% 45.49/29.60 inference(bind,[status(th)],[])).
% 45.49/29.60 tff(147,plain,
% 45.49/29.60 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)) | ((X = false) & (Y = not1(false))))) <=> ![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))),
% 45.49/29.60 inference(quant_intro,[status(thm)],[146])).
% 45.49/29.60 tff(148,plain,
% 45.49/29.60 (^[X: $i, Y: $i] : rewrite((forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)))) <=> (forallprefers(X, Y) <=> (((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)) | ((X = false) & (Y = not1(false))))))),
% 45.49/29.60 inference(bind,[status(th)],[])).
% 45.49/29.60 tff(149,plain,
% 45.49/29.60 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)))) <=> ![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)) | ((X = false) & (Y = not1(false)))))),
% 45.49/29.60 inference(quant_intro,[status(thm)],[148])).
% 45.49/29.60 tff(150,plain,
% 45.49/29.60 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)))) <=> ![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 45.49/29.60 inference(rewrite,[status(thm)],[])).
% 45.49/29.60 tff(151,plain,
% 45.49/29.60 (^[X: $i, Y: $i] : rewrite((forallprefers(X, Y) <=> ((((~d(X)) & d(Y)) | (((d(X) & d(Y)) & (~bool(X))) & bool(Y))) | ((X = false) & (Y = true)))) <=> (forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)))))),
% 45.49/29.60 inference(bind,[status(th)],[])).
% 45.49/29.60 tff(152,plain,
% 45.49/29.60 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((((~d(X)) & d(Y)) | (((d(X) & d(Y)) & (~bool(X))) & bool(Y))) | ((X = false) & (Y = true)))) <=> ![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 45.49/29.60 inference(quant_intro,[status(thm)],[151])).
% 45.49/29.60 tff(153,axiom,(![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((((~d(X)) & d(Y)) | (((d(X) & d(Y)) & (~bool(X))) & bool(Y))) | ((X = false) & (Y = true))))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','def_forallprefers')).
% 45.49/29.60 tff(154,plain,
% 45.49/29.60 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[153, 152])).
% 45.49/29.60 tff(155,plain,
% 45.49/29.60 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[154, 150])).
% 45.49/29.60 tff(156,plain,
% 45.49/29.60 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)) | ((X = false) & (Y = not1(false)))))),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[155, 149])).
% 45.49/29.60 tff(157,plain,(
% 45.49/29.60 ![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)) | ((X = false) & (Y = not1(false)))))),
% 45.49/29.60 inference(skolemize,[status(sab)],[156])).
% 45.49/29.60 tff(158,plain,
% 45.49/29.60 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[157, 147])).
% 45.49/29.60 tff(159,plain,
% 45.49/29.60 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))),
% 45.49/29.60 inference(modus_ponens,[status(thm)],[158, 145])).
% 45.49/29.60 tff(160,plain,
% 45.49/29.60 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(phi(apply(P!7, tptp_fun_X_3(P!7))), false) <=> ((~((~d(false)) | d(phi(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(false = not1(false))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = false)))) | (~((~d(false)) | (~bool(false)) | (~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | bool(phi(apply(P!7, tptp_fun_X_3(P!7))))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(phi(apply(P!7, tptp_fun_X_3(P!7))), false) <=> ((~((~d(false)) | d(phi(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(false = not1(false))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = false)))) | (~((~d(false)) | (~bool(false)) | (~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | bool(phi(apply(P!7, tptp_fun_X_3(P!7)))))))))),
% 45.51/29.60 inference(rewrite,[status(thm)],[])).
% 45.51/29.60 tff(161,plain,
% 45.51/29.60 ((forallprefers(phi(apply(P!7, tptp_fun_X_3(P!7))), false) <=> ((~(d(phi(apply(P!7, tptp_fun_X_3(P!7)))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(phi(apply(P!7, tptp_fun_X_3(P!7)))) | (~d(phi(apply(P!7, tptp_fun_X_3(P!7))))))) | (~((~(phi(apply(P!7, tptp_fun_X_3(P!7))) = false)) | (~(false = not1(false))))))) <=> (forallprefers(phi(apply(P!7, tptp_fun_X_3(P!7))), false) <=> ((~((~d(false)) | d(phi(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(false = not1(false))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = false)))) | (~((~d(false)) | (~bool(false)) | (~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | bool(phi(apply(P!7, tptp_fun_X_3(P!7))))))))),
% 45.51/29.60 inference(rewrite,[status(thm)],[])).
% 45.51/29.60 tff(162,plain,
% 45.51/29.60 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(phi(apply(P!7, tptp_fun_X_3(P!7))), false) <=> ((~(d(phi(apply(P!7, tptp_fun_X_3(P!7)))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(phi(apply(P!7, tptp_fun_X_3(P!7)))) | (~d(phi(apply(P!7, tptp_fun_X_3(P!7))))))) | (~((~(phi(apply(P!7, tptp_fun_X_3(P!7))) = false)) | (~(false = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(phi(apply(P!7, tptp_fun_X_3(P!7))), false) <=> ((~((~d(false)) | d(phi(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(false = not1(false))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = false)))) | (~((~d(false)) | (~bool(false)) | (~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | bool(phi(apply(P!7, tptp_fun_X_3(P!7)))))))))),
% 45.51/29.60 inference(monotonicity,[status(thm)],[161])).
% 45.51/29.60 tff(163,plain,
% 45.51/29.60 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(phi(apply(P!7, tptp_fun_X_3(P!7))), false) <=> ((~(d(phi(apply(P!7, tptp_fun_X_3(P!7)))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(phi(apply(P!7, tptp_fun_X_3(P!7)))) | (~d(phi(apply(P!7, tptp_fun_X_3(P!7))))))) | (~((~(phi(apply(P!7, tptp_fun_X_3(P!7))) = false)) | (~(false = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(phi(apply(P!7, tptp_fun_X_3(P!7))), false) <=> ((~((~d(false)) | d(phi(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(false = not1(false))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = false)))) | (~((~d(false)) | (~bool(false)) | (~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | bool(phi(apply(P!7, tptp_fun_X_3(P!7)))))))))),
% 45.51/29.60 inference(transitivity,[status(thm)],[162, 160])).
% 45.51/29.60 tff(164,plain,
% 45.51/29.60 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(phi(apply(P!7, tptp_fun_X_3(P!7))), false) <=> ((~(d(phi(apply(P!7, tptp_fun_X_3(P!7)))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(phi(apply(P!7, tptp_fun_X_3(P!7)))) | (~d(phi(apply(P!7, tptp_fun_X_3(P!7))))))) | (~((~(phi(apply(P!7, tptp_fun_X_3(P!7))) = false)) | (~(false = not1(false)))))))),
% 45.51/29.60 inference(quant_inst,[status(thm)],[])).
% 45.51/29.60 tff(165,plain,
% 45.51/29.60 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(phi(apply(P!7, tptp_fun_X_3(P!7))), false) <=> ((~((~d(false)) | d(phi(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(false = not1(false))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = false)))) | (~((~d(false)) | (~bool(false)) | (~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | bool(phi(apply(P!7, tptp_fun_X_3(P!7))))))))),
% 45.51/29.60 inference(modus_ponens,[status(thm)],[164, 163])).
% 45.51/29.60 tff(166,plain,
% 45.51/29.60 (forallprefers(phi(apply(P!7, tptp_fun_X_3(P!7))), false) <=> ((~((~d(false)) | d(phi(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(false = not1(false))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = false)))) | (~((~d(false)) | (~bool(false)) | (~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | bool(phi(apply(P!7, tptp_fun_X_3(P!7)))))))),
% 45.51/29.60 inference(unit_resolution,[status(thm)],[165, 159])).
% 45.51/29.60 tff(167,plain,
% 45.51/29.60 (^[B: $i] : refl((lazy_impl(false, B) = not1(false)) <=> (lazy_impl(false, B) = not1(false)))),
% 45.51/29.60 inference(bind,[status(th)],[])).
% 45.51/29.60 tff(168,plain,
% 45.51/29.60 (![B: $i] : (lazy_impl(false, B) = not1(false)) <=> ![B: $i] : (lazy_impl(false, B) = not1(false))),
% 45.51/29.60 inference(quant_intro,[status(thm)],[167])).
% 45.51/29.60 tff(169,plain,
% 45.51/29.60 (^[B: $i] : rewrite((lazy_impl(false, B) = true) <=> (lazy_impl(false, B) = not1(false)))),
% 45.51/29.60 inference(bind,[status(th)],[])).
% 45.51/29.60 tff(170,plain,
% 45.51/29.60 (![B: $i] : (lazy_impl(false, B) = true) <=> ![B: $i] : (lazy_impl(false, B) = not1(false))),
% 45.51/29.60 inference(quant_intro,[status(thm)],[169])).
% 45.51/29.60 tff(171,plain,
% 45.51/29.60 (![B: $i] : (lazy_impl(false, B) = true) <=> ![B: $i] : (lazy_impl(false, B) = true)),
% 45.51/29.60 inference(rewrite,[status(thm)],[])).
% 45.51/29.60 tff(172,axiom,(![B: $i] : (lazy_impl(false, B) = true)), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','lazy_impl_axiom2')).
% 45.51/29.60 tff(173,plain,
% 45.51/29.60 (![B: $i] : (lazy_impl(false, B) = true)),
% 45.51/29.60 inference(modus_ponens,[status(thm)],[172, 171])).
% 45.51/29.60 tff(174,plain,
% 45.51/29.60 (![B: $i] : (lazy_impl(false, B) = not1(false))),
% 45.51/29.60 inference(modus_ponens,[status(thm)],[173, 170])).
% 45.51/29.60 tff(175,plain,(
% 45.51/29.60 ![B: $i] : (lazy_impl(false, B) = not1(false))),
% 45.51/29.60 inference(skolemize,[status(sab)],[174])).
% 45.51/29.60 tff(176,plain,
% 45.51/29.60 (![B: $i] : (lazy_impl(false, B) = not1(false))),
% 45.51/29.60 inference(modus_ponens,[status(thm)],[175, 168])).
% 45.51/29.60 tff(177,plain,
% 45.51/29.60 ((~![B: $i] : (lazy_impl(false, B) = not1(false))) | (lazy_impl(false, P!6) = not1(false))),
% 45.51/29.60 inference(quant_inst,[status(thm)],[])).
% 45.51/29.60 tff(178,plain,
% 45.51/29.60 (lazy_impl(false, P!6) = not1(false)),
% 45.51/29.60 inference(unit_resolution,[status(thm)],[177, 176])).
% 45.51/29.60 tff(179,assumption,(prop(P!6) = false), introduced(assumption)).
% 45.51/29.60 tff(180,plain,
% 45.51/29.60 (lazy_impl(prop(P!6), P!6) = lazy_impl(false, P!6)),
% 45.51/29.60 inference(monotonicity,[status(thm)],[179])).
% 45.51/29.60 tff(181,plain,
% 45.51/29.60 (lazy_impl(prop(P!6), P!6) = not1(false)),
% 45.51/29.60 inference(transitivity,[status(thm)],[180, 178])).
% 45.51/29.60 tff(182,plain,
% 45.51/29.60 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))) | (lazy_impl(prop(P!6), P!6) = not1(false))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))) | (lazy_impl(prop(P!6), P!6) = not1(false)))))),
% 45.51/29.60 inference(rewrite,[status(thm)],[])).
% 45.51/29.60 tff(183,plain,
% 45.51/29.60 ((forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(false) | (~d(false)))) | (~((~(false = false)) | (~(lazy_impl(prop(P!6), P!6) = not1(false))))))) <=> (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))) | (lazy_impl(prop(P!6), P!6) = not1(false))))),
% 45.51/29.61 inference(rewrite,[status(thm)],[])).
% 45.51/29.61 tff(184,plain,
% 45.51/29.61 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(false) | (~d(false)))) | (~((~(false = false)) | (~(lazy_impl(prop(P!6), P!6) = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))) | (lazy_impl(prop(P!6), P!6) = not1(false)))))),
% 45.51/29.61 inference(monotonicity,[status(thm)],[183])).
% 45.51/29.61 tff(185,plain,
% 45.51/29.61 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(false) | (~d(false)))) | (~((~(false = false)) | (~(lazy_impl(prop(P!6), P!6) = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))) | (lazy_impl(prop(P!6), P!6) = not1(false)))))),
% 45.51/29.61 inference(transitivity,[status(thm)],[184, 182])).
% 45.51/29.61 tff(186,plain,
% 45.51/29.61 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(false) | (~d(false)))) | (~((~(false = false)) | (~(lazy_impl(prop(P!6), P!6) = not1(false)))))))),
% 45.51/29.61 inference(quant_inst,[status(thm)],[])).
% 45.51/29.61 tff(187,plain,
% 45.51/29.61 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))) | (lazy_impl(prop(P!6), P!6) = not1(false))))),
% 45.51/29.61 inference(modus_ponens,[status(thm)],[186, 185])).
% 45.51/29.61 tff(188,plain,
% 45.51/29.61 (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))) | (lazy_impl(prop(P!6), P!6) = not1(false)))),
% 45.51/29.61 inference(unit_resolution,[status(thm)],[187, 159])).
% 45.51/29.61 tff(189,plain,
% 45.51/29.61 (^[P: $i] : refl((f7(P) = lazy_impl(prop(P), P)) <=> (f7(P) = lazy_impl(prop(P), P)))),
% 45.51/29.61 inference(bind,[status(th)],[])).
% 45.51/29.61 tff(190,plain,
% 45.51/29.61 (![P: $i] : (f7(P) = lazy_impl(prop(P), P)) <=> ![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 45.51/29.61 inference(quant_intro,[status(thm)],[189])).
% 45.51/29.61 tff(191,plain,
% 45.51/29.61 (![P: $i] : (f7(P) = lazy_impl(prop(P), P)) <=> ![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 45.51/29.61 inference(rewrite,[status(thm)],[])).
% 45.51/29.61 tff(192,axiom,(![P: $i] : (f7(P) = lazy_impl(prop(P), P))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','def_f7')).
% 45.51/29.61 tff(193,plain,
% 45.51/29.61 (![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 45.51/29.61 inference(modus_ponens,[status(thm)],[192, 191])).
% 45.51/29.61 tff(194,plain,(
% 45.51/29.61 ![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 45.51/29.61 inference(skolemize,[status(sab)],[193])).
% 45.51/29.61 tff(195,plain,
% 45.51/29.61 (![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 45.51/29.61 inference(modus_ponens,[status(thm)],[194, 190])).
% 45.51/29.61 tff(196,plain,
% 45.51/29.61 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(P!6) = lazy_impl(prop(P!6), P!6))),
% 45.51/29.61 inference(quant_inst,[status(thm)],[])).
% 45.51/29.61 tff(197,plain,
% 45.51/29.61 (f7(P!6) = lazy_impl(prop(P!6), P!6)),
% 45.51/29.61 inference(unit_resolution,[status(thm)],[196, 195])).
% 45.51/29.61 tff(198,plain,
% 45.51/29.61 (lazy_impl(prop(P!6), P!6) = f7(P!6)),
% 45.51/29.61 inference(symmetry,[status(thm)],[197])).
% 45.51/29.61 tff(199,plain,
% 45.51/29.61 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(false) = lazy_impl(prop(false), false))),
% 45.51/29.61 inference(quant_inst,[status(thm)],[])).
% 45.51/29.61 tff(200,plain,
% 45.51/29.61 (f7(false) = lazy_impl(prop(false), false)),
% 45.51/29.61 inference(unit_resolution,[status(thm)],[199, 195])).
% 45.51/29.61 tff(201,plain,
% 45.51/29.61 (lazy_impl(prop(false), false) = f7(false)),
% 45.51/29.61 inference(symmetry,[status(thm)],[200])).
% 45.51/29.61 tff(202,plain,
% 45.51/29.61 (lazy_impl(prop(false), false) = lazy_impl(not1(false), false)),
% 45.51/29.61 inference(monotonicity,[status(thm)],[131])).
% 45.51/29.61 tff(203,plain,
% 45.51/29.61 (lazy_impl(not1(false), false) = lazy_impl(prop(false), false)),
% 45.51/29.61 inference(symmetry,[status(thm)],[202])).
% 45.51/29.61 tff(204,plain,
% 45.51/29.61 (phi(false) = lazy_impl(not1(false), false)),
% 45.51/29.61 inference(symmetry,[status(thm)],[35])).
% 45.51/29.61 tff(205,plain,
% 45.51/29.61 (false = phi(false)),
% 45.51/29.61 inference(symmetry,[status(thm)],[23])).
% 45.51/29.61 tff(206,plain,
% 45.51/29.61 (false = f7(false)),
% 45.51/29.61 inference(transitivity,[status(thm)],[205, 204, 203, 201])).
% 45.51/29.61 tff(207,plain,
% 45.51/29.61 (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> forallprefers(f7(false), f7(P!6))),
% 45.51/29.61 inference(monotonicity,[status(thm)],[206, 198])).
% 45.51/29.61 tff(208,plain,
% 45.51/29.61 (forallprefers(f7(false), f7(P!6)) <=> forallprefers(false, lazy_impl(prop(P!6), P!6))),
% 45.51/29.61 inference(symmetry,[status(thm)],[207])).
% 45.51/29.61 tff(209,plain,
% 45.51/29.61 ((~forallprefers(f7(false), f7(P!6))) <=> (~forallprefers(false, lazy_impl(prop(P!6), P!6)))),
% 45.51/29.61 inference(monotonicity,[status(thm)],[208])).
% 45.51/29.61 tff(210,plain,
% 45.51/29.61 (^[P1: $i] : refl((~forallprefers(f7(P1), f7(P!6))) <=> (~forallprefers(f7(P1), f7(P!6))))),
% 45.51/29.61 inference(bind,[status(th)],[])).
% 45.51/29.61 tff(211,plain,
% 45.51/29.61 (![P1: $i] : (~forallprefers(f7(P1), f7(P!6))) <=> ![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 45.51/29.61 inference(quant_intro,[status(thm)],[210])).
% 45.51/29.61 tff(212,plain,
% 45.51/29.61 (((false2 = phi(f7(P!6))) & ![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))) <=> ((false2 = phi(f7(P!6))) & ![P1: $i] : (~forallprefers(f7(P1), f7(P!6))))),
% 45.51/29.61 inference(rewrite,[status(thm)],[])).
% 45.51/29.61 tff(213,plain,
% 45.51/29.61 (?[P: $i] : ((false2 = phi(f7(P))) & (~?[P1: $i] : forallprefers(f7(P1), f7(P)))) <=> ?[P: $i] : ((false2 = phi(f7(P))) & (~?[P1: $i] : forallprefers(f7(P1), f7(P))))),
% 45.51/29.61 inference(rewrite,[status(thm)],[])).
% 45.51/29.61 tff(214,axiom,(?[P: $i] : ((false2 = phi(f7(P))) & (~?[P1: $i] : forallprefers(f7(P1), f7(P))))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','def_false2')).
% 45.51/29.61 tff(215,plain,
% 45.51/29.61 (?[P: $i] : ((false2 = phi(f7(P))) & (~?[P1: $i] : forallprefers(f7(P1), f7(P))))),
% 45.51/29.61 inference(modus_ponens,[status(thm)],[214, 213])).
% 45.51/29.61 tff(216,plain,
% 45.51/29.61 ((false2 = phi(f7(P!6))) & ![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 45.51/29.61 inference(modus_ponens,[status(thm)],[215, 212])).
% 45.51/29.61 tff(217,plain,
% 45.51/29.61 (![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 45.51/29.61 inference(and_elim,[status(thm)],[216])).
% 45.51/29.61 tff(218,plain,
% 45.51/29.61 (![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 45.51/29.61 inference(modus_ponens,[status(thm)],[217, 211])).
% 45.51/29.61 tff(219,plain,
% 45.51/29.61 ((~![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))) | (~forallprefers(f7(false), f7(P!6)))),
% 45.51/29.61 inference(quant_inst,[status(thm)],[])).
% 45.51/29.61 tff(220,plain,
% 45.51/29.61 (~forallprefers(f7(false), f7(P!6))),
% 45.51/29.61 inference(unit_resolution,[status(thm)],[219, 218])).
% 45.51/29.61 tff(221,plain,
% 45.51/29.61 (~forallprefers(false, lazy_impl(prop(P!6), P!6))),
% 45.51/29.61 inference(modus_ponens,[status(thm)],[220, 209])).
% 45.51/29.61 tff(222,plain,
% 45.51/29.61 ((~(forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))) | (lazy_impl(prop(P!6), P!6) = not1(false))))) | forallprefers(false, lazy_impl(prop(P!6), P!6)) | (~((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))) | (lazy_impl(prop(P!6), P!6) = not1(false))))),
% 45.51/29.61 inference(tautology,[status(thm)],[])).
% 45.51/29.61 tff(223,plain,
% 45.51/29.61 (~((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))) | (lazy_impl(prop(P!6), P!6) = not1(false)))),
% 45.51/29.61 inference(unit_resolution,[status(thm)],[222, 221, 188])).
% 45.51/29.61 tff(224,plain,
% 45.51/29.61 (((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))) | (lazy_impl(prop(P!6), P!6) = not1(false))) | (~(lazy_impl(prop(P!6), P!6) = not1(false)))),
% 45.51/29.61 inference(tautology,[status(thm)],[])).
% 45.51/29.61 tff(225,plain,
% 45.51/29.61 (~(lazy_impl(prop(P!6), P!6) = not1(false))),
% 45.51/29.61 inference(unit_resolution,[status(thm)],[224, 223])).
% 45.51/29.61 tff(226,plain,
% 45.51/29.61 ($false),
% 45.51/29.61 inference(unit_resolution,[status(thm)],[225, 181])).
% 45.51/29.61 tff(227,plain,(~(prop(P!6) = false)), inference(lemma,lemma(discharge,[]))).
% 45.51/29.61 tff(228,plain,
% 45.51/29.61 (^[X: $i] : refl(((prop(X) = false) <=> (~bool(X))) <=> ((prop(X) = false) <=> (~bool(X))))),
% 45.51/29.61 inference(bind,[status(th)],[])).
% 45.51/29.61 tff(229,plain,
% 45.51/29.61 (![X: $i] : ((prop(X) = false) <=> (~bool(X))) <=> ![X: $i] : ((prop(X) = false) <=> (~bool(X)))),
% 45.51/29.61 inference(quant_intro,[status(thm)],[228])).
% 45.51/29.61 tff(230,plain,
% 45.51/29.61 (![X: $i] : ((prop(X) = false) <=> (~bool(X))) <=> ![X: $i] : ((prop(X) = false) <=> (~bool(X)))),
% 45.51/29.61 inference(rewrite,[status(thm)],[])).
% 45.51/29.61 tff(231,axiom,(![X: $i] : ((prop(X) = false) <=> (~bool(X)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','prop_false')).
% 45.51/29.61 tff(232,plain,
% 45.51/29.61 (![X: $i] : ((prop(X) = false) <=> (~bool(X)))),
% 45.51/29.61 inference(modus_ponens,[status(thm)],[231, 230])).
% 45.51/29.61 tff(233,plain,(
% 45.51/29.61 ![X: $i] : ((prop(X) = false) <=> (~bool(X)))),
% 45.51/29.61 inference(skolemize,[status(sab)],[232])).
% 45.51/29.61 tff(234,plain,
% 45.51/29.61 (![X: $i] : ((prop(X) = false) <=> (~bool(X)))),
% 45.51/29.61 inference(modus_ponens,[status(thm)],[233, 229])).
% 45.51/29.61 tff(235,plain,
% 45.51/29.61 ((~![X: $i] : ((prop(X) = false) <=> (~bool(X)))) | ((prop(P!6) = false) <=> (~bool(P!6)))),
% 45.51/29.61 inference(quant_inst,[status(thm)],[])).
% 45.51/29.61 tff(236,plain,
% 45.51/29.61 ((prop(P!6) = false) <=> (~bool(P!6))),
% 45.51/29.61 inference(unit_resolution,[status(thm)],[235, 234])).
% 45.51/29.61 tff(237,plain,
% 45.51/29.61 ((~((prop(P!6) = false) <=> (~bool(P!6)))) | (prop(P!6) = false) | bool(P!6)),
% 45.51/29.61 inference(tautology,[status(thm)],[])).
% 45.51/29.61 tff(238,plain,
% 45.51/29.61 ((prop(P!6) = false) | bool(P!6)),
% 45.51/29.61 inference(unit_resolution,[status(thm)],[237, 236])).
% 45.51/29.61 tff(239,plain,
% 45.51/29.61 (bool(P!6)),
% 45.51/29.61 inference(unit_resolution,[status(thm)],[238, 227])).
% 45.51/29.61 tff(240,plain,
% 45.51/29.61 (^[X: $i] : refl((bool(X) <=> ((X = false) | (X = not1(false)))) <=> (bool(X) <=> ((X = false) | (X = not1(false)))))),
% 45.51/29.61 inference(bind,[status(th)],[])).
% 45.51/29.61 tff(241,plain,
% 45.51/29.61 (![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false)))) <=> ![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))),
% 45.51/29.61 inference(quant_intro,[status(thm)],[240])).
% 45.51/29.61 tff(242,plain,
% 45.51/29.61 (^[X: $i] : rewrite((bool(X) <=> ((X = false) | (X = true))) <=> (bool(X) <=> ((X = false) | (X = not1(false)))))),
% 45.51/29.61 inference(bind,[status(th)],[])).
% 45.51/29.61 tff(243,plain,
% 45.51/29.61 (![X: $i] : (bool(X) <=> ((X = false) | (X = true))) <=> ![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))),
% 45.51/29.61 inference(quant_intro,[status(thm)],[242])).
% 45.51/29.61 tff(244,plain,
% 45.51/29.61 (![X: $i] : (bool(X) <=> ((X = false) | (X = true))) <=> ![X: $i] : (bool(X) <=> ((X = false) | (X = true)))),
% 45.51/29.61 inference(rewrite,[status(thm)],[])).
% 45.51/29.61 tff(245,axiom,(![X: $i] : (bool(X) <=> ((X = false) | (X = true)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','def_bool')).
% 45.51/29.61 tff(246,plain,
% 45.51/29.61 (![X: $i] : (bool(X) <=> ((X = false) | (X = true)))),
% 45.51/29.61 inference(modus_ponens,[status(thm)],[245, 244])).
% 45.51/29.61 tff(247,plain,
% 45.51/29.61 (![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))),
% 45.51/29.61 inference(modus_ponens,[status(thm)],[246, 243])).
% 45.51/29.61 tff(248,plain,(
% 45.51/29.61 ![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))),
% 45.51/29.61 inference(skolemize,[status(sab)],[247])).
% 45.51/29.61 tff(249,plain,
% 45.51/29.61 (![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))),
% 45.51/29.61 inference(modus_ponens,[status(thm)],[248, 241])).
% 45.51/29.61 tff(250,plain,
% 45.51/29.61 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(P!6) <=> ((P!6 = false) | (P!6 = not1(false))))),
% 45.51/29.61 inference(quant_inst,[status(thm)],[])).
% 45.51/29.61 tff(251,plain,
% 45.51/29.61 (bool(P!6) <=> ((P!6 = false) | (P!6 = not1(false)))),
% 45.51/29.61 inference(unit_resolution,[status(thm)],[250, 249])).
% 45.51/29.61 tff(252,plain,
% 45.51/29.61 ((~(bool(P!6) <=> ((P!6 = false) | (P!6 = not1(false))))) | (~bool(P!6)) | ((P!6 = false) | (P!6 = not1(false)))),
% 45.51/29.61 inference(tautology,[status(thm)],[])).
% 45.51/29.61 tff(253,plain,
% 45.51/29.61 ((~bool(P!6)) | ((P!6 = false) | (P!6 = not1(false)))),
% 45.51/29.61 inference(unit_resolution,[status(thm)],[252, 251])).
% 45.51/29.61 tff(254,plain,
% 45.51/29.61 ((P!6 = false) | (P!6 = not1(false))),
% 45.51/29.61 inference(unit_resolution,[status(thm)],[253, 239])).
% 45.51/29.61 tff(255,plain,
% 45.51/29.61 ((~![X: $i] : ((prop(X) = not1(false)) <=> bool(X))) | ((prop(not1(false)) = not1(false)) <=> bool(not1(false)))),
% 45.51/29.61 inference(quant_inst,[status(thm)],[])).
% 45.51/29.61 tff(256,plain,
% 45.51/29.61 ((prop(not1(false)) = not1(false)) <=> bool(not1(false))),
% 45.51/29.61 inference(unit_resolution,[status(thm)],[255, 126])).
% 45.51/29.61 tff(257,plain,
% 45.51/29.61 ((false = not1(false)) <=> (not1(false) = false)),
% 45.51/29.61 inference(commutativity,[status(thm)],[])).
% 45.51/29.61 tff(258,plain,
% 45.51/29.61 ((not1(true) = false) <=> (not1(not1(false)) = false)),
% 45.51/29.61 inference(rewrite,[status(thm)],[])).
% 45.51/29.61 tff(259,plain,
% 45.51/29.61 ((not1(true) = false) <=> (not1(true) = false)),
% 45.51/29.61 inference(rewrite,[status(thm)],[])).
% 45.51/29.61 tff(260,axiom,(not1(true) = false), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','not1_axiom3')).
% 45.51/29.61 tff(261,plain,
% 45.51/29.61 (not1(true) = false),
% 45.51/29.61 inference(modus_ponens,[status(thm)],[260, 259])).
% 45.51/29.61 tff(262,plain,
% 45.51/29.61 (not1(not1(false)) = false),
% 45.51/29.61 inference(modus_ponens,[status(thm)],[261, 258])).
% 45.51/29.61 tff(263,plain,
% 45.51/29.61 ((not1(not1(false)) = phi(not1(false))) <=> (false = not1(false))),
% 45.51/29.61 inference(monotonicity,[status(thm)],[262, 48])).
% 45.51/29.61 tff(264,plain,
% 45.51/29.61 ((not1(not1(false)) = phi(not1(false))) <=> (not1(false) = false)),
% 45.51/29.61 inference(transitivity,[status(thm)],[263, 257])).
% 45.51/29.61 tff(265,plain,
% 45.51/29.61 ((not1(false) = false) <=> (not1(not1(false)) = phi(not1(false)))),
% 45.51/29.61 inference(symmetry,[status(thm)],[264])).
% 45.51/29.61 tff(266,plain,
% 45.51/29.61 ((~(not1(false) = false)) <=> (~(not1(not1(false)) = phi(not1(false))))),
% 45.51/29.61 inference(monotonicity,[status(thm)],[265])).
% 45.51/29.61 tff(267,plain,
% 45.51/29.61 (~(not1(not1(false)) = phi(not1(false)))),
% 45.51/29.61 inference(modus_ponens,[status(thm)],[60, 266])).
% 45.51/29.61 tff(268,plain,
% 45.51/29.61 (((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | (bool(not1(false)) | (not1(not1(false)) = phi(not1(false))))) <=> ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | bool(not1(false)) | (not1(not1(false)) = phi(not1(false))))),
% 45.51/29.61 inference(rewrite,[status(thm)],[])).
% 45.51/29.61 tff(269,plain,
% 45.51/29.61 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | (bool(not1(false)) | (not1(not1(false)) = phi(not1(false))))),
% 45.51/29.61 inference(quant_inst,[status(thm)],[])).
% 45.51/29.61 tff(270,plain,
% 45.51/29.61 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | bool(not1(false)) | (not1(not1(false)) = phi(not1(false)))),
% 45.51/29.61 inference(modus_ponens,[status(thm)],[269, 268])).
% 45.51/29.61 tff(271,plain,
% 45.51/29.61 (bool(not1(false)) | (not1(not1(false)) = phi(not1(false)))),
% 45.51/29.61 inference(unit_resolution,[status(thm)],[270, 71])).
% 45.51/29.61 tff(272,plain,
% 45.51/29.61 (bool(not1(false))),
% 45.51/29.61 inference(unit_resolution,[status(thm)],[271, 267])).
% 45.51/29.61 tff(273,plain,
% 45.51/29.61 ((~((prop(not1(false)) = not1(false)) <=> bool(not1(false)))) | (prop(not1(false)) = not1(false)) | (~bool(not1(false)))),
% 45.51/29.61 inference(tautology,[status(thm)],[])).
% 45.51/29.61 tff(274,plain,
% 45.51/29.61 ((~((prop(not1(false)) = not1(false)) <=> bool(not1(false)))) | (prop(not1(false)) = not1(false))),
% 45.51/29.61 inference(unit_resolution,[status(thm)],[273, 272])).
% 45.51/29.61 tff(275,plain,
% 45.51/29.61 (prop(not1(false)) = not1(false)),
% 45.51/29.61 inference(unit_resolution,[status(thm)],[274, 256])).
% 45.51/29.61 tff(276,plain,
% 45.51/29.61 (lazy_impl(prop(not1(false)), not1(false)) = lazy_impl(not1(false), not1(false))),
% 45.51/29.61 inference(monotonicity,[status(thm)],[275])).
% 45.51/29.61 tff(277,plain,
% 45.51/29.61 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(not1(false)) = lazy_impl(prop(not1(false)), not1(false)))),
% 45.51/29.61 inference(quant_inst,[status(thm)],[])).
% 45.51/29.61 tff(278,plain,
% 45.51/29.61 (f7(not1(false)) = lazy_impl(prop(not1(false)), not1(false))),
% 45.51/29.61 inference(unit_resolution,[status(thm)],[277, 195])).
% 45.51/29.61 tff(279,assumption,(P!6 = not1(false)), introduced(assumption)).
% 45.51/29.61 tff(280,plain,
% 45.51/29.61 (f7(P!6) = f7(not1(false))),
% 45.51/29.61 inference(monotonicity,[status(thm)],[279])).
% 45.51/29.61 tff(281,plain,
% 45.51/29.61 (lazy_impl(prop(P!6), P!6) = not1(false)),
% 45.51/29.61 inference(transitivity,[status(thm)],[198, 280, 278, 276, 50, 48])).
% 45.51/29.61 tff(282,plain,
% 45.51/29.61 ($false),
% 45.51/29.61 inference(unit_resolution,[status(thm)],[225, 281])).
% 45.51/29.61 tff(283,plain,(~(P!6 = not1(false))), inference(lemma,lemma(discharge,[]))).
% 45.51/29.61 tff(284,plain,
% 45.51/29.61 ((~((P!6 = false) | (P!6 = not1(false)))) | (P!6 = false) | (P!6 = not1(false))),
% 45.51/29.61 inference(tautology,[status(thm)],[])).
% 45.51/29.61 tff(285,plain,
% 45.51/29.61 ((~((P!6 = false) | (P!6 = not1(false)))) | (P!6 = false)),
% 45.51/29.61 inference(unit_resolution,[status(thm)],[284, 283])).
% 45.51/29.61 tff(286,plain,
% 45.51/29.61 (P!6 = false),
% 45.51/29.61 inference(unit_resolution,[status(thm)],[285, 254])).
% 45.51/29.61 tff(287,plain,
% 45.51/29.61 (f7(P!6) = f7(false)),
% 45.51/29.61 inference(monotonicity,[status(thm)],[286])).
% 45.51/29.61 tff(288,plain,
% 45.51/29.61 (f7(false) = f7(P!6)),
% 45.51/29.61 inference(symmetry,[status(thm)],[287])).
% 45.51/29.61 tff(289,plain,
% 45.51/29.61 (false = f7(P!6)),
% 45.51/29.61 inference(transitivity,[status(thm)],[205, 204, 203, 201, 288])).
% 45.51/29.61 tff(290,plain,
% 45.51/29.61 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(apply(P!7, tptp_fun_X_3(P!7))) = lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))))),
% 45.51/29.61 inference(quant_inst,[status(thm)],[])).
% 45.51/29.61 tff(291,plain,
% 45.51/29.61 (f7(apply(P!7, tptp_fun_X_3(P!7))) = lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))),
% 45.51/29.61 inference(unit_resolution,[status(thm)],[290, 195])).
% 45.51/29.61 tff(292,plain,
% 45.51/29.61 (lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))) = f7(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.51/29.61 inference(symmetry,[status(thm)],[291])).
% 45.51/29.61 tff(293,plain,
% 45.51/29.61 ((~![X: $i] : ((prop(X) = not1(false)) <=> bool(X))) | ((prop(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)) <=> bool(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.51/29.61 inference(quant_inst,[status(thm)],[])).
% 45.51/29.61 tff(294,plain,
% 45.51/29.61 ((prop(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)) <=> bool(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.51/29.61 inference(unit_resolution,[status(thm)],[293, 126])).
% 45.51/29.61 tff(295,plain,
% 45.51/29.61 (^[P: $i, R: $i] : refl((~((~(f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R)))) | (~![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R)))))) <=> (~((~(f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R)))) | (~![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R)))))))),
% 45.51/29.61 inference(bind,[status(th)],[])).
% 45.51/29.61 tff(296,plain,
% 45.51/29.61 (![P: $i, R: $i] : (~((~(f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R)))) | (~![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R)))))) <=> ![P: $i, R: $i] : (~((~(f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R)))) | (~![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R))))))),
% 45.51/29.61 inference(quant_intro,[status(thm)],[295])).
% 45.51/29.61 tff(297,plain,
% 45.51/29.61 (^[P: $i, R: $i] : rewrite((~((~(f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R)))) | (~![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R)))))) <=> (~((~(f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R)))) | (~![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R)))))))),
% 45.51/29.61 inference(bind,[status(th)],[])).
% 45.51/29.61 tff(298,plain,
% 45.51/29.61 (![P: $i, R: $i] : (~((~(f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R)))) | (~![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R)))))) <=> ![P: $i, R: $i] : (~((~(f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R)))) | (~![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R))))))),
% 45.51/29.61 inference(quant_intro,[status(thm)],[297])).
% 45.51/29.61 tff(299,plain,
% 45.51/29.61 (![P: $i, R: $i] : (~((~(f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R)))) | (~![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R)))))) <=> ![P: $i, R: $i] : (~((~(f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R)))) | (~![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R))))))),
% 45.51/29.61 inference(transitivity,[status(thm)],[298, 296])).
% 45.51/29.61 tff(300,plain,
% 45.51/29.61 (^[P: $i, R: $i] : rewrite(((f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R))) & ![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R)))) <=> (~((~(f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R)))) | (~![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R)))))))),
% 45.51/29.61 inference(bind,[status(th)],[])).
% 45.51/29.61 tff(301,plain,
% 45.51/29.61 (![P: $i, R: $i] : ((f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R))) & ![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R)))) <=> ![P: $i, R: $i] : (~((~(f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R)))) | (~![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R))))))),
% 45.51/29.61 inference(quant_intro,[status(thm)],[300])).
% 45.51/29.61 tff(302,plain,
% 45.51/29.61 (![P: $i, R: $i] : ?[X: $i] : ((f5(P, R) = phi(f4(P, X, R))) & (~?[X1: $i] : forallprefers(f4(P, X1, R), f4(P, X, R)))) <=> ![P: $i, R: $i] : ?[X: $i] : ((f5(P, R) = phi(f4(P, X, R))) & (~?[X1: $i] : forallprefers(f4(P, X1, R), f4(P, X, R))))),
% 45.51/29.61 inference(rewrite,[status(thm)],[])).
% 45.51/29.61 tff(303,axiom,(![P: $i, R: $i] : ?[X: $i] : ((f5(P, R) = phi(f4(P, X, R))) & (~?[X1: $i] : forallprefers(f4(P, X1, R), f4(P, X, R))))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','def_f5')).
% 45.51/29.61 tff(304,plain,
% 45.51/29.61 (![P: $i, R: $i] : ?[X: $i] : ((f5(P, R) = phi(f4(P, X, R))) & (~?[X1: $i] : forallprefers(f4(P, X1, R), f4(P, X, R))))),
% 45.51/29.61 inference(modus_ponens,[status(thm)],[303, 302])).
% 45.51/29.61 tff(305,plain,(
% 45.51/29.61 ![P: $i, R: $i] : ((f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R))) & ![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R))))),
% 45.51/29.61 inference(skolemize,[status(sab)],[304])).
% 45.51/29.61 tff(306,plain,
% 45.51/29.61 (![P: $i, R: $i] : (~((~(f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R)))) | (~![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R))))))),
% 45.51/29.61 inference(modus_ponens,[status(thm)],[305, 301])).
% 45.51/29.61 tff(307,plain,
% 45.51/29.61 (![P: $i, R: $i] : (~((~(f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R)))) | (~![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R))))))),
% 45.51/29.61 inference(modus_ponens,[status(thm)],[306, 299])).
% 45.51/29.61 tff(308,plain,
% 45.51/29.61 ((~![P: $i, R: $i] : (~((~(f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R)))) | (~![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R))))))) | (~((~(f5(P!7, tptp_fun_R_5(P!7)) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))) | (~![X1: $i] : (~forallprefers(f4(P!7, X1, tptp_fun_R_5(P!7)), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))))))),
% 45.51/29.61 inference(quant_inst,[status(thm)],[])).
% 45.51/29.61 tff(309,plain,
% 45.51/29.61 (~((~(f5(P!7, tptp_fun_R_5(P!7)) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))) | (~![X1: $i] : (~forallprefers(f4(P!7, X1, tptp_fun_R_5(P!7)), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))))),
% 45.51/29.61 inference(unit_resolution,[status(thm)],[308, 307])).
% 45.51/29.61 tff(310,plain,
% 45.51/29.61 (((~(f5(P!7, tptp_fun_R_5(P!7)) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))) | (~![X1: $i] : (~forallprefers(f4(P!7, X1, tptp_fun_R_5(P!7)), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))))) | (f5(P!7, tptp_fun_R_5(P!7)) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 45.51/29.61 inference(tautology,[status(thm)],[])).
% 45.51/29.61 tff(311,plain,
% 45.51/29.61 (f5(P!7, tptp_fun_R_5(P!7)) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.51/29.61 inference(unit_resolution,[status(thm)],[310, 309])).
% 45.51/29.61 tff(312,plain,
% 45.51/29.61 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f5(P!7, tptp_fun_R_5(P!7))),
% 45.51/29.61 inference(symmetry,[status(thm)],[311])).
% 45.51/29.61 tff(313,plain,
% 45.51/29.61 (bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) <=> bool(f5(P!7, tptp_fun_R_5(P!7)))),
% 45.51/29.61 inference(monotonicity,[status(thm)],[312])).
% 45.51/29.61 tff(314,plain,
% 45.51/29.61 (bool(f5(P!7, tptp_fun_R_5(P!7))) <=> bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 45.51/29.61 inference(symmetry,[status(thm)],[313])).
% 45.51/29.61 tff(315,plain,
% 45.51/29.61 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(lazy_impl(prop(false), impl(f5(P!7, false), false))) <=> ((lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false))))),
% 45.51/29.61 inference(quant_inst,[status(thm)],[])).
% 45.51/29.61 tff(316,plain,
% 45.51/29.61 (bool(lazy_impl(prop(false), impl(f5(P!7, false), false))) <=> ((lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false)))),
% 45.51/29.61 inference(unit_resolution,[status(thm)],[315, 249])).
% 45.51/29.61 tff(317,plain,
% 45.51/29.61 (^[P: $i, R: $i] : refl((f6(P, R) = lazy_impl(prop(R), impl(f5(P, R), R))) <=> (f6(P, R) = lazy_impl(prop(R), impl(f5(P, R), R))))),
% 45.51/29.61 inference(bind,[status(th)],[])).
% 45.51/29.61 tff(318,plain,
% 45.51/29.61 (![P: $i, R: $i] : (f6(P, R) = lazy_impl(prop(R), impl(f5(P, R), R))) <=> ![P: $i, R: $i] : (f6(P, R) = lazy_impl(prop(R), impl(f5(P, R), R)))),
% 45.51/29.61 inference(quant_intro,[status(thm)],[317])).
% 45.51/29.61 tff(319,plain,
% 45.51/29.61 (![P: $i, R: $i] : (f6(P, R) = lazy_impl(prop(R), impl(f5(P, R), R))) <=> ![P: $i, R: $i] : (f6(P, R) = lazy_impl(prop(R), impl(f5(P, R), R)))),
% 45.51/29.61 inference(rewrite,[status(thm)],[])).
% 45.51/29.61 tff(320,axiom,(![P: $i, R: $i] : (f6(P, R) = lazy_impl(prop(R), impl(f5(P, R), R)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','def_f6')).
% 45.51/29.61 tff(321,plain,
% 45.51/29.61 (![P: $i, R: $i] : (f6(P, R) = lazy_impl(prop(R), impl(f5(P, R), R)))),
% 45.51/29.61 inference(modus_ponens,[status(thm)],[320, 319])).
% 45.51/29.61 tff(322,plain,(
% 45.51/29.61 ![P: $i, R: $i] : (f6(P, R) = lazy_impl(prop(R), impl(f5(P, R), R)))),
% 45.51/29.61 inference(skolemize,[status(sab)],[321])).
% 45.51/29.61 tff(323,plain,
% 45.51/29.61 (![P: $i, R: $i] : (f6(P, R) = lazy_impl(prop(R), impl(f5(P, R), R)))),
% 45.51/29.61 inference(modus_ponens,[status(thm)],[322, 318])).
% 45.51/29.61 tff(324,plain,
% 45.51/29.61 ((~![P: $i, R: $i] : (f6(P, R) = lazy_impl(prop(R), impl(f5(P, R), R)))) | (f6(P!7, tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.51/29.61 inference(quant_inst,[status(thm)],[])).
% 45.51/29.61 tff(325,plain,
% 45.51/29.61 (f6(P!7, tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.51/29.61 inference(unit_resolution,[status(thm)],[324, 323])).
% 45.51/29.61 tff(326,plain,
% 45.51/29.61 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = f6(P!7, tptp_fun_R_5(P!7))),
% 45.51/29.61 inference(symmetry,[status(thm)],[325])).
% 45.51/29.61 tff(327,plain,
% 45.51/29.61 (d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> d(f6(P!7, tptp_fun_R_5(P!7)))),
% 45.51/29.61 inference(monotonicity,[status(thm)],[326])).
% 45.51/29.61 tff(328,plain,
% 45.51/29.61 (d(f6(P!7, tptp_fun_R_5(P!7))) <=> d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.51/29.61 inference(symmetry,[status(thm)],[327])).
% 45.51/29.61 tff(329,plain,
% 45.51/29.61 ((exists2(P!7) = exists1(P!7)) <=> (exists1(P!7) = exists2(P!7))),
% 45.51/29.61 inference(commutativity,[status(thm)],[])).
% 45.51/29.61 tff(330,plain,
% 45.51/29.61 (^[P: $i] : refl((~((~(exists1(P) = phi(apply(P, tptp_fun_X_3(P))))) | (~![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P))))))) <=> (~((~(exists1(P) = phi(apply(P, tptp_fun_X_3(P))))) | (~![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P))))))))),
% 45.51/29.61 inference(bind,[status(th)],[])).
% 45.51/29.61 tff(331,plain,
% 45.51/29.61 (![P: $i] : (~((~(exists1(P) = phi(apply(P, tptp_fun_X_3(P))))) | (~![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P))))))) <=> ![P: $i] : (~((~(exists1(P) = phi(apply(P, tptp_fun_X_3(P))))) | (~![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P)))))))),
% 45.51/29.61 inference(quant_intro,[status(thm)],[330])).
% 45.51/29.61 tff(332,plain,
% 45.51/29.61 (^[P: $i] : rewrite((~((~(exists1(P) = phi(apply(P, tptp_fun_X_3(P))))) | (~![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P))))))) <=> (~((~(exists1(P) = phi(apply(P, tptp_fun_X_3(P))))) | (~![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P))))))))),
% 45.51/29.61 inference(bind,[status(th)],[])).
% 45.51/29.61 tff(333,plain,
% 45.51/29.61 (![P: $i] : (~((~(exists1(P) = phi(apply(P, tptp_fun_X_3(P))))) | (~![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P))))))) <=> ![P: $i] : (~((~(exists1(P) = phi(apply(P, tptp_fun_X_3(P))))) | (~![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P)))))))),
% 45.51/29.61 inference(quant_intro,[status(thm)],[332])).
% 45.51/29.61 tff(334,plain,
% 45.51/29.61 (![P: $i] : (~((~(exists1(P) = phi(apply(P, tptp_fun_X_3(P))))) | (~![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P))))))) <=> ![P: $i] : (~((~(exists1(P) = phi(apply(P, tptp_fun_X_3(P))))) | (~![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P)))))))),
% 45.51/29.61 inference(transitivity,[status(thm)],[333, 331])).
% 45.51/29.61 tff(335,plain,
% 45.51/29.61 (^[P: $i] : rewrite(((exists1(P) = phi(apply(P, tptp_fun_X_3(P)))) & ![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P))))) <=> (~((~(exists1(P) = phi(apply(P, tptp_fun_X_3(P))))) | (~![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P))))))))),
% 45.51/29.61 inference(bind,[status(th)],[])).
% 45.51/29.61 tff(336,plain,
% 45.51/29.61 (![P: $i] : ((exists1(P) = phi(apply(P, tptp_fun_X_3(P)))) & ![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P))))) <=> ![P: $i] : (~((~(exists1(P) = phi(apply(P, tptp_fun_X_3(P))))) | (~![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P)))))))),
% 45.51/29.61 inference(quant_intro,[status(thm)],[335])).
% 45.51/29.61 tff(337,plain,
% 45.51/29.61 (![P: $i] : ?[X: $i] : ((exists1(P) = phi(apply(P, X))) & (~?[X1: $i] : existsprefers(apply(P, X1), apply(P, X)))) <=> ![P: $i] : ?[X: $i] : ((exists1(P) = phi(apply(P, X))) & (~?[X1: $i] : existsprefers(apply(P, X1), apply(P, X))))),
% 45.51/29.61 inference(rewrite,[status(thm)],[])).
% 45.51/29.61 tff(338,axiom,(![P: $i] : ?[X: $i] : ((exists1(P) = phi(apply(P, X))) & (~?[X1: $i] : existsprefers(apply(P, X1), apply(P, X))))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','exists1_axiom1')).
% 45.51/29.61 tff(339,plain,
% 45.51/29.61 (![P: $i] : ?[X: $i] : ((exists1(P) = phi(apply(P, X))) & (~?[X1: $i] : existsprefers(apply(P, X1), apply(P, X))))),
% 45.51/29.61 inference(modus_ponens,[status(thm)],[338, 337])).
% 45.51/29.61 tff(340,plain,(
% 45.51/29.61 ![P: $i] : ((exists1(P) = phi(apply(P, tptp_fun_X_3(P)))) & ![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P)))))),
% 45.51/29.61 inference(skolemize,[status(sab)],[339])).
% 45.51/29.61 tff(341,plain,
% 45.51/29.61 (![P: $i] : (~((~(exists1(P) = phi(apply(P, tptp_fun_X_3(P))))) | (~![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P)))))))),
% 45.51/29.61 inference(modus_ponens,[status(thm)],[340, 336])).
% 45.51/29.61 tff(342,plain,
% 45.51/29.61 (![P: $i] : (~((~(exists1(P) = phi(apply(P, tptp_fun_X_3(P))))) | (~![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P)))))))),
% 45.51/29.61 inference(modus_ponens,[status(thm)],[341, 334])).
% 45.51/29.61 tff(343,plain,
% 45.51/29.61 ((~![P: $i] : (~((~(exists1(P) = phi(apply(P, tptp_fun_X_3(P))))) | (~![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P)))))))) | (~((~(exists1(P!7) = phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~![X1: $i] : (~existsprefers(apply(P!7, X1), apply(P!7, tptp_fun_X_3(P!7)))))))),
% 45.51/29.61 inference(quant_inst,[status(thm)],[])).
% 45.51/29.61 tff(344,plain,
% 45.51/29.61 (~((~(exists1(P!7) = phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~![X1: $i] : (~existsprefers(apply(P!7, X1), apply(P!7, tptp_fun_X_3(P!7))))))),
% 45.51/29.61 inference(unit_resolution,[status(thm)],[343, 342])).
% 45.51/29.61 tff(345,plain,
% 45.51/29.61 (((~(exists1(P!7) = phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~![X1: $i] : (~existsprefers(apply(P!7, X1), apply(P!7, tptp_fun_X_3(P!7)))))) | (exists1(P!7) = phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.51/29.61 inference(tautology,[status(thm)],[])).
% 45.51/29.61 tff(346,plain,
% 45.51/29.61 (exists1(P!7) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.51/29.61 inference(unit_resolution,[status(thm)],[345, 344])).
% 45.51/29.62 tff(347,plain,
% 45.51/29.62 (phi(apply(P!7, tptp_fun_X_3(P!7))) = exists1(P!7)),
% 45.51/29.62 inference(symmetry,[status(thm)],[346])).
% 45.51/29.62 tff(348,assumption,(~bool(apply(P!7, tptp_fun_X_3(P!7)))), introduced(assumption)).
% 45.51/29.62 tff(349,plain,
% 45.51/29.62 (^[A: $i, B: $i] : refl((bool(A) | (impl(A, B) = phi(A))) <=> (bool(A) | (impl(A, B) = phi(A))))),
% 45.51/29.62 inference(bind,[status(th)],[])).
% 45.51/29.62 tff(350,plain,
% 45.51/29.62 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A))) <=> ![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 45.51/29.62 inference(quant_intro,[status(thm)],[349])).
% 45.51/29.62 tff(351,plain,
% 45.51/29.62 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A))) <=> ![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 45.51/29.62 inference(rewrite,[status(thm)],[])).
% 45.51/29.62 tff(352,plain,
% 45.51/29.62 (^[A: $i, B: $i] : rewrite(((~bool(A)) => (impl(A, B) = phi(A))) <=> (bool(A) | (impl(A, B) = phi(A))))),
% 45.51/29.62 inference(bind,[status(th)],[])).
% 45.51/29.62 tff(353,plain,
% 45.51/29.62 (![A: $i, B: $i] : ((~bool(A)) => (impl(A, B) = phi(A))) <=> ![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 45.51/29.62 inference(quant_intro,[status(thm)],[352])).
% 45.51/29.62 tff(354,axiom,(![A: $i, B: $i] : ((~bool(A)) => (impl(A, B) = phi(A)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','impl_axiom1')).
% 45.51/29.62 tff(355,plain,
% 45.51/29.62 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 45.51/29.62 inference(modus_ponens,[status(thm)],[354, 353])).
% 45.51/29.62 tff(356,plain,
% 45.51/29.62 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 45.51/29.62 inference(modus_ponens,[status(thm)],[355, 351])).
% 45.51/29.62 tff(357,plain,(
% 45.51/29.62 ![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 45.51/29.62 inference(skolemize,[status(sab)],[356])).
% 45.51/29.62 tff(358,plain,
% 45.51/29.62 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 45.51/29.62 inference(modus_ponens,[status(thm)],[357, 350])).
% 45.51/29.62 tff(359,plain,
% 45.51/29.62 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = phi(apply(P!7, tptp_fun_X_3(P!7)))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = phi(apply(P!7, tptp_fun_X_3(P!7)))))),
% 45.51/29.62 inference(rewrite,[status(thm)],[])).
% 45.51/29.62 tff(360,plain,
% 45.51/29.62 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = phi(apply(P!7, tptp_fun_X_3(P!7)))))),
% 45.51/29.62 inference(quant_inst,[status(thm)],[])).
% 45.51/29.62 tff(361,plain,
% 45.51/29.62 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.51/29.62 inference(modus_ponens,[status(thm)],[360, 359])).
% 45.51/29.62 tff(362,plain,
% 45.51/29.62 (bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.51/29.62 inference(unit_resolution,[status(thm)],[361, 358])).
% 45.51/29.62 tff(363,plain,
% 45.51/29.62 (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.51/29.62 inference(unit_resolution,[status(thm)],[362, 348])).
% 45.51/29.62 tff(364,assumption,(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = phi(apply(P!7, tptp_fun_X_3(P!7)))), introduced(assumption)).
% 45.51/29.62 tff(365,assumption,(~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))), introduced(assumption)).
% 45.51/29.62 tff(366,plain,
% 45.51/29.62 (d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) <=> d(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.51/29.62 inference(monotonicity,[status(thm)],[364])).
% 45.51/29.62 tff(367,plain,
% 45.51/29.62 (d(phi(apply(P!7, tptp_fun_X_3(P!7)))) <=> d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))),
% 45.51/29.62 inference(symmetry,[status(thm)],[366])).
% 45.51/29.62 tff(368,assumption,(~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))))), introduced(assumption)).
% 45.51/29.62 tff(369,plain,
% 45.51/29.62 (((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))))) | (phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))),
% 45.51/29.62 inference(tautology,[status(thm)],[])).
% 45.53/29.62 tff(370,plain,
% 45.53/29.62 (phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))),
% 45.53/29.62 inference(unit_resolution,[status(thm)],[369, 368])).
% 45.53/29.62 tff(371,plain,
% 45.53/29.62 (apply(P!7, tptp_fun_X_3(P!7)) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.53/29.62 inference(symmetry,[status(thm)],[370])).
% 45.53/29.62 tff(372,plain,
% 45.53/29.62 (d(apply(P!7, tptp_fun_X_3(P!7))) <=> d(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.53/29.62 inference(monotonicity,[status(thm)],[371])).
% 45.53/29.62 tff(373,plain,
% 45.53/29.62 (d(apply(P!7, tptp_fun_X_3(P!7))) <=> d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))),
% 45.53/29.62 inference(transitivity,[status(thm)],[372, 367])).
% 45.53/29.62 tff(374,plain,
% 45.53/29.62 (((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))))) | d(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.53/29.62 inference(tautology,[status(thm)],[])).
% 45.53/29.62 tff(375,plain,
% 45.53/29.62 (d(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.53/29.62 inference(unit_resolution,[status(thm)],[374, 368])).
% 45.53/29.62 tff(376,plain,
% 45.53/29.62 (d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))),
% 45.53/29.62 inference(modus_ponens,[status(thm)],[375, 373])).
% 45.53/29.62 tff(377,plain,
% 45.53/29.62 ($false),
% 45.53/29.62 inference(unit_resolution,[status(thm)],[365, 376])).
% 45.53/29.62 tff(378,plain,(((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))))) | d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = phi(apply(P!7, tptp_fun_X_3(P!7)))))), inference(lemma,lemma(discharge,[]))).
% 45.53/29.62 tff(379,plain,
% 45.53/29.62 ((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))))),
% 45.53/29.62 inference(unit_resolution,[status(thm)],[378, 365, 364])).
% 45.53/29.62 tff(380,plain,
% 45.53/29.62 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))))) | (~(d(apply(P!7, tptp_fun_X_3(P!7))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))))) | (~(d(apply(P!7, tptp_fun_X_3(P!7))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err)))))),
% 45.53/29.62 inference(rewrite,[status(thm)],[])).
% 45.53/29.62 tff(381,plain,
% 45.53/29.62 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))))) | (~(d(apply(P!7, tptp_fun_X_3(P!7))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err)))))),
% 45.53/29.62 inference(quant_inst,[status(thm)],[])).
% 45.53/29.62 tff(382,plain,
% 45.53/29.62 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))))) | (~(d(apply(P!7, tptp_fun_X_3(P!7))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err))))),
% 45.53/29.62 inference(modus_ponens,[status(thm)],[381, 380])).
% 45.53/29.62 tff(383,plain,
% 45.53/29.62 ((~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))))) | (~(d(apply(P!7, tptp_fun_X_3(P!7))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err))))),
% 45.53/29.62 inference(unit_resolution,[status(thm)],[382, 17])).
% 45.53/29.62 tff(384,plain,
% 45.53/29.62 (~(d(apply(P!7, tptp_fun_X_3(P!7))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err)))),
% 45.53/29.62 inference(unit_resolution,[status(thm)],[383, 379])).
% 45.53/29.62 tff(385,plain,
% 45.53/29.62 ((d(apply(P!7, tptp_fun_X_3(P!7))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err))) | (phi(apply(P!7, tptp_fun_X_3(P!7))) = err)),
% 45.53/29.62 inference(tautology,[status(thm)],[])).
% 45.53/29.62 tff(386,plain,
% 45.53/29.62 (phi(apply(P!7, tptp_fun_X_3(P!7))) = err),
% 45.53/29.62 inference(unit_resolution,[status(thm)],[385, 384])).
% 45.53/29.62 tff(387,plain,
% 45.53/29.62 (err = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.53/29.62 inference(symmetry,[status(thm)],[386])).
% 45.53/29.62 tff(388,plain,
% 45.53/29.62 (d(err) <=> d(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.53/29.62 inference(monotonicity,[status(thm)],[387])).
% 45.53/29.62 tff(389,plain,
% 45.53/29.62 (d(phi(apply(P!7, tptp_fun_X_3(P!7)))) <=> d(err)),
% 45.53/29.62 inference(symmetry,[status(thm)],[388])).
% 45.53/29.62 tff(390,plain,
% 45.53/29.62 ((~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) <=> (~d(err))),
% 45.53/29.62 inference(monotonicity,[status(thm)],[389])).
% 45.53/29.62 tff(391,plain,
% 45.53/29.62 ((~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))) <=> (~d(phi(apply(P!7, tptp_fun_X_3(P!7)))))),
% 45.53/29.62 inference(monotonicity,[status(thm)],[366])).
% 45.53/29.62 tff(392,plain,
% 45.53/29.62 (~d(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.53/29.62 inference(modus_ponens,[status(thm)],[365, 391])).
% 45.53/29.62 tff(393,plain,
% 45.53/29.62 (~d(err)),
% 45.53/29.62 inference(modus_ponens,[status(thm)],[392, 390])).
% 45.53/29.62 tff(394,plain,
% 45.53/29.62 (d(err) <=> d(err)),
% 45.53/29.62 inference(rewrite,[status(thm)],[])).
% 45.53/29.62 tff(395,plain,
% 45.53/29.62 (d(err)),
% 45.53/29.62 inference(and_elim,[status(thm)],[2])).
% 45.53/29.62 tff(396,plain,
% 45.53/29.62 (d(err)),
% 45.53/29.62 inference(modus_ponens,[status(thm)],[395, 394])).
% 45.53/29.62 tff(397,plain,
% 45.53/29.62 ($false),
% 45.53/29.62 inference(unit_resolution,[status(thm)],[396, 393])).
% 45.53/29.62 tff(398,plain,(d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = phi(apply(P!7, tptp_fun_X_3(P!7)))))), inference(lemma,lemma(discharge,[]))).
% 45.53/29.62 tff(399,plain,
% 45.53/29.62 (d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))),
% 45.53/29.62 inference(unit_resolution,[status(thm)],[398, 363])).
% 45.53/29.62 tff(400,plain,
% 45.53/29.62 (bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) <=> bool(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.53/29.62 inference(monotonicity,[status(thm)],[363])).
% 45.53/29.62 tff(401,plain,
% 45.53/29.62 (bool(phi(apply(P!7, tptp_fun_X_3(P!7)))) <=> bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))),
% 45.53/29.62 inference(symmetry,[status(thm)],[400])).
% 45.53/29.62 tff(402,plain,
% 45.53/29.62 (bool(apply(P!7, tptp_fun_X_3(P!7))) <=> bool(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.53/29.62 inference(monotonicity,[status(thm)],[371])).
% 45.53/29.62 tff(403,plain,
% 45.53/29.62 (bool(apply(P!7, tptp_fun_X_3(P!7))) <=> bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))),
% 45.53/29.62 inference(transitivity,[status(thm)],[402, 401])).
% 45.53/29.62 tff(404,plain,
% 45.53/29.62 ((~bool(apply(P!7, tptp_fun_X_3(P!7)))) <=> (~bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))))),
% 45.53/29.62 inference(monotonicity,[status(thm)],[403])).
% 45.53/29.62 tff(405,plain,
% 45.53/29.62 (~bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))),
% 45.53/29.62 inference(modus_ponens,[status(thm)],[348, 404])).
% 45.53/29.62 tff(406,plain,
% 45.53/29.62 (^[P: $i, X: $i, R: $i] : refl((f4(P, X, R) = impl(apply(P, X), R)) <=> (f4(P, X, R) = impl(apply(P, X), R)))),
% 45.53/29.62 inference(bind,[status(th)],[])).
% 45.53/29.62 tff(407,plain,
% 45.53/29.62 (![P: $i, X: $i, R: $i] : (f4(P, X, R) = impl(apply(P, X), R)) <=> ![P: $i, X: $i, R: $i] : (f4(P, X, R) = impl(apply(P, X), R))),
% 45.53/29.62 inference(quant_intro,[status(thm)],[406])).
% 45.53/29.62 tff(408,plain,
% 45.53/29.62 (![P: $i, X: $i, R: $i] : (f4(P, X, R) = impl(apply(P, X), R)) <=> ![P: $i, X: $i, R: $i] : (f4(P, X, R) = impl(apply(P, X), R))),
% 45.53/29.62 inference(rewrite,[status(thm)],[])).
% 45.53/29.62 tff(409,axiom,(![P: $i, X: $i, R: $i] : (f4(P, X, R) = impl(apply(P, X), R))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','def_f4')).
% 45.53/29.62 tff(410,plain,
% 45.53/29.62 (![P: $i, X: $i, R: $i] : (f4(P, X, R) = impl(apply(P, X), R))),
% 45.53/29.62 inference(modus_ponens,[status(thm)],[409, 408])).
% 45.53/29.62 tff(411,plain,(
% 45.53/29.62 ![P: $i, X: $i, R: $i] : (f4(P, X, R) = impl(apply(P, X), R))),
% 45.53/29.62 inference(skolemize,[status(sab)],[410])).
% 45.53/29.62 tff(412,plain,
% 45.53/29.62 (![P: $i, X: $i, R: $i] : (f4(P, X, R) = impl(apply(P, X), R))),
% 45.53/29.62 inference(modus_ponens,[status(thm)],[411, 407])).
% 45.53/29.62 tff(413,plain,
% 45.53/29.62 ((~![P: $i, X: $i, R: $i] : (f4(P, X, R) = impl(apply(P, X), R))) | (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 45.53/29.62 inference(quant_inst,[status(thm)],[])).
% 45.53/29.62 tff(414,plain,
% 45.53/29.62 (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))),
% 45.53/29.62 inference(unit_resolution,[status(thm)],[413, 412])).
% 45.53/29.62 tff(415,plain,
% 45.53/29.62 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))),
% 45.53/29.62 inference(symmetry,[status(thm)],[414])).
% 45.53/29.62 tff(416,plain,
% 45.53/29.62 (bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> bool(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.53/29.62 inference(monotonicity,[status(thm)],[415])).
% 45.53/29.62 tff(417,plain,
% 45.53/29.62 (bool(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) <=> bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 45.53/29.62 inference(symmetry,[status(thm)],[416])).
% 45.53/29.62 tff(418,plain,
% 45.53/29.62 (((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | ((~bool(not1(false))) | (impl(false, not1(false)) = not1(false)))) <=> ((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | (~bool(not1(false))) | (impl(false, not1(false)) = not1(false)))),
% 45.53/29.62 inference(rewrite,[status(thm)],[])).
% 45.53/29.62 tff(419,plain,
% 45.53/29.62 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | ((~bool(not1(false))) | (impl(false, not1(false)) = not1(false)))),
% 45.53/29.62 inference(quant_inst,[status(thm)],[])).
% 45.53/29.62 tff(420,plain,
% 45.53/29.62 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | (~bool(not1(false))) | (impl(false, not1(false)) = not1(false))),
% 45.53/29.62 inference(modus_ponens,[status(thm)],[419, 418])).
% 45.53/29.62 tff(421,plain,
% 45.53/29.62 (impl(false, not1(false)) = not1(false)),
% 45.53/29.62 inference(unit_resolution,[status(thm)],[420, 89, 272])).
% 45.53/29.62 tff(422,plain,
% 45.53/29.62 ((d(err) | (~(phi(err) = err))) | (~d(err))),
% 45.53/29.62 inference(tautology,[status(thm)],[])).
% 45.53/29.62 tff(423,plain,
% 45.53/29.62 (d(err) | (~(phi(err) = err))),
% 45.53/29.62 inference(unit_resolution,[status(thm)],[422, 396])).
% 45.53/29.62 tff(424,plain,
% 45.53/29.62 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(err)) | (~(phi(err) = err)))) | (~(d(err) | (~(phi(err) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(err)) | (~(phi(err) = err)))) | (~(d(err) | (~(phi(err) = err)))))),
% 45.53/29.62 inference(rewrite,[status(thm)],[])).
% 45.53/29.62 tff(425,plain,
% 45.53/29.62 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(err)) | (~(phi(err) = err)))) | (~(d(err) | (~(phi(err) = err)))))),
% 45.53/29.62 inference(quant_inst,[status(thm)],[])).
% 45.53/29.62 tff(426,plain,
% 45.53/29.62 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(err)) | (~(phi(err) = err)))) | (~(d(err) | (~(phi(err) = err))))),
% 45.53/29.62 inference(modus_ponens,[status(thm)],[425, 424])).
% 45.53/29.62 tff(427,plain,
% 45.53/29.62 (~((~d(err)) | (~(phi(err) = err)))),
% 45.53/29.62 inference(unit_resolution,[status(thm)],[426, 17, 423])).
% 45.53/29.62 tff(428,plain,
% 45.53/29.62 (((~d(err)) | (~(phi(err) = err))) | (phi(err) = err)),
% 45.53/29.62 inference(tautology,[status(thm)],[])).
% 45.53/29.62 tff(429,plain,
% 45.53/29.62 (phi(err) = err),
% 45.53/29.62 inference(unit_resolution,[status(thm)],[428, 427])).
% 45.53/29.62 tff(430,plain,
% 45.53/29.62 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), err) = phi(err))),
% 45.53/29.62 inference(quant_inst,[status(thm)],[])).
% 45.53/29.62 tff(431,plain,
% 45.53/29.62 (lazy_impl(not1(false), err) = phi(err)),
% 45.53/29.62 inference(unit_resolution,[status(thm)],[430, 33])).
% 45.53/29.62 tff(432,assumption,(~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false)), introduced(assumption)).
% 45.53/29.62 tff(433,plain,
% 45.53/29.62 ((not1(false) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) <=> (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = not1(false))),
% 45.53/29.62 inference(commutativity,[status(thm)],[])).
% 45.53/29.62 tff(434,plain,
% 45.53/29.62 (d(lazy_impl(prop(P!6), P!6)) <=> d(f7(P!6))),
% 45.53/29.62 inference(monotonicity,[status(thm)],[198])).
% 45.53/29.62 tff(435,plain,
% 45.53/29.62 (d(f7(P!6)) <=> d(lazy_impl(prop(P!6), P!6))),
% 45.53/29.62 inference(symmetry,[status(thm)],[434])).
% 45.53/29.62 tff(436,plain,
% 45.53/29.62 (f7(P!6) = false),
% 45.53/29.62 inference(transitivity,[status(thm)],[287, 200, 202, 35, 23])).
% 45.53/29.62 tff(437,plain,
% 45.53/29.62 (d(f7(P!6)) <=> d(false)),
% 45.53/29.62 inference(monotonicity,[status(thm)],[436])).
% 45.53/29.62 tff(438,plain,
% 45.53/29.62 (d(false) <=> d(f7(P!6))),
% 45.53/29.62 inference(symmetry,[status(thm)],[437])).
% 45.53/29.62 tff(439,plain,
% 45.53/29.62 (d(false) <=> d(lazy_impl(prop(P!6), P!6))),
% 45.53/29.62 inference(transitivity,[status(thm)],[438, 435])).
% 45.53/29.62 tff(440,plain,
% 45.53/29.62 (d(lazy_impl(prop(P!6), P!6))),
% 45.53/29.62 inference(modus_ponens,[status(thm)],[5, 439])).
% 45.53/29.62 tff(441,plain,
% 45.53/29.62 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~((~(lazy_impl(prop(P!6), P!6) = not1(false))) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~((~(lazy_impl(prop(P!6), P!6) = not1(false))) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false)))))))),
% 45.53/29.62 inference(rewrite,[status(thm)],[])).
% 45.53/29.62 tff(442,plain,
% 45.53/29.62 ((forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~((~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(lazy_impl(prop(P!6), P!6) = not1(false))))))) <=> (forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~((~(lazy_impl(prop(P!6), P!6) = not1(false))) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false))))))),
% 45.53/29.62 inference(rewrite,[status(thm)],[])).
% 45.53/29.62 tff(443,plain,
% 45.53/29.62 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~((~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(lazy_impl(prop(P!6), P!6) = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~((~(lazy_impl(prop(P!6), P!6) = not1(false))) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false)))))))),
% 45.53/29.62 inference(monotonicity,[status(thm)],[442])).
% 45.53/29.62 tff(444,plain,
% 45.53/29.62 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~((~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(lazy_impl(prop(P!6), P!6) = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~((~(lazy_impl(prop(P!6), P!6) = not1(false))) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false)))))))),
% 45.53/29.62 inference(transitivity,[status(thm)],[443, 441])).
% 45.53/29.62 tff(445,plain,
% 45.53/29.62 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~((~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(lazy_impl(prop(P!6), P!6) = not1(false)))))))),
% 45.53/29.62 inference(quant_inst,[status(thm)],[])).
% 45.53/29.62 tff(446,plain,
% 45.53/29.62 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~((~(lazy_impl(prop(P!6), P!6) = not1(false))) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false))))))),
% 45.53/29.62 inference(modus_ponens,[status(thm)],[445, 444])).
% 45.53/29.62 tff(447,plain,
% 45.53/29.62 (forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~((~(lazy_impl(prop(P!6), P!6) = not1(false))) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false)))))),
% 45.53/29.62 inference(unit_resolution,[status(thm)],[446, 159])).
% 45.53/29.62 tff(448,plain,
% 45.53/29.62 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.53/29.62 inference(quant_inst,[status(thm)],[])).
% 45.53/29.62 tff(449,plain,
% 45.53/29.62 (f7(tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 45.53/29.62 inference(unit_resolution,[status(thm)],[448, 195])).
% 45.53/29.62 tff(450,plain,
% 45.53/29.62 (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = f7(tptp_fun_R_5(P!7))),
% 45.53/29.62 inference(symmetry,[status(thm)],[449])).
% 45.53/29.62 tff(451,plain,
% 45.53/29.62 (forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6)) <=> forallprefers(f7(tptp_fun_R_5(P!7)), f7(P!6))),
% 45.53/29.62 inference(monotonicity,[status(thm)],[450, 198])).
% 45.53/29.62 tff(452,plain,
% 45.53/29.62 (forallprefers(f7(tptp_fun_R_5(P!7)), f7(P!6)) <=> forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6))),
% 45.53/29.62 inference(symmetry,[status(thm)],[451])).
% 45.53/29.62 tff(453,plain,
% 45.53/29.62 ((~forallprefers(f7(tptp_fun_R_5(P!7)), f7(P!6))) <=> (~forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6)))),
% 45.53/29.62 inference(monotonicity,[status(thm)],[452])).
% 45.53/29.62 tff(454,plain,
% 45.53/29.62 ((~![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))) | (~forallprefers(f7(tptp_fun_R_5(P!7)), f7(P!6)))),
% 45.53/29.62 inference(quant_inst,[status(thm)],[])).
% 45.53/29.62 tff(455,plain,
% 45.53/29.62 (~forallprefers(f7(tptp_fun_R_5(P!7)), f7(P!6))),
% 45.53/29.62 inference(unit_resolution,[status(thm)],[454, 218])).
% 45.53/29.62 tff(456,plain,
% 45.53/29.62 (~forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6))),
% 45.53/29.62 inference(modus_ponens,[status(thm)],[455, 453])).
% 45.53/29.62 tff(457,plain,
% 45.53/29.62 ((~(forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~((~(lazy_impl(prop(P!6), P!6) = not1(false))) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false))))))) | forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6)) | (~((~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~((~(lazy_impl(prop(P!6), P!6) = not1(false))) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false))))))),
% 45.53/29.62 inference(tautology,[status(thm)],[])).
% 45.53/29.62 tff(458,plain,
% 45.53/29.62 (~((~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~((~(lazy_impl(prop(P!6), P!6) = not1(false))) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false)))))),
% 45.53/29.62 inference(unit_resolution,[status(thm)],[457, 456, 447])).
% 45.53/29.62 tff(459,plain,
% 45.53/29.62 (((~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~((~(lazy_impl(prop(P!6), P!6) = not1(false))) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false))))) | (d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))),
% 45.53/29.62 inference(tautology,[status(thm)],[])).
% 45.53/29.62 tff(460,plain,
% 45.53/29.62 (d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6)))),
% 45.53/29.62 inference(unit_resolution,[status(thm)],[459, 458])).
% 45.53/29.62 tff(461,plain,
% 45.53/29.62 ((~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))) | d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6)))),
% 45.53/29.62 inference(tautology,[status(thm)],[])).
% 45.53/29.62 tff(462,plain,
% 45.53/29.62 (d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6)))),
% 45.53/29.62 inference(unit_resolution,[status(thm)],[461, 460])).
% 45.53/29.62 tff(463,plain,
% 45.53/29.62 (d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.53/29.62 inference(unit_resolution,[status(thm)],[462, 440])).
% 45.53/29.62 tff(464,plain,
% 45.53/29.62 ((d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~(phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.53/29.62 inference(tautology,[status(thm)],[])).
% 45.53/29.62 tff(465,plain,
% 45.53/29.63 (d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~(phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err))),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[464, 463])).
% 45.53/29.63 tff(466,plain,
% 45.53/29.63 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~(phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~(phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)))))),
% 45.53/29.63 inference(rewrite,[status(thm)],[])).
% 45.53/29.63 tff(467,plain,
% 45.53/29.63 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~(phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)))))),
% 45.53/29.63 inference(quant_inst,[status(thm)],[])).
% 45.53/29.63 tff(468,plain,
% 45.53/29.63 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~(phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err))))),
% 45.53/29.63 inference(modus_ponens,[status(thm)],[467, 466])).
% 45.53/29.63 tff(469,plain,
% 45.53/29.63 (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[468, 17, 465])).
% 45.53/29.63 tff(470,plain,
% 45.53/29.63 (((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.53/29.63 inference(tautology,[status(thm)],[])).
% 45.53/29.63 tff(471,plain,
% 45.53/29.63 (phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[470, 469])).
% 45.53/29.63 tff(472,assumption,(~(bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) <=> ((apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))))), introduced(assumption)).
% 45.53/29.63 tff(473,plain,
% 45.53/29.63 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) <=> ((apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))))),
% 45.53/29.63 inference(quant_inst,[status(thm)],[])).
% 45.53/29.63 tff(474,plain,
% 45.53/29.63 ($false),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[473, 249, 472])).
% 45.53/29.63 tff(475,plain,(bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) <=> ((apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 45.53/29.63 tff(476,assumption,(~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))))), introduced(assumption)).
% 45.53/29.63 tff(477,plain,
% 45.53/29.63 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = phi(apply(P!7, tptp_fun_X_4(not1(false), P!7)))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = phi(apply(P!7, tptp_fun_X_4(not1(false), P!7)))))),
% 45.53/29.63 inference(rewrite,[status(thm)],[])).
% 45.53/29.63 tff(478,plain,
% 45.53/29.63 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = phi(apply(P!7, tptp_fun_X_4(not1(false), P!7)))))),
% 45.53/29.63 inference(quant_inst,[status(thm)],[])).
% 45.53/29.63 tff(479,plain,
% 45.53/29.63 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))))),
% 45.53/29.63 inference(modus_ponens,[status(thm)],[478, 477])).
% 45.53/29.63 tff(480,plain,
% 45.53/29.63 (bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))))),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[479, 358])).
% 45.53/29.63 tff(481,plain,
% 45.53/29.63 (bool(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[480, 476])).
% 45.53/29.63 tff(482,plain,
% 45.53/29.63 ((~(bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) <=> ((apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))))) | (~bool(apply(P!7, tptp_fun_X_4(not1(false), P!7)))) | ((apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false)))),
% 45.53/29.63 inference(tautology,[status(thm)],[])).
% 45.53/29.63 tff(483,plain,
% 45.53/29.63 ((apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[482, 481, 475])).
% 45.53/29.63 tff(484,plain,
% 45.53/29.63 ((~((apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false)))) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))),
% 45.53/29.63 inference(tautology,[status(thm)],[])).
% 45.53/29.63 tff(485,plain,
% 45.53/29.63 (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false)),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[484, 432, 483])).
% 45.53/29.63 tff(486,plain,
% 45.53/29.63 (d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) <=> d(not1(false))),
% 45.53/29.63 inference(monotonicity,[status(thm)],[485])).
% 45.53/29.63 tff(487,plain,
% 45.53/29.63 (d(not1(false)) <=> d(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.53/29.63 inference(symmetry,[status(thm)],[486])).
% 45.53/29.63 tff(488,plain,
% 45.53/29.63 (d(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.53/29.63 inference(modus_ponens,[status(thm)],[40, 487])).
% 45.53/29.63 tff(489,plain,
% 45.53/29.63 (bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) <=> ((apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false)))),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[473, 249])).
% 45.53/29.63 tff(490,plain,
% 45.53/29.63 ((~(bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) <=> ((apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))))) | ((apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false)))),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[482, 481])).
% 45.53/29.63 tff(491,plain,
% 45.53/29.63 ((apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[490, 489])).
% 45.53/29.63 tff(492,plain,
% 45.53/29.63 ((~((apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false)))) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[484, 432])).
% 45.53/29.63 tff(493,plain,
% 45.53/29.63 (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false)),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[492, 491])).
% 45.53/29.63 tff(494,assumption,(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = apply(P!7, tptp_fun_X_4(not1(false), P!7))), introduced(assumption)).
% 45.53/29.63 tff(495,plain,
% 45.53/29.63 (phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = not1(false)),
% 45.53/29.63 inference(transitivity,[status(thm)],[494, 493])).
% 45.53/29.63 tff(496,plain,
% 45.53/29.63 ((impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = phi(apply(P!7, tptp_fun_X_4(not1(false), P!7)))) <=> (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = not1(false))),
% 45.53/29.63 inference(monotonicity,[status(thm)],[495])).
% 45.53/29.63 tff(497,plain,
% 45.53/29.63 ((impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = not1(false)) <=> (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))))),
% 45.53/29.63 inference(symmetry,[status(thm)],[496])).
% 45.53/29.63 tff(498,plain,
% 45.53/29.63 (((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | ((~bool(not1(false))) | (impl(not1(false), not1(false)) = not1(false)))) <=> ((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | (~bool(not1(false))) | (impl(not1(false), not1(false)) = not1(false)))),
% 45.53/29.63 inference(rewrite,[status(thm)],[])).
% 45.53/29.63 tff(499,plain,
% 45.53/29.63 ((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | ((~bool(not1(false))) | (impl(not1(false), not1(false)) = not1(false)))),
% 45.53/29.63 inference(quant_inst,[status(thm)],[])).
% 45.53/29.63 tff(500,plain,
% 45.53/29.63 ((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | (~bool(not1(false))) | (impl(not1(false), not1(false)) = not1(false))),
% 45.53/29.63 inference(modus_ponens,[status(thm)],[499, 498])).
% 45.53/29.63 tff(501,plain,
% 45.53/29.63 (impl(not1(false), not1(false)) = not1(false)),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[500, 110, 272])).
% 45.53/29.63 tff(502,plain,
% 45.53/29.63 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = impl(not1(false), not1(false))),
% 45.53/29.63 inference(monotonicity,[status(thm)],[493])).
% 45.53/29.63 tff(503,plain,
% 45.53/29.63 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = not1(false)),
% 45.53/29.63 inference(transitivity,[status(thm)],[502, 501])).
% 45.53/29.63 tff(504,plain,
% 45.53/29.63 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = phi(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.53/29.63 inference(modus_ponens,[status(thm)],[503, 497])).
% 45.53/29.63 tff(505,plain,
% 45.53/29.63 ($false),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[476, 504])).
% 45.53/29.63 tff(506,plain,((impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = phi(apply(P!7, tptp_fun_X_4(not1(false), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = apply(P!7, tptp_fun_X_4(not1(false), P!7)))) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false)), inference(lemma,lemma(discharge,[]))).
% 45.53/29.63 tff(507,plain,
% 45.53/29.63 (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[506, 432, 476])).
% 45.53/29.63 tff(508,plain,
% 45.53/29.63 (((~d(apply(P!7, tptp_fun_X_4(not1(false), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = apply(P!7, tptp_fun_X_4(not1(false), P!7))))) | (phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.53/29.63 inference(tautology,[status(thm)],[])).
% 45.53/29.63 tff(509,plain,
% 45.53/29.63 ((~d(apply(P!7, tptp_fun_X_4(not1(false), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = apply(P!7, tptp_fun_X_4(not1(false), P!7))))),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[508, 507])).
% 45.53/29.63 tff(510,plain,
% 45.53/29.63 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(apply(P!7, tptp_fun_X_4(not1(false), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = apply(P!7, tptp_fun_X_4(not1(false), P!7)))))) | (~(d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(apply(P!7, tptp_fun_X_4(not1(false), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = apply(P!7, tptp_fun_X_4(not1(false), P!7)))))) | (~(d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err)))))),
% 45.53/29.63 inference(rewrite,[status(thm)],[])).
% 45.53/29.63 tff(511,plain,
% 45.53/29.63 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(apply(P!7, tptp_fun_X_4(not1(false), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = apply(P!7, tptp_fun_X_4(not1(false), P!7)))))) | (~(d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err)))))),
% 45.53/29.63 inference(quant_inst,[status(thm)],[])).
% 45.53/29.63 tff(512,plain,
% 45.53/29.63 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(apply(P!7, tptp_fun_X_4(not1(false), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = apply(P!7, tptp_fun_X_4(not1(false), P!7)))))) | (~(d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err))))),
% 45.53/29.63 inference(modus_ponens,[status(thm)],[511, 510])).
% 45.53/29.63 tff(513,plain,
% 45.53/29.63 ((~((~d(apply(P!7, tptp_fun_X_4(not1(false), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = apply(P!7, tptp_fun_X_4(not1(false), P!7)))))) | (~(d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err))))),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[512, 17])).
% 45.53/29.63 tff(514,plain,
% 45.53/29.63 (~(d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err)))),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[513, 509])).
% 45.53/29.63 tff(515,plain,
% 45.53/29.63 ((d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err))) | (~d(apply(P!7, tptp_fun_X_4(not1(false), P!7))))),
% 45.53/29.63 inference(tautology,[status(thm)],[])).
% 45.53/29.63 tff(516,plain,
% 45.53/29.63 (~d(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[515, 514])).
% 45.53/29.63 tff(517,plain,
% 45.53/29.63 ($false),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[516, 488])).
% 45.53/29.63 tff(518,plain,((apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false) | (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))))), inference(lemma,lemma(discharge,[]))).
% 45.53/29.63 tff(519,plain,
% 45.53/29.63 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = phi(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[518, 432])).
% 45.53/29.63 tff(520,plain,
% 45.53/29.63 ((~![P: $i, X: $i, R: $i] : (f4(P, X, R) = impl(apply(P, X), R))) | (f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)))),
% 45.53/29.63 inference(quant_inst,[status(thm)],[])).
% 45.53/29.63 tff(521,plain,
% 45.53/29.63 (f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[520, 412])).
% 45.53/29.63 tff(522,plain,
% 45.53/29.63 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))),
% 45.53/29.63 inference(symmetry,[status(thm)],[521])).
% 45.53/29.63 tff(523,assumption,(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = phi(apply(P!7, tptp_fun_X_4(not1(false), P!7)))), introduced(assumption)).
% 45.53/29.63 tff(524,plain,
% 45.53/29.63 (phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))),
% 45.53/29.63 inference(symmetry,[status(thm)],[523])).
% 45.53/29.63 tff(525,assumption,(~(impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false))))), introduced(assumption)).
% 45.53/29.63 tff(526,plain,
% 45.53/29.63 ((~![P: $i, R: $i] : (~((~(f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R)))) | (~![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R))))))) | (~((~(f5(P!7, not1(false)) = phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))))) | (~![X1: $i] : (~forallprefers(f4(P!7, X1, not1(false)), f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))))))),
% 45.53/29.63 inference(quant_inst,[status(thm)],[])).
% 45.53/29.63 tff(527,plain,
% 45.53/29.63 (~((~(f5(P!7, not1(false)) = phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))))) | (~![X1: $i] : (~forallprefers(f4(P!7, X1, not1(false)), f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))))))),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[526, 307])).
% 45.53/29.63 tff(528,plain,
% 45.53/29.63 (((~(f5(P!7, not1(false)) = phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))))) | (~![X1: $i] : (~forallprefers(f4(P!7, X1, not1(false)), f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))))) | (f5(P!7, not1(false)) = phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))))),
% 45.53/29.63 inference(tautology,[status(thm)],[])).
% 45.53/29.63 tff(529,plain,
% 45.53/29.63 (f5(P!7, not1(false)) = phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[528, 527])).
% 45.53/29.63 tff(530,plain,
% 45.53/29.63 (phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = f5(P!7, not1(false))),
% 45.53/29.63 inference(symmetry,[status(thm)],[529])).
% 45.53/29.63 tff(531,assumption,(~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))), introduced(assumption)).
% 45.53/29.63 tff(532,plain,
% 45.53/29.63 (((~d(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))) | (~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))))) | (phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 45.53/29.63 inference(tautology,[status(thm)],[])).
% 45.53/29.63 tff(533,plain,
% 45.53/29.63 ((~d(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))) | (~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))))),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[532, 531])).
% 45.53/29.63 tff(534,plain,
% 45.53/29.63 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))) | (~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))))) | (~(d(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) | (~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))) | (~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))))) | (~(d(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) | (~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err)))))),
% 45.53/29.63 inference(rewrite,[status(thm)],[])).
% 45.53/29.63 tff(535,plain,
% 45.53/29.63 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))) | (~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))))) | (~(d(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) | (~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err)))))),
% 45.53/29.63 inference(quant_inst,[status(thm)],[])).
% 45.53/29.63 tff(536,plain,
% 45.53/29.63 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))) | (~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))))) | (~(d(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) | (~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err))))),
% 45.53/29.63 inference(modus_ponens,[status(thm)],[535, 534])).
% 45.53/29.63 tff(537,plain,
% 45.53/29.63 ((~((~d(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))) | (~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))))) | (~(d(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) | (~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err))))),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[536, 17])).
% 45.53/29.63 tff(538,plain,
% 45.53/29.63 (~(d(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) | (~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err)))),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[537, 533])).
% 45.53/29.63 tff(539,plain,
% 45.53/29.63 ((d(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) | (~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err))) | (phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err)),
% 45.53/29.63 inference(tautology,[status(thm)],[])).
% 45.53/29.63 tff(540,plain,
% 45.53/29.63 (phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[539, 538])).
% 45.53/29.63 tff(541,assumption,(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err), introduced(assumption)).
% 45.53/29.63 tff(542,plain,
% 45.53/29.63 (f5(P!7, not1(false)) = err),
% 45.53/29.63 inference(transitivity,[status(thm)],[529, 541])).
% 45.53/29.63 tff(543,plain,
% 45.53/29.63 (phi(f5(P!7, not1(false))) = phi(err)),
% 45.53/29.63 inference(monotonicity,[status(thm)],[542])).
% 45.53/29.63 tff(544,plain,
% 45.53/29.63 (bool(f5(P!7, not1(false))) <=> bool(err)),
% 45.53/29.63 inference(monotonicity,[status(thm)],[542])).
% 45.53/29.63 tff(545,plain,
% 45.53/29.63 (bool(err) <=> bool(f5(P!7, not1(false)))),
% 45.53/29.63 inference(symmetry,[status(thm)],[544])).
% 45.53/29.63 tff(546,plain,
% 45.53/29.63 ((~bool(err)) <=> (~bool(f5(P!7, not1(false))))),
% 45.53/29.63 inference(monotonicity,[status(thm)],[545])).
% 45.53/29.63 tff(547,assumption,(~(bool(err) <=> ((err = false) | (err = not1(false))))), introduced(assumption)).
% 45.53/29.63 tff(548,plain,
% 45.53/29.63 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(err) <=> ((err = false) | (err = not1(false))))),
% 45.53/29.63 inference(quant_inst,[status(thm)],[])).
% 45.53/29.63 tff(549,plain,
% 45.53/29.63 ($false),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[548, 249, 547])).
% 45.53/29.63 tff(550,plain,(bool(err) <=> ((err = false) | (err = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 45.53/29.63 tff(551,plain,
% 45.53/29.63 ((err = false) <=> (false = err)),
% 45.53/29.63 inference(commutativity,[status(thm)],[])).
% 45.53/29.63 tff(552,plain,
% 45.53/29.63 ((false = err) <=> (err = false)),
% 45.53/29.63 inference(symmetry,[status(thm)],[551])).
% 45.53/29.63 tff(553,plain,
% 45.53/29.63 ((~(false = err)) <=> (~(err = false))),
% 45.53/29.63 inference(monotonicity,[status(thm)],[552])).
% 45.53/29.63 tff(554,plain,
% 45.53/29.63 ((~(false = err)) <=> (~(false = err))),
% 45.53/29.63 inference(rewrite,[status(thm)],[])).
% 45.53/29.63 tff(555,plain,
% 45.53/29.63 (~(false = err)),
% 45.53/29.63 inference(and_elim,[status(thm)],[56])).
% 45.53/29.63 tff(556,plain,
% 45.53/29.63 (~(false = err)),
% 45.53/29.63 inference(modus_ponens,[status(thm)],[555, 554])).
% 45.53/29.63 tff(557,plain,
% 45.53/29.63 (~(err = false)),
% 45.53/29.63 inference(modus_ponens,[status(thm)],[556, 553])).
% 45.53/29.63 tff(558,assumption,(err = not1(false)), introduced(assumption)).
% 45.53/29.63 tff(559,plain,
% 45.53/29.63 (not1(false) = err),
% 45.53/29.63 inference(symmetry,[status(thm)],[558])).
% 45.53/29.63 tff(560,plain,
% 45.53/29.63 ((~(true = err)) <=> (~(not1(false) = err))),
% 45.53/29.63 inference(rewrite,[status(thm)],[])).
% 45.53/29.63 tff(561,plain,
% 45.53/29.63 ((~(true = err)) <=> (~(true = err))),
% 45.53/29.63 inference(rewrite,[status(thm)],[])).
% 45.53/29.63 tff(562,plain,
% 45.53/29.63 (~(true = err)),
% 45.53/29.63 inference(and_elim,[status(thm)],[57])).
% 45.53/29.63 tff(563,plain,
% 45.53/29.63 (~(true = err)),
% 45.53/29.63 inference(modus_ponens,[status(thm)],[562, 561])).
% 45.53/29.63 tff(564,plain,
% 45.53/29.63 (~(not1(false) = err)),
% 45.53/29.63 inference(modus_ponens,[status(thm)],[563, 560])).
% 45.53/29.63 tff(565,plain,
% 45.53/29.63 ($false),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[564, 559])).
% 45.53/29.63 tff(566,plain,(~(err = not1(false))), inference(lemma,lemma(discharge,[]))).
% 45.53/29.63 tff(567,plain,
% 45.53/29.63 ((~((err = false) | (err = not1(false)))) | (err = false) | (err = not1(false))),
% 45.53/29.63 inference(tautology,[status(thm)],[])).
% 45.53/29.63 tff(568,plain,
% 45.53/29.63 ((~((err = false) | (err = not1(false)))) | (err = false)),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[567, 566])).
% 45.53/29.63 tff(569,plain,
% 45.53/29.63 (~((err = false) | (err = not1(false)))),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[568, 557])).
% 45.53/29.63 tff(570,plain,
% 45.53/29.63 ((~(bool(err) <=> ((err = false) | (err = not1(false))))) | (~bool(err)) | ((err = false) | (err = not1(false)))),
% 45.53/29.63 inference(tautology,[status(thm)],[])).
% 45.53/29.63 tff(571,plain,
% 45.53/29.63 (~bool(err)),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[570, 569, 550])).
% 45.53/29.63 tff(572,plain,
% 45.53/29.63 (~bool(f5(P!7, not1(false)))),
% 45.53/29.63 inference(modus_ponens,[status(thm)],[571, 546])).
% 45.53/29.63 tff(573,plain,
% 45.53/29.63 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(f5(P!7, not1(false))) | (impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false)))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(f5(P!7, not1(false))) | (impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false)))))),
% 45.53/29.63 inference(rewrite,[status(thm)],[])).
% 45.53/29.63 tff(574,plain,
% 45.53/29.63 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(f5(P!7, not1(false))) | (impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false)))))),
% 45.53/29.63 inference(quant_inst,[status(thm)],[])).
% 45.53/29.63 tff(575,plain,
% 45.53/29.63 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(f5(P!7, not1(false))) | (impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false))))),
% 45.53/29.63 inference(modus_ponens,[status(thm)],[574, 573])).
% 45.53/29.63 tff(576,plain,
% 45.53/29.63 (bool(f5(P!7, not1(false))) | (impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false))))),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[575, 358])).
% 45.53/29.63 tff(577,plain,
% 45.53/29.63 (impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false)))),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[576, 572])).
% 45.53/29.63 tff(578,plain,
% 45.53/29.63 (impl(f5(P!7, not1(false)), not1(false)) = err),
% 45.53/29.63 inference(transitivity,[status(thm)],[577, 543, 429])).
% 45.53/29.63 tff(579,plain,
% 45.53/29.63 (lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = lazy_impl(not1(false), err)),
% 45.53/29.63 inference(monotonicity,[status(thm)],[275, 578])).
% 45.53/29.63 tff(580,plain,
% 45.53/29.63 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))))),
% 45.53/29.63 inference(quant_inst,[status(thm)],[])).
% 45.53/29.63 tff(581,plain,
% 45.53/29.63 (lazy_impl(not1(false), f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[580, 33])).
% 45.53/29.63 tff(582,plain,
% 45.53/29.63 (lazy_impl(not1(false), impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))) = lazy_impl(not1(false), f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 45.53/29.63 inference(monotonicity,[status(thm)],[522])).
% 45.53/29.63 tff(583,plain,
% 45.53/29.63 (lazy_impl(not1(false), impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))) = f5(P!7, not1(false))),
% 45.53/29.63 inference(transitivity,[status(thm)],[582, 581, 530])).
% 45.53/29.63 tff(584,plain,
% 45.53/29.63 (impl(lazy_impl(not1(false), impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))), not1(false)) = impl(f5(P!7, not1(false)), not1(false))),
% 45.53/29.63 inference(monotonicity,[status(thm)],[583])).
% 45.53/29.63 tff(585,plain,
% 45.53/29.63 (lazy_impl(prop(not1(false)), impl(lazy_impl(not1(false), impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))), not1(false))) = lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))),
% 45.53/29.63 inference(monotonicity,[status(thm)],[584])).
% 45.53/29.63 tff(586,plain,
% 45.53/29.63 ((~![P: $i, Q: $i, R: $i] : (f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R)))) | (f2(not1(false), apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = lazy_impl(prop(not1(false)), impl(lazy_impl(not1(false), impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))), not1(false))))),
% 45.53/29.63 inference(quant_inst,[status(thm)],[])).
% 45.53/29.63 tff(587,plain,
% 45.53/29.63 (f2(not1(false), apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = lazy_impl(prop(not1(false)), impl(lazy_impl(not1(false), impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))), not1(false)))),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[586, 141])).
% 45.53/29.63 tff(588,assumption,(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false), introduced(assumption)).
% 45.53/29.63 tff(589,plain,
% 45.53/29.63 (false = apply(P!7, tptp_fun_X_4(not1(false), P!7))),
% 45.53/29.63 inference(symmetry,[status(thm)],[588])).
% 45.53/29.63 tff(590,plain,
% 45.53/29.63 (f2(not1(false), false, not1(false)) = f2(not1(false), apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))),
% 45.53/29.63 inference(monotonicity,[status(thm)],[589])).
% 45.53/29.63 tff(591,plain,
% 45.53/29.63 ((~![P: $i, Q: $i, R: $i] : (f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R)))) | (f2(not1(false), false, not1(false)) = lazy_impl(prop(not1(false)), impl(lazy_impl(not1(false), impl(false, not1(false))), not1(false))))),
% 45.53/29.63 inference(quant_inst,[status(thm)],[])).
% 45.53/29.63 tff(592,plain,
% 45.53/29.63 (f2(not1(false), false, not1(false)) = lazy_impl(prop(not1(false)), impl(lazy_impl(not1(false), impl(false, not1(false))), not1(false)))),
% 45.53/29.63 inference(unit_resolution,[status(thm)],[591, 141])).
% 45.53/29.63 tff(593,plain,
% 45.53/29.63 (lazy_impl(prop(not1(false)), impl(lazy_impl(not1(false), impl(false, not1(false))), not1(false))) = f2(not1(false), false, not1(false))),
% 45.53/29.63 inference(symmetry,[status(thm)],[592])).
% 45.53/29.63 tff(594,plain,
% 45.53/29.63 (lazy_impl(not1(false), impl(false, not1(false))) = lazy_impl(not1(false), not1(false))),
% 45.53/29.63 inference(monotonicity,[status(thm)],[421])).
% 45.53/29.63 tff(595,plain,
% 45.53/29.63 (lazy_impl(not1(false), impl(false, not1(false))) = not1(false)),
% 45.53/29.64 inference(transitivity,[status(thm)],[594, 50, 48])).
% 45.53/29.64 tff(596,plain,
% 45.53/29.64 (impl(lazy_impl(not1(false), impl(false, not1(false))), not1(false)) = impl(not1(false), not1(false))),
% 45.53/29.64 inference(monotonicity,[status(thm)],[595])).
% 45.53/29.64 tff(597,plain,
% 45.53/29.64 (impl(not1(false), not1(false)) = impl(lazy_impl(not1(false), impl(false, not1(false))), not1(false))),
% 45.53/29.64 inference(symmetry,[status(thm)],[596])).
% 45.53/29.64 tff(598,plain,
% 45.53/29.64 (not1(false) = impl(not1(false), not1(false))),
% 45.53/29.64 inference(symmetry,[status(thm)],[501])).
% 45.53/29.64 tff(599,plain,
% 45.53/29.64 (not1(false) = impl(lazy_impl(not1(false), impl(false, not1(false))), not1(false))),
% 45.53/29.64 inference(transitivity,[status(thm)],[598, 597])).
% 45.53/29.64 tff(600,plain,
% 45.53/29.64 (not1(false) = prop(not1(false))),
% 45.53/29.64 inference(symmetry,[status(thm)],[275])).
% 45.53/29.64 tff(601,plain,
% 45.53/29.64 (lazy_impl(not1(false), not1(false)) = lazy_impl(prop(not1(false)), impl(lazy_impl(not1(false), impl(false, not1(false))), not1(false)))),
% 45.53/29.64 inference(monotonicity,[status(thm)],[600, 599])).
% 45.53/29.64 tff(602,plain,
% 45.53/29.64 (phi(not1(false)) = lazy_impl(not1(false), not1(false))),
% 45.53/29.64 inference(symmetry,[status(thm)],[50])).
% 45.53/29.64 tff(603,plain,
% 45.53/29.64 (not1(false) = phi(not1(false))),
% 45.53/29.64 inference(symmetry,[status(thm)],[48])).
% 45.53/29.64 tff(604,plain,
% 45.53/29.64 (not1(false) = err),
% 45.53/29.64 inference(transitivity,[status(thm)],[603, 602, 601, 593, 590, 587, 585, 579, 431, 429])).
% 45.53/29.64 tff(605,plain,
% 45.53/29.64 ($false),
% 45.53/29.64 inference(unit_resolution,[status(thm)],[564, 604])).
% 45.53/29.64 tff(606,plain,((~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false)) | (~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err))), inference(lemma,lemma(discharge,[]))).
% 45.53/29.64 tff(607,plain,
% 45.53/29.64 (~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false)),
% 45.53/29.64 inference(unit_resolution,[status(thm)],[606, 540])).
% 45.53/29.64 tff(608,plain,
% 45.53/29.64 ((f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)) = phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))) <=> (phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 45.53/29.64 inference(commutativity,[status(thm)],[])).
% 45.53/29.64 tff(609,plain,
% 45.53/29.64 (err = phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 45.53/29.64 inference(symmetry,[status(thm)],[540])).
% 45.53/29.64 tff(610,plain,
% 45.53/29.64 (phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))),
% 45.53/29.64 inference(transitivity,[status(thm)],[524, 522])).
% 45.53/29.64 tff(611,plain,
% 45.53/29.64 ((phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err) <=> (f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)) = phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))))),
% 45.53/29.64 inference(monotonicity,[status(thm)],[610, 609])).
% 45.53/29.64 tff(612,plain,
% 45.53/29.64 ((phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err) <=> (phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 45.53/29.64 inference(transitivity,[status(thm)],[611, 608])).
% 45.53/29.64 tff(613,plain,
% 45.53/29.64 ((phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) <=> (phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err)),
% 45.53/29.64 inference(symmetry,[status(thm)],[612])).
% 45.53/29.64 tff(614,plain,
% 45.53/29.64 ((~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))) <=> (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err))),
% 45.53/29.64 inference(monotonicity,[status(thm)],[613])).
% 45.53/29.64 tff(615,plain,
% 45.53/29.64 (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err)),
% 45.53/29.64 inference(modus_ponens,[status(thm)],[531, 614])).
% 45.53/29.64 tff(616,plain,
% 45.53/29.64 ((d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err))) | (phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err)),
% 45.53/29.64 inference(tautology,[status(thm)],[])).
% 45.53/29.64 tff(617,plain,
% 45.53/29.64 (d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err))),
% 45.53/29.64 inference(unit_resolution,[status(thm)],[616, 615])).
% 45.53/29.64 tff(618,plain,
% 45.53/29.64 (~((~d(apply(P!7, tptp_fun_X_4(not1(false), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = apply(P!7, tptp_fun_X_4(not1(false), P!7)))))),
% 45.53/29.64 inference(unit_resolution,[status(thm)],[513, 617])).
% 45.53/29.64 tff(619,plain,
% 45.53/29.64 (phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = apply(P!7, tptp_fun_X_4(not1(false), P!7))),
% 45.53/29.64 inference(unit_resolution,[status(thm)],[508, 618])).
% 45.53/29.64 tff(620,plain,
% 45.53/29.64 (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = phi(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.53/29.64 inference(symmetry,[status(thm)],[619])).
% 45.53/29.64 tff(621,plain,
% 45.53/29.64 (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))),
% 45.53/29.64 inference(transitivity,[status(thm)],[620, 524, 522])).
% 45.53/29.64 tff(622,plain,
% 45.53/29.64 (d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) <=> d(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 45.53/29.64 inference(monotonicity,[status(thm)],[621])).
% 45.53/29.64 tff(623,plain,
% 45.53/29.64 (d(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) <=> d(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.53/29.64 inference(symmetry,[status(thm)],[622])).
% 45.53/29.64 tff(624,plain,
% 45.53/29.64 ((~d(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))) <=> (~d(apply(P!7, tptp_fun_X_4(not1(false), P!7))))),
% 45.53/29.64 inference(monotonicity,[status(thm)],[623])).
% 45.53/29.64 tff(625,plain,
% 45.53/29.64 ((d(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) | (~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err))) | (~d(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))))),
% 45.53/29.64 inference(tautology,[status(thm)],[])).
% 45.53/29.64 tff(626,plain,
% 45.53/29.64 (~d(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 45.53/29.64 inference(unit_resolution,[status(thm)],[625, 538])).
% 45.53/29.64 tff(627,plain,
% 45.53/29.64 (~d(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.53/29.64 inference(modus_ponens,[status(thm)],[626, 624])).
% 45.53/29.64 tff(628,plain,
% 45.53/29.64 (((~d(apply(P!7, tptp_fun_X_4(not1(false), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = apply(P!7, tptp_fun_X_4(not1(false), P!7))))) | d(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.53/29.64 inference(tautology,[status(thm)],[])).
% 45.53/29.64 tff(629,plain,
% 45.53/29.64 (d(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.53/29.64 inference(unit_resolution,[status(thm)],[628, 618])).
% 45.53/29.64 tff(630,plain,
% 45.53/29.64 ($false),
% 45.53/29.64 inference(unit_resolution,[status(thm)],[629, 627])).
% 45.53/29.64 tff(631,plain,((~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))))) | (phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))), inference(lemma,lemma(discharge,[]))).
% 45.53/29.64 tff(632,plain,
% 45.53/29.64 (~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))))),
% 45.53/29.64 inference(unit_resolution,[status(thm)],[631, 531])).
% 45.53/29.64 tff(633,plain,
% 45.53/29.64 (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.53/29.64 inference(unit_resolution,[status(thm)],[506, 632, 607])).
% 45.53/29.64 tff(634,plain,
% 45.53/29.64 ((~d(apply(P!7, tptp_fun_X_4(not1(false), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = apply(P!7, tptp_fun_X_4(not1(false), P!7))))),
% 45.53/29.64 inference(unit_resolution,[status(thm)],[508, 633])).
% 45.53/29.64 tff(635,plain,
% 45.53/29.64 (~(d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err)))),
% 45.53/29.64 inference(unit_resolution,[status(thm)],[512, 17, 634])).
% 45.53/29.64 tff(636,plain,
% 45.53/29.64 (phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err),
% 45.53/29.64 inference(unit_resolution,[status(thm)],[616, 635])).
% 45.53/29.64 tff(637,plain,
% 45.53/29.64 (bool(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.53/29.64 inference(unit_resolution,[status(thm)],[480, 632])).
% 45.53/29.64 tff(638,plain,
% 45.53/29.64 ((apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))),
% 45.53/29.64 inference(unit_resolution,[status(thm)],[482, 637, 475])).
% 45.53/29.64 tff(639,plain,
% 45.53/29.64 (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false)),
% 45.53/29.64 inference(unit_resolution,[status(thm)],[484, 638, 607])).
% 45.53/29.64 tff(640,plain,
% 45.53/29.64 (not1(false) = apply(P!7, tptp_fun_X_4(not1(false), P!7))),
% 45.53/29.64 inference(symmetry,[status(thm)],[639])).
% 45.53/29.64 tff(641,plain,
% 45.53/29.64 (phi(not1(false)) = phi(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.53/29.64 inference(monotonicity,[status(thm)],[640])).
% 45.53/29.64 tff(642,plain,
% 45.53/29.64 (not1(false) = err),
% 45.53/29.64 inference(transitivity,[status(thm)],[603, 641, 636])).
% 45.53/29.64 tff(643,plain,
% 45.53/29.64 ($false),
% 45.53/29.64 inference(unit_resolution,[status(thm)],[564, 642])).
% 45.53/29.64 tff(644,plain,(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))), inference(lemma,lemma(discharge,[]))).
% 45.53/29.64 tff(645,plain,
% 45.53/29.64 (f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)) = phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 45.53/29.64 inference(symmetry,[status(thm)],[644])).
% 45.53/29.64 tff(646,plain,
% 45.53/29.64 (f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)) = f5(P!7, not1(false))),
% 45.53/29.64 inference(transitivity,[status(thm)],[645, 530])).
% 45.53/29.64 tff(647,plain,
% 45.53/29.64 (phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = phi(f5(P!7, not1(false)))),
% 45.53/29.64 inference(monotonicity,[status(thm)],[646])).
% 45.53/29.64 tff(648,plain,
% 45.53/29.64 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))),
% 45.53/29.64 inference(monotonicity,[status(thm)],[421])).
% 45.53/29.64 tff(649,plain,
% 45.53/29.64 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))) = apply(P!7, tptp_fun_X_4(not1(false), P!7))),
% 45.53/29.64 inference(transitivity,[status(thm)],[648, 523, 494])).
% 45.53/29.64 tff(650,plain,
% 45.53/29.64 (impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))),
% 45.53/29.64 inference(monotonicity,[status(thm)],[649])).
% 45.53/29.64 tff(651,plain,
% 45.53/29.64 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false)))),
% 45.53/29.64 inference(symmetry,[status(thm)],[648])).
% 45.53/29.64 tff(652,plain,
% 45.53/29.64 (f5(P!7, not1(false)) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false)))),
% 45.53/29.64 inference(transitivity,[status(thm)],[529, 644, 521, 651])).
% 45.53/29.64 tff(653,plain,
% 45.53/29.64 (impl(f5(P!7, not1(false)), not1(false)) = impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))),
% 45.53/29.64 inference(monotonicity,[status(thm)],[652])).
% 45.53/29.64 tff(654,plain,
% 45.53/29.64 (impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false)))),
% 45.53/29.64 inference(transitivity,[status(thm)],[653, 650, 522, 645, 647])).
% 45.53/29.64 tff(655,plain,
% 45.53/29.64 ($false),
% 45.53/29.64 inference(unit_resolution,[status(thm)],[525, 654])).
% 45.53/29.64 tff(656,plain,((~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = apply(P!7, tptp_fun_X_4(not1(false), P!7)))) | (impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false)))) | (~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = phi(apply(P!7, tptp_fun_X_4(not1(false), P!7)))))), inference(lemma,lemma(discharge,[]))).
% 45.53/29.64 tff(657,plain,
% 45.53/29.64 (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.53/29.64 inference(unit_resolution,[status(thm)],[656, 525, 523])).
% 45.53/29.64 tff(658,plain,
% 45.53/29.64 ((~d(apply(P!7, tptp_fun_X_4(not1(false), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = apply(P!7, tptp_fun_X_4(not1(false), P!7))))),
% 45.53/29.64 inference(unit_resolution,[status(thm)],[508, 657])).
% 45.53/29.64 tff(659,plain,
% 45.53/29.64 (~(d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err)))),
% 45.53/29.64 inference(unit_resolution,[status(thm)],[513, 658])).
% 45.53/29.64 tff(660,plain,
% 45.53/29.64 (phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err),
% 45.53/29.64 inference(unit_resolution,[status(thm)],[616, 659])).
% 45.53/29.64 tff(661,plain,
% 45.53/29.64 (err = phi(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.53/29.64 inference(symmetry,[status(thm)],[660])).
% 45.53/29.64 tff(662,plain,
% 45.53/29.64 (f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)) = err),
% 45.53/29.64 inference(transitivity,[status(thm)],[521, 523, 660])).
% 45.53/29.64 tff(663,plain,
% 45.53/29.64 (phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = phi(err)),
% 45.53/29.64 inference(monotonicity,[status(thm)],[662])).
% 45.53/29.64 tff(664,plain,
% 45.53/29.64 (f5(P!7, not1(false)) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))),
% 45.53/29.64 inference(transitivity,[status(thm)],[529, 663, 429, 661, 524, 522])).
% 45.53/29.64 tff(665,plain,
% 45.53/29.64 (bool(f5(P!7, not1(false))) <=> bool(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 45.53/29.64 inference(monotonicity,[status(thm)],[664])).
% 45.53/29.64 tff(666,plain,
% 45.53/29.64 (bool(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) <=> bool(f5(P!7, not1(false)))),
% 45.53/29.64 inference(symmetry,[status(thm)],[665])).
% 45.53/29.64 tff(667,plain,
% 45.53/29.64 ((~bool(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))) <=> (~bool(f5(P!7, not1(false))))),
% 45.53/29.64 inference(monotonicity,[status(thm)],[666])).
% 45.53/29.64 tff(668,plain,
% 45.53/29.64 (bool(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) <=> bool(err)),
% 45.53/29.64 inference(monotonicity,[status(thm)],[662])).
% 45.53/29.64 tff(669,plain,
% 45.53/29.64 (bool(err) <=> bool(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 45.53/29.64 inference(symmetry,[status(thm)],[668])).
% 45.53/29.64 tff(670,plain,
% 45.53/29.64 ((~bool(err)) <=> (~bool(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))))),
% 45.53/29.64 inference(monotonicity,[status(thm)],[669])).
% 45.53/29.64 tff(671,plain,
% 45.53/29.64 (~bool(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 45.53/29.64 inference(modus_ponens,[status(thm)],[571, 670])).
% 45.53/29.64 tff(672,plain,
% 45.53/29.64 (~bool(f5(P!7, not1(false)))),
% 45.53/29.64 inference(modus_ponens,[status(thm)],[671, 667])).
% 45.53/29.64 tff(673,plain,
% 45.53/29.64 (bool(f5(P!7, not1(false)))),
% 45.53/29.64 inference(unit_resolution,[status(thm)],[576, 525])).
% 45.53/29.64 tff(674,plain,
% 45.53/29.64 ($false),
% 45.53/29.64 inference(unit_resolution,[status(thm)],[673, 672])).
% 45.53/29.64 tff(675,plain,((impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false)))) | (~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = phi(apply(P!7, tptp_fun_X_4(not1(false), P!7)))))), inference(lemma,lemma(discharge,[]))).
% 45.53/29.64 tff(676,plain,
% 45.53/29.64 (impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false)))),
% 45.53/29.64 inference(unit_resolution,[status(thm)],[675, 519])).
% 45.53/29.64 tff(677,plain,
% 45.53/29.64 (phi(f5(P!7, not1(false))) = impl(f5(P!7, not1(false)), not1(false))),
% 45.53/29.64 inference(symmetry,[status(thm)],[676])).
% 45.53/29.64 tff(678,plain,
% 45.53/29.64 (phi(f5(P!7, not1(false))) = phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 45.53/29.64 inference(symmetry,[status(thm)],[647])).
% 45.53/29.64 tff(679,plain,
% 45.53/29.64 (impl(f5(P!7, not1(false)), not1(false)) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))),
% 45.53/29.64 inference(transitivity,[status(thm)],[676, 678, 644])).
% 45.53/29.64 tff(680,plain,
% 45.53/29.64 (phi(impl(f5(P!7, not1(false)), not1(false))) = phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 45.53/29.64 inference(monotonicity,[status(thm)],[679])).
% 45.53/29.64 tff(681,plain,
% 45.53/29.64 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), impl(f5(P!7, not1(false)), not1(false))) = phi(impl(f5(P!7, not1(false)), not1(false))))),
% 45.53/29.64 inference(quant_inst,[status(thm)],[])).
% 45.53/29.64 tff(682,plain,
% 45.53/29.64 (lazy_impl(not1(false), impl(f5(P!7, not1(false)), not1(false))) = phi(impl(f5(P!7, not1(false)), not1(false)))),
% 45.53/29.64 inference(unit_resolution,[status(thm)],[681, 33])).
% 45.53/29.64 tff(683,plain,
% 45.53/29.64 (lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = lazy_impl(not1(false), impl(f5(P!7, not1(false)), not1(false)))),
% 45.53/29.64 inference(monotonicity,[status(thm)],[275])).
% 45.53/29.64 tff(684,plain,
% 45.53/29.64 (lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = impl(f5(P!7, not1(false)), not1(false))),
% 45.53/29.64 inference(transitivity,[status(thm)],[683, 682, 680, 647, 677])).
% 45.53/29.64 tff(685,plain,
% 45.53/29.64 (d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) <=> d(impl(f5(P!7, not1(false)), not1(false)))),
% 45.53/29.64 inference(monotonicity,[status(thm)],[684])).
% 45.53/29.64 tff(686,plain,
% 45.53/29.64 (d(impl(f5(P!7, not1(false)), not1(false))) <=> d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))),
% 45.53/29.64 inference(symmetry,[status(thm)],[685])).
% 45.53/29.64 tff(687,plain,
% 45.53/29.64 (f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)) = impl(f5(P!7, not1(false)), not1(false))),
% 45.53/29.64 inference(transitivity,[status(thm)],[645, 647, 677])).
% 45.53/29.64 tff(688,plain,
% 45.53/29.64 (d(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) <=> d(impl(f5(P!7, not1(false)), not1(false)))),
% 45.53/29.64 inference(monotonicity,[status(thm)],[687])).
% 45.53/29.64 tff(689,assumption,(~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err)), introduced(assumption)).
% 45.53/29.64 tff(690,plain,
% 45.53/29.64 (d(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) | (~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err))),
% 45.53/29.64 inference(unit_resolution,[status(thm)],[539, 689])).
% 45.53/29.64 tff(691,plain,
% 45.53/29.64 (~((~d(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))) | (~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))))),
% 45.53/29.64 inference(unit_resolution,[status(thm)],[537, 690])).
% 45.53/29.64 tff(692,plain,
% 45.53/29.64 (((~d(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))) | (~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))))) | d(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 45.53/29.64 inference(tautology,[status(thm)],[])).
% 45.53/29.64 tff(693,plain,
% 45.53/29.64 (d(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 45.53/29.64 inference(unit_resolution,[status(thm)],[692, 691])).
% 45.53/29.64 tff(694,plain,
% 45.53/29.64 (d(impl(f5(P!7, not1(false)), not1(false)))),
% 45.53/29.64 inference(modus_ponens,[status(thm)],[693, 688])).
% 45.53/29.64 tff(695,plain,
% 45.53/29.64 (d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))),
% 45.53/29.64 inference(modus_ponens,[status(thm)],[694, 686])).
% 45.53/29.64 tff(696,plain,
% 45.53/29.64 (phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = phi(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.53/29.64 inference(transitivity,[status(thm)],[644, 521, 519])).
% 45.53/29.64 tff(697,plain,
% 45.53/29.64 ((phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err) <=> (phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err)),
% 45.53/29.64 inference(monotonicity,[status(thm)],[696])).
% 45.53/29.64 tff(698,plain,
% 45.53/29.64 ((~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err)) <=> (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err))),
% 45.53/29.64 inference(monotonicity,[status(thm)],[697])).
% 45.53/29.64 tff(699,plain,
% 45.53/29.64 (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err)),
% 45.53/29.64 inference(modus_ponens,[status(thm)],[689, 698])).
% 45.53/29.64 tff(700,plain,
% 45.53/29.64 (d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err))),
% 45.53/29.64 inference(unit_resolution,[status(thm)],[616, 699])).
% 45.53/29.64 tff(701,plain,
% 45.53/29.64 (~((~d(apply(P!7, tptp_fun_X_4(not1(false), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = apply(P!7, tptp_fun_X_4(not1(false), P!7)))))),
% 45.53/29.64 inference(unit_resolution,[status(thm)],[513, 700])).
% 45.53/29.64 tff(702,plain,
% 45.53/29.64 (phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = apply(P!7, tptp_fun_X_4(not1(false), P!7))),
% 45.53/29.64 inference(unit_resolution,[status(thm)],[508, 701])).
% 45.53/29.64 tff(703,plain,
% 45.53/29.64 (phi(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))) = phi(f5(P!7, not1(false)))),
% 45.53/29.64 inference(monotonicity,[status(thm)],[530])).
% 45.53/29.64 tff(704,plain,
% 45.53/29.64 (phi(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))) = phi(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.53/29.64 inference(transitivity,[status(thm)],[703, 678, 644, 521, 519])).
% 45.53/29.64 tff(705,plain,
% 45.53/29.64 ((phi(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))) = err) <=> (phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err)),
% 45.53/29.64 inference(monotonicity,[status(thm)],[704])).
% 45.53/29.64 tff(706,plain,
% 45.53/29.64 ((phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err) <=> (phi(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))) = err)),
% 45.53/29.64 inference(symmetry,[status(thm)],[705])).
% 45.53/29.64 tff(707,plain,
% 45.53/29.64 ((~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err)) <=> (~(phi(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))) = err))),
% 45.53/29.64 inference(monotonicity,[status(thm)],[706])).
% 45.53/29.64 tff(708,plain,
% 45.53/29.64 (~(phi(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))) = err)),
% 45.53/29.64 inference(modus_ponens,[status(thm)],[699, 707])).
% 45.53/29.64 tff(709,plain,
% 45.53/29.64 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(impl(f5(P!7, not1(false)), not1(false))) <=> ((impl(f5(P!7, not1(false)), not1(false)) = false) | (impl(f5(P!7, not1(false)), not1(false)) = not1(false))))),
% 45.53/29.64 inference(quant_inst,[status(thm)],[])).
% 45.53/29.64 tff(710,plain,
% 45.53/29.64 (bool(impl(f5(P!7, not1(false)), not1(false))) <=> ((impl(f5(P!7, not1(false)), not1(false)) = false) | (impl(f5(P!7, not1(false)), not1(false)) = not1(false)))),
% 45.53/29.64 inference(unit_resolution,[status(thm)],[709, 249])).
% 45.53/29.64 tff(711,plain,
% 45.53/29.64 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))) = f5(P!7, not1(false))),
% 45.53/29.64 inference(transitivity,[status(thm)],[648, 522, 645, 530])).
% 45.53/29.64 tff(712,plain,
% 45.53/29.64 (impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)) = impl(f5(P!7, not1(false)), not1(false))),
% 45.53/29.64 inference(monotonicity,[status(thm)],[711])).
% 45.53/29.64 tff(713,plain,
% 45.53/29.64 (lazy_impl(prop(not1(false)), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))) = lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))),
% 45.53/29.64 inference(monotonicity,[status(thm)],[712])).
% 45.53/29.64 tff(714,plain,
% 45.53/29.64 (lazy_impl(prop(not1(false)), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))) = impl(f5(P!7, not1(false)), not1(false))),
% 45.53/29.64 inference(transitivity,[status(thm)],[713, 683, 682, 680, 647, 677])).
% 45.53/29.64 tff(715,plain,
% 45.53/29.64 (bool(lazy_impl(prop(not1(false)), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)))) <=> bool(impl(f5(P!7, not1(false)), not1(false)))),
% 45.53/29.64 inference(monotonicity,[status(thm)],[714])).
% 45.53/29.64 tff(716,plain,
% 45.53/29.64 (lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = lazy_impl(prop(not1(false)), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)))),
% 45.53/29.64 inference(symmetry,[status(thm)],[713])).
% 45.53/29.64 tff(717,plain,
% 45.53/29.64 (bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) <=> bool(lazy_impl(prop(not1(false)), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))))),
% 45.53/29.64 inference(monotonicity,[status(thm)],[716])).
% 45.53/29.64 tff(718,plain,
% 45.53/29.64 (bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) <=> bool(impl(f5(P!7, not1(false)), not1(false)))),
% 45.53/29.64 inference(transitivity,[status(thm)],[717, 715])).
% 45.53/29.64 tff(719,plain,
% 45.53/29.64 (bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> bool(f6(P!7, tptp_fun_R_5(P!7)))),
% 45.53/29.64 inference(monotonicity,[status(thm)],[326])).
% 45.53/29.64 tff(720,plain,
% 45.53/29.64 (bool(f6(P!7, tptp_fun_R_5(P!7))) <=> bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.53/29.64 inference(symmetry,[status(thm)],[719])).
% 45.53/29.64 tff(721,plain,
% 45.53/29.64 ((~![B: $i] : (lazy_impl(false, B) = not1(false))) | (lazy_impl(false, impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))),
% 45.53/29.64 inference(quant_inst,[status(thm)],[])).
% 45.53/29.64 tff(722,plain,
% 45.53/29.64 (lazy_impl(false, impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false)),
% 45.53/29.64 inference(unit_resolution,[status(thm)],[721, 176])).
% 45.53/29.64 tff(723,assumption,(prop(tptp_fun_R_5(P!7)) = false), introduced(assumption)).
% 45.53/29.64 tff(724,plain,
% 45.53/29.64 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(false, impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.53/29.64 inference(monotonicity,[status(thm)],[723])).
% 45.53/29.64 tff(725,plain,
% 45.53/29.64 (f6(P!7, tptp_fun_R_5(P!7)) = not1(false)),
% 45.53/29.64 inference(transitivity,[status(thm)],[325, 724, 722])).
% 45.53/29.64 tff(726,plain,
% 45.53/29.64 (bool(f6(P!7, tptp_fun_R_5(P!7))) <=> bool(not1(false))),
% 45.53/29.64 inference(monotonicity,[status(thm)],[725])).
% 45.53/29.64 tff(727,plain,
% 45.53/29.64 (bool(not1(false)) <=> bool(f6(P!7, tptp_fun_R_5(P!7)))),
% 45.53/29.64 inference(symmetry,[status(thm)],[726])).
% 45.53/29.64 tff(728,plain,
% 45.53/29.64 (bool(not1(false)) <=> bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.53/29.64 inference(transitivity,[status(thm)],[727, 720])).
% 45.53/29.64 tff(729,plain,
% 45.53/29.64 (bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.53/29.64 inference(modus_ponens,[status(thm)],[272, 728])).
% 45.53/29.64 tff(730,assumption,(d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))), introduced(assumption)).
% 45.53/29.64 tff(731,plain,
% 45.53/29.64 (d(f6(P!7, tptp_fun_R_5(P!7))) <=> d(not1(false))),
% 45.53/29.64 inference(monotonicity,[status(thm)],[725])).
% 45.53/29.64 tff(732,plain,
% 45.53/29.64 (d(not1(false)) <=> d(f6(P!7, tptp_fun_R_5(P!7)))),
% 45.53/29.64 inference(symmetry,[status(thm)],[731])).
% 45.53/29.64 tff(733,plain,
% 45.53/29.64 (d(not1(false)) <=> d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.53/29.64 inference(transitivity,[status(thm)],[732, 328])).
% 45.53/29.64 tff(734,plain,
% 45.53/29.64 (d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.53/29.64 inference(modus_ponens,[status(thm)],[40, 733])).
% 45.53/29.64 tff(735,plain,
% 45.53/29.64 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~((~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))) | (~(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = false)))) | (~(d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~((~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))) | (~(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = false)))) | (~(d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))))))))),
% 45.53/29.64 inference(rewrite,[status(thm)],[])).
% 45.53/29.64 tff(736,plain,
% 45.53/29.64 ((forallprefers(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~(d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))))) | (~((~(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))))))) <=> (forallprefers(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~((~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))) | (~(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = false)))) | (~(d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))))))))),
% 45.53/29.65 inference(rewrite,[status(thm)],[])).
% 45.53/29.65 tff(737,plain,
% 45.53/29.65 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~(d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))))) | (~((~(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~((~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))) | (~(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = false)))) | (~(d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))))))))),
% 45.53/29.65 inference(monotonicity,[status(thm)],[736])).
% 45.53/29.65 tff(738,plain,
% 45.53/29.65 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~(d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))))) | (~((~(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~((~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))) | (~(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = false)))) | (~(d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))))))))),
% 45.53/29.65 inference(transitivity,[status(thm)],[737, 735])).
% 45.53/29.65 tff(739,plain,
% 45.53/29.65 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~(d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))))) | (~((~(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false)))))))),
% 45.53/29.65 inference(quant_inst,[status(thm)],[])).
% 45.53/29.65 tff(740,plain,
% 45.53/29.65 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~((~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))) | (~(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = false)))) | (~(d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))))))))),
% 45.53/29.65 inference(modus_ponens,[status(thm)],[739, 738])).
% 45.53/29.65 tff(741,plain,
% 45.53/29.65 (forallprefers(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~((~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))) | (~(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = false)))) | (~(d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))))))),
% 45.53/29.65 inference(unit_resolution,[status(thm)],[740, 159])).
% 45.53/29.65 tff(742,plain,
% 45.53/29.65 ((~![P: $i, R: $i] : (f6(P, R) = lazy_impl(prop(R), impl(f5(P, R), R)))) | (f6(P!7, not1(false)) = lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))),
% 45.53/29.65 inference(quant_inst,[status(thm)],[])).
% 45.53/29.65 tff(743,plain,
% 45.53/29.65 (f6(P!7, not1(false)) = lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))),
% 45.53/29.65 inference(unit_resolution,[status(thm)],[742, 323])).
% 45.53/29.65 tff(744,plain,
% 45.53/29.65 (lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = f6(P!7, not1(false))),
% 45.53/29.65 inference(symmetry,[status(thm)],[743])).
% 45.53/29.65 tff(745,plain,
% 45.53/29.65 (forallprefers(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> forallprefers(f6(P!7, not1(false)), f6(P!7, tptp_fun_R_5(P!7)))),
% 45.53/29.65 inference(monotonicity,[status(thm)],[744, 326])).
% 45.53/29.65 tff(746,plain,
% 45.53/29.65 (forallprefers(f6(P!7, not1(false)), f6(P!7, tptp_fun_R_5(P!7))) <=> forallprefers(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.53/29.65 inference(symmetry,[status(thm)],[745])).
% 45.53/29.65 tff(747,plain,
% 45.53/29.65 ((~forallprefers(f6(P!7, not1(false)), f6(P!7, tptp_fun_R_5(P!7)))) <=> (~forallprefers(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 45.53/29.65 inference(monotonicity,[status(thm)],[746])).
% 45.53/29.65 tff(748,plain,
% 45.53/29.65 (^[P: $i] : refl((~((~(exists2(P) = phi(f6(P, tptp_fun_R_5(P))))) | (~![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P))))))) <=> (~((~(exists2(P) = phi(f6(P, tptp_fun_R_5(P))))) | (~![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P))))))))),
% 45.53/29.65 inference(bind,[status(th)],[])).
% 45.53/29.65 tff(749,plain,
% 45.53/29.65 (![P: $i] : (~((~(exists2(P) = phi(f6(P, tptp_fun_R_5(P))))) | (~![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P))))))) <=> ![P: $i] : (~((~(exists2(P) = phi(f6(P, tptp_fun_R_5(P))))) | (~![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P)))))))),
% 45.53/29.65 inference(quant_intro,[status(thm)],[748])).
% 45.53/29.65 tff(750,plain,
% 45.53/29.65 (^[P: $i] : rewrite((~((~(exists2(P) = phi(f6(P, tptp_fun_R_5(P))))) | (~![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P))))))) <=> (~((~(exists2(P) = phi(f6(P, tptp_fun_R_5(P))))) | (~![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P))))))))),
% 45.53/29.65 inference(bind,[status(th)],[])).
% 45.53/29.65 tff(751,plain,
% 45.53/29.65 (![P: $i] : (~((~(exists2(P) = phi(f6(P, tptp_fun_R_5(P))))) | (~![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P))))))) <=> ![P: $i] : (~((~(exists2(P) = phi(f6(P, tptp_fun_R_5(P))))) | (~![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P)))))))),
% 45.53/29.65 inference(quant_intro,[status(thm)],[750])).
% 45.53/29.65 tff(752,plain,
% 45.53/29.65 (![P: $i] : (~((~(exists2(P) = phi(f6(P, tptp_fun_R_5(P))))) | (~![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P))))))) <=> ![P: $i] : (~((~(exists2(P) = phi(f6(P, tptp_fun_R_5(P))))) | (~![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P)))))))),
% 45.53/29.65 inference(transitivity,[status(thm)],[751, 749])).
% 45.53/29.65 tff(753,plain,
% 45.53/29.65 (^[P: $i] : rewrite(((exists2(P) = phi(f6(P, tptp_fun_R_5(P)))) & ![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P))))) <=> (~((~(exists2(P) = phi(f6(P, tptp_fun_R_5(P))))) | (~![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P))))))))),
% 45.53/29.65 inference(bind,[status(th)],[])).
% 45.53/29.65 tff(754,plain,
% 45.53/29.65 (![P: $i] : ((exists2(P) = phi(f6(P, tptp_fun_R_5(P)))) & ![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P))))) <=> ![P: $i] : (~((~(exists2(P) = phi(f6(P, tptp_fun_R_5(P))))) | (~![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P)))))))),
% 45.53/29.65 inference(quant_intro,[status(thm)],[753])).
% 45.53/29.65 tff(755,plain,
% 45.53/29.65 (![P: $i] : ?[R: $i] : ((exists2(P) = phi(f6(P, R))) & (~?[R1: $i] : forallprefers(f6(P, R1), f6(P, R)))) <=> ![P: $i] : ?[R: $i] : ((exists2(P) = phi(f6(P, R))) & (~?[R1: $i] : forallprefers(f6(P, R1), f6(P, R))))),
% 45.53/29.65 inference(rewrite,[status(thm)],[])).
% 45.53/29.65 tff(756,axiom,(![P: $i] : ?[R: $i] : ((exists2(P) = phi(f6(P, R))) & (~?[R1: $i] : forallprefers(f6(P, R1), f6(P, R))))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','def_exists2')).
% 45.53/29.65 tff(757,plain,
% 45.53/29.65 (![P: $i] : ?[R: $i] : ((exists2(P) = phi(f6(P, R))) & (~?[R1: $i] : forallprefers(f6(P, R1), f6(P, R))))),
% 45.53/29.65 inference(modus_ponens,[status(thm)],[756, 755])).
% 45.53/29.65 tff(758,plain,(
% 45.53/29.65 ![P: $i] : ((exists2(P) = phi(f6(P, tptp_fun_R_5(P)))) & ![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P)))))),
% 45.53/29.65 inference(skolemize,[status(sab)],[757])).
% 45.53/29.65 tff(759,plain,
% 45.53/29.65 (![P: $i] : (~((~(exists2(P) = phi(f6(P, tptp_fun_R_5(P))))) | (~![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P)))))))),
% 45.53/29.65 inference(modus_ponens,[status(thm)],[758, 754])).
% 45.53/29.65 tff(760,plain,
% 45.53/29.65 (![P: $i] : (~((~(exists2(P) = phi(f6(P, tptp_fun_R_5(P))))) | (~![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P)))))))),
% 45.53/29.65 inference(modus_ponens,[status(thm)],[759, 752])).
% 45.53/29.65 tff(761,plain,
% 45.53/29.65 ((~![P: $i] : (~((~(exists2(P) = phi(f6(P, tptp_fun_R_5(P))))) | (~![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P)))))))) | (~((~(exists2(P!7) = phi(f6(P!7, tptp_fun_R_5(P!7))))) | (~![R1: $i] : (~forallprefers(f6(P!7, R1), f6(P!7, tptp_fun_R_5(P!7)))))))),
% 45.53/29.65 inference(quant_inst,[status(thm)],[])).
% 45.53/29.65 tff(762,plain,
% 45.53/29.65 (~((~(exists2(P!7) = phi(f6(P!7, tptp_fun_R_5(P!7))))) | (~![R1: $i] : (~forallprefers(f6(P!7, R1), f6(P!7, tptp_fun_R_5(P!7))))))),
% 45.53/29.65 inference(unit_resolution,[status(thm)],[761, 760])).
% 45.53/29.65 tff(763,plain,
% 45.53/29.65 (((~(exists2(P!7) = phi(f6(P!7, tptp_fun_R_5(P!7))))) | (~![R1: $i] : (~forallprefers(f6(P!7, R1), f6(P!7, tptp_fun_R_5(P!7)))))) | ![R1: $i] : (~forallprefers(f6(P!7, R1), f6(P!7, tptp_fun_R_5(P!7))))),
% 45.53/29.65 inference(tautology,[status(thm)],[])).
% 45.53/29.65 tff(764,plain,
% 45.53/29.65 (![R1: $i] : (~forallprefers(f6(P!7, R1), f6(P!7, tptp_fun_R_5(P!7))))),
% 45.53/29.65 inference(unit_resolution,[status(thm)],[763, 762])).
% 45.53/29.65 tff(765,plain,
% 45.53/29.65 ((~![R1: $i] : (~forallprefers(f6(P!7, R1), f6(P!7, tptp_fun_R_5(P!7))))) | (~forallprefers(f6(P!7, not1(false)), f6(P!7, tptp_fun_R_5(P!7))))),
% 45.53/29.65 inference(quant_inst,[status(thm)],[])).
% 45.53/29.65 tff(766,plain,
% 45.53/29.65 (~forallprefers(f6(P!7, not1(false)), f6(P!7, tptp_fun_R_5(P!7)))),
% 45.53/29.65 inference(unit_resolution,[status(thm)],[765, 764])).
% 45.53/29.65 tff(767,plain,
% 45.53/29.65 (~forallprefers(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.53/29.65 inference(modus_ponens,[status(thm)],[766, 747])).
% 45.53/29.65 tff(768,plain,
% 45.53/29.65 ((~(forallprefers(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~((~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))) | (~(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = false)))) | (~(d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))))))))) | forallprefers(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~((~((~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))) | (~(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = false)))) | (~(d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))))))))),
% 45.53/29.65 inference(tautology,[status(thm)],[])).
% 45.53/29.65 tff(769,plain,
% 45.53/29.65 (~((~((~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))) | (~(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = false)))) | (~(d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))))))),
% 45.53/29.65 inference(unit_resolution,[status(thm)],[768, 767, 741])).
% 45.53/29.65 tff(770,plain,
% 45.53/29.65 (((~((~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))) | (~(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = false)))) | (~(d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))))))) | ((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))))),
% 45.53/29.65 inference(tautology,[status(thm)],[])).
% 45.53/29.65 tff(771,plain,
% 45.53/29.65 ((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))))),
% 45.53/29.65 inference(unit_resolution,[status(thm)],[770, 769])).
% 45.53/29.65 tff(772,plain,
% 45.53/29.65 ((~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))))),
% 45.53/29.65 inference(tautology,[status(thm)],[])).
% 45.53/29.65 tff(773,plain,
% 45.53/29.65 ((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) | (~d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))))),
% 45.53/29.65 inference(unit_resolution,[status(thm)],[772, 771])).
% 45.53/29.65 tff(774,plain,
% 45.53/29.65 (bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))),
% 45.53/29.65 inference(unit_resolution,[status(thm)],[773, 734, 730, 729])).
% 45.53/29.65 tff(775,plain,
% 45.53/29.65 (bool(impl(f5(P!7, not1(false)), not1(false)))),
% 45.53/29.65 inference(modus_ponens,[status(thm)],[774, 718])).
% 45.53/29.65 tff(776,plain,
% 45.53/29.65 ((~(bool(impl(f5(P!7, not1(false)), not1(false))) <=> ((impl(f5(P!7, not1(false)), not1(false)) = false) | (impl(f5(P!7, not1(false)), not1(false)) = not1(false))))) | (~bool(impl(f5(P!7, not1(false)), not1(false)))) | ((impl(f5(P!7, not1(false)), not1(false)) = false) | (impl(f5(P!7, not1(false)), not1(false)) = not1(false)))),
% 45.53/29.65 inference(tautology,[status(thm)],[])).
% 45.53/29.65 tff(777,plain,
% 45.53/29.65 ((~(bool(impl(f5(P!7, not1(false)), not1(false))) <=> ((impl(f5(P!7, not1(false)), not1(false)) = false) | (impl(f5(P!7, not1(false)), not1(false)) = not1(false))))) | ((impl(f5(P!7, not1(false)), not1(false)) = false) | (impl(f5(P!7, not1(false)), not1(false)) = not1(false)))),
% 45.53/29.65 inference(unit_resolution,[status(thm)],[776, 775])).
% 45.53/29.65 tff(778,plain,
% 45.53/29.65 ((impl(f5(P!7, not1(false)), not1(false)) = false) | (impl(f5(P!7, not1(false)), not1(false)) = not1(false))),
% 45.53/29.65 inference(unit_resolution,[status(thm)],[777, 710])).
% 45.53/29.65 tff(779,plain,
% 45.53/29.65 (impl(f5(P!7, not1(false)), not1(false)) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))),
% 45.53/29.65 inference(transitivity,[status(thm)],[676, 678, 644, 521])).
% 45.53/29.65 tff(780,plain,
% 45.53/29.65 ((impl(f5(P!7, not1(false)), not1(false)) = false) <=> (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = false)),
% 45.53/29.65 inference(monotonicity,[status(thm)],[779])).
% 45.53/29.65 tff(781,plain,
% 45.53/29.65 ((impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = false) <=> (impl(f5(P!7, not1(false)), not1(false)) = false)),
% 45.53/29.65 inference(symmetry,[status(thm)],[780])).
% 45.53/29.65 tff(782,plain,
% 45.53/29.65 ((~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = false)) <=> (~(impl(f5(P!7, not1(false)), not1(false)) = false))),
% 45.53/29.65 inference(monotonicity,[status(thm)],[781])).
% 45.53/29.65 tff(783,plain,
% 45.53/29.65 (phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))),
% 45.53/29.65 inference(symmetry,[status(thm)],[519])).
% 45.53/29.65 tff(784,plain,
% 45.53/29.65 (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = phi(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.53/29.65 inference(symmetry,[status(thm)],[494])).
% 45.53/29.65 tff(785,plain,
% 45.53/29.65 (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))),
% 45.53/29.65 inference(transitivity,[status(thm)],[784, 783])).
% 45.53/29.65 tff(786,plain,
% 45.53/29.65 ((apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false) <=> (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = false)),
% 45.53/29.65 inference(monotonicity,[status(thm)],[785])).
% 45.53/29.65 tff(787,plain,
% 45.53/29.65 ((~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false)) <=> (~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = false))),
% 45.53/29.65 inference(monotonicity,[status(thm)],[786])).
% 45.53/29.65 tff(788,plain,
% 45.53/29.65 (~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = false)),
% 45.53/29.65 inference(modus_ponens,[status(thm)],[432, 787])).
% 45.53/29.65 tff(789,plain,
% 45.53/29.65 (~(impl(f5(P!7, not1(false)), not1(false)) = false)),
% 45.53/29.65 inference(modus_ponens,[status(thm)],[788, 782])).
% 45.53/29.65 tff(790,plain,
% 45.53/29.65 ((~((impl(f5(P!7, not1(false)), not1(false)) = false) | (impl(f5(P!7, not1(false)), not1(false)) = not1(false)))) | (impl(f5(P!7, not1(false)), not1(false)) = false) | (impl(f5(P!7, not1(false)), not1(false)) = not1(false))),
% 45.53/29.65 inference(tautology,[status(thm)],[])).
% 45.53/29.65 tff(791,plain,
% 45.53/29.65 (impl(f5(P!7, not1(false)), not1(false)) = not1(false)),
% 45.53/29.65 inference(unit_resolution,[status(thm)],[790, 789, 778])).
% 45.53/29.65 tff(792,plain,
% 45.53/29.65 (not1(false) = impl(f5(P!7, not1(false)), not1(false))),
% 45.53/29.65 inference(symmetry,[status(thm)],[791])).
% 45.53/29.65 tff(793,plain,
% 45.53/29.65 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(apply(P!7, tptp_fun_X_3(P!7))) <=> ((apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = not1(false))))),
% 45.53/29.65 inference(quant_inst,[status(thm)],[])).
% 45.53/29.65 tff(794,plain,
% 45.53/29.65 (bool(apply(P!7, tptp_fun_X_3(P!7))) <=> ((apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = not1(false)))),
% 45.53/29.65 inference(unit_resolution,[status(thm)],[793, 249])).
% 45.53/29.65 tff(795,assumption,(~(phi(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))) = err)), introduced(assumption)).
% 45.53/29.65 tff(796,plain,
% 45.53/29.65 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(impl(f5(P!7, not1(false)), not1(false)), false2), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) <=> ((~(d(impl(impl(f5(P!7, not1(false)), not1(false)), false2)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~(bool(impl(impl(f5(P!7, not1(false)), not1(false)), false2)) | (~d(impl(impl(f5(P!7, not1(false)), not1(false)), false2))) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))) | (~(impl(impl(f5(P!7, not1(false)), not1(false)), false2) = false))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(impl(f5(P!7, not1(false)), not1(false)), false2), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) <=> ((~(d(impl(impl(f5(P!7, not1(false)), not1(false)), false2)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~(bool(impl(impl(f5(P!7, not1(false)), not1(false)), false2)) | (~d(impl(impl(f5(P!7, not1(false)), not1(false)), false2))) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))) | (~(impl(impl(f5(P!7, not1(false)), not1(false)), false2) = false)))))))),
% 45.53/29.65 inference(rewrite,[status(thm)],[])).
% 45.53/29.65 tff(797,plain,
% 45.53/29.65 ((forallprefers(impl(impl(f5(P!7, not1(false)), not1(false)), false2), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) <=> ((~(d(impl(impl(f5(P!7, not1(false)), not1(false)), false2)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | bool(impl(impl(f5(P!7, not1(false)), not1(false)), false2)) | (~d(impl(impl(f5(P!7, not1(false)), not1(false)), false2))))) | (~((~(impl(impl(f5(P!7, not1(false)), not1(false)), false2) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))))))) <=> (forallprefers(impl(impl(f5(P!7, not1(false)), not1(false)), false2), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) <=> ((~(d(impl(impl(f5(P!7, not1(false)), not1(false)), false2)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~(bool(impl(impl(f5(P!7, not1(false)), not1(false)), false2)) | (~d(impl(impl(f5(P!7, not1(false)), not1(false)), false2))) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))) | (~(impl(impl(f5(P!7, not1(false)), not1(false)), false2) = false))))))),
% 45.53/29.65 inference(rewrite,[status(thm)],[])).
% 45.53/29.65 tff(798,plain,
% 45.53/29.65 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(impl(f5(P!7, not1(false)), not1(false)), false2), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) <=> ((~(d(impl(impl(f5(P!7, not1(false)), not1(false)), false2)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | bool(impl(impl(f5(P!7, not1(false)), not1(false)), false2)) | (~d(impl(impl(f5(P!7, not1(false)), not1(false)), false2))))) | (~((~(impl(impl(f5(P!7, not1(false)), not1(false)), false2) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(impl(f5(P!7, not1(false)), not1(false)), false2), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) <=> ((~(d(impl(impl(f5(P!7, not1(false)), not1(false)), false2)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~(bool(impl(impl(f5(P!7, not1(false)), not1(false)), false2)) | (~d(impl(impl(f5(P!7, not1(false)), not1(false)), false2))) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))) | (~(impl(impl(f5(P!7, not1(false)), not1(false)), false2) = false)))))))),
% 45.53/29.66 inference(monotonicity,[status(thm)],[797])).
% 45.53/29.66 tff(799,plain,
% 45.53/29.66 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(impl(f5(P!7, not1(false)), not1(false)), false2), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) <=> ((~(d(impl(impl(f5(P!7, not1(false)), not1(false)), false2)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | bool(impl(impl(f5(P!7, not1(false)), not1(false)), false2)) | (~d(impl(impl(f5(P!7, not1(false)), not1(false)), false2))))) | (~((~(impl(impl(f5(P!7, not1(false)), not1(false)), false2) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(impl(f5(P!7, not1(false)), not1(false)), false2), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) <=> ((~(d(impl(impl(f5(P!7, not1(false)), not1(false)), false2)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~(bool(impl(impl(f5(P!7, not1(false)), not1(false)), false2)) | (~d(impl(impl(f5(P!7, not1(false)), not1(false)), false2))) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))) | (~(impl(impl(f5(P!7, not1(false)), not1(false)), false2) = false)))))))),
% 45.53/29.66 inference(transitivity,[status(thm)],[798, 796])).
% 45.53/29.66 tff(800,plain,
% 45.53/29.66 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(impl(f5(P!7, not1(false)), not1(false)), false2), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) <=> ((~(d(impl(impl(f5(P!7, not1(false)), not1(false)), false2)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | bool(impl(impl(f5(P!7, not1(false)), not1(false)), false2)) | (~d(impl(impl(f5(P!7, not1(false)), not1(false)), false2))))) | (~((~(impl(impl(f5(P!7, not1(false)), not1(false)), false2) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false)))))))),
% 45.53/29.66 inference(quant_inst,[status(thm)],[])).
% 45.53/29.66 tff(801,plain,
% 45.53/29.66 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(impl(f5(P!7, not1(false)), not1(false)), false2), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) <=> ((~(d(impl(impl(f5(P!7, not1(false)), not1(false)), false2)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~(bool(impl(impl(f5(P!7, not1(false)), not1(false)), false2)) | (~d(impl(impl(f5(P!7, not1(false)), not1(false)), false2))) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))) | (~(impl(impl(f5(P!7, not1(false)), not1(false)), false2) = false))))))),
% 45.53/29.66 inference(modus_ponens,[status(thm)],[800, 799])).
% 45.53/29.66 tff(802,plain,
% 45.53/29.66 (forallprefers(impl(impl(f5(P!7, not1(false)), not1(false)), false2), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) <=> ((~(d(impl(impl(f5(P!7, not1(false)), not1(false)), false2)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~(bool(impl(impl(f5(P!7, not1(false)), not1(false)), false2)) | (~d(impl(impl(f5(P!7, not1(false)), not1(false)), false2))) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))) | (~(impl(impl(f5(P!7, not1(false)), not1(false)), false2) = false)))))),
% 45.53/29.66 inference(unit_resolution,[status(thm)],[801, 159])).
% 45.53/29.66 tff(803,plain,
% 45.53/29.66 ((~![P: $i, X: $i, R: $i] : (f4(P, X, R) = impl(apply(P, X), R))) | (f4(P!7, tptp_fun_X_4(false, P!7), false) = impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))),
% 45.53/29.66 inference(quant_inst,[status(thm)],[])).
% 45.53/29.66 tff(804,plain,
% 45.53/29.66 (f4(P!7, tptp_fun_X_4(false, P!7), false) = impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)),
% 45.53/29.66 inference(unit_resolution,[status(thm)],[803, 412])).
% 45.53/29.66 tff(805,plain,
% 45.53/29.66 (impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = f4(P!7, tptp_fun_X_4(false, P!7), false)),
% 45.53/29.66 inference(symmetry,[status(thm)],[804])).
% 45.53/29.66 tff(806,plain,
% 45.53/29.66 ((~![P: $i, X: $i, R: $i] : (f4(P, X, R) = impl(apply(P, X), R))) | (f4(P!7, tptp_fun_X_4(not1(false), P!7), false) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), false))),
% 45.53/29.66 inference(quant_inst,[status(thm)],[])).
% 45.53/29.66 tff(807,plain,
% 45.53/29.66 (f4(P!7, tptp_fun_X_4(not1(false), P!7), false) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), false)),
% 45.53/29.66 inference(unit_resolution,[status(thm)],[806, 412])).
% 45.53/29.66 tff(808,plain,
% 45.53/29.66 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), false) = f4(P!7, tptp_fun_X_4(not1(false), P!7), false)),
% 45.53/29.66 inference(symmetry,[status(thm)],[807])).
% 45.53/29.66 tff(809,plain,
% 45.53/29.66 (impl(f5(P!7, not1(false)), impl(false, false)) = impl(f5(P!7, not1(false)), not1(false))),
% 45.53/29.66 inference(monotonicity,[status(thm)],[93])).
% 45.53/29.66 tff(810,plain,
% 45.53/29.66 (impl(f5(P!7, not1(false)), not1(false)) = impl(f5(P!7, not1(false)), impl(false, false))),
% 45.53/29.66 inference(symmetry,[status(thm)],[809])).
% 45.53/29.66 tff(811,plain,
% 45.53/29.66 (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = impl(f5(P!7, not1(false)), impl(false, false))),
% 45.53/29.66 inference(transitivity,[status(thm)],[784, 783, 522, 645, 647, 677, 810])).
% 45.53/29.66 tff(812,plain,
% 45.53/29.66 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), false) = impl(impl(f5(P!7, not1(false)), impl(false, false)), false)),
% 45.53/29.66 inference(monotonicity,[status(thm)],[811])).
% 45.53/29.66 tff(813,plain,
% 45.53/29.66 (impl(impl(f5(P!7, not1(false)), impl(false, false)), false) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), false)),
% 45.53/29.66 inference(symmetry,[status(thm)],[812])).
% 45.53/29.66 tff(814,plain,
% 45.53/29.66 (phi(f7(P!6)) = phi(false)),
% 45.53/29.66 inference(monotonicity,[status(thm)],[436])).
% 45.53/29.66 tff(815,plain,
% 45.53/29.66 (false2 = phi(f7(P!6))),
% 45.53/29.66 inference(and_elim,[status(thm)],[216])).
% 45.53/29.66 tff(816,plain,
% 45.53/29.66 (false2 = false),
% 45.53/29.66 inference(transitivity,[status(thm)],[815, 814, 23])).
% 45.53/29.66 tff(817,plain,
% 45.53/29.66 (impl(impl(f5(P!7, not1(false)), not1(false)), false2) = impl(impl(f5(P!7, not1(false)), impl(false, false)), false)),
% 45.53/29.66 inference(monotonicity,[status(thm)],[810, 816])).
% 45.53/29.66 tff(818,plain,
% 45.53/29.66 (impl(impl(f5(P!7, not1(false)), not1(false)), false2) = f4(P!7, tptp_fun_X_4(not1(false), P!7), false)),
% 45.53/29.66 inference(transitivity,[status(thm)],[817, 813, 808])).
% 45.53/29.66 tff(819,plain,
% 45.53/29.66 (forallprefers(impl(impl(f5(P!7, not1(false)), not1(false)), false2), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) <=> forallprefers(f4(P!7, tptp_fun_X_4(not1(false), P!7), false), f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 45.53/29.66 inference(monotonicity,[status(thm)],[818, 805])).
% 45.53/29.66 tff(820,plain,
% 45.53/29.66 (forallprefers(f4(P!7, tptp_fun_X_4(not1(false), P!7), false), f4(P!7, tptp_fun_X_4(false, P!7), false)) <=> forallprefers(impl(impl(f5(P!7, not1(false)), not1(false)), false2), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))),
% 45.53/29.66 inference(symmetry,[status(thm)],[819])).
% 45.53/29.66 tff(821,plain,
% 45.53/29.66 ((~forallprefers(f4(P!7, tptp_fun_X_4(not1(false), P!7), false), f4(P!7, tptp_fun_X_4(false, P!7), false))) <=> (~forallprefers(impl(impl(f5(P!7, not1(false)), not1(false)), false2), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)))),
% 45.53/29.66 inference(monotonicity,[status(thm)],[820])).
% 45.53/29.66 tff(822,plain,
% 45.53/29.66 ((~![P: $i, R: $i] : (~((~(f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R)))) | (~![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R))))))) | (~((~(f5(P!7, false) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~![X1: $i] : (~forallprefers(f4(P!7, X1, false), f4(P!7, tptp_fun_X_4(false, P!7), false))))))),
% 45.53/29.66 inference(quant_inst,[status(thm)],[])).
% 45.53/29.66 tff(823,plain,
% 45.53/29.66 (~((~(f5(P!7, false) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~![X1: $i] : (~forallprefers(f4(P!7, X1, false), f4(P!7, tptp_fun_X_4(false, P!7), false)))))),
% 45.53/29.66 inference(unit_resolution,[status(thm)],[822, 307])).
% 45.53/29.66 tff(824,plain,
% 45.53/29.66 (((~(f5(P!7, false) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~![X1: $i] : (~forallprefers(f4(P!7, X1, false), f4(P!7, tptp_fun_X_4(false, P!7), false))))) | ![X1: $i] : (~forallprefers(f4(P!7, X1, false), f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 45.53/29.66 inference(tautology,[status(thm)],[])).
% 45.53/29.66 tff(825,plain,
% 45.53/29.66 (![X1: $i] : (~forallprefers(f4(P!7, X1, false), f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 45.53/29.66 inference(unit_resolution,[status(thm)],[824, 823])).
% 45.53/29.66 tff(826,plain,
% 45.53/29.66 ((~![X1: $i] : (~forallprefers(f4(P!7, X1, false), f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~forallprefers(f4(P!7, tptp_fun_X_4(not1(false), P!7), false), f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 45.53/29.66 inference(quant_inst,[status(thm)],[])).
% 45.53/29.66 tff(827,plain,
% 45.53/29.66 (~forallprefers(f4(P!7, tptp_fun_X_4(not1(false), P!7), false), f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 45.53/29.66 inference(unit_resolution,[status(thm)],[826, 825])).
% 45.53/29.66 tff(828,plain,
% 45.53/29.66 (~forallprefers(impl(impl(f5(P!7, not1(false)), not1(false)), false2), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))),
% 45.53/29.66 inference(modus_ponens,[status(thm)],[827, 821])).
% 45.53/29.66 tff(829,plain,
% 45.53/29.66 ((~(forallprefers(impl(impl(f5(P!7, not1(false)), not1(false)), false2), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) <=> ((~(d(impl(impl(f5(P!7, not1(false)), not1(false)), false2)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~(bool(impl(impl(f5(P!7, not1(false)), not1(false)), false2)) | (~d(impl(impl(f5(P!7, not1(false)), not1(false)), false2))) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))) | (~(impl(impl(f5(P!7, not1(false)), not1(false)), false2) = false))))))) | forallprefers(impl(impl(f5(P!7, not1(false)), not1(false)), false2), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) | (~((~(d(impl(impl(f5(P!7, not1(false)), not1(false)), false2)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~(bool(impl(impl(f5(P!7, not1(false)), not1(false)), false2)) | (~d(impl(impl(f5(P!7, not1(false)), not1(false)), false2))) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))) | (~(impl(impl(f5(P!7, not1(false)), not1(false)), false2) = false))))))),
% 45.53/29.66 inference(tautology,[status(thm)],[])).
% 45.53/29.66 tff(830,plain,
% 45.53/29.66 (~((~(d(impl(impl(f5(P!7, not1(false)), not1(false)), false2)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~(bool(impl(impl(f5(P!7, not1(false)), not1(false)), false2)) | (~d(impl(impl(f5(P!7, not1(false)), not1(false)), false2))) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))) | (~(impl(impl(f5(P!7, not1(false)), not1(false)), false2) = false)))))),
% 45.53/29.66 inference(unit_resolution,[status(thm)],[829, 828, 802])).
% 45.53/29.66 tff(831,plain,
% 45.53/29.66 (((~(d(impl(impl(f5(P!7, not1(false)), not1(false)), false2)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~(bool(impl(impl(f5(P!7, not1(false)), not1(false)), false2)) | (~d(impl(impl(f5(P!7, not1(false)), not1(false)), false2))) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))) | (~(impl(impl(f5(P!7, not1(false)), not1(false)), false2) = false))))) | ((~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))) | (~(impl(impl(f5(P!7, not1(false)), not1(false)), false2) = false)))),
% 45.53/29.66 inference(tautology,[status(thm)],[])).
% 45.53/29.66 tff(832,plain,
% 45.53/29.66 ((~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))) | (~(impl(impl(f5(P!7, not1(false)), not1(false)), false2) = false))),
% 45.53/29.66 inference(unit_resolution,[status(thm)],[831, 830])).
% 45.53/29.66 tff(833,plain,
% 45.53/29.66 (impl(f5(P!7, not1(false)), impl(false, false)) = not1(false)),
% 45.53/29.66 inference(transitivity,[status(thm)],[809, 791])).
% 45.53/29.66 tff(834,plain,
% 45.53/29.66 (impl(impl(f5(P!7, not1(false)), impl(false, false)), false) = impl(not1(false), false)),
% 45.53/29.66 inference(monotonicity,[status(thm)],[833])).
% 45.53/29.66 tff(835,plain,
% 45.53/29.66 (impl(impl(f5(P!7, not1(false)), not1(false)), false2) = false),
% 45.53/29.66 inference(transitivity,[status(thm)],[817, 834, 114])).
% 45.53/29.66 tff(836,plain,
% 45.53/29.66 ((~((~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))) | (~(impl(impl(f5(P!7, not1(false)), not1(false)), false2) = false)))) | (~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))) | (~(impl(impl(f5(P!7, not1(false)), not1(false)), false2) = false))),
% 45.53/29.66 inference(tautology,[status(thm)],[])).
% 45.53/29.66 tff(837,plain,
% 45.53/29.66 (~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))),
% 45.53/29.66 inference(unit_resolution,[status(thm)],[836, 835, 832])).
% 45.53/29.66 tff(838,plain,
% 45.53/29.66 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(false), impl(f5(P!7, false), false)), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))))) | (~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(false), impl(f5(P!7, false), false)), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))))) | (~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))))))),
% 45.53/29.66 inference(rewrite,[status(thm)],[])).
% 45.53/29.66 tff(839,plain,
% 45.53/29.66 ((forallprefers(lazy_impl(prop(false), impl(f5(P!7, false), false)), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))))) | (~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))))))) <=> (forallprefers(lazy_impl(prop(false), impl(f5(P!7, false), false)), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))))) | (~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))))))),
% 45.53/29.66 inference(rewrite,[status(thm)],[])).
% 45.53/29.66 tff(840,plain,
% 45.53/29.66 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(false), impl(f5(P!7, false), false)), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))))) | (~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(false), impl(f5(P!7, false), false)), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))))) | (~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))))))),
% 45.53/29.66 inference(monotonicity,[status(thm)],[839])).
% 45.53/29.66 tff(841,plain,
% 45.53/29.66 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(false), impl(f5(P!7, false), false)), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))))) | (~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(false), impl(f5(P!7, false), false)), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))))) | (~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))))))),
% 45.53/29.67 inference(transitivity,[status(thm)],[840, 838])).
% 45.53/29.67 tff(842,plain,
% 45.53/29.67 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(false), impl(f5(P!7, false), false)), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))))) | (~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false)))))))),
% 45.53/29.67 inference(quant_inst,[status(thm)],[])).
% 45.53/29.67 tff(843,plain,
% 45.53/29.67 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(false), impl(f5(P!7, false), false)), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))))) | (~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))))))),
% 45.53/29.67 inference(modus_ponens,[status(thm)],[842, 841])).
% 45.53/29.67 tff(844,plain,
% 45.53/29.67 (forallprefers(lazy_impl(prop(false), impl(f5(P!7, false), false)), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))))) | (~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))))),
% 45.53/29.67 inference(unit_resolution,[status(thm)],[843, 159])).
% 45.53/29.67 tff(845,plain,
% 45.53/29.67 ((~![P: $i, R: $i] : (f6(P, R) = lazy_impl(prop(R), impl(f5(P, R), R)))) | (f6(P!7, false) = lazy_impl(prop(false), impl(f5(P!7, false), false)))),
% 45.53/29.67 inference(quant_inst,[status(thm)],[])).
% 45.53/29.67 tff(846,plain,
% 45.53/29.67 (f6(P!7, false) = lazy_impl(prop(false), impl(f5(P!7, false), false))),
% 45.53/29.67 inference(unit_resolution,[status(thm)],[845, 323])).
% 45.53/29.67 tff(847,plain,
% 45.53/29.67 (lazy_impl(prop(false), impl(f5(P!7, false), false)) = f6(P!7, false)),
% 45.53/29.67 inference(symmetry,[status(thm)],[846])).
% 45.53/29.67 tff(848,plain,
% 45.53/29.67 (forallprefers(lazy_impl(prop(false), impl(f5(P!7, false), false)), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> forallprefers(f6(P!7, false), f6(P!7, tptp_fun_R_5(P!7)))),
% 45.53/29.67 inference(monotonicity,[status(thm)],[847, 326])).
% 45.53/29.67 tff(849,plain,
% 45.53/29.67 (forallprefers(f6(P!7, false), f6(P!7, tptp_fun_R_5(P!7))) <=> forallprefers(lazy_impl(prop(false), impl(f5(P!7, false), false)), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.53/29.67 inference(symmetry,[status(thm)],[848])).
% 45.53/29.67 tff(850,plain,
% 45.53/29.67 ((~forallprefers(f6(P!7, false), f6(P!7, tptp_fun_R_5(P!7)))) <=> (~forallprefers(lazy_impl(prop(false), impl(f5(P!7, false), false)), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 45.53/29.67 inference(monotonicity,[status(thm)],[849])).
% 45.53/29.67 tff(851,plain,
% 45.53/29.67 ((~![R1: $i] : (~forallprefers(f6(P!7, R1), f6(P!7, tptp_fun_R_5(P!7))))) | (~forallprefers(f6(P!7, false), f6(P!7, tptp_fun_R_5(P!7))))),
% 45.53/29.67 inference(quant_inst,[status(thm)],[])).
% 45.53/29.67 tff(852,plain,
% 45.53/29.67 (~forallprefers(f6(P!7, false), f6(P!7, tptp_fun_R_5(P!7)))),
% 45.53/29.67 inference(unit_resolution,[status(thm)],[851, 764])).
% 45.53/29.67 tff(853,plain,
% 45.53/29.67 (~forallprefers(lazy_impl(prop(false), impl(f5(P!7, false), false)), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.53/29.67 inference(modus_ponens,[status(thm)],[852, 850])).
% 45.53/29.67 tff(854,plain,
% 45.53/29.67 ((~(forallprefers(lazy_impl(prop(false), impl(f5(P!7, false), false)), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))))) | (~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))))))) | forallprefers(lazy_impl(prop(false), impl(f5(P!7, false), false)), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~((~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))))) | (~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))))))),
% 45.53/29.67 inference(tautology,[status(thm)],[])).
% 45.53/29.67 tff(855,plain,
% 45.53/29.67 (~((~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))))) | (~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))))),
% 45.53/29.67 inference(unit_resolution,[status(thm)],[854, 853, 844])).
% 45.53/29.67 tff(856,plain,
% 45.53/29.67 (((~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))))) | (~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))))) | (d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))),
% 45.53/29.67 inference(tautology,[status(thm)],[])).
% 45.53/29.67 tff(857,plain,
% 45.53/29.67 (d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 45.53/29.67 inference(unit_resolution,[status(thm)],[856, 855])).
% 45.53/29.67 tff(858,plain,
% 45.53/29.67 ((~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 45.53/29.67 inference(tautology,[status(thm)],[])).
% 45.53/29.67 tff(859,plain,
% 45.53/29.67 (d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 45.53/29.67 inference(unit_resolution,[status(thm)],[858, 857])).
% 45.53/29.67 tff(860,plain,
% 45.53/29.67 (d(lazy_impl(prop(false), impl(f5(P!7, false), false)))),
% 45.53/29.67 inference(unit_resolution,[status(thm)],[859, 734])).
% 45.53/29.67 tff(861,plain,
% 45.53/29.67 (((~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))))) | (~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))))) | ((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))))),
% 45.53/29.67 inference(tautology,[status(thm)],[])).
% 45.53/29.67 tff(862,plain,
% 45.53/29.67 ((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false)))),
% 45.53/29.67 inference(unit_resolution,[status(thm)],[861, 855])).
% 45.53/29.67 tff(863,plain,
% 45.53/29.67 ((~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false)))),
% 45.53/29.67 inference(tautology,[status(thm)],[])).
% 45.53/29.67 tff(864,plain,
% 45.53/29.67 ((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false)))),
% 45.53/29.67 inference(unit_resolution,[status(thm)],[863, 862])).
% 45.53/29.67 tff(865,plain,
% 45.53/29.67 (bool(lazy_impl(prop(false), impl(f5(P!7, false), false)))),
% 45.53/29.67 inference(unit_resolution,[status(thm)],[864, 860, 729, 734])).
% 45.53/29.67 tff(866,plain,
% 45.53/29.67 ((~(bool(lazy_impl(prop(false), impl(f5(P!7, false), false))) <=> ((lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false))))) | (~bool(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | ((lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false)))),
% 45.53/29.67 inference(tautology,[status(thm)],[])).
% 45.53/29.67 tff(867,plain,
% 45.53/29.67 ((~(bool(lazy_impl(prop(false), impl(f5(P!7, false), false))) <=> ((lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false))))) | ((lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false)))),
% 45.53/29.67 inference(unit_resolution,[status(thm)],[866, 865])).
% 45.53/29.67 tff(868,plain,
% 45.53/29.67 ((lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false))),
% 45.53/29.67 inference(unit_resolution,[status(thm)],[867, 316])).
% 45.53/29.67 tff(869,plain,
% 45.53/29.67 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false)),
% 45.53/29.67 inference(transitivity,[status(thm)],[724, 722])).
% 45.53/29.67 tff(870,plain,
% 45.53/29.67 (((~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))))) | (~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))))) | ((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))))),
% 45.53/29.67 inference(tautology,[status(thm)],[])).
% 45.53/29.67 tff(871,plain,
% 45.53/29.67 ((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false)))),
% 45.53/29.67 inference(unit_resolution,[status(thm)],[870, 855])).
% 45.53/29.67 tff(872,plain,
% 45.53/29.67 ((~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))))) | (~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false)))),
% 45.53/29.67 inference(tautology,[status(thm)],[])).
% 45.53/29.67 tff(873,plain,
% 45.53/29.67 ((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false)))),
% 45.53/29.67 inference(unit_resolution,[status(thm)],[872, 871])).
% 45.53/29.67 tff(874,plain,
% 45.53/29.67 (~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)),
% 45.53/29.67 inference(unit_resolution,[status(thm)],[873, 869])).
% 45.53/29.67 tff(875,plain,
% 45.53/29.67 ((~((lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false)))) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false))),
% 45.53/29.67 inference(tautology,[status(thm)],[])).
% 45.53/29.67 tff(876,plain,
% 45.53/29.67 ((~((lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false)))) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false))),
% 45.53/29.67 inference(unit_resolution,[status(thm)],[875, 874])).
% 45.53/29.67 tff(877,plain,
% 45.53/29.67 (lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false)),
% 45.53/29.67 inference(unit_resolution,[status(thm)],[876, 868])).
% 45.53/29.67 tff(878,plain,
% 45.53/29.67 (phi(f6(P!7, tptp_fun_R_5(P!7))) = phi(not1(false))),
% 45.53/29.67 inference(monotonicity,[status(thm)],[725])).
% 45.53/29.67 tff(879,plain,
% 45.53/29.67 (((~(exists2(P!7) = phi(f6(P!7, tptp_fun_R_5(P!7))))) | (~![R1: $i] : (~forallprefers(f6(P!7, R1), f6(P!7, tptp_fun_R_5(P!7)))))) | (exists2(P!7) = phi(f6(P!7, tptp_fun_R_5(P!7))))),
% 45.53/29.67 inference(tautology,[status(thm)],[])).
% 45.53/29.67 tff(880,plain,
% 45.53/29.67 (exists2(P!7) = phi(f6(P!7, tptp_fun_R_5(P!7)))),
% 45.53/29.67 inference(unit_resolution,[status(thm)],[879, 762])).
% 45.53/29.67 tff(881,plain,
% 45.53/29.67 (exists2(P!7) = not1(false)),
% 45.53/29.67 inference(transitivity,[status(thm)],[880, 878, 48])).
% 45.53/29.67 tff(882,plain,
% 45.53/29.67 ((exists1(P!7) = exists2(P!7)) <=> (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))),
% 45.53/29.67 inference(monotonicity,[status(thm)],[346, 881])).
% 45.53/29.67 tff(883,plain,
% 45.53/29.67 ((~(exists1(P!7) = exists2(P!7))) <=> (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)))),
% 45.53/29.67 inference(monotonicity,[status(thm)],[882])).
% 45.53/29.67 tff(884,plain,
% 45.53/29.67 ((![X1: $i, X2: $i] : ((~((~bool(apply(P!7, X1))) & (~bool(apply(P!7, X2))))) | (apply(P!7, X1) = apply(P!7, X2))) & (~(exists1(P!7) = exists2(P!7)))) <=> (![X1: $i, X2: $i] : ((~((~bool(apply(P!7, X1))) & (~bool(apply(P!7, X2))))) | (apply(P!7, X1) = apply(P!7, X2))) & (~(exists1(P!7) = exists2(P!7))))),
% 45.53/29.67 inference(rewrite,[status(thm)],[])).
% 45.53/29.67 tff(885,plain,
% 45.53/29.67 ((~![P: $i] : ((~![X1: $i, X2: $i] : ((~((~bool(apply(P, X1))) & (~bool(apply(P, X2))))) | (apply(P, X1) = apply(P, X2)))) | (exists1(P) = exists2(P)))) <=> (~![P: $i] : ((~![X1: $i, X2: $i] : ((~((~bool(apply(P, X1))) & (~bool(apply(P, X2))))) | (apply(P, X1) = apply(P, X2)))) | (exists1(P) = exists2(P))))),
% 45.53/29.67 inference(rewrite,[status(thm)],[])).
% 45.53/29.67 tff(886,plain,
% 45.53/29.67 ((~![P: $i] : (![X1: $i, X2: $i] : (((~bool(apply(P, X1))) & (~bool(apply(P, X2)))) => (apply(P, X1) = apply(P, X2))) => (exists1(P) = exists2(P)))) <=> (~![P: $i] : ((~![X1: $i, X2: $i] : ((~((~bool(apply(P, X1))) & (~bool(apply(P, X2))))) | (apply(P, X1) = apply(P, X2)))) | (exists1(P) = exists2(P))))),
% 45.53/29.67 inference(rewrite,[status(thm)],[])).
% 45.53/29.67 tff(887,axiom,(~![P: $i] : (![X1: $i, X2: $i] : (((~bool(apply(P, X1))) & (~bool(apply(P, X2)))) => (apply(P, X1) = apply(P, X2))) => (exists1(P) = exists2(P)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','exists1_exists2')).
% 45.53/29.67 tff(888,plain,
% 45.53/29.67 (~![P: $i] : ((~![X1: $i, X2: $i] : ((~((~bool(apply(P, X1))) & (~bool(apply(P, X2))))) | (apply(P, X1) = apply(P, X2)))) | (exists1(P) = exists2(P)))),
% 45.53/29.67 inference(modus_ponens,[status(thm)],[887, 886])).
% 45.53/29.67 tff(889,plain,
% 45.53/29.67 (~![P: $i] : ((~![X1: $i, X2: $i] : ((~((~bool(apply(P, X1))) & (~bool(apply(P, X2))))) | (apply(P, X1) = apply(P, X2)))) | (exists1(P) = exists2(P)))),
% 45.53/29.67 inference(modus_ponens,[status(thm)],[888, 885])).
% 45.53/29.67 tff(890,plain,
% 45.53/29.67 (~![P: $i] : ((~![X1: $i, X2: $i] : ((~((~bool(apply(P, X1))) & (~bool(apply(P, X2))))) | (apply(P, X1) = apply(P, X2)))) | (exists1(P) = exists2(P)))),
% 45.53/29.67 inference(modus_ponens,[status(thm)],[889, 885])).
% 45.53/29.67 tff(891,plain,
% 45.53/29.67 (~![P: $i] : ((~![X1: $i, X2: $i] : ((~((~bool(apply(P, X1))) & (~bool(apply(P, X2))))) | (apply(P, X1) = apply(P, X2)))) | (exists1(P) = exists2(P)))),
% 45.53/29.67 inference(modus_ponens,[status(thm)],[890, 885])).
% 45.53/29.67 tff(892,plain,
% 45.53/29.67 (~![P: $i] : ((~![X1: $i, X2: $i] : ((~((~bool(apply(P, X1))) & (~bool(apply(P, X2))))) | (apply(P, X1) = apply(P, X2)))) | (exists1(P) = exists2(P)))),
% 45.53/29.67 inference(modus_ponens,[status(thm)],[891, 885])).
% 45.53/29.67 tff(893,plain,
% 45.53/29.67 (~![P: $i] : ((~![X1: $i, X2: $i] : ((~((~bool(apply(P, X1))) & (~bool(apply(P, X2))))) | (apply(P, X1) = apply(P, X2)))) | (exists1(P) = exists2(P)))),
% 45.53/29.67 inference(modus_ponens,[status(thm)],[892, 885])).
% 45.53/29.67 tff(894,plain,
% 45.53/29.67 (~![P: $i] : ((~![X1: $i, X2: $i] : ((~((~bool(apply(P, X1))) & (~bool(apply(P, X2))))) | (apply(P, X1) = apply(P, X2)))) | (exists1(P) = exists2(P)))),
% 45.53/29.67 inference(modus_ponens,[status(thm)],[893, 885])).
% 45.53/29.67 tff(895,plain,
% 45.53/29.67 (~![P: $i] : ((~![X1: $i, X2: $i] : ((~((~bool(apply(P, X1))) & (~bool(apply(P, X2))))) | (apply(P, X1) = apply(P, X2)))) | (exists1(P) = exists2(P)))),
% 45.53/29.67 inference(modus_ponens,[status(thm)],[894, 885])).
% 45.53/29.67 tff(896,plain,
% 45.53/29.67 (![X1: $i, X2: $i] : ((~((~bool(apply(P!7, X1))) & (~bool(apply(P!7, X2))))) | (apply(P!7, X1) = apply(P!7, X2))) & (~(exists1(P!7) = exists2(P!7)))),
% 45.53/29.67 inference(modus_ponens,[status(thm)],[895, 884])).
% 45.53/29.67 tff(897,plain,
% 45.53/29.67 (~(exists1(P!7) = exists2(P!7))),
% 45.53/29.67 inference(and_elim,[status(thm)],[896])).
% 45.53/29.67 tff(898,plain,
% 45.53/29.67 (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))),
% 45.53/29.67 inference(modus_ponens,[status(thm)],[897, 883])).
% 45.53/29.67 tff(899,assumption,(lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false)), introduced(assumption)).
% 45.53/29.67 tff(900,plain,
% 45.53/29.67 (lazy_impl(not1(false), impl(f5(P!7, false), false)) = lazy_impl(prop(false), impl(f5(P!7, false), false))),
% 45.53/29.67 inference(monotonicity,[status(thm)],[132])).
% 45.53/29.67 tff(901,plain,
% 45.53/29.67 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), impl(f5(P!7, false), false)) = phi(impl(f5(P!7, false), false)))),
% 45.53/29.67 inference(quant_inst,[status(thm)],[])).
% 45.53/29.67 tff(902,plain,
% 45.53/29.67 (lazy_impl(not1(false), impl(f5(P!7, false), false)) = phi(impl(f5(P!7, false), false))),
% 45.53/29.67 inference(unit_resolution,[status(thm)],[901, 33])).
% 45.53/29.67 tff(903,plain,
% 45.53/29.67 (phi(impl(f5(P!7, false), false)) = lazy_impl(not1(false), impl(f5(P!7, false), false))),
% 45.53/29.67 inference(symmetry,[status(thm)],[902])).
% 45.53/29.67 tff(904,plain,
% 45.53/29.67 (phi(f7(P!6)) = false2),
% 45.53/29.67 inference(symmetry,[status(thm)],[815])).
% 45.53/29.67 tff(905,plain,
% 45.53/29.67 (phi(false) = phi(f7(P!6))),
% 45.53/29.67 inference(symmetry,[status(thm)],[814])).
% 45.53/29.67 tff(906,plain,
% 45.53/29.67 (false = false2),
% 45.53/29.67 inference(transitivity,[status(thm)],[205, 905, 904])).
% 45.53/29.67 tff(907,plain,
% 45.53/29.67 (((~(f5(P!7, false) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~![X1: $i] : (~forallprefers(f4(P!7, X1, false), f4(P!7, tptp_fun_X_4(false, P!7), false))))) | (f5(P!7, false) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 45.53/29.67 inference(tautology,[status(thm)],[])).
% 45.53/29.67 tff(908,plain,
% 45.53/29.67 (f5(P!7, false) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 45.53/29.67 inference(unit_resolution,[status(thm)],[907, 823])).
% 45.53/29.67 tff(909,plain,
% 45.53/29.67 (impl(f5(P!7, false), false) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)),
% 45.53/29.67 inference(monotonicity,[status(thm)],[908, 906])).
% 45.53/29.67 tff(910,plain,
% 45.53/29.67 (impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2) = impl(f5(P!7, false), false)),
% 45.53/29.67 inference(symmetry,[status(thm)],[909])).
% 45.53/29.67 tff(911,plain,
% 45.53/29.67 (phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = phi(impl(f5(P!7, false), false))),
% 45.53/29.67 inference(monotonicity,[status(thm)],[910])).
% 45.53/29.67 tff(912,plain,
% 45.53/29.67 (phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = not1(false)),
% 45.53/29.67 inference(transitivity,[status(thm)],[911, 903, 900, 899])).
% 45.53/29.67 tff(913,plain,
% 45.53/29.67 ((phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err) <=> (not1(false) = err)),
% 45.53/29.67 inference(monotonicity,[status(thm)],[912])).
% 45.53/29.67 tff(914,plain,
% 45.53/29.67 ((not1(false) = err) <=> (phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err)),
% 45.53/29.67 inference(symmetry,[status(thm)],[913])).
% 45.53/29.67 tff(915,plain,
% 45.53/29.67 ((~(not1(false) = err)) <=> (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err))),
% 45.53/29.67 inference(monotonicity,[status(thm)],[914])).
% 45.53/29.67 tff(916,plain,
% 45.53/29.67 (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err)),
% 45.53/29.67 inference(modus_ponens,[status(thm)],[564, 915])).
% 45.53/29.67 tff(917,plain,
% 45.53/29.67 ((d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err))) | (phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err)),
% 45.53/29.67 inference(tautology,[status(thm)],[])).
% 45.53/29.67 tff(918,plain,
% 45.53/29.67 (d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err))),
% 45.53/29.67 inference(unit_resolution,[status(thm)],[917, 916])).
% 45.53/29.67 tff(919,plain,
% 45.53/29.67 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~(d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err)))) | (~((~d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~(d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err)))) | (~((~d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))))))),
% 45.53/29.67 inference(rewrite,[status(thm)],[])).
% 45.53/29.67 tff(920,plain,
% 45.53/29.67 (((~((~d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))))) | (~(d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err))))) <=> ((~(d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err)))) | (~((~d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))))))),
% 45.53/29.67 inference(rewrite,[status(thm)],[])).
% 45.53/29.67 tff(921,plain,
% 45.53/29.67 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))))) | (~(d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~(d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err)))) | (~((~d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)))))))),
% 45.53/29.67 inference(monotonicity,[status(thm)],[920])).
% 45.53/29.67 tff(922,plain,
% 45.53/29.67 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))))) | (~(d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~(d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err)))) | (~((~d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))))))),
% 45.53/29.68 inference(transitivity,[status(thm)],[921, 919])).
% 45.53/29.68 tff(923,plain,
% 45.53/29.68 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))))) | (~(d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err)))))),
% 45.53/29.68 inference(quant_inst,[status(thm)],[])).
% 45.53/29.68 tff(924,plain,
% 45.53/29.68 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~(d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err)))) | (~((~d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)))))),
% 45.53/29.68 inference(modus_ponens,[status(thm)],[923, 922])).
% 45.53/29.68 tff(925,plain,
% 45.53/29.68 ((~(d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err)))) | (~((~d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)))))),
% 45.53/29.68 inference(unit_resolution,[status(thm)],[924, 17])).
% 45.53/29.68 tff(926,plain,
% 45.53/29.68 (~((~d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))))),
% 45.53/29.68 inference(unit_resolution,[status(thm)],[925, 918])).
% 45.53/29.68 tff(927,plain,
% 45.53/29.68 (((~d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)))) | (phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))),
% 45.53/29.68 inference(tautology,[status(thm)],[])).
% 45.53/29.68 tff(928,plain,
% 45.53/29.68 (phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)),
% 45.53/29.68 inference(unit_resolution,[status(thm)],[927, 926])).
% 45.53/29.68 tff(929,plain,
% 45.53/29.68 (impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2) = phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))),
% 45.53/29.68 inference(symmetry,[status(thm)],[928])).
% 45.53/29.68 tff(930,plain,
% 45.53/29.68 (impl(impl(false, false), false) = impl(not1(false), false)),
% 45.53/29.68 inference(monotonicity,[status(thm)],[93])).
% 45.53/29.68 tff(931,plain,
% 45.53/29.68 (impl(impl(false, false), false) = false),
% 45.53/29.68 inference(transitivity,[status(thm)],[930, 114])).
% 45.53/29.68 tff(932,plain,
% 45.53/29.68 (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f5(P!7, false)),
% 45.53/29.68 inference(symmetry,[status(thm)],[908])).
% 45.53/29.68 tff(933,assumption,(~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))), introduced(assumption)).
% 45.53/29.68 tff(934,plain,
% 45.53/29.68 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), false) = phi(apply(P!7, tptp_fun_X_3(P!7)))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), false) = phi(apply(P!7, tptp_fun_X_3(P!7)))))),
% 45.53/29.68 inference(rewrite,[status(thm)],[])).
% 45.53/29.68 tff(935,plain,
% 45.53/29.68 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), false) = phi(apply(P!7, tptp_fun_X_3(P!7)))))),
% 45.53/29.68 inference(quant_inst,[status(thm)],[])).
% 45.53/29.68 tff(936,plain,
% 45.53/29.68 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), false) = phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.53/29.68 inference(modus_ponens,[status(thm)],[935, 934])).
% 45.53/29.68 tff(937,plain,
% 45.53/29.68 (bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), false) = phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.53/29.68 inference(unit_resolution,[status(thm)],[936, 358])).
% 45.53/29.68 tff(938,plain,
% 45.53/29.68 (impl(apply(P!7, tptp_fun_X_3(P!7)), false) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.53/29.68 inference(unit_resolution,[status(thm)],[937, 348])).
% 45.53/29.68 tff(939,plain,
% 45.53/29.68 (d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) <=> d(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.53/29.68 inference(monotonicity,[status(thm)],[938])).
% 45.53/29.68 tff(940,plain,
% 45.53/29.68 (d(phi(apply(P!7, tptp_fun_X_3(P!7)))) <=> d(impl(apply(P!7, tptp_fun_X_3(P!7)), false))),
% 45.53/29.68 inference(symmetry,[status(thm)],[939])).
% 45.53/29.68 tff(941,plain,
% 45.53/29.68 (d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) <=> d(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.53/29.68 inference(monotonicity,[status(thm)],[363])).
% 45.53/29.68 tff(942,plain,
% 45.53/29.68 (d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) <=> d(impl(apply(P!7, tptp_fun_X_3(P!7)), false))),
% 45.53/29.68 inference(transitivity,[status(thm)],[941, 940])).
% 45.53/29.68 tff(943,plain,
% 45.53/29.68 (d(impl(apply(P!7, tptp_fun_X_3(P!7)), false))),
% 45.53/29.68 inference(modus_ponens,[status(thm)],[399, 942])).
% 45.53/29.68 tff(944,plain,
% 45.53/29.68 (bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) <=> bool(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.53/29.68 inference(monotonicity,[status(thm)],[938])).
% 45.53/29.68 tff(945,plain,
% 45.53/29.68 (bool(phi(apply(P!7, tptp_fun_X_3(P!7)))) <=> bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false))),
% 45.53/29.68 inference(symmetry,[status(thm)],[944])).
% 45.53/29.68 tff(946,plain,
% 45.53/29.68 ((~bool(phi(apply(P!7, tptp_fun_X_3(P!7))))) <=> (~bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)))),
% 45.53/29.68 inference(monotonicity,[status(thm)],[945])).
% 45.53/29.68 tff(947,plain,
% 45.53/29.68 (d(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.53/29.68 inference(modus_ponens,[status(thm)],[399, 941])).
% 45.53/29.68 tff(948,plain,
% 45.53/29.68 ((d(phi(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(phi(apply(P!7, tptp_fun_X_3(P!7)))) = err))) | (~d(phi(apply(P!7, tptp_fun_X_3(P!7)))))),
% 45.53/29.68 inference(tautology,[status(thm)],[])).
% 45.53/29.68 tff(949,plain,
% 45.53/29.68 (d(phi(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(phi(apply(P!7, tptp_fun_X_3(P!7)))) = err))),
% 45.53/29.68 inference(unit_resolution,[status(thm)],[948, 947])).
% 45.53/29.68 tff(950,plain,
% 45.53/29.68 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~(phi(phi(apply(P!7, tptp_fun_X_3(P!7)))) = phi(apply(P!7, tptp_fun_X_3(P!7))))))) | (~(d(phi(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(phi(apply(P!7, tptp_fun_X_3(P!7)))) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~(phi(phi(apply(P!7, tptp_fun_X_3(P!7)))) = phi(apply(P!7, tptp_fun_X_3(P!7))))))) | (~(d(phi(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(phi(apply(P!7, tptp_fun_X_3(P!7)))) = err)))))),
% 45.53/29.68 inference(rewrite,[status(thm)],[])).
% 45.53/29.68 tff(951,plain,
% 45.53/29.68 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~(phi(phi(apply(P!7, tptp_fun_X_3(P!7)))) = phi(apply(P!7, tptp_fun_X_3(P!7))))))) | (~(d(phi(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(phi(apply(P!7, tptp_fun_X_3(P!7)))) = err)))))),
% 45.53/29.68 inference(quant_inst,[status(thm)],[])).
% 45.53/29.68 tff(952,plain,
% 45.53/29.68 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~(phi(phi(apply(P!7, tptp_fun_X_3(P!7)))) = phi(apply(P!7, tptp_fun_X_3(P!7))))))) | (~(d(phi(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(phi(apply(P!7, tptp_fun_X_3(P!7)))) = err))))),
% 45.53/29.68 inference(modus_ponens,[status(thm)],[951, 950])).
% 45.53/29.68 tff(953,plain,
% 45.53/29.68 ((~((~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~(phi(phi(apply(P!7, tptp_fun_X_3(P!7)))) = phi(apply(P!7, tptp_fun_X_3(P!7))))))) | (~(d(phi(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(phi(apply(P!7, tptp_fun_X_3(P!7)))) = err))))),
% 45.53/29.68 inference(unit_resolution,[status(thm)],[952, 17])).
% 45.53/29.68 tff(954,plain,
% 45.53/29.68 (~((~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~(phi(phi(apply(P!7, tptp_fun_X_3(P!7)))) = phi(apply(P!7, tptp_fun_X_3(P!7))))))),
% 45.53/29.68 inference(unit_resolution,[status(thm)],[953, 949])).
% 45.53/29.68 tff(955,plain,
% 45.53/29.68 (((~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~(phi(phi(apply(P!7, tptp_fun_X_3(P!7)))) = phi(apply(P!7, tptp_fun_X_3(P!7)))))) | (phi(phi(apply(P!7, tptp_fun_X_3(P!7)))) = phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.53/29.68 inference(tautology,[status(thm)],[])).
% 45.53/29.68 tff(956,plain,
% 45.53/29.68 (phi(phi(apply(P!7, tptp_fun_X_3(P!7)))) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.53/29.68 inference(unit_resolution,[status(thm)],[955, 954])).
% 45.53/29.68 tff(957,assumption,(impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false)))), introduced(assumption)).
% 45.53/29.68 tff(958,assumption,(impl(f5(P!7, not1(false)), not1(false)) = not1(false)), introduced(assumption)).
% 45.53/29.68 tff(959,plain,
% 45.53/29.68 ((not1(false) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) <=> (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false))),
% 45.53/29.68 inference(commutativity,[status(thm)],[])).
% 45.53/29.68 tff(960,plain,
% 45.53/29.68 (phi(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 45.53/29.68 inference(monotonicity,[status(thm)],[805])).
% 45.53/29.68 tff(961,assumption,(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))), introduced(assumption)).
% 45.53/29.68 tff(962,plain,
% 45.53/29.68 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(err) | (impl(err, false) = phi(err)))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(err) | (impl(err, false) = phi(err)))),
% 45.53/29.68 inference(rewrite,[status(thm)],[])).
% 45.53/29.68 tff(963,plain,
% 45.53/29.68 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(err) | (impl(err, false) = phi(err)))),
% 45.53/29.68 inference(quant_inst,[status(thm)],[])).
% 45.53/29.68 tff(964,plain,
% 45.53/29.68 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(err) | (impl(err, false) = phi(err))),
% 45.53/29.68 inference(modus_ponens,[status(thm)],[963, 962])).
% 45.53/29.68 tff(965,plain,
% 45.53/29.68 (impl(err, false) = phi(err)),
% 45.53/29.68 inference(unit_resolution,[status(thm)],[964, 358, 571])).
% 45.53/29.68 tff(966,plain,
% 45.53/29.68 (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = apply(P!7, tptp_fun_X_3(P!7))),
% 45.53/29.68 inference(transitivity,[status(thm)],[364, 961])).
% 45.53/29.68 tff(967,plain,
% 45.53/29.68 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))),
% 45.53/29.68 inference(monotonicity,[status(thm)],[966])).
% 45.53/29.68 tff(968,plain,
% 45.53/29.68 (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 45.53/29.68 inference(symmetry,[status(thm)],[967])).
% 45.53/29.68 tff(969,plain,
% 45.53/29.68 (phi(apply(P!7, tptp_fun_X_3(P!7))) = impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))),
% 45.53/29.68 inference(symmetry,[status(thm)],[364])).
% 45.53/29.68 tff(970,assumption,(impl(apply(P!7, tptp_fun_X_3(P!7)), false) = phi(apply(P!7, tptp_fun_X_3(P!7)))), introduced(assumption)).
% 45.53/29.68 tff(971,plain,
% 45.53/29.68 (impl(apply(P!7, tptp_fun_X_3(P!7)), false) = apply(P!7, tptp_fun_X_3(P!7))),
% 45.53/29.68 inference(transitivity,[status(thm)],[970, 961])).
% 45.53/29.68 tff(972,plain,
% 45.53/29.68 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), false), impl(impl(false, false), false)) = impl(apply(P!7, tptp_fun_X_3(P!7)), false)),
% 45.53/29.68 inference(monotonicity,[status(thm)],[971, 931])).
% 45.53/29.68 tff(973,plain,
% 45.53/29.68 (impl(not1(false), false) = impl(impl(false, false), false)),
% 45.53/29.68 inference(symmetry,[status(thm)],[930])).
% 45.53/29.68 tff(974,plain,
% 45.53/29.68 (false = impl(impl(false, false), false)),
% 45.53/29.68 inference(transitivity,[status(thm)],[115, 973])).
% 45.53/29.68 tff(975,plain,
% 45.53/29.68 (phi(apply(P!7, tptp_fun_X_3(P!7))) = impl(apply(P!7, tptp_fun_X_3(P!7)), false)),
% 45.53/29.68 inference(symmetry,[status(thm)],[970])).
% 45.53/29.68 tff(976,plain,
% 45.53/29.68 (impl(phi(apply(P!7, tptp_fun_X_3(P!7))), false) = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), false), impl(impl(false, false), false))),
% 45.53/29.68 inference(monotonicity,[status(thm)],[975, 974])).
% 45.53/29.68 tff(977,plain,
% 45.53/29.68 (impl(phi(apply(P!7, tptp_fun_X_3(P!7))), false) = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 45.53/29.68 inference(transitivity,[status(thm)],[976, 972, 970, 969, 968])).
% 45.53/29.68 tff(978,plain,
% 45.53/29.68 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(err) | (impl(err, tptp_fun_R_5(P!7)) = phi(err)))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(err) | (impl(err, tptp_fun_R_5(P!7)) = phi(err)))),
% 45.53/29.68 inference(rewrite,[status(thm)],[])).
% 45.53/29.68 tff(979,plain,
% 45.53/29.68 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(err) | (impl(err, tptp_fun_R_5(P!7)) = phi(err)))),
% 45.53/29.68 inference(quant_inst,[status(thm)],[])).
% 45.53/29.68 tff(980,plain,
% 45.53/29.68 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(err) | (impl(err, tptp_fun_R_5(P!7)) = phi(err))),
% 45.53/29.68 inference(modus_ponens,[status(thm)],[979, 978])).
% 45.53/29.68 tff(981,plain,
% 45.53/29.68 (impl(err, tptp_fun_R_5(P!7)) = phi(err)),
% 45.53/29.68 inference(unit_resolution,[status(thm)],[980, 358, 571])).
% 45.53/29.68 tff(982,plain,
% 45.53/29.68 (phi(err) = impl(err, tptp_fun_R_5(P!7))),
% 45.53/29.68 inference(symmetry,[status(thm)],[981])).
% 45.53/29.68 tff(983,plain,
% 45.53/29.68 (err = phi(err)),
% 45.53/29.68 inference(symmetry,[status(thm)],[429])).
% 45.53/29.68 tff(984,plain,
% 45.53/29.68 (err = impl(err, tptp_fun_R_5(P!7))),
% 45.53/29.68 inference(transitivity,[status(thm)],[983, 982])).
% 45.53/29.68 tff(985,plain,
% 45.53/29.68 (impl(err, impl(phi(apply(P!7, tptp_fun_X_3(P!7))), false)) = impl(impl(err, tptp_fun_R_5(P!7)), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.53/29.68 inference(monotonicity,[status(thm)],[984, 977])).
% 45.53/29.68 tff(986,plain,
% 45.53/29.68 (impl(impl(err, tptp_fun_R_5(P!7)), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(err, impl(phi(apply(P!7, tptp_fun_X_3(P!7))), false))),
% 45.53/29.68 inference(symmetry,[status(thm)],[985])).
% 45.53/29.68 tff(987,plain,
% 45.53/29.68 (impl(err, tptp_fun_R_5(P!7)) = err),
% 45.53/29.68 inference(transitivity,[status(thm)],[981, 429])).
% 45.53/29.68 tff(988,plain,
% 45.53/29.68 (bool(impl(err, tptp_fun_R_5(P!7))) <=> bool(err)),
% 45.53/29.68 inference(monotonicity,[status(thm)],[987])).
% 45.53/29.68 tff(989,plain,
% 45.53/29.68 (bool(err) <=> bool(impl(err, tptp_fun_R_5(P!7)))),
% 45.53/29.68 inference(symmetry,[status(thm)],[988])).
% 45.53/29.68 tff(990,plain,
% 45.53/29.68 ((~bool(err)) <=> (~bool(impl(err, tptp_fun_R_5(P!7))))),
% 45.53/29.68 inference(monotonicity,[status(thm)],[989])).
% 45.53/29.68 tff(991,plain,
% 45.53/29.68 (~bool(impl(err, tptp_fun_R_5(P!7)))),
% 45.53/29.68 inference(modus_ponens,[status(thm)],[571, 990])).
% 45.53/29.68 tff(992,plain,
% 45.53/29.68 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(err, tptp_fun_R_5(P!7))) | (impl(impl(err, tptp_fun_R_5(P!7)), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = phi(impl(err, tptp_fun_R_5(P!7)))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(err, tptp_fun_R_5(P!7))) | (impl(impl(err, tptp_fun_R_5(P!7)), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = phi(impl(err, tptp_fun_R_5(P!7)))))),
% 45.53/29.68 inference(rewrite,[status(thm)],[])).
% 45.53/29.68 tff(993,plain,
% 45.53/29.68 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(err, tptp_fun_R_5(P!7))) | (impl(impl(err, tptp_fun_R_5(P!7)), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = phi(impl(err, tptp_fun_R_5(P!7)))))),
% 45.53/29.68 inference(quant_inst,[status(thm)],[])).
% 45.53/29.68 tff(994,plain,
% 45.53/29.68 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(err, tptp_fun_R_5(P!7))) | (impl(impl(err, tptp_fun_R_5(P!7)), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = phi(impl(err, tptp_fun_R_5(P!7))))),
% 45.53/29.68 inference(modus_ponens,[status(thm)],[993, 992])).
% 45.53/29.68 tff(995,plain,
% 45.53/29.68 (bool(impl(err, tptp_fun_R_5(P!7))) | (impl(impl(err, tptp_fun_R_5(P!7)), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = phi(impl(err, tptp_fun_R_5(P!7))))),
% 45.53/29.68 inference(unit_resolution,[status(thm)],[994, 358])).
% 45.53/29.68 tff(996,plain,
% 45.53/29.68 (impl(impl(err, tptp_fun_R_5(P!7)), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = phi(impl(err, tptp_fun_R_5(P!7)))),
% 45.53/29.68 inference(unit_resolution,[status(thm)],[995, 991])).
% 45.53/29.68 tff(997,plain,
% 45.53/29.68 (phi(impl(err, tptp_fun_R_5(P!7))) = impl(impl(err, tptp_fun_R_5(P!7)), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.53/29.68 inference(symmetry,[status(thm)],[996])).
% 45.53/29.68 tff(998,plain,
% 45.53/29.68 (phi(impl(err, tptp_fun_R_5(P!7))) = phi(err)),
% 45.53/29.68 inference(monotonicity,[status(thm)],[987])).
% 45.53/29.68 tff(999,plain,
% 45.53/29.68 (phi(err) = phi(impl(err, tptp_fun_R_5(P!7)))),
% 45.53/29.68 inference(symmetry,[status(thm)],[998])).
% 45.53/29.68 tff(1000,plain,
% 45.53/29.68 (err = impl(err, impl(phi(apply(P!7, tptp_fun_X_3(P!7))), false))),
% 45.53/29.68 inference(transitivity,[status(thm)],[983, 999, 997, 986])).
% 45.53/29.68 tff(1001,plain,
% 45.53/29.68 (impl(err, false) = impl(impl(err, impl(phi(apply(P!7, tptp_fun_X_3(P!7))), false)), false)),
% 45.53/29.68 inference(monotonicity,[status(thm)],[1000])).
% 45.53/29.68 tff(1002,plain,
% 45.53/29.68 (impl(impl(err, impl(phi(apply(P!7, tptp_fun_X_3(P!7))), false)), false) = impl(err, false)),
% 45.53/29.68 inference(symmetry,[status(thm)],[1001])).
% 45.53/29.68 tff(1003,assumption,(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err), introduced(assumption)).
% 45.53/29.68 tff(1004,plain,
% 45.53/29.68 (err = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 45.53/29.68 inference(symmetry,[status(thm)],[1003])).
% 45.53/29.68 tff(1005,plain,
% 45.53/29.68 (impl(err, impl(phi(apply(P!7, tptp_fun_X_3(P!7))), false)) = f5(P!7, false)),
% 45.53/29.68 inference(transitivity,[status(thm)],[985, 996, 998, 429, 1004, 932])).
% 45.53/29.68 tff(1006,plain,
% 45.53/29.68 (impl(impl(err, impl(phi(apply(P!7, tptp_fun_X_3(P!7))), false)), false) = impl(f5(P!7, false), false)),
% 45.53/29.68 inference(monotonicity,[status(thm)],[1005])).
% 45.53/29.68 tff(1007,plain,
% 45.53/29.68 (impl(f5(P!7, false), false) = impl(impl(err, impl(phi(apply(P!7, tptp_fun_X_3(P!7))), false)), false)),
% 45.53/29.68 inference(symmetry,[status(thm)],[1006])).
% 45.53/29.68 tff(1008,plain,
% 45.53/29.68 (phi(impl(f5(P!7, false), false)) = phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))),
% 45.53/29.68 inference(symmetry,[status(thm)],[911])).
% 45.53/29.68 tff(1009,plain,
% 45.53/29.68 (lazy_impl(prop(false), impl(f5(P!7, false), false)) = lazy_impl(not1(false), impl(f5(P!7, false), false))),
% 45.53/29.68 inference(symmetry,[status(thm)],[900])).
% 45.53/29.68 tff(1010,plain,
% 45.53/29.68 (not1(false) = lazy_impl(prop(false), impl(f5(P!7, false), false))),
% 45.53/29.68 inference(symmetry,[status(thm)],[899])).
% 45.53/29.68 tff(1011,plain,
% 45.53/29.68 (phi(f5(P!7, not1(false))) = impl(f5(P!7, not1(false)), not1(false))),
% 45.53/29.68 inference(symmetry,[status(thm)],[957])).
% 45.53/29.68 tff(1012,plain,
% 45.53/29.68 (phi(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))) = err),
% 45.53/29.68 inference(transitivity,[status(thm)],[703, 1011, 958, 1010, 1009, 902, 1008, 928, 910, 1007, 1002, 965, 429])).
% 45.53/29.68 tff(1013,plain,
% 45.53/29.68 ($false),
% 45.53/29.68 inference(unit_resolution,[status(thm)],[795, 1012])).
% 45.53/29.68 tff(1014,plain,((~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err)) | (phi(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))) = err) | (~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false))) | (~(impl(f5(P!7, not1(false)), not1(false)) = not1(false))) | (~(impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false))))) | (~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~(impl(apply(P!7, tptp_fun_X_3(P!7)), false) = phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))))), inference(lemma,lemma(discharge,[]))).
% 45.53/29.68 tff(1015,plain,
% 45.53/29.68 (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err)),
% 45.53/29.68 inference(unit_resolution,[status(thm)],[1014, 961, 899, 958, 957, 363, 938, 795])).
% 45.53/29.68 tff(1016,plain,
% 45.53/29.68 ((d(f4(P!7, tptp_fun_X_4(false, P!7), false)) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err))) | (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err)),
% 45.53/29.68 inference(tautology,[status(thm)],[])).
% 45.53/29.68 tff(1017,plain,
% 45.53/29.68 (d(f4(P!7, tptp_fun_X_4(false, P!7), false)) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err))),
% 45.53/29.68 inference(unit_resolution,[status(thm)],[1016, 1015])).
% 45.53/29.68 tff(1018,plain,
% 45.53/29.68 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false))))) | (~(d(f4(P!7, tptp_fun_X_4(false, P!7), false)) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false))))) | (~(d(f4(P!7, tptp_fun_X_4(false, P!7), false)) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err)))))),
% 45.53/29.68 inference(rewrite,[status(thm)],[])).
% 45.53/29.68 tff(1019,plain,
% 45.53/29.68 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false))))) | (~(d(f4(P!7, tptp_fun_X_4(false, P!7), false)) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err)))))),
% 45.53/29.68 inference(quant_inst,[status(thm)],[])).
% 45.53/29.68 tff(1020,plain,
% 45.53/29.68 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false))))) | (~(d(f4(P!7, tptp_fun_X_4(false, P!7), false)) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err))))),
% 45.53/29.68 inference(modus_ponens,[status(thm)],[1019, 1018])).
% 45.53/29.68 tff(1021,plain,
% 45.53/29.68 ((~((~d(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false))))) | (~(d(f4(P!7, tptp_fun_X_4(false, P!7), false)) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err))))),
% 45.53/29.68 inference(unit_resolution,[status(thm)],[1020, 17])).
% 45.53/29.68 tff(1022,plain,
% 45.53/29.68 (~((~d(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 45.53/29.68 inference(unit_resolution,[status(thm)],[1021, 1017])).
% 45.53/29.68 tff(1023,plain,
% 45.53/29.68 (((~d(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 45.53/29.68 inference(tautology,[status(thm)],[])).
% 45.53/29.68 tff(1024,plain,
% 45.53/29.68 (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false)),
% 45.53/29.68 inference(unit_resolution,[status(thm)],[1023, 1022])).
% 45.53/29.68 tff(1025,plain,
% 45.53/29.68 (f4(P!7, tptp_fun_X_4(false, P!7), false) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 45.53/29.68 inference(symmetry,[status(thm)],[1024])).
% 45.53/29.68 tff(1026,plain,
% 45.53/29.68 (impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)) = impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)),
% 45.53/29.68 inference(monotonicity,[status(thm)],[114])).
% 45.53/29.68 tff(1027,plain,
% 45.53/29.68 (impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)) = f5(P!7, false)),
% 45.53/29.68 inference(transitivity,[status(thm)],[1026, 805, 1025, 932])).
% 45.53/29.68 tff(1028,plain,
% 45.53/29.68 (impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false) = impl(f5(P!7, false), false)),
% 45.53/29.68 inference(monotonicity,[status(thm)],[1027])).
% 45.53/29.68 tff(1029,plain,
% 45.53/29.68 (impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false))),
% 45.53/29.68 inference(symmetry,[status(thm)],[1026])).
% 45.53/29.68 tff(1030,plain,
% 45.53/29.68 (impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false) = impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false)),
% 45.53/29.68 inference(monotonicity,[status(thm)],[1029])).
% 45.53/29.68 tff(1031,plain,
% 45.53/29.68 (impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false) = not1(false)),
% 45.53/29.68 inference(transitivity,[status(thm)],[1030, 1028, 909, 929, 911, 903, 900, 899])).
% 45.53/29.68 tff(1032,plain,
% 45.53/29.68 ((impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false) = phi(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) <=> (not1(false) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 45.53/29.68 inference(monotonicity,[status(thm)],[1031, 960])).
% 45.53/29.68 tff(1033,plain,
% 45.53/29.68 ((impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false) = phi(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) <=> (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false))),
% 45.53/29.68 inference(transitivity,[status(thm)],[1032, 959])).
% 45.53/29.68 tff(1034,plain,
% 45.53/29.68 ((phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false)) <=> (impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false) = phi(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)))),
% 45.53/29.69 inference(symmetry,[status(thm)],[1033])).
% 45.53/29.69 tff(1035,plain,
% 45.53/29.69 ((~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false))) <=> (~(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false) = phi(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))),
% 45.53/29.69 inference(monotonicity,[status(thm)],[1034])).
% 45.53/29.69 tff(1036,plain,
% 45.53/29.69 (impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 45.53/29.69 inference(transitivity,[status(thm)],[805, 1025])).
% 45.53/29.69 tff(1037,plain,
% 45.53/29.69 ((impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false)) <=> (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false))),
% 45.53/29.69 inference(monotonicity,[status(thm)],[1036])).
% 45.53/29.69 tff(1038,plain,
% 45.53/29.69 ((~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))) <=> (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false)))),
% 45.53/29.69 inference(monotonicity,[status(thm)],[1037])).
% 45.53/29.69 tff(1039,plain,
% 45.53/29.69 (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false))),
% 45.53/29.69 inference(modus_ponens,[status(thm)],[933, 1038])).
% 45.53/29.69 tff(1040,plain,
% 45.53/29.69 (~(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false) = phi(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)))),
% 45.53/29.69 inference(modus_ponens,[status(thm)],[1039, 1035])).
% 45.53/29.69 tff(1041,plain,
% 45.53/29.69 (apply(P!7, tptp_fun_X_3(P!7)) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.53/29.69 inference(symmetry,[status(thm)],[961])).
% 45.53/29.69 tff(1042,plain,
% 45.53/29.69 (bool(apply(P!7, tptp_fun_X_3(P!7))) <=> bool(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.53/29.69 inference(monotonicity,[status(thm)],[1041])).
% 45.53/29.69 tff(1043,plain,
% 45.53/29.69 (bool(apply(P!7, tptp_fun_X_3(P!7))) <=> bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false))),
% 45.53/29.69 inference(transitivity,[status(thm)],[1042, 945])).
% 45.53/29.69 tff(1044,plain,
% 45.53/29.69 ((~bool(apply(P!7, tptp_fun_X_3(P!7)))) <=> (~bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)))),
% 45.53/29.69 inference(monotonicity,[status(thm)],[1043])).
% 45.53/29.69 tff(1045,plain,
% 45.53/29.69 (~bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false))),
% 45.53/29.69 inference(modus_ponens,[status(thm)],[348, 1044])).
% 45.53/29.69 tff(1046,plain,
% 45.53/29.69 (d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) <=> d(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 45.53/29.69 inference(monotonicity,[status(thm)],[805])).
% 45.53/29.69 tff(1047,plain,
% 45.53/29.69 (d(f4(P!7, tptp_fun_X_4(false, P!7), false)) <=> d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))),
% 45.53/29.69 inference(symmetry,[status(thm)],[1046])).
% 45.53/29.69 tff(1048,plain,
% 45.53/29.69 (((~d(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false)))) | d(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 45.53/29.69 inference(tautology,[status(thm)],[])).
% 45.53/29.69 tff(1049,plain,
% 45.53/29.69 (d(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 45.53/29.69 inference(unit_resolution,[status(thm)],[1048, 1022])).
% 45.53/29.69 tff(1050,plain,
% 45.53/29.69 (d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))),
% 45.53/29.69 inference(modus_ponens,[status(thm)],[1049, 1047])).
% 45.53/29.69 tff(1051,plain,
% 45.53/29.69 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), false), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) <=> ((~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), false) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))))) | (~(bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), false), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) <=> ((~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), false) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))))) | (~(bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false))))))))),
% 45.53/29.69 inference(rewrite,[status(thm)],[])).
% 45.53/29.69 tff(1052,plain,
% 45.53/29.69 ((forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), false), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) <=> ((~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false))))) | (~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), false) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))))))) <=> (forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), false), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) <=> ((~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), false) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))))) | (~(bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)))))))),
% 45.53/29.69 inference(rewrite,[status(thm)],[])).
% 45.53/29.69 tff(1053,plain,
% 45.53/29.69 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), false), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) <=> ((~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false))))) | (~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), false) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), false), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) <=> ((~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), false) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))))) | (~(bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false))))))))),
% 45.53/29.69 inference(monotonicity,[status(thm)],[1052])).
% 45.53/29.69 tff(1054,plain,
% 45.53/29.69 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), false), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) <=> ((~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false))))) | (~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), false) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), false), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) <=> ((~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), false) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))))) | (~(bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false))))))))),
% 45.53/29.69 inference(transitivity,[status(thm)],[1053, 1051])).
% 45.53/29.69 tff(1055,plain,
% 45.53/29.69 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), false), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) <=> ((~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false))))) | (~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), false) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false)))))))),
% 45.53/29.69 inference(quant_inst,[status(thm)],[])).
% 45.53/29.69 tff(1056,plain,
% 45.53/29.69 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), false), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) <=> ((~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), false) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))))) | (~(bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)))))))),
% 45.53/29.69 inference(modus_ponens,[status(thm)],[1055, 1054])).
% 45.53/29.69 tff(1057,plain,
% 45.53/29.69 (forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), false), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) <=> ((~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), false) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))))) | (~(bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false))))))),
% 45.53/29.69 inference(unit_resolution,[status(thm)],[1056, 159])).
% 45.53/29.69 tff(1058,plain,
% 45.53/29.69 ((~![P: $i, X: $i, R: $i] : (f4(P, X, R) = impl(apply(P, X), R))) | (f4(P!7, tptp_fun_X_3(P!7), false) = impl(apply(P!7, tptp_fun_X_3(P!7)), false))),
% 45.53/29.69 inference(quant_inst,[status(thm)],[])).
% 45.53/29.69 tff(1059,plain,
% 45.53/29.69 (f4(P!7, tptp_fun_X_3(P!7), false) = impl(apply(P!7, tptp_fun_X_3(P!7)), false)),
% 45.53/29.69 inference(unit_resolution,[status(thm)],[1058, 412])).
% 45.53/29.69 tff(1060,plain,
% 45.53/29.69 (impl(apply(P!7, tptp_fun_X_3(P!7)), false) = f4(P!7, tptp_fun_X_3(P!7), false)),
% 45.53/29.69 inference(symmetry,[status(thm)],[1059])).
% 45.53/29.69 tff(1061,plain,
% 45.53/29.69 (forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), false), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) <=> forallprefers(f4(P!7, tptp_fun_X_3(P!7), false), f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 45.53/29.69 inference(monotonicity,[status(thm)],[1060, 805])).
% 45.53/29.69 tff(1062,plain,
% 45.53/29.69 (forallprefers(f4(P!7, tptp_fun_X_3(P!7), false), f4(P!7, tptp_fun_X_4(false, P!7), false)) <=> forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), false), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))),
% 45.53/29.69 inference(symmetry,[status(thm)],[1061])).
% 45.53/29.69 tff(1063,plain,
% 45.53/29.69 ((~forallprefers(f4(P!7, tptp_fun_X_3(P!7), false), f4(P!7, tptp_fun_X_4(false, P!7), false))) <=> (~forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), false), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)))),
% 45.53/29.69 inference(monotonicity,[status(thm)],[1062])).
% 45.53/29.69 tff(1064,plain,
% 45.53/29.69 ((~![X1: $i] : (~forallprefers(f4(P!7, X1, false), f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~forallprefers(f4(P!7, tptp_fun_X_3(P!7), false), f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 45.53/29.69 inference(quant_inst,[status(thm)],[])).
% 45.53/29.69 tff(1065,plain,
% 45.53/29.69 (~forallprefers(f4(P!7, tptp_fun_X_3(P!7), false), f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 45.53/29.69 inference(unit_resolution,[status(thm)],[1064, 825])).
% 45.53/29.69 tff(1066,plain,
% 45.53/29.69 (~forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), false), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))),
% 45.53/29.69 inference(modus_ponens,[status(thm)],[1065, 1063])).
% 45.53/29.69 tff(1067,plain,
% 45.53/29.69 ((~(forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), false), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) <=> ((~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), false) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))))) | (~(bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)))))))) | forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), false), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) | (~((~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), false) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))))) | (~(bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)))))))),
% 45.53/29.69 inference(tautology,[status(thm)],[])).
% 45.53/29.69 tff(1068,plain,
% 45.53/29.69 (~((~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), false) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))))) | (~(bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false))))))),
% 45.53/29.69 inference(unit_resolution,[status(thm)],[1067, 1066, 1057])).
% 45.53/29.69 tff(1069,plain,
% 45.53/29.69 (((~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), false) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))))) | (~(bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)))))) | (bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false))))),
% 45.53/29.69 inference(tautology,[status(thm)],[])).
% 45.53/29.69 tff(1070,plain,
% 45.53/29.69 (bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)))),
% 45.53/29.69 inference(unit_resolution,[status(thm)],[1069, 1068])).
% 45.53/29.69 tff(1071,plain,
% 45.53/29.69 ((~(bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false))))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)))),
% 45.53/29.69 inference(tautology,[status(thm)],[])).
% 45.53/29.69 tff(1072,plain,
% 45.53/29.69 (bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)))),
% 45.53/29.69 inference(unit_resolution,[status(thm)],[1071, 1070])).
% 45.53/29.69 tff(1073,plain,
% 45.53/29.69 (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))),
% 45.53/29.69 inference(unit_resolution,[status(thm)],[1072, 1050, 1045, 943])).
% 45.53/29.69 tff(1074,plain,
% 45.53/29.69 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) | (impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false) = phi(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) | (impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false) = phi(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))),
% 45.53/29.69 inference(rewrite,[status(thm)],[])).
% 45.53/29.69 tff(1075,plain,
% 45.53/29.69 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) | (impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false) = phi(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))),
% 45.53/29.69 inference(quant_inst,[status(thm)],[])).
% 45.53/29.69 tff(1076,plain,
% 45.53/29.69 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) | (impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false) = phi(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)))),
% 45.53/29.69 inference(modus_ponens,[status(thm)],[1075, 1074])).
% 45.53/29.69 tff(1077,plain,
% 45.53/29.69 (bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) | (impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false) = phi(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)))),
% 45.53/29.69 inference(unit_resolution,[status(thm)],[1076, 358])).
% 45.53/29.69 tff(1078,plain,
% 45.53/29.69 ($false),
% 45.53/29.69 inference(unit_resolution,[status(thm)],[1077, 1073, 1040])).
% 45.53/29.69 tff(1079,plain,((~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))) | (~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false))) | (impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false)) | (~(impl(f5(P!7, not1(false)), not1(false)) = not1(false))) | (~(impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false))))) | (phi(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))) = err) | bool(apply(P!7, tptp_fun_X_3(P!7)))), inference(lemma,lemma(discharge,[]))).
% 45.53/29.69 tff(1080,plain,
% 45.53/29.69 (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))),
% 45.53/29.69 inference(unit_resolution,[status(thm)],[1079, 348, 933, 958, 957, 795, 899])).
% 45.53/29.69 tff(1081,plain,
% 45.53/29.69 ((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))))),
% 45.53/29.69 inference(unit_resolution,[status(thm)],[369, 1080])).
% 45.53/29.69 tff(1082,plain,
% 45.53/29.69 (~(d(apply(P!7, tptp_fun_X_3(P!7))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err)))),
% 45.53/29.69 inference(unit_resolution,[status(thm)],[383, 1081])).
% 45.53/29.69 tff(1083,plain,
% 45.53/29.69 (phi(apply(P!7, tptp_fun_X_3(P!7))) = err),
% 45.53/29.69 inference(unit_resolution,[status(thm)],[385, 1082])).
% 45.53/29.69 tff(1084,assumption,(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))) = not1(false)), introduced(assumption)).
% 45.53/29.69 tff(1085,plain,
% 45.53/29.69 (lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = lazy_impl(not1(false), phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.53/29.69 inference(monotonicity,[status(thm)],[1084])).
% 45.53/29.69 tff(1086,plain,
% 45.53/29.69 (lazy_impl(not1(false), phi(apply(P!7, tptp_fun_X_3(P!7)))) = lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.53/29.69 inference(symmetry,[status(thm)],[1085])).
% 45.53/29.69 tff(1087,plain,
% 45.53/29.69 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), phi(apply(P!7, tptp_fun_X_3(P!7)))) = phi(phi(apply(P!7, tptp_fun_X_3(P!7)))))),
% 45.53/29.69 inference(quant_inst,[status(thm)],[])).
% 45.53/29.69 tff(1088,plain,
% 45.53/29.69 (lazy_impl(not1(false), phi(apply(P!7, tptp_fun_X_3(P!7)))) = phi(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.53/29.69 inference(unit_resolution,[status(thm)],[1087, 33])).
% 45.53/29.69 tff(1089,plain,
% 45.53/29.69 (phi(phi(apply(P!7, tptp_fun_X_3(P!7)))) = lazy_impl(not1(false), phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.53/29.69 inference(symmetry,[status(thm)],[1088])).
% 45.53/29.69 tff(1090,assumption,(phi(phi(apply(P!7, tptp_fun_X_3(P!7)))) = phi(apply(P!7, tptp_fun_X_3(P!7)))), introduced(assumption)).
% 45.53/29.69 tff(1091,plain,
% 45.53/29.69 (phi(apply(P!7, tptp_fun_X_3(P!7))) = phi(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.53/29.69 inference(symmetry,[status(thm)],[1090])).
% 45.53/29.69 tff(1092,assumption,(phi(apply(P!7, tptp_fun_X_3(P!7))) = err), introduced(assumption)).
% 45.53/29.69 tff(1093,plain,
% 45.53/29.69 (err = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.53/29.69 inference(symmetry,[status(thm)],[1092])).
% 45.53/29.69 tff(1094,plain,
% 45.53/29.69 (err = lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.53/29.69 inference(transitivity,[status(thm)],[1093, 1091, 1089, 1086])).
% 45.53/29.69 tff(1095,plain,
% 45.53/29.69 (bool(err) <=> bool(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))))),
% 45.53/29.69 inference(monotonicity,[status(thm)],[1094])).
% 45.53/29.69 tff(1096,plain,
% 45.53/29.69 (bool(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))) <=> bool(err)),
% 45.53/29.69 inference(symmetry,[status(thm)],[1095])).
% 45.53/29.69 tff(1097,plain,
% 45.53/29.69 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))), false) <=> ((~((~(false = not1(false))) | (~(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))))))) | (~((~d(false)) | d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))), false) <=> ((~((~(false = not1(false))) | (~(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))))))) | (~((~d(false)) | d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))))))))),
% 45.53/29.69 inference(rewrite,[status(thm)],[])).
% 45.53/29.69 tff(1098,plain,
% 45.53/29.69 ((forallprefers(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))), false) <=> ((~(d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))))))) | (~((~(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = false)) | (~(false = not1(false))))))) <=> (forallprefers(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))), false) <=> ((~((~(false = not1(false))) | (~(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))))))) | (~((~d(false)) | d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))))))))),
% 45.53/29.69 inference(rewrite,[status(thm)],[])).
% 45.53/29.69 tff(1099,plain,
% 45.53/29.69 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))), false) <=> ((~(d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))))))) | (~((~(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = false)) | (~(false = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))), false) <=> ((~((~(false = not1(false))) | (~(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))))))) | (~((~d(false)) | d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))))))))),
% 45.53/29.69 inference(monotonicity,[status(thm)],[1098])).
% 45.53/29.69 tff(1100,plain,
% 45.53/29.69 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))), false) <=> ((~(d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))))))) | (~((~(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = false)) | (~(false = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))), false) <=> ((~((~(false = not1(false))) | (~(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))))))) | (~((~d(false)) | d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))))))))),
% 45.53/29.69 inference(transitivity,[status(thm)],[1099, 1097])).
% 45.53/29.69 tff(1101,plain,
% 45.53/29.69 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))), false) <=> ((~(d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))))))) | (~((~(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = false)) | (~(false = not1(false)))))))),
% 45.53/29.70 inference(quant_inst,[status(thm)],[])).
% 45.53/29.70 tff(1102,plain,
% 45.53/29.70 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))), false) <=> ((~((~(false = not1(false))) | (~(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))))))) | (~((~d(false)) | d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))))))))),
% 45.53/29.70 inference(modus_ponens,[status(thm)],[1101, 1100])).
% 45.53/29.70 tff(1103,plain,
% 45.53/29.70 (forallprefers(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))), false) <=> ((~((~(false = not1(false))) | (~(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))))))) | (~((~d(false)) | d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))))))),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[1102, 159])).
% 45.53/29.70 tff(1104,plain,
% 45.53/29.70 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(phi(apply(P!7, tptp_fun_X_3(P!7)))) = lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))))),
% 45.53/29.70 inference(quant_inst,[status(thm)],[])).
% 45.53/29.70 tff(1105,plain,
% 45.53/29.70 (f7(phi(apply(P!7, tptp_fun_X_3(P!7)))) = lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[1104, 195])).
% 45.53/29.70 tff(1106,plain,
% 45.53/29.70 (lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = f7(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.53/29.70 inference(symmetry,[status(thm)],[1105])).
% 45.53/29.70 tff(1107,plain,
% 45.53/29.70 (forallprefers(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))), false) <=> forallprefers(f7(phi(apply(P!7, tptp_fun_X_3(P!7)))), f7(P!6))),
% 45.53/29.70 inference(monotonicity,[status(thm)],[1106, 289])).
% 45.53/29.70 tff(1108,plain,
% 45.53/29.70 (forallprefers(f7(phi(apply(P!7, tptp_fun_X_3(P!7)))), f7(P!6)) <=> forallprefers(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))), false)),
% 45.53/29.70 inference(symmetry,[status(thm)],[1107])).
% 45.53/29.70 tff(1109,plain,
% 45.53/29.70 ((~forallprefers(f7(phi(apply(P!7, tptp_fun_X_3(P!7)))), f7(P!6))) <=> (~forallprefers(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))), false))),
% 45.53/29.70 inference(monotonicity,[status(thm)],[1108])).
% 45.53/29.70 tff(1110,plain,
% 45.53/29.70 ((~![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))) | (~forallprefers(f7(phi(apply(P!7, tptp_fun_X_3(P!7)))), f7(P!6)))),
% 45.53/29.70 inference(quant_inst,[status(thm)],[])).
% 45.53/29.70 tff(1111,plain,
% 45.53/29.70 (~forallprefers(f7(phi(apply(P!7, tptp_fun_X_3(P!7)))), f7(P!6))),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[1110, 218])).
% 45.53/29.70 tff(1112,plain,
% 45.53/29.70 (~forallprefers(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))), false)),
% 45.53/29.70 inference(modus_ponens,[status(thm)],[1111, 1109])).
% 45.53/29.70 tff(1113,plain,
% 45.53/29.70 ((~(forallprefers(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))), false) <=> ((~((~(false = not1(false))) | (~(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))))))) | (~((~d(false)) | d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))))))))) | forallprefers(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))), false) | (~((~((~(false = not1(false))) | (~(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))))))) | (~((~d(false)) | d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))))))))),
% 45.53/29.70 inference(tautology,[status(thm)],[])).
% 45.53/29.70 tff(1114,plain,
% 45.53/29.70 (~((~((~(false = not1(false))) | (~(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))))))) | (~((~d(false)) | d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))))))),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[1113, 1112, 1103])).
% 45.53/29.70 tff(1115,plain,
% 45.53/29.70 (((~((~(false = not1(false))) | (~(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))))))) | (~((~d(false)) | d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))))))) | ((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))))))),
% 45.53/29.70 inference(tautology,[status(thm)],[])).
% 45.53/29.70 tff(1116,plain,
% 45.53/29.70 ((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))))),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[1115, 1114])).
% 45.53/29.70 tff(1117,plain,
% 45.53/29.70 (((~((~(false = not1(false))) | (~(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))))))) | (~((~d(false)) | d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))))))) | ((~d(false)) | d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))))),
% 45.53/29.70 inference(tautology,[status(thm)],[])).
% 45.53/29.70 tff(1118,plain,
% 45.53/29.70 ((~d(false)) | d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))))),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[1117, 1114])).
% 45.53/29.70 tff(1119,plain,
% 45.53/29.70 ((~((~d(false)) | d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))))) | (~d(false)) | d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))))),
% 45.53/29.70 inference(tautology,[status(thm)],[])).
% 45.53/29.70 tff(1120,plain,
% 45.53/29.70 ((~((~d(false)) | d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))))) | d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))))),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[1119, 5])).
% 45.53/29.70 tff(1121,plain,
% 45.53/29.70 (d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))))),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[1120, 1118])).
% 45.53/29.70 tff(1122,plain,
% 45.53/29.70 ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))))))) | (~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))))),
% 45.53/29.70 inference(tautology,[status(thm)],[])).
% 45.53/29.70 tff(1123,plain,
% 45.53/29.70 ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))))))) | bool(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~d(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))))),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[1122, 5, 76])).
% 45.53/29.70 tff(1124,plain,
% 45.53/29.70 (bool(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))))),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[1123, 1121, 1116])).
% 45.53/29.70 tff(1125,plain,
% 45.53/29.70 (bool(err)),
% 45.53/29.70 inference(modus_ponens,[status(thm)],[1124, 1096])).
% 45.53/29.70 tff(1126,plain,
% 45.53/29.70 ($false),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[571, 1125])).
% 45.53/29.70 tff(1127,plain,((~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err)) | (~(phi(phi(apply(P!7, tptp_fun_X_3(P!7)))) = phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))) = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 45.53/29.70 tff(1128,plain,
% 45.53/29.70 (~(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))) = not1(false))),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[1127, 1083, 956])).
% 45.53/29.70 tff(1129,plain,
% 45.53/29.70 ((~![X: $i] : ((prop(X) = not1(false)) <=> bool(X))) | ((prop(phi(apply(P!7, tptp_fun_X_3(P!7)))) = not1(false)) <=> bool(phi(apply(P!7, tptp_fun_X_3(P!7)))))),
% 45.53/29.70 inference(quant_inst,[status(thm)],[])).
% 45.53/29.70 tff(1130,plain,
% 45.53/29.70 ((prop(phi(apply(P!7, tptp_fun_X_3(P!7)))) = not1(false)) <=> bool(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[1129, 126])).
% 45.53/29.70 tff(1131,plain,
% 45.53/29.70 ((~((prop(phi(apply(P!7, tptp_fun_X_3(P!7)))) = not1(false)) <=> bool(phi(apply(P!7, tptp_fun_X_3(P!7)))))) | (prop(phi(apply(P!7, tptp_fun_X_3(P!7)))) = not1(false)) | (~bool(phi(apply(P!7, tptp_fun_X_3(P!7)))))),
% 45.53/29.70 inference(tautology,[status(thm)],[])).
% 45.53/29.70 tff(1132,plain,
% 45.53/29.70 ((prop(phi(apply(P!7, tptp_fun_X_3(P!7)))) = not1(false)) | (~bool(phi(apply(P!7, tptp_fun_X_3(P!7)))))),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[1131, 1130])).
% 45.53/29.70 tff(1133,plain,
% 45.53/29.70 (~bool(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[1132, 1128])).
% 45.53/29.70 tff(1134,plain,
% 45.53/29.70 (~bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false))),
% 45.53/29.70 inference(modus_ponens,[status(thm)],[1133, 946])).
% 45.53/29.70 tff(1135,assumption,(~((~d(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false))))), introduced(assumption)).
% 45.53/29.70 tff(1136,plain,
% 45.53/29.70 (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false)),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[1023, 1135])).
% 45.53/29.70 tff(1137,plain,
% 45.53/29.70 (f4(P!7, tptp_fun_X_4(false, P!7), false) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 45.53/29.70 inference(symmetry,[status(thm)],[1136])).
% 45.53/29.70 tff(1138,plain,
% 45.53/29.70 (impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)) = f5(P!7, false)),
% 45.53/29.70 inference(transitivity,[status(thm)],[1026, 805, 1137, 932])).
% 45.53/29.70 tff(1139,plain,
% 45.53/29.70 (impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false) = impl(f5(P!7, false), false)),
% 45.53/29.70 inference(monotonicity,[status(thm)],[1138])).
% 45.53/29.70 tff(1140,plain,
% 45.53/29.70 (impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false) = not1(false)),
% 45.53/29.70 inference(transitivity,[status(thm)],[1030, 1139, 909, 929, 911, 903, 900, 899])).
% 45.53/29.70 tff(1141,plain,
% 45.53/29.70 ((impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false) = phi(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) <=> (not1(false) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 45.53/29.70 inference(monotonicity,[status(thm)],[1140, 960])).
% 45.53/29.70 tff(1142,plain,
% 45.53/29.70 ((impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false) = phi(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) <=> (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false))),
% 45.53/29.70 inference(transitivity,[status(thm)],[1141, 959])).
% 45.53/29.70 tff(1143,plain,
% 45.53/29.70 ((phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false)) <=> (impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false) = phi(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)))),
% 45.53/29.70 inference(symmetry,[status(thm)],[1142])).
% 45.53/29.70 tff(1144,plain,
% 45.53/29.70 ((~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false))) <=> (~(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false) = phi(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))),
% 45.53/29.70 inference(monotonicity,[status(thm)],[1143])).
% 45.53/29.70 tff(1145,plain,
% 45.53/29.70 (impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 45.53/29.70 inference(transitivity,[status(thm)],[805, 1137])).
% 45.53/29.70 tff(1146,plain,
% 45.53/29.70 ((impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false)) <=> (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false))),
% 45.53/29.70 inference(monotonicity,[status(thm)],[1145])).
% 45.53/29.70 tff(1147,plain,
% 45.53/29.70 ((~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))) <=> (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false)))),
% 45.53/29.70 inference(monotonicity,[status(thm)],[1146])).
% 45.53/29.70 tff(1148,plain,
% 45.53/29.70 (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false))),
% 45.53/29.70 inference(modus_ponens,[status(thm)],[933, 1147])).
% 45.53/29.70 tff(1149,plain,
% 45.53/29.70 (~(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false) = phi(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)))),
% 45.53/29.70 inference(modus_ponens,[status(thm)],[1148, 1144])).
% 45.53/29.70 tff(1150,assumption,(d(impl(apply(P!7, tptp_fun_X_3(P!7)), false))), introduced(assumption)).
% 45.53/29.70 tff(1151,assumption,(~bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false))), introduced(assumption)).
% 45.53/29.70 tff(1152,plain,
% 45.53/29.70 (d(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[1048, 1135])).
% 45.53/29.70 tff(1153,plain,
% 45.53/29.70 (d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))),
% 45.53/29.70 inference(modus_ponens,[status(thm)],[1152, 1047])).
% 45.53/29.70 tff(1154,plain,
% 45.53/29.70 (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[1072, 1153, 1151, 1150])).
% 45.53/29.70 tff(1155,plain,
% 45.53/29.70 ($false),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[1077, 1154, 1149])).
% 45.53/29.70 tff(1156,plain,(((~d(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false)))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false))) | (~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false))) | (impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))), inference(lemma,lemma(discharge,[]))).
% 45.53/29.70 tff(1157,plain,
% 45.53/29.70 ((~d(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[1156, 1134, 943, 899, 933])).
% 45.53/29.70 tff(1158,plain,
% 45.53/29.70 (~(d(f4(P!7, tptp_fun_X_4(false, P!7), false)) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err)))),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[1021, 1157])).
% 45.53/29.70 tff(1159,plain,
% 45.53/29.70 (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[1016, 1158])).
% 45.53/29.70 tff(1160,plain,
% 45.53/29.70 (err = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 45.53/29.70 inference(symmetry,[status(thm)],[1159])).
% 45.53/29.70 tff(1161,plain,
% 45.53/29.70 (impl(apply(P!7, tptp_fun_X_3(P!7)), false) = f5(P!7, false)),
% 45.53/29.70 inference(transitivity,[status(thm)],[938, 1083, 1160, 932])).
% 45.53/29.70 tff(1162,plain,
% 45.53/29.70 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), false), impl(impl(false, false), false)) = impl(f5(P!7, false), false)),
% 45.53/29.70 inference(monotonicity,[status(thm)],[1161, 931])).
% 45.53/29.70 tff(1163,plain,
% 45.53/29.70 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), false), false) = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), false), impl(impl(false, false), false))),
% 45.53/29.70 inference(monotonicity,[status(thm)],[974])).
% 45.53/29.70 tff(1164,plain,
% 45.53/29.70 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), false), false) = phi(impl(apply(P!7, tptp_fun_X_3(P!7)), false))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), false), false) = phi(impl(apply(P!7, tptp_fun_X_3(P!7)), false))))),
% 45.53/29.70 inference(rewrite,[status(thm)],[])).
% 45.53/29.70 tff(1165,plain,
% 45.53/29.70 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), false), false) = phi(impl(apply(P!7, tptp_fun_X_3(P!7)), false))))),
% 45.53/29.70 inference(quant_inst,[status(thm)],[])).
% 45.53/29.70 tff(1166,plain,
% 45.53/29.70 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), false), false) = phi(impl(apply(P!7, tptp_fun_X_3(P!7)), false)))),
% 45.53/29.70 inference(modus_ponens,[status(thm)],[1165, 1164])).
% 45.53/29.70 tff(1167,plain,
% 45.53/29.70 (bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), false), false) = phi(impl(apply(P!7, tptp_fun_X_3(P!7)), false)))),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[1166, 358])).
% 45.53/29.70 tff(1168,plain,
% 45.53/29.70 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), false), false) = phi(impl(apply(P!7, tptp_fun_X_3(P!7)), false))),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[1167, 1134])).
% 45.53/29.70 tff(1169,plain,
% 45.53/29.70 (phi(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), false), false)),
% 45.53/29.70 inference(symmetry,[status(thm)],[1168])).
% 45.53/29.70 tff(1170,plain,
% 45.53/29.70 (phi(apply(P!7, tptp_fun_X_3(P!7))) = impl(apply(P!7, tptp_fun_X_3(P!7)), false)),
% 45.53/29.70 inference(symmetry,[status(thm)],[938])).
% 45.53/29.70 tff(1171,plain,
% 45.53/29.70 (phi(phi(apply(P!7, tptp_fun_X_3(P!7)))) = phi(impl(apply(P!7, tptp_fun_X_3(P!7)), false))),
% 45.53/29.70 inference(monotonicity,[status(thm)],[1170])).
% 45.53/29.70 tff(1172,plain,
% 45.53/29.70 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = phi(apply(P!7, tptp_fun_X_3(P!7)))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = phi(apply(P!7, tptp_fun_X_3(P!7)))))),
% 45.53/29.70 inference(rewrite,[status(thm)],[])).
% 45.53/29.70 tff(1173,plain,
% 45.53/29.70 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = phi(apply(P!7, tptp_fun_X_3(P!7)))))),
% 45.53/29.70 inference(quant_inst,[status(thm)],[])).
% 45.53/29.70 tff(1174,plain,
% 45.53/29.70 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.53/29.70 inference(modus_ponens,[status(thm)],[1173, 1172])).
% 45.53/29.70 tff(1175,plain,
% 45.53/29.70 (bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[1174, 358])).
% 45.53/29.70 tff(1176,plain,
% 45.53/29.70 (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[1175, 348])).
% 45.53/29.70 tff(1177,plain,
% 45.53/29.70 (phi(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = phi(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.53/29.70 inference(monotonicity,[status(thm)],[1176])).
% 45.53/29.70 tff(1178,plain,
% 45.53/29.70 (d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) <=> d(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.53/29.70 inference(monotonicity,[status(thm)],[1176])).
% 45.53/29.70 tff(1179,plain,
% 45.53/29.70 (d(phi(apply(P!7, tptp_fun_X_3(P!7)))) <=> d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 45.53/29.70 inference(symmetry,[status(thm)],[1178])).
% 45.53/29.70 tff(1180,plain,
% 45.53/29.70 (d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) <=> d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 45.53/29.70 inference(transitivity,[status(thm)],[941, 1179])).
% 45.53/29.70 tff(1181,plain,
% 45.53/29.70 (d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 45.53/29.70 inference(modus_ponens,[status(thm)],[399, 1180])).
% 45.53/29.70 tff(1182,plain,
% 45.53/29.70 ((d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~(phi(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))),
% 45.53/29.70 inference(tautology,[status(thm)],[])).
% 45.53/29.70 tff(1183,plain,
% 45.53/29.70 (d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~(phi(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err))),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[1182, 1181])).
% 45.53/29.70 tff(1184,plain,
% 45.53/29.70 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (~(phi(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~(phi(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (~(phi(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~(phi(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err)))))),
% 45.53/29.70 inference(rewrite,[status(thm)],[])).
% 45.53/29.70 tff(1185,plain,
% 45.53/29.70 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (~(phi(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~(phi(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err)))))),
% 45.53/29.70 inference(quant_inst,[status(thm)],[])).
% 45.53/29.70 tff(1186,plain,
% 45.53/29.70 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (~(phi(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~(phi(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err))))),
% 45.53/29.70 inference(modus_ponens,[status(thm)],[1185, 1184])).
% 45.53/29.70 tff(1187,plain,
% 45.53/29.70 ((~((~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (~(phi(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~(phi(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err))))),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[1186, 17])).
% 45.53/29.70 tff(1188,plain,
% 45.53/29.70 (~((~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (~(phi(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[1187, 1183])).
% 45.53/29.70 tff(1189,plain,
% 45.53/29.70 (((~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (~(phi(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))) | (phi(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 45.53/29.70 inference(tautology,[status(thm)],[])).
% 45.53/29.70 tff(1190,plain,
% 45.53/29.70 (phi(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[1189, 1188])).
% 45.53/29.70 tff(1191,plain,
% 45.53/29.70 (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = phi(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 45.53/29.70 inference(symmetry,[status(thm)],[1190])).
% 45.53/29.70 tff(1192,plain,
% 45.53/29.70 (phi(apply(P!7, tptp_fun_X_3(P!7))) = impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))),
% 45.53/29.70 inference(symmetry,[status(thm)],[1176])).
% 45.53/29.70 tff(1193,plain,
% 45.53/29.70 (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)),
% 45.53/29.70 inference(transitivity,[status(thm)],[1192, 1191, 1177, 1171, 1169, 1163, 1162, 909, 929, 911, 903, 900, 899])).
% 45.53/29.70 tff(1194,assumption,(~(phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))), introduced(assumption)).
% 45.53/29.70 tff(1195,plain,
% 45.53/29.70 ($false),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[1194, 1193])).
% 45.53/29.70 tff(1196,plain,(bool(apply(P!7, tptp_fun_X_3(P!7))) | (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)) | (~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false))) | (impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false)) | (~(impl(f5(P!7, not1(false)), not1(false)) = not1(false))) | (~(impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false))))) | (phi(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))) = err)), inference(lemma,lemma(discharge,[]))).
% 45.53/29.70 tff(1197,plain,
% 45.53/29.70 (bool(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[1196, 898, 877, 837, 791, 676, 795])).
% 45.53/29.70 tff(1198,plain,
% 45.53/29.70 ((~(bool(apply(P!7, tptp_fun_X_3(P!7))) <=> ((apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = not1(false))))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | ((apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = not1(false)))),
% 45.53/29.70 inference(tautology,[status(thm)],[])).
% 45.53/29.70 tff(1199,plain,
% 45.53/29.70 ((~(bool(apply(P!7, tptp_fun_X_3(P!7))) <=> ((apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = not1(false))))) | ((apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = not1(false)))),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[1198, 1197])).
% 45.53/29.70 tff(1200,plain,
% 45.53/29.70 ((apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = not1(false))),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[1199, 794])).
% 45.53/29.70 tff(1201,plain,
% 45.53/29.70 (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = impl(f5(P!7, not1(false)), not1(false))),
% 45.53/29.70 inference(transitivity,[status(thm)],[784, 783, 522, 645, 647, 677])).
% 45.53/29.70 tff(1202,plain,
% 45.53/29.70 (bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) <=> bool(impl(f5(P!7, not1(false)), not1(false)))),
% 45.53/29.70 inference(monotonicity,[status(thm)],[1201])).
% 45.53/29.70 tff(1203,plain,
% 45.53/29.70 (bool(impl(f5(P!7, not1(false)), not1(false))) <=> bool(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.53/29.70 inference(symmetry,[status(thm)],[1202])).
% 45.53/29.70 tff(1204,plain,
% 45.53/29.70 (bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) <=> bool(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.53/29.70 inference(transitivity,[status(thm)],[717, 715, 1203])).
% 45.53/29.70 tff(1205,plain,
% 45.53/29.70 (bool(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.53/29.70 inference(modus_ponens,[status(thm)],[774, 1204])).
% 45.53/29.70 tff(1206,plain,
% 45.53/29.70 ((~bool(apply(P!7, tptp_fun_X_4(not1(false), P!7)))) | ((apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false)))),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[482, 475])).
% 45.53/29.70 tff(1207,plain,
% 45.53/29.70 ((apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))),
% 45.53/29.70 inference(unit_resolution,[status(thm)],[1206, 1205])).
% 45.53/29.71 tff(1208,plain,
% 45.53/29.71 (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false)),
% 45.53/29.71 inference(unit_resolution,[status(thm)],[484, 1207, 432])).
% 45.53/29.71 tff(1209,plain,
% 45.53/29.71 (^[X: $i, Y: $i] : refl((existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = not1(false))) | (~(Y = false)))))) <=> (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = not1(false))) | (~(Y = false)))))))),
% 45.53/29.71 inference(bind,[status(th)],[])).
% 45.53/29.71 tff(1210,plain,
% 45.53/29.71 (![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = not1(false))) | (~(Y = false)))))) <=> ![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = not1(false))) | (~(Y = false))))))),
% 45.53/29.71 inference(quant_intro,[status(thm)],[1209])).
% 45.53/29.71 tff(1211,plain,
% 45.53/29.71 (^[X: $i, Y: $i] : rewrite((existsprefers(X, Y) <=> (((~d(X)) & d(Y)) | ((X = not1(false)) & (Y = false)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)))) <=> (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = not1(false))) | (~(Y = false)))))))),
% 45.53/29.71 inference(bind,[status(th)],[])).
% 45.53/29.71 tff(1212,plain,
% 45.53/29.71 (![X: $i, Y: $i] : (existsprefers(X, Y) <=> (((~d(X)) & d(Y)) | ((X = not1(false)) & (Y = false)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)))) <=> ![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = not1(false))) | (~(Y = false))))))),
% 45.53/29.71 inference(quant_intro,[status(thm)],[1211])).
% 45.53/29.71 tff(1213,plain,
% 45.53/29.71 (^[X: $i, Y: $i] : rewrite((existsprefers(X, Y) <=> (((~d(X)) & d(Y)) | ((X = true) & (Y = false)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)))) <=> (existsprefers(X, Y) <=> (((~d(X)) & d(Y)) | ((X = not1(false)) & (Y = false)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)))))),
% 45.53/29.71 inference(bind,[status(th)],[])).
% 45.53/29.71 tff(1214,plain,
% 45.53/29.71 (![X: $i, Y: $i] : (existsprefers(X, Y) <=> (((~d(X)) & d(Y)) | ((X = true) & (Y = false)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)))) <=> ![X: $i, Y: $i] : (existsprefers(X, Y) <=> (((~d(X)) & d(Y)) | ((X = not1(false)) & (Y = false)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 45.53/29.71 inference(quant_intro,[status(thm)],[1213])).
% 45.53/29.71 tff(1215,plain,
% 45.53/29.71 (![X: $i, Y: $i] : (existsprefers(X, Y) <=> (((~d(X)) & d(Y)) | ((X = true) & (Y = false)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)))) <=> ![X: $i, Y: $i] : (existsprefers(X, Y) <=> (((~d(X)) & d(Y)) | ((X = true) & (Y = false)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 45.53/29.71 inference(rewrite,[status(thm)],[])).
% 45.53/29.71 tff(1216,plain,
% 45.53/29.71 (^[X: $i, Y: $i] : rewrite((existsprefers(X, Y) <=> ((((~d(X)) & d(Y)) | (((d(X) & d(Y)) & (~bool(X))) & bool(Y))) | ((X = true) & (Y = false)))) <=> (existsprefers(X, Y) <=> (((~d(X)) & d(Y)) | ((X = true) & (Y = false)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)))))),
% 45.53/29.71 inference(bind,[status(th)],[])).
% 45.53/29.71 tff(1217,plain,
% 45.53/29.71 (![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((((~d(X)) & d(Y)) | (((d(X) & d(Y)) & (~bool(X))) & bool(Y))) | ((X = true) & (Y = false)))) <=> ![X: $i, Y: $i] : (existsprefers(X, Y) <=> (((~d(X)) & d(Y)) | ((X = true) & (Y = false)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 45.53/29.71 inference(quant_intro,[status(thm)],[1216])).
% 45.53/29.71 tff(1218,axiom,(![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((((~d(X)) & d(Y)) | (((d(X) & d(Y)) & (~bool(X))) & bool(Y))) | ((X = true) & (Y = false))))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','def_existsprefers')).
% 45.53/29.71 tff(1219,plain,
% 45.53/29.71 (![X: $i, Y: $i] : (existsprefers(X, Y) <=> (((~d(X)) & d(Y)) | ((X = true) & (Y = false)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 45.53/29.71 inference(modus_ponens,[status(thm)],[1218, 1217])).
% 45.53/29.71 tff(1220,plain,
% 45.53/29.71 (![X: $i, Y: $i] : (existsprefers(X, Y) <=> (((~d(X)) & d(Y)) | ((X = true) & (Y = false)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 45.53/29.71 inference(modus_ponens,[status(thm)],[1219, 1215])).
% 45.53/29.71 tff(1221,plain,
% 45.53/29.71 (![X: $i, Y: $i] : (existsprefers(X, Y) <=> (((~d(X)) & d(Y)) | ((X = not1(false)) & (Y = false)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 45.53/29.71 inference(modus_ponens,[status(thm)],[1220, 1214])).
% 45.53/29.71 tff(1222,plain,(
% 45.53/29.71 ![X: $i, Y: $i] : (existsprefers(X, Y) <=> (((~d(X)) & d(Y)) | ((X = not1(false)) & (Y = false)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 45.53/29.71 inference(skolemize,[status(sab)],[1221])).
% 45.53/29.71 tff(1223,plain,
% 45.53/29.71 (![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = not1(false))) | (~(Y = false))))))),
% 45.53/29.71 inference(modus_ponens,[status(thm)],[1222, 1212])).
% 45.53/29.71 tff(1224,plain,
% 45.53/29.71 (![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = not1(false))) | (~(Y = false))))))),
% 45.53/29.71 inference(modus_ponens,[status(thm)],[1223, 1210])).
% 45.53/29.71 tff(1225,plain,
% 45.53/29.71 (((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = not1(false))) | (~(Y = false))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(not1(false), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))))) | (~(d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_4(not1(false), P!7))))))))) <=> ((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = not1(false))) | (~(Y = false))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(not1(false), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))))) | (~(d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_4(not1(false), P!7)))))))))),
% 45.53/29.71 inference(rewrite,[status(thm)],[])).
% 45.53/29.71 tff(1226,plain,
% 45.53/29.71 ((existsprefers(apply(P!7, tptp_fun_X_4(not1(false), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_4(not1(false), P!7)))))) | (~((~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))) | (~(apply(P!7, tptp_fun_X_3(P!7)) = false)))))) <=> (existsprefers(apply(P!7, tptp_fun_X_4(not1(false), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))))) | (~(d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_4(not1(false), P!7))))))))),
% 45.53/29.71 inference(rewrite,[status(thm)],[])).
% 45.53/29.71 tff(1227,plain,
% 45.53/29.71 (((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = not1(false))) | (~(Y = false))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(not1(false), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_4(not1(false), P!7)))))) | (~((~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))) | (~(apply(P!7, tptp_fun_X_3(P!7)) = false))))))) <=> ((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = not1(false))) | (~(Y = false))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(not1(false), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))))) | (~(d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_4(not1(false), P!7)))))))))),
% 45.53/29.71 inference(monotonicity,[status(thm)],[1226])).
% 45.53/29.71 tff(1228,plain,
% 45.53/29.71 (((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = not1(false))) | (~(Y = false))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(not1(false), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_4(not1(false), P!7)))))) | (~((~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))) | (~(apply(P!7, tptp_fun_X_3(P!7)) = false))))))) <=> ((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = not1(false))) | (~(Y = false))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(not1(false), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))))) | (~(d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_4(not1(false), P!7)))))))))),
% 45.53/29.71 inference(transitivity,[status(thm)],[1227, 1225])).
% 45.53/29.71 tff(1229,plain,
% 45.53/29.71 ((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = not1(false))) | (~(Y = false))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(not1(false), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_4(not1(false), P!7)))))) | (~((~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))) | (~(apply(P!7, tptp_fun_X_3(P!7)) = false))))))),
% 45.53/29.71 inference(quant_inst,[status(thm)],[])).
% 45.53/29.71 tff(1230,plain,
% 45.53/29.71 ((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = not1(false))) | (~(Y = false))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(not1(false), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))))) | (~(d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_4(not1(false), P!7))))))))),
% 45.53/29.71 inference(modus_ponens,[status(thm)],[1229, 1228])).
% 45.53/29.71 tff(1231,plain,
% 45.53/29.71 (existsprefers(apply(P!7, tptp_fun_X_4(not1(false), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))))) | (~(d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_4(not1(false), P!7)))))))),
% 45.53/29.71 inference(unit_resolution,[status(thm)],[1230, 1224])).
% 45.53/29.71 tff(1232,plain,
% 45.53/29.71 (((~(exists1(P!7) = phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~![X1: $i] : (~existsprefers(apply(P!7, X1), apply(P!7, tptp_fun_X_3(P!7)))))) | ![X1: $i] : (~existsprefers(apply(P!7, X1), apply(P!7, tptp_fun_X_3(P!7))))),
% 45.62/29.71 inference(tautology,[status(thm)],[])).
% 45.62/29.71 tff(1233,plain,
% 45.62/29.71 (![X1: $i] : (~existsprefers(apply(P!7, X1), apply(P!7, tptp_fun_X_3(P!7))))),
% 45.62/29.71 inference(unit_resolution,[status(thm)],[1232, 344])).
% 45.62/29.71 tff(1234,plain,
% 45.62/29.71 ((~![X1: $i] : (~existsprefers(apply(P!7, X1), apply(P!7, tptp_fun_X_3(P!7))))) | (~existsprefers(apply(P!7, tptp_fun_X_4(not1(false), P!7)), apply(P!7, tptp_fun_X_3(P!7))))),
% 45.62/29.71 inference(quant_inst,[status(thm)],[])).
% 45.62/29.71 tff(1235,plain,
% 45.62/29.71 (~existsprefers(apply(P!7, tptp_fun_X_4(not1(false), P!7)), apply(P!7, tptp_fun_X_3(P!7)))),
% 45.62/29.71 inference(unit_resolution,[status(thm)],[1234, 1233])).
% 45.62/29.71 tff(1236,plain,
% 45.62/29.71 ((~(existsprefers(apply(P!7, tptp_fun_X_4(not1(false), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))))) | (~(d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_4(not1(false), P!7))))))))) | existsprefers(apply(P!7, tptp_fun_X_4(not1(false), P!7)), apply(P!7, tptp_fun_X_3(P!7))) | (~((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))))) | (~(d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_4(not1(false), P!7))))))))),
% 45.62/29.71 inference(tautology,[status(thm)],[])).
% 45.62/29.71 tff(1237,plain,
% 45.62/29.71 ((~(existsprefers(apply(P!7, tptp_fun_X_4(not1(false), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))))) | (~(d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_4(not1(false), P!7))))))))) | (~((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))))) | (~(d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_4(not1(false), P!7))))))))),
% 45.62/29.71 inference(unit_resolution,[status(thm)],[1236, 1235])).
% 45.62/29.71 tff(1238,plain,
% 45.62/29.71 (~((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))))) | (~(d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_4(not1(false), P!7)))))))),
% 45.62/29.71 inference(unit_resolution,[status(thm)],[1237, 1231])).
% 45.62/29.71 tff(1239,plain,
% 45.62/29.71 (((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))))) | (~(d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_4(not1(false), P!7))))))) | ((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))))),
% 45.62/29.71 inference(tautology,[status(thm)],[])).
% 45.62/29.71 tff(1240,plain,
% 45.62/29.71 ((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false)))),
% 45.62/29.71 inference(unit_resolution,[status(thm)],[1239, 1238])).
% 45.62/29.71 tff(1241,plain,
% 45.62/29.71 ((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))))) | (~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false)))),
% 45.62/29.71 inference(tautology,[status(thm)],[])).
% 45.62/29.71 tff(1242,plain,
% 45.62/29.71 ((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false)))),
% 45.62/29.71 inference(unit_resolution,[status(thm)],[1241, 1240])).
% 45.62/29.71 tff(1243,plain,
% 45.62/29.71 (~(apply(P!7, tptp_fun_X_3(P!7)) = false)),
% 45.62/29.71 inference(unit_resolution,[status(thm)],[1242, 1208])).
% 45.62/29.71 tff(1244,plain,
% 45.62/29.71 ((~((apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = not1(false)))) | (apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = not1(false))),
% 45.62/29.71 inference(tautology,[status(thm)],[])).
% 45.62/29.71 tff(1245,plain,
% 45.62/29.71 ((~((apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = not1(false)))) | (apply(P!7, tptp_fun_X_3(P!7)) = not1(false))),
% 45.62/29.71 inference(unit_resolution,[status(thm)],[1244, 1243])).
% 45.62/29.71 tff(1246,plain,
% 45.62/29.71 (apply(P!7, tptp_fun_X_3(P!7)) = not1(false)),
% 45.62/29.71 inference(unit_resolution,[status(thm)],[1245, 1200])).
% 45.62/29.71 tff(1247,plain,
% 45.62/29.71 (apply(P!7, tptp_fun_X_3(P!7)) = impl(f5(P!7, not1(false)), not1(false))),
% 45.62/29.71 inference(transitivity,[status(thm)],[1246, 792])).
% 45.62/29.71 tff(1248,plain,
% 45.62/29.71 (phi(apply(P!7, tptp_fun_X_3(P!7))) = phi(impl(f5(P!7, not1(false)), not1(false)))),
% 45.62/29.71 inference(monotonicity,[status(thm)],[1247])).
% 45.62/29.71 tff(1249,plain,
% 45.62/29.71 (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)),
% 45.62/29.71 inference(transitivity,[status(thm)],[1248, 680, 647, 677, 791])).
% 45.62/29.71 tff(1250,plain,
% 45.62/29.71 ($false),
% 45.62/29.71 inference(unit_resolution,[status(thm)],[898, 1249])).
% 45.62/29.71 tff(1251,plain,((~(prop(tptp_fun_R_5(P!7)) = false)) | (phi(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))) = err) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false) | (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = apply(P!7, tptp_fun_X_4(not1(false), P!7)))) | (~d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))))), inference(lemma,lemma(discharge,[]))).
% 45.62/29.71 tff(1252,plain,
% 45.62/29.71 (~(prop(tptp_fun_R_5(P!7)) = false)),
% 45.62/29.71 inference(unit_resolution,[status(thm)],[1251, 708, 432, 702, 695])).
% 45.62/29.71 tff(1253,plain,
% 45.62/29.71 ((~![X: $i] : ((prop(X) = false) <=> (~bool(X)))) | ((prop(tptp_fun_R_5(P!7)) = false) <=> (~bool(tptp_fun_R_5(P!7))))),
% 45.62/29.71 inference(quant_inst,[status(thm)],[])).
% 45.62/29.71 tff(1254,plain,
% 45.62/29.71 ((prop(tptp_fun_R_5(P!7)) = false) <=> (~bool(tptp_fun_R_5(P!7)))),
% 45.62/29.71 inference(unit_resolution,[status(thm)],[1253, 234])).
% 45.62/29.71 tff(1255,plain,
% 45.62/29.71 ((~((prop(tptp_fun_R_5(P!7)) = false) <=> (~bool(tptp_fun_R_5(P!7))))) | (prop(tptp_fun_R_5(P!7)) = false) | bool(tptp_fun_R_5(P!7))),
% 45.62/29.71 inference(tautology,[status(thm)],[])).
% 45.62/29.71 tff(1256,plain,
% 45.62/29.71 ((prop(tptp_fun_R_5(P!7)) = false) | bool(tptp_fun_R_5(P!7))),
% 45.62/29.71 inference(unit_resolution,[status(thm)],[1255, 1254])).
% 45.62/29.71 tff(1257,plain,
% 45.62/29.71 (bool(tptp_fun_R_5(P!7))),
% 45.62/29.71 inference(unit_resolution,[status(thm)],[1256, 1252])).
% 45.62/29.71 tff(1258,plain,
% 45.62/29.71 (((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | ((~bool(tptp_fun_R_5(P!7))) | (impl(not1(false), tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)))) <=> ((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | (~bool(tptp_fun_R_5(P!7))) | (impl(not1(false), tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)))),
% 45.62/29.71 inference(rewrite,[status(thm)],[])).
% 45.62/29.71 tff(1259,plain,
% 45.62/29.71 ((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | ((~bool(tptp_fun_R_5(P!7))) | (impl(not1(false), tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)))),
% 45.62/29.71 inference(quant_inst,[status(thm)],[])).
% 45.62/29.71 tff(1260,plain,
% 45.62/29.71 ((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | (~bool(tptp_fun_R_5(P!7))) | (impl(not1(false), tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))),
% 45.62/29.71 inference(modus_ponens,[status(thm)],[1259, 1258])).
% 45.62/29.71 tff(1261,plain,
% 45.62/29.71 ((~bool(tptp_fun_R_5(P!7))) | (impl(not1(false), tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))),
% 45.62/29.71 inference(unit_resolution,[status(thm)],[1260, 110])).
% 45.62/29.71 tff(1262,plain,
% 45.62/29.71 (impl(not1(false), tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)),
% 45.62/29.71 inference(unit_resolution,[status(thm)],[1261, 1257])).
% 45.62/29.71 tff(1263,plain,
% 45.62/29.71 (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = phi(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.62/29.71 inference(symmetry,[status(thm)],[702])).
% 45.62/29.71 tff(1264,plain,
% 45.62/29.71 (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = impl(f5(P!7, not1(false)), not1(false))),
% 45.62/29.71 inference(transitivity,[status(thm)],[1263, 783, 522, 645, 647, 677])).
% 45.62/29.71 tff(1265,plain,
% 45.62/29.71 (bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) <=> bool(impl(f5(P!7, not1(false)), not1(false)))),
% 45.62/29.71 inference(monotonicity,[status(thm)],[1264])).
% 45.62/29.71 tff(1266,plain,
% 45.62/29.71 (d(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.62/29.71 inference(unit_resolution,[status(thm)],[628, 701])).
% 45.62/29.71 tff(1267,plain,
% 45.62/29.71 (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))),
% 45.62/29.71 inference(transitivity,[status(thm)],[1263, 783])).
% 45.62/29.71 tff(1268,plain,
% 45.62/29.71 ((apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false) <=> (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = false)),
% 45.62/29.71 inference(monotonicity,[status(thm)],[1267])).
% 45.62/29.71 tff(1269,plain,
% 45.62/29.71 ((~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false)) <=> (~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = false))),
% 45.62/29.71 inference(monotonicity,[status(thm)],[1268])).
% 45.62/29.71 tff(1270,plain,
% 45.62/29.71 (~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = false)),
% 45.62/29.71 inference(modus_ponens,[status(thm)],[432, 1269])).
% 45.62/29.71 tff(1271,assumption,(~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = false)), introduced(assumption)).
% 45.62/29.71 tff(1272,assumption,(bool(tptp_fun_R_5(P!7))), introduced(assumption)).
% 45.62/29.71 tff(1273,plain,
% 45.62/29.71 ((~![X: $i] : ((prop(X) = not1(false)) <=> bool(X))) | ((prop(tptp_fun_R_5(P!7)) = not1(false)) <=> bool(tptp_fun_R_5(P!7)))),
% 45.62/29.71 inference(quant_inst,[status(thm)],[])).
% 45.62/29.71 tff(1274,plain,
% 45.62/29.71 ((prop(tptp_fun_R_5(P!7)) = not1(false)) <=> bool(tptp_fun_R_5(P!7))),
% 45.62/29.71 inference(unit_resolution,[status(thm)],[1273, 126])).
% 45.62/29.71 tff(1275,plain,
% 45.62/29.71 ((~((prop(tptp_fun_R_5(P!7)) = not1(false)) <=> bool(tptp_fun_R_5(P!7)))) | (prop(tptp_fun_R_5(P!7)) = not1(false)) | (~bool(tptp_fun_R_5(P!7)))),
% 45.62/29.71 inference(tautology,[status(thm)],[])).
% 45.62/29.71 tff(1276,plain,
% 45.62/29.71 ((prop(tptp_fun_R_5(P!7)) = not1(false)) | (~bool(tptp_fun_R_5(P!7)))),
% 45.62/29.71 inference(unit_resolution,[status(thm)],[1275, 1274])).
% 45.62/29.71 tff(1277,plain,
% 45.62/29.71 (prop(tptp_fun_R_5(P!7)) = not1(false)),
% 45.62/29.71 inference(unit_resolution,[status(thm)],[1276, 1272])).
% 45.62/29.71 tff(1278,plain,
% 45.62/29.71 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(tptp_fun_R_5(P!7)) <=> ((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = not1(false))))),
% 45.62/29.71 inference(quant_inst,[status(thm)],[])).
% 45.62/29.71 tff(1279,plain,
% 45.62/29.71 (bool(tptp_fun_R_5(P!7)) <=> ((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = not1(false)))),
% 45.62/29.71 inference(unit_resolution,[status(thm)],[1278, 249])).
% 45.62/29.71 tff(1280,plain,
% 45.62/29.71 ((~(bool(tptp_fun_R_5(P!7)) <=> ((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = not1(false))))) | (~bool(tptp_fun_R_5(P!7))) | ((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = not1(false)))),
% 45.62/29.71 inference(tautology,[status(thm)],[])).
% 45.62/29.71 tff(1281,plain,
% 45.62/29.71 ((~bool(tptp_fun_R_5(P!7))) | ((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = not1(false)))),
% 45.62/29.71 inference(unit_resolution,[status(thm)],[1280, 1279])).
% 45.62/29.71 tff(1282,plain,
% 45.62/29.71 ((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = not1(false))),
% 45.62/29.71 inference(unit_resolution,[status(thm)],[1281, 1272])).
% 45.62/29.71 tff(1283,plain,
% 45.62/29.71 (((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | ((~bool(tptp_fun_R_5(P!7))) | (impl(false, tptp_fun_R_5(P!7)) = not1(false)))) <=> ((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | (~bool(tptp_fun_R_5(P!7))) | (impl(false, tptp_fun_R_5(P!7)) = not1(false)))),
% 45.62/29.71 inference(rewrite,[status(thm)],[])).
% 45.62/29.71 tff(1284,plain,
% 45.62/29.71 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | ((~bool(tptp_fun_R_5(P!7))) | (impl(false, tptp_fun_R_5(P!7)) = not1(false)))),
% 45.62/29.71 inference(quant_inst,[status(thm)],[])).
% 45.62/29.71 tff(1285,plain,
% 45.62/29.71 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | (~bool(tptp_fun_R_5(P!7))) | (impl(false, tptp_fun_R_5(P!7)) = not1(false))),
% 45.62/29.71 inference(modus_ponens,[status(thm)],[1284, 1283])).
% 45.62/29.71 tff(1286,plain,
% 45.62/29.71 ((~bool(tptp_fun_R_5(P!7))) | (impl(false, tptp_fun_R_5(P!7)) = not1(false))),
% 45.62/29.71 inference(unit_resolution,[status(thm)],[1285, 89])).
% 45.62/29.71 tff(1287,plain,
% 45.62/29.71 (impl(false, tptp_fun_R_5(P!7)) = not1(false)),
% 45.62/29.71 inference(unit_resolution,[status(thm)],[1286, 1272])).
% 45.62/29.71 tff(1288,plain,
% 45.62/29.71 (impl(not1(false), tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)),
% 45.62/29.71 inference(unit_resolution,[status(thm)],[1261, 1272])).
% 45.62/29.71 tff(1289,plain,
% 45.62/29.71 (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.71 inference(symmetry,[status(thm)],[471])).
% 45.62/29.71 tff(1290,assumption,(prop(tptp_fun_R_5(P!7)) = not1(false)), introduced(assumption)).
% 45.62/29.71 tff(1291,plain,
% 45.62/29.71 (not1(false) = prop(tptp_fun_R_5(P!7))),
% 45.62/29.71 inference(symmetry,[status(thm)],[1290])).
% 45.62/29.71 tff(1292,plain,
% 45.62/29.71 (lazy_impl(not1(false), tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 45.62/29.71 inference(monotonicity,[status(thm)],[1291])).
% 45.62/29.71 tff(1293,plain,
% 45.62/29.71 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7)))),
% 45.62/29.71 inference(quant_inst,[status(thm)],[])).
% 45.62/29.71 tff(1294,plain,
% 45.62/29.71 (lazy_impl(not1(false), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))),
% 45.62/29.71 inference(unit_resolution,[status(thm)],[1293, 33])).
% 45.62/29.71 tff(1295,plain,
% 45.62/29.71 (phi(tptp_fun_R_5(P!7)) = lazy_impl(not1(false), tptp_fun_R_5(P!7))),
% 45.62/29.71 inference(symmetry,[status(thm)],[1294])).
% 45.62/29.71 tff(1296,plain,
% 45.62/29.71 (phi(tptp_fun_R_5(P!7)) = phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.71 inference(transitivity,[status(thm)],[1295, 1292, 1289])).
% 45.62/29.71 tff(1297,plain,
% 45.62/29.71 ((phi(tptp_fun_R_5(P!7)) = err) <=> (phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)),
% 45.62/29.71 inference(monotonicity,[status(thm)],[1296])).
% 45.62/29.71 tff(1298,plain,
% 45.62/29.71 ((phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err) <=> (phi(tptp_fun_R_5(P!7)) = err)),
% 45.62/29.71 inference(symmetry,[status(thm)],[1297])).
% 45.62/29.71 tff(1299,plain,
% 45.62/29.71 ((phi(tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) <=> (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7)))),
% 45.62/29.71 inference(commutativity,[status(thm)],[])).
% 45.62/29.71 tff(1300,plain,
% 45.62/29.71 (phi(apply(P!7, tptp_fun_X_3(P!7))) = impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))),
% 45.62/29.71 inference(symmetry,[status(thm)],[363])).
% 45.62/29.71 tff(1301,plain,
% 45.62/29.71 (err = impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))),
% 45.62/29.71 inference(transitivity,[status(thm)],[1093, 1300])).
% 45.62/29.71 tff(1302,plain,
% 45.62/29.71 (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = lazy_impl(not1(false), tptp_fun_R_5(P!7))),
% 45.62/29.71 inference(symmetry,[status(thm)],[1292])).
% 45.62/29.71 tff(1303,plain,
% 45.62/29.71 (phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = phi(tptp_fun_R_5(P!7))),
% 45.62/29.71 inference(transitivity,[status(thm)],[471, 1302, 1294])).
% 45.62/29.71 tff(1304,plain,
% 45.62/29.71 ((phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err) <=> (phi(tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.71 inference(monotonicity,[status(thm)],[1303, 1301])).
% 45.62/29.72 tff(1305,plain,
% 45.62/29.72 ((phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err) <=> (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7)))),
% 45.62/29.72 inference(transitivity,[status(thm)],[1304, 1299])).
% 45.62/29.72 tff(1306,plain,
% 45.62/29.72 ((impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))) <=> (phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)),
% 45.62/29.72 inference(symmetry,[status(thm)],[1305])).
% 45.62/29.72 tff(1307,plain,
% 45.62/29.72 (impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false)))),
% 45.62/29.72 inference(unit_resolution,[status(thm)],[675, 523])).
% 45.62/29.72 tff(1308,plain,
% 45.62/29.72 (err = exists1(P!7)),
% 45.62/29.72 inference(transitivity,[status(thm)],[1093, 347])).
% 45.62/29.72 tff(1309,plain,
% 45.62/29.72 (phi(f6(P!7, tptp_fun_R_5(P!7))) = exists2(P!7)),
% 45.62/29.72 inference(symmetry,[status(thm)],[880])).
% 45.62/29.72 tff(1310,plain,
% 45.62/29.72 ((phi(f6(P!7, tptp_fun_R_5(P!7))) = err) <=> (exists2(P!7) = exists1(P!7))),
% 45.62/29.72 inference(monotonicity,[status(thm)],[1309, 1308])).
% 45.62/29.72 tff(1311,plain,
% 45.62/29.72 ((phi(f6(P!7, tptp_fun_R_5(P!7))) = err) <=> (exists1(P!7) = exists2(P!7))),
% 45.62/29.72 inference(transitivity,[status(thm)],[1310, 329])).
% 45.62/29.72 tff(1312,plain,
% 45.62/29.72 ((exists1(P!7) = exists2(P!7)) <=> (phi(f6(P!7, tptp_fun_R_5(P!7))) = err)),
% 45.62/29.72 inference(symmetry,[status(thm)],[1311])).
% 45.62/29.72 tff(1313,plain,
% 45.62/29.72 ((~(exists1(P!7) = exists2(P!7))) <=> (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = err))),
% 45.62/29.72 inference(monotonicity,[status(thm)],[1312])).
% 45.62/29.72 tff(1314,plain,
% 45.62/29.72 (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = err)),
% 45.62/29.72 inference(modus_ponens,[status(thm)],[897, 1313])).
% 45.62/29.72 tff(1315,plain,
% 45.62/29.72 ((d(f6(P!7, tptp_fun_R_5(P!7))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = err))) | (phi(f6(P!7, tptp_fun_R_5(P!7))) = err)),
% 45.62/29.72 inference(tautology,[status(thm)],[])).
% 45.62/29.72 tff(1316,plain,
% 45.62/29.72 (d(f6(P!7, tptp_fun_R_5(P!7))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = err))),
% 45.62/29.72 inference(unit_resolution,[status(thm)],[1315, 1314])).
% 45.62/29.72 tff(1317,plain,
% 45.62/29.72 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(f6(P!7, tptp_fun_R_5(P!7)))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = f6(P!7, tptp_fun_R_5(P!7)))))) | (~(d(f6(P!7, tptp_fun_R_5(P!7))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(f6(P!7, tptp_fun_R_5(P!7)))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = f6(P!7, tptp_fun_R_5(P!7)))))) | (~(d(f6(P!7, tptp_fun_R_5(P!7))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = err)))))),
% 45.62/29.72 inference(rewrite,[status(thm)],[])).
% 45.62/29.72 tff(1318,plain,
% 45.62/29.72 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(f6(P!7, tptp_fun_R_5(P!7)))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = f6(P!7, tptp_fun_R_5(P!7)))))) | (~(d(f6(P!7, tptp_fun_R_5(P!7))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = err)))))),
% 45.62/29.72 inference(quant_inst,[status(thm)],[])).
% 45.62/29.72 tff(1319,plain,
% 45.62/29.72 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(f6(P!7, tptp_fun_R_5(P!7)))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = f6(P!7, tptp_fun_R_5(P!7)))))) | (~(d(f6(P!7, tptp_fun_R_5(P!7))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = err))))),
% 45.62/29.72 inference(modus_ponens,[status(thm)],[1318, 1317])).
% 45.62/29.72 tff(1320,plain,
% 45.62/29.72 ((~((~d(f6(P!7, tptp_fun_R_5(P!7)))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = f6(P!7, tptp_fun_R_5(P!7)))))) | (~(d(f6(P!7, tptp_fun_R_5(P!7))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = err))))),
% 45.62/29.72 inference(unit_resolution,[status(thm)],[1319, 17])).
% 45.62/29.72 tff(1321,plain,
% 45.62/29.72 (~((~d(f6(P!7, tptp_fun_R_5(P!7)))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = f6(P!7, tptp_fun_R_5(P!7)))))),
% 45.62/29.72 inference(unit_resolution,[status(thm)],[1320, 1316])).
% 45.62/29.72 tff(1322,plain,
% 45.62/29.72 (((~d(f6(P!7, tptp_fun_R_5(P!7)))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = f6(P!7, tptp_fun_R_5(P!7))))) | d(f6(P!7, tptp_fun_R_5(P!7)))),
% 45.62/29.72 inference(tautology,[status(thm)],[])).
% 45.62/29.72 tff(1323,plain,
% 45.62/29.72 (d(f6(P!7, tptp_fun_R_5(P!7)))),
% 45.62/29.72 inference(unit_resolution,[status(thm)],[1322, 1321])).
% 45.62/29.72 tff(1324,plain,
% 45.62/29.72 (d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.62/29.72 inference(modus_ponens,[status(thm)],[1323, 328])).
% 45.62/29.72 tff(1325,plain,
% 45.62/29.72 (d(lazy_impl(prop(false), impl(f5(P!7, false), false)))),
% 45.62/29.72 inference(unit_resolution,[status(thm)],[859, 1324])).
% 45.62/29.72 tff(1326,assumption,(impl(false, tptp_fun_R_5(P!7)) = not1(false)), introduced(assumption)).
% 45.62/29.72 tff(1327,assumption,((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = not1(false))), introduced(assumption)).
% 45.62/29.72 tff(1328,assumption,(impl(not1(false), tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)), introduced(assumption)).
% 45.62/29.72 tff(1329,plain,
% 45.62/29.72 ((err = phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)),
% 45.62/29.72 inference(commutativity,[status(thm)],[])).
% 45.62/29.72 tff(1330,plain,
% 45.62/29.72 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.62/29.72 inference(quant_inst,[status(thm)],[])).
% 45.62/29.72 tff(1331,plain,
% 45.62/29.72 (lazy_impl(not1(false), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.72 inference(unit_resolution,[status(thm)],[1330, 33])).
% 45.62/29.72 tff(1332,plain,
% 45.62/29.72 (lazy_impl(not1(false), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.72 inference(monotonicity,[status(thm)],[1291])).
% 45.62/29.72 tff(1333,plain,
% 45.62/29.72 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(not1(false), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.72 inference(symmetry,[status(thm)],[1332])).
% 45.62/29.72 tff(1334,plain,
% 45.62/29.72 (((~d(f6(P!7, tptp_fun_R_5(P!7)))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = f6(P!7, tptp_fun_R_5(P!7))))) | (phi(f6(P!7, tptp_fun_R_5(P!7))) = f6(P!7, tptp_fun_R_5(P!7)))),
% 45.62/29.72 inference(tautology,[status(thm)],[])).
% 45.62/29.72 tff(1335,plain,
% 45.62/29.72 (phi(f6(P!7, tptp_fun_R_5(P!7))) = f6(P!7, tptp_fun_R_5(P!7))),
% 45.62/29.72 inference(unit_resolution,[status(thm)],[1334, 1321])).
% 45.62/29.72 tff(1336,plain,
% 45.62/29.72 (exists2(P!7) = phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.72 inference(transitivity,[status(thm)],[880, 1335, 325, 1333, 1331])).
% 45.62/29.72 tff(1337,plain,
% 45.62/29.72 (exists1(P!7) = err),
% 45.62/29.72 inference(transitivity,[status(thm)],[346, 1092])).
% 45.62/29.72 tff(1338,plain,
% 45.62/29.72 ((exists1(P!7) = exists2(P!7)) <=> (err = phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.62/29.72 inference(monotonicity,[status(thm)],[1337, 1336])).
% 45.62/29.72 tff(1339,plain,
% 45.62/29.72 ((exists1(P!7) = exists2(P!7)) <=> (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)),
% 45.62/29.72 inference(transitivity,[status(thm)],[1338, 1329])).
% 45.62/29.72 tff(1340,plain,
% 45.62/29.72 ((~(exists1(P!7) = exists2(P!7))) <=> (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err))),
% 45.62/29.72 inference(monotonicity,[status(thm)],[1339])).
% 45.62/29.72 tff(1341,plain,
% 45.62/29.72 (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)),
% 45.62/29.72 inference(modus_ponens,[status(thm)],[897, 1340])).
% 45.62/29.72 tff(1342,plain,
% 45.62/29.72 ((d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err))) | (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)),
% 45.62/29.72 inference(tautology,[status(thm)],[])).
% 45.62/29.72 tff(1343,plain,
% 45.62/29.72 (d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err))),
% 45.62/29.72 inference(unit_resolution,[status(thm)],[1342, 1341])).
% 45.62/29.72 tff(1344,plain,
% 45.62/29.72 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~(d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~(d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)))))),
% 45.62/29.72 inference(rewrite,[status(thm)],[])).
% 45.62/29.72 tff(1345,plain,
% 45.62/29.72 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~(d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)))))),
% 45.62/29.72 inference(quant_inst,[status(thm)],[])).
% 45.62/29.72 tff(1346,plain,
% 45.62/29.72 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~(d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err))))),
% 45.62/29.72 inference(modus_ponens,[status(thm)],[1345, 1344])).
% 45.62/29.72 tff(1347,plain,
% 45.62/29.72 ((~((~d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~(d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err))))),
% 45.62/29.72 inference(unit_resolution,[status(thm)],[1346, 17])).
% 45.62/29.72 tff(1348,plain,
% 45.62/29.72 (~((~d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 45.62/29.72 inference(unit_resolution,[status(thm)],[1347, 1343])).
% 45.62/29.72 tff(1349,plain,
% 45.62/29.72 (((~d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.72 inference(tautology,[status(thm)],[])).
% 45.62/29.72 tff(1350,plain,
% 45.62/29.72 (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 45.62/29.72 inference(unit_resolution,[status(thm)],[1349, 1348])).
% 45.62/29.72 tff(1351,plain,
% 45.62/29.72 ((~![X: $i] : ((prop(X) = false) <=> (~bool(X)))) | ((prop(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = false) <=> (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))),
% 45.62/29.72 inference(quant_inst,[status(thm)],[])).
% 45.62/29.72 tff(1352,plain,
% 45.62/29.72 ((prop(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = false) <=> (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 45.62/29.72 inference(unit_resolution,[status(thm)],[1351, 234])).
% 45.62/29.72 tff(1353,assumption,(~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))), introduced(assumption)).
% 45.62/29.72 tff(1354,plain,
% 45.62/29.72 ((~((prop(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = false) <=> (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (prop(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = false) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.62/29.72 inference(tautology,[status(thm)],[])).
% 45.62/29.72 tff(1355,plain,
% 45.62/29.72 ((~((prop(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = false) <=> (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (prop(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = false)),
% 45.62/29.72 inference(unit_resolution,[status(thm)],[1354, 1353])).
% 45.62/29.72 tff(1356,plain,
% 45.62/29.72 (prop(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = false),
% 45.62/29.72 inference(unit_resolution,[status(thm)],[1355, 1352])).
% 45.62/29.72 tff(1357,plain,
% 45.62/29.72 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))))),
% 45.62/29.72 inference(quant_inst,[status(thm)],[])).
% 45.62/29.72 tff(1358,plain,
% 45.62/29.72 (bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false)))),
% 45.62/29.72 inference(unit_resolution,[status(thm)],[1357, 249])).
% 45.62/29.72 tff(1359,plain,
% 45.62/29.72 ((~(bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~((lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))))),
% 45.62/29.72 inference(tautology,[status(thm)],[])).
% 45.62/29.72 tff(1360,plain,
% 45.62/29.72 ((~(bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))))) | (~((lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))))),
% 45.62/29.72 inference(unit_resolution,[status(thm)],[1359, 1353])).
% 45.62/29.72 tff(1361,plain,
% 45.62/29.72 (~((lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false)))),
% 45.62/29.72 inference(unit_resolution,[status(thm)],[1360, 1358])).
% 45.62/29.72 tff(1362,plain,
% 45.62/29.72 (((lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false)))),
% 45.62/29.72 inference(tautology,[status(thm)],[])).
% 45.62/29.72 tff(1363,plain,
% 45.62/29.72 (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))),
% 45.62/29.72 inference(unit_resolution,[status(thm)],[1362, 1361])).
% 45.62/29.72 tff(1364,assumption,(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false), introduced(assumption)).
% 45.62/29.72 tff(1365,plain,
% 45.62/29.72 (f5(P!7, tptp_fun_R_5(P!7)) = false),
% 45.62/29.72 inference(transitivity,[status(thm)],[311, 1364])).
% 45.62/29.72 tff(1366,plain,
% 45.62/29.72 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = impl(false, tptp_fun_R_5(P!7))),
% 45.62/29.72 inference(monotonicity,[status(thm)],[1365])).
% 45.62/29.72 tff(1367,plain,
% 45.62/29.72 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = not1(false)),
% 45.62/29.72 inference(transitivity,[status(thm)],[1366, 1326])).
% 45.62/29.72 tff(1368,plain,
% 45.62/29.72 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(not1(false), not1(false))),
% 45.62/29.72 inference(monotonicity,[status(thm)],[1290, 1367])).
% 45.62/29.72 tff(1369,plain,
% 45.62/29.72 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false)),
% 45.62/29.72 inference(transitivity,[status(thm)],[1368, 50, 48])).
% 45.62/29.72 tff(1370,assumption,(~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))), introduced(assumption)).
% 45.62/29.72 tff(1371,plain,
% 45.62/29.72 ($false),
% 45.62/29.72 inference(unit_resolution,[status(thm)],[1370, 1369])).
% 45.62/29.72 tff(1372,plain,((~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false)) | (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false)) | (~(impl(false, tptp_fun_R_5(P!7)) = not1(false))) | (~(prop(tptp_fun_R_5(P!7)) = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 45.62/29.72 tff(1373,plain,
% 45.62/29.72 (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false)),
% 45.62/29.72 inference(unit_resolution,[status(thm)],[1372, 1363, 1326, 1290])).
% 45.62/29.72 tff(1374,assumption,(~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))), introduced(assumption)).
% 45.62/29.72 tff(1375,assumption,(~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false)), introduced(assumption)).
% 45.62/29.72 tff(1376,assumption,((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false))), introduced(assumption)).
% 45.62/29.72 tff(1377,assumption,(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false), introduced(assumption)).
% 45.62/29.72 tff(1378,plain,
% 45.62/29.72 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = impl(false, tptp_fun_R_5(P!7))),
% 45.62/29.72 inference(monotonicity,[status(thm)],[1377])).
% 45.62/29.72 tff(1379,plain,
% 45.62/29.72 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)),
% 45.62/29.72 inference(transitivity,[status(thm)],[1378, 1326])).
% 45.62/29.72 tff(1380,plain,
% 45.62/29.72 ($false),
% 45.62/29.72 inference(unit_resolution,[status(thm)],[1374, 1379])).
% 45.62/29.72 tff(1381,plain,((~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false)) | (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)) | (~(impl(false, tptp_fun_R_5(P!7)) = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 45.62/29.72 tff(1382,plain,
% 45.62/29.72 (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false)),
% 45.62/29.72 inference(unit_resolution,[status(thm)],[1381, 1374, 1326])).
% 45.62/29.72 tff(1383,plain,
% 45.62/29.72 ((~((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false)))) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false))),
% 45.62/29.72 inference(tautology,[status(thm)],[])).
% 45.62/29.72 tff(1384,plain,
% 45.62/29.72 (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false)),
% 45.62/29.72 inference(unit_resolution,[status(thm)],[1383, 1382, 1376])).
% 45.62/29.72 tff(1385,plain,
% 45.62/29.72 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = impl(not1(false), tptp_fun_R_5(P!7))),
% 45.62/29.72 inference(monotonicity,[status(thm)],[1384])).
% 45.62/29.72 tff(1386,plain,
% 45.62/29.72 (impl(not1(false), tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))),
% 45.62/29.72 inference(symmetry,[status(thm)],[1385])).
% 45.62/29.72 tff(1387,plain,
% 45.62/29.72 (tptp_fun_R_5(P!7) = impl(not1(false), tptp_fun_R_5(P!7))),
% 45.62/29.72 inference(symmetry,[status(thm)],[1328])).
% 45.62/29.72 tff(1388,plain,
% 45.62/29.72 (tptp_fun_R_5(P!7) = impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))),
% 45.62/29.72 inference(transitivity,[status(thm)],[1387, 1386])).
% 45.62/29.72 tff(1389,plain,
% 45.62/29.72 ((tptp_fun_R_5(P!7) = not1(false)) <=> (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))),
% 45.62/29.72 inference(monotonicity,[status(thm)],[1388])).
% 45.62/29.72 tff(1390,plain,
% 45.62/29.72 ((impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)) <=> (tptp_fun_R_5(P!7) = not1(false))),
% 45.62/29.72 inference(symmetry,[status(thm)],[1389])).
% 45.62/29.72 tff(1391,plain,
% 45.62/29.72 ((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))) <=> (~(tptp_fun_R_5(P!7) = not1(false)))),
% 45.62/29.72 inference(monotonicity,[status(thm)],[1390])).
% 45.62/29.72 tff(1392,plain,
% 45.62/29.72 (~(tptp_fun_R_5(P!7) = not1(false))),
% 45.62/29.72 inference(modus_ponens,[status(thm)],[1374, 1391])).
% 45.62/29.72 tff(1393,plain,
% 45.62/29.72 ((~((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = not1(false)))) | (tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = not1(false))),
% 45.62/29.72 inference(tautology,[status(thm)],[])).
% 45.62/29.72 tff(1394,plain,
% 45.62/29.72 (tptp_fun_R_5(P!7) = false),
% 45.62/29.72 inference(unit_resolution,[status(thm)],[1393, 1392, 1327])).
% 45.62/29.72 tff(1395,plain,
% 45.62/29.72 (false = tptp_fun_R_5(P!7)),
% 45.62/29.72 inference(symmetry,[status(thm)],[1394])).
% 45.62/29.72 tff(1396,plain,
% 45.62/29.72 (phi(false) = phi(tptp_fun_R_5(P!7))),
% 45.62/29.72 inference(monotonicity,[status(thm)],[1395])).
% 45.62/29.72 tff(1397,plain,
% 45.62/29.72 (phi(tptp_fun_R_5(P!7)) = phi(false)),
% 45.62/29.72 inference(symmetry,[status(thm)],[1396])).
% 45.62/29.72 tff(1398,plain,
% 45.62/29.72 (tptp_fun_R_5(P!7) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))),
% 45.62/29.72 inference(transitivity,[status(thm)],[1387, 1386, 415])).
% 45.62/29.72 tff(1399,plain,
% 45.62/29.72 (phi(tptp_fun_R_5(P!7)) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.62/29.72 inference(monotonicity,[status(thm)],[1398])).
% 45.62/29.72 tff(1400,plain,
% 45.62/29.72 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = phi(tptp_fun_R_5(P!7))),
% 45.62/29.72 inference(symmetry,[status(thm)],[1399])).
% 45.62/29.72 tff(1401,plain,
% 45.62/29.72 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false),
% 45.62/29.72 inference(transitivity,[status(thm)],[1400, 1397, 23])).
% 45.62/29.72 tff(1402,plain,
% 45.62/29.72 ($false),
% 45.62/29.72 inference(unit_resolution,[status(thm)],[1375, 1401])).
% 45.62/29.72 tff(1403,plain,((impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (~(impl(not1(false), tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))) | (~((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = not1(false)))) | (~((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false)))) | (~(impl(false, tptp_fun_R_5(P!7)) = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 45.62/29.72 tff(1404,plain,
% 45.62/29.72 (~((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false)))),
% 45.62/29.72 inference(unit_resolution,[status(thm)],[1403, 1375, 1328, 1374, 1327, 1326])).
% 45.62/29.72 tff(1405,assumption,(~(bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) <=> ((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false))))), introduced(assumption)).
% 45.62/29.72 tff(1406,plain,
% 45.62/29.72 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) <=> ((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false))))),
% 45.62/29.72 inference(quant_inst,[status(thm)],[])).
% 45.62/29.72 tff(1407,plain,
% 45.62/29.72 ($false),
% 45.62/29.72 inference(unit_resolution,[status(thm)],[1406, 249, 1405])).
% 45.62/29.72 tff(1408,plain,(bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) <=> ((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 45.62/29.72 tff(1409,plain,
% 45.62/29.72 ((~(bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) <=> ((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false))))) | (~bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | ((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false)))),
% 45.62/29.72 inference(tautology,[status(thm)],[])).
% 45.62/29.72 tff(1410,plain,
% 45.62/29.72 ((~bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | ((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false)))),
% 45.62/29.72 inference(unit_resolution,[status(thm)],[1409, 1408])).
% 45.62/29.72 tff(1411,plain,
% 45.62/29.72 (~bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 45.62/29.72 inference(unit_resolution,[status(thm)],[1410, 1404])).
% 45.62/29.72 tff(1412,assumption,(~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))), introduced(assumption)).
% 45.62/29.72 tff(1413,assumption,(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))), introduced(assumption)).
% 45.62/29.72 tff(1414,plain,
% 45.62/29.72 (phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))),
% 45.62/29.72 inference(symmetry,[status(thm)],[1413])).
% 45.62/29.72 tff(1415,plain,
% 45.62/29.72 ((f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) <=> (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.62/29.72 inference(commutativity,[status(thm)],[])).
% 45.62/29.72 tff(1416,plain,
% 45.62/29.72 (((~d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.62/29.72 inference(tautology,[status(thm)],[])).
% 45.62/29.72 tff(1417,plain,
% 45.62/29.72 ((~d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1416, 1412])).
% 45.62/29.73 tff(1418,plain,
% 45.62/29.73 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))))) | (~(d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))))) | (~(d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = err)))))),
% 45.62/29.73 inference(rewrite,[status(thm)],[])).
% 45.62/29.73 tff(1419,plain,
% 45.62/29.73 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))))) | (~(d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = err)))))),
% 45.62/29.73 inference(quant_inst,[status(thm)],[])).
% 45.62/29.73 tff(1420,plain,
% 45.62/29.73 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))))) | (~(d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = err))))),
% 45.62/29.73 inference(modus_ponens,[status(thm)],[1419, 1418])).
% 45.62/29.73 tff(1421,plain,
% 45.62/29.73 ((~((~d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))))) | (~(d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = err))))),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1420, 17])).
% 45.62/29.73 tff(1422,plain,
% 45.62/29.73 (~(d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = err)))),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1421, 1417])).
% 45.62/29.73 tff(1423,plain,
% 45.62/29.73 ((d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = err))) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = err)),
% 45.62/29.73 inference(tautology,[status(thm)],[])).
% 45.62/29.73 tff(1424,plain,
% 45.62/29.73 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = err),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1423, 1422])).
% 45.62/29.73 tff(1425,plain,
% 45.62/29.73 (err = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.62/29.73 inference(symmetry,[status(thm)],[1424])).
% 45.62/29.73 tff(1426,plain,
% 45.62/29.73 (phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))),
% 45.62/29.73 inference(transitivity,[status(thm)],[1414, 415])).
% 45.62/29.73 tff(1427,plain,
% 45.62/29.73 ((phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err) <=> (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 45.62/29.73 inference(monotonicity,[status(thm)],[1426, 1425])).
% 45.62/29.73 tff(1428,plain,
% 45.62/29.73 ((phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err) <=> (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.62/29.73 inference(transitivity,[status(thm)],[1427, 1415])).
% 45.62/29.73 tff(1429,plain,
% 45.62/29.73 ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) <=> (phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err)),
% 45.62/29.73 inference(symmetry,[status(thm)],[1428])).
% 45.62/29.73 tff(1430,plain,
% 45.62/29.73 ((~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) <=> (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err))),
% 45.62/29.73 inference(monotonicity,[status(thm)],[1429])).
% 45.62/29.73 tff(1431,plain,
% 45.62/29.73 (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err)),
% 45.62/29.73 inference(modus_ponens,[status(thm)],[1412, 1430])).
% 45.62/29.73 tff(1432,plain,
% 45.62/29.73 ((d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err))) | (phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err)),
% 45.62/29.73 inference(tautology,[status(thm)],[])).
% 45.62/29.73 tff(1433,plain,
% 45.62/29.73 (d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err))),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1432, 1431])).
% 45.62/29.73 tff(1434,plain,
% 45.62/29.73 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err)))))),
% 45.62/29.73 inference(rewrite,[status(thm)],[])).
% 45.62/29.73 tff(1435,plain,
% 45.62/29.73 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err)))))),
% 45.62/29.73 inference(quant_inst,[status(thm)],[])).
% 45.62/29.73 tff(1436,plain,
% 45.62/29.73 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err))))),
% 45.62/29.73 inference(modus_ponens,[status(thm)],[1435, 1434])).
% 45.62/29.73 tff(1437,plain,
% 45.62/29.73 ((~((~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err))))),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1436, 17])).
% 45.62/29.73 tff(1438,plain,
% 45.62/29.73 (~((~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1437, 1433])).
% 45.62/29.73 tff(1439,plain,
% 45.62/29.73 (((~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))) | (phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 45.62/29.73 inference(tautology,[status(thm)],[])).
% 45.62/29.73 tff(1440,plain,
% 45.62/29.73 (phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1439, 1438])).
% 45.62/29.73 tff(1441,plain,
% 45.62/29.73 (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 45.62/29.73 inference(symmetry,[status(thm)],[1440])).
% 45.62/29.73 tff(1442,plain,
% 45.62/29.73 (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))),
% 45.62/29.73 inference(transitivity,[status(thm)],[1441, 1414, 415])).
% 45.62/29.73 tff(1443,plain,
% 45.62/29.73 (phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.62/29.73 inference(monotonicity,[status(thm)],[1442])).
% 45.62/29.73 tff(1444,plain,
% 45.62/29.73 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 45.62/29.73 inference(symmetry,[status(thm)],[1443])).
% 45.62/29.73 tff(1445,plain,
% 45.62/29.73 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))),
% 45.62/29.73 inference(transitivity,[status(thm)],[1444, 1414, 415])).
% 45.62/29.73 tff(1446,plain,
% 45.62/29.73 ($false),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1412, 1445])).
% 45.62/29.73 tff(1447,plain,((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))), inference(lemma,lemma(discharge,[]))).
% 45.62/29.73 tff(1448,plain,
% 45.62/29.73 (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1447, 1412])).
% 45.62/29.73 tff(1449,plain,
% 45.62/29.73 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))),
% 45.62/29.73 inference(rewrite,[status(thm)],[])).
% 45.62/29.73 tff(1450,plain,
% 45.62/29.73 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))),
% 45.62/29.73 inference(quant_inst,[status(thm)],[])).
% 45.62/29.73 tff(1451,plain,
% 45.62/29.73 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))),
% 45.62/29.73 inference(modus_ponens,[status(thm)],[1450, 1449])).
% 45.62/29.73 tff(1452,plain,
% 45.62/29.73 (bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1451, 358])).
% 45.62/29.73 tff(1453,plain,
% 45.62/29.73 (bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1452, 1448])).
% 45.62/29.73 tff(1454,assumption,(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))), introduced(assumption)).
% 45.62/29.73 tff(1455,plain,
% 45.62/29.73 (phi(tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))),
% 45.62/29.73 inference(symmetry,[status(thm)],[1454])).
% 45.62/29.73 tff(1456,plain,
% 45.62/29.73 ((phi(tptp_fun_R_5(P!7)) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) <=> (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7)))),
% 45.62/29.73 inference(commutativity,[status(thm)],[])).
% 45.62/29.73 tff(1457,plain,
% 45.62/29.73 ((err = not1(false)) <=> (not1(false) = err)),
% 45.62/29.73 inference(commutativity,[status(thm)],[])).
% 45.62/29.73 tff(1458,plain,
% 45.62/29.73 ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false)) <=> (err = not1(false))),
% 45.62/29.73 inference(monotonicity,[status(thm)],[1424])).
% 45.62/29.73 tff(1459,plain,
% 45.62/29.73 ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false)) <=> (not1(false) = err)),
% 45.62/29.73 inference(transitivity,[status(thm)],[1458, 1457])).
% 45.62/29.73 tff(1460,plain,
% 45.62/29.73 ((not1(false) = err) <=> (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false))),
% 45.62/29.73 inference(symmetry,[status(thm)],[1459])).
% 45.62/29.73 tff(1461,plain,
% 45.62/29.73 ((~(not1(false) = err)) <=> (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false)))),
% 45.62/29.73 inference(monotonicity,[status(thm)],[1460])).
% 45.62/29.73 tff(1462,plain,
% 45.62/29.73 (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false))),
% 45.62/29.73 inference(modus_ponens,[status(thm)],[564, 1461])).
% 45.62/29.73 tff(1463,plain,
% 45.62/29.73 ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) <=> (err = false)),
% 45.62/29.73 inference(monotonicity,[status(thm)],[1424])).
% 45.62/29.73 tff(1464,plain,
% 45.62/29.73 ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) <=> (false = err)),
% 45.62/29.73 inference(transitivity,[status(thm)],[1463, 551])).
% 45.62/29.73 tff(1465,plain,
% 45.62/29.73 ((false = err) <=> (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false)),
% 45.62/29.73 inference(symmetry,[status(thm)],[1464])).
% 45.62/29.73 tff(1466,plain,
% 45.62/29.73 ((~(false = err)) <=> (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false))),
% 45.62/29.73 inference(monotonicity,[status(thm)],[1465])).
% 45.62/29.73 tff(1467,plain,
% 45.62/29.73 (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false)),
% 45.62/29.73 inference(modus_ponens,[status(thm)],[556, 1466])).
% 45.62/29.73 tff(1468,plain,
% 45.62/29.73 ((~((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false)))) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false))),
% 45.62/29.73 inference(tautology,[status(thm)],[])).
% 45.62/29.73 tff(1469,plain,
% 45.62/29.73 (~((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false)))),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1468, 1467, 1462])).
% 45.62/29.73 tff(1470,assumption,(~(bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) <=> ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false))))), introduced(assumption)).
% 45.62/29.73 tff(1471,plain,
% 45.62/29.73 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) <=> ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false))))),
% 45.62/29.73 inference(quant_inst,[status(thm)],[])).
% 45.62/29.73 tff(1472,plain,
% 45.62/29.73 ($false),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1471, 249, 1470])).
% 45.62/29.73 tff(1473,plain,(bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) <=> ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 45.62/29.73 tff(1474,plain,
% 45.62/29.73 ((~(bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) <=> ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false))))) | (~bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))) | ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false)))),
% 45.62/29.73 inference(tautology,[status(thm)],[])).
% 45.62/29.73 tff(1475,plain,
% 45.62/29.73 ((~bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))) | ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false)))),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1474, 1473])).
% 45.62/29.73 tff(1476,plain,
% 45.62/29.73 (~bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1475, 1469])).
% 45.62/29.73 tff(1477,assumption,(bool(f5(P!7, tptp_fun_R_5(P!7)))), introduced(assumption)).
% 45.62/29.73 tff(1478,plain,
% 45.62/29.73 (bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 45.62/29.73 inference(modus_ponens,[status(thm)],[1477, 314])).
% 45.62/29.73 tff(1479,assumption,(~bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))), introduced(assumption)).
% 45.62/29.73 tff(1480,plain,
% 45.62/29.73 ($false),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1479, 1478])).
% 45.62/29.73 tff(1481,plain,((~bool(f5(P!7, tptp_fun_R_5(P!7)))) | bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))), inference(lemma,lemma(discharge,[]))).
% 45.62/29.73 tff(1482,plain,
% 45.62/29.73 (~bool(f5(P!7, tptp_fun_R_5(P!7)))),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1481, 1476])).
% 45.62/29.73 tff(1483,plain,
% 45.62/29.73 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(f5(P!7, tptp_fun_R_5(P!7))) | (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(f5(P!7, tptp_fun_R_5(P!7)))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(f5(P!7, tptp_fun_R_5(P!7))) | (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(f5(P!7, tptp_fun_R_5(P!7)))))),
% 45.62/29.73 inference(rewrite,[status(thm)],[])).
% 45.62/29.73 tff(1484,plain,
% 45.62/29.73 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(f5(P!7, tptp_fun_R_5(P!7))) | (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(f5(P!7, tptp_fun_R_5(P!7)))))),
% 45.62/29.73 inference(quant_inst,[status(thm)],[])).
% 45.62/29.73 tff(1485,plain,
% 45.62/29.73 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(f5(P!7, tptp_fun_R_5(P!7))) | (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(f5(P!7, tptp_fun_R_5(P!7))))),
% 45.62/29.73 inference(modus_ponens,[status(thm)],[1484, 1483])).
% 45.62/29.73 tff(1486,plain,
% 45.62/29.73 (bool(f5(P!7, tptp_fun_R_5(P!7))) | (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(f5(P!7, tptp_fun_R_5(P!7))))),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1485, 358])).
% 45.62/29.73 tff(1487,plain,
% 45.62/29.73 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(f5(P!7, tptp_fun_R_5(P!7)))),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1486, 1482])).
% 45.62/29.73 tff(1488,plain,
% 45.62/29.73 (phi(f5(P!7, tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 45.62/29.73 inference(symmetry,[status(thm)],[1487])).
% 45.62/29.73 tff(1489,plain,
% 45.62/29.73 (f5(P!7, tptp_fun_R_5(P!7)) = err),
% 45.62/29.73 inference(transitivity,[status(thm)],[311, 1424])).
% 45.62/29.73 tff(1490,plain,
% 45.62/29.73 (phi(f5(P!7, tptp_fun_R_5(P!7))) = phi(err)),
% 45.62/29.73 inference(monotonicity,[status(thm)],[1489])).
% 45.62/29.73 tff(1491,plain,
% 45.62/29.73 (phi(err) = phi(f5(P!7, tptp_fun_R_5(P!7)))),
% 45.62/29.73 inference(symmetry,[status(thm)],[1490])).
% 45.62/29.73 tff(1492,plain,
% 45.62/29.73 (err = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 45.62/29.73 inference(transitivity,[status(thm)],[983, 1491, 1488])).
% 45.62/29.73 tff(1493,plain,
% 45.62/29.73 ((phi(tptp_fun_R_5(P!7)) = err) <=> (phi(tptp_fun_R_5(P!7)) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.73 inference(monotonicity,[status(thm)],[1492])).
% 45.62/29.73 tff(1494,plain,
% 45.62/29.73 ((phi(tptp_fun_R_5(P!7)) = err) <=> (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7)))),
% 45.62/29.73 inference(transitivity,[status(thm)],[1493, 1456])).
% 45.62/29.73 tff(1495,plain,
% 45.62/29.73 ((impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))) <=> (phi(tptp_fun_R_5(P!7)) = err)),
% 45.62/29.73 inference(symmetry,[status(thm)],[1494])).
% 45.62/29.73 tff(1496,plain,
% 45.62/29.73 ((~(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7)))) <=> (~(phi(tptp_fun_R_5(P!7)) = err))),
% 45.62/29.73 inference(monotonicity,[status(thm)],[1495])).
% 45.62/29.73 tff(1497,plain,
% 45.62/29.73 (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))),
% 45.62/29.73 inference(transitivity,[status(thm)],[414, 1454])).
% 45.62/29.73 tff(1498,plain,
% 45.62/29.73 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 45.62/29.73 inference(transitivity,[status(thm)],[1424, 983, 1491, 1488])).
% 45.62/29.73 tff(1499,plain,
% 45.62/29.73 ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) <=> (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7)))),
% 45.62/29.73 inference(monotonicity,[status(thm)],[1498, 1497])).
% 45.62/29.73 tff(1500,plain,
% 45.62/29.73 ((~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) <=> (~(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))))),
% 45.62/29.73 inference(monotonicity,[status(thm)],[1499])).
% 45.62/29.73 tff(1501,plain,
% 45.62/29.73 (~(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7)))),
% 45.62/29.73 inference(modus_ponens,[status(thm)],[1412, 1500])).
% 45.62/29.73 tff(1502,plain,
% 45.62/29.73 (~(phi(tptp_fun_R_5(P!7)) = err)),
% 45.62/29.73 inference(modus_ponens,[status(thm)],[1501, 1496])).
% 45.62/29.73 tff(1503,plain,
% 45.62/29.73 ((d(tptp_fun_R_5(P!7)) | (~(phi(tptp_fun_R_5(P!7)) = err))) | (phi(tptp_fun_R_5(P!7)) = err)),
% 45.62/29.73 inference(tautology,[status(thm)],[])).
% 45.62/29.73 tff(1504,plain,
% 45.62/29.73 (d(tptp_fun_R_5(P!7)) | (~(phi(tptp_fun_R_5(P!7)) = err))),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1503, 1502])).
% 45.62/29.73 tff(1505,plain,
% 45.62/29.73 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(tptp_fun_R_5(P!7))) | (~(phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))))) | (~(d(tptp_fun_R_5(P!7)) | (~(phi(tptp_fun_R_5(P!7)) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(tptp_fun_R_5(P!7))) | (~(phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))))) | (~(d(tptp_fun_R_5(P!7)) | (~(phi(tptp_fun_R_5(P!7)) = err)))))),
% 45.62/29.73 inference(rewrite,[status(thm)],[])).
% 45.62/29.73 tff(1506,plain,
% 45.62/29.73 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(tptp_fun_R_5(P!7))) | (~(phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))))) | (~(d(tptp_fun_R_5(P!7)) | (~(phi(tptp_fun_R_5(P!7)) = err)))))),
% 45.62/29.73 inference(quant_inst,[status(thm)],[])).
% 45.62/29.73 tff(1507,plain,
% 45.62/29.73 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(tptp_fun_R_5(P!7))) | (~(phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))))) | (~(d(tptp_fun_R_5(P!7)) | (~(phi(tptp_fun_R_5(P!7)) = err))))),
% 45.62/29.73 inference(modus_ponens,[status(thm)],[1506, 1505])).
% 45.62/29.73 tff(1508,plain,
% 45.62/29.73 ((~((~d(tptp_fun_R_5(P!7))) | (~(phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))))) | (~(d(tptp_fun_R_5(P!7)) | (~(phi(tptp_fun_R_5(P!7)) = err))))),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1507, 17])).
% 45.62/29.73 tff(1509,plain,
% 45.62/29.73 (~((~d(tptp_fun_R_5(P!7))) | (~(phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))))),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1508, 1504])).
% 45.62/29.73 tff(1510,plain,
% 45.62/29.73 (((~d(tptp_fun_R_5(P!7))) | (~(phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)))) | (phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))),
% 45.62/29.73 inference(tautology,[status(thm)],[])).
% 45.62/29.73 tff(1511,plain,
% 45.62/29.73 (phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1510, 1509])).
% 45.62/29.73 tff(1512,plain,
% 45.62/29.73 (tptp_fun_R_5(P!7) = phi(tptp_fun_R_5(P!7))),
% 45.62/29.73 inference(symmetry,[status(thm)],[1511])).
% 45.62/29.73 tff(1513,plain,
% 45.62/29.73 (tptp_fun_R_5(P!7) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))),
% 45.62/29.73 inference(transitivity,[status(thm)],[1512, 1455, 415])).
% 45.62/29.73 tff(1514,plain,
% 45.62/29.73 (phi(tptp_fun_R_5(P!7)) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.62/29.73 inference(monotonicity,[status(thm)],[1513])).
% 45.62/29.73 tff(1515,plain,
% 45.62/29.73 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = phi(tptp_fun_R_5(P!7))),
% 45.62/29.73 inference(symmetry,[status(thm)],[1514])).
% 45.62/29.73 tff(1516,plain,
% 45.62/29.73 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))),
% 45.62/29.73 inference(transitivity,[status(thm)],[1487, 1490, 429, 1425, 1515])).
% 45.62/29.73 tff(1517,plain,
% 45.62/29.73 ($false),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1501, 1516])).
% 45.62/29.73 tff(1518,plain,((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7)))) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))), inference(lemma,lemma(discharge,[]))).
% 45.62/29.73 tff(1519,plain,
% 45.62/29.73 (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7)))),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1518, 1412])).
% 45.62/29.73 tff(1520,plain,
% 45.62/29.73 (^[A: $i, B: $i] : refl((bool(B) | (~bool(A)) | (impl(A, B) = phi(B))) <=> (bool(B) | (~bool(A)) | (impl(A, B) = phi(B))))),
% 45.62/29.73 inference(bind,[status(th)],[])).
% 45.62/29.73 tff(1521,plain,
% 45.62/29.73 (![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B))) <=> ![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))),
% 45.62/29.73 inference(quant_intro,[status(thm)],[1520])).
% 45.62/29.73 tff(1522,plain,
% 45.62/29.73 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((bool(A) & (~bool(B))) <=> (~(bool(B) | (~bool(A))))), ((~(bool(A) & (~bool(B)))) <=> (~(~(bool(B) | (~bool(A))))))), rewrite((~(~(bool(B) | (~bool(A))))) <=> (bool(B) | (~bool(A)))), ((~(bool(A) & (~bool(B)))) <=> (bool(B) | (~bool(A))))), (((~(bool(A) & (~bool(B)))) | (impl(A, B) = phi(B))) <=> ((bool(B) | (~bool(A))) | (impl(A, B) = phi(B))))), rewrite(((bool(B) | (~bool(A))) | (impl(A, B) = phi(B))) <=> (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))), (((~(bool(A) & (~bool(B)))) | (impl(A, B) = phi(B))) <=> (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))))),
% 45.62/29.73 inference(bind,[status(th)],[])).
% 45.62/29.73 tff(1523,plain,
% 45.62/29.73 (![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (impl(A, B) = phi(B))) <=> ![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))),
% 45.62/29.73 inference(quant_intro,[status(thm)],[1522])).
% 45.62/29.73 tff(1524,plain,
% 45.62/29.73 (![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (impl(A, B) = phi(B))) <=> ![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (impl(A, B) = phi(B)))),
% 45.62/29.73 inference(rewrite,[status(thm)],[])).
% 45.62/29.73 tff(1525,plain,
% 45.62/29.73 (^[A: $i, B: $i] : rewrite(((bool(A) & (~bool(B))) => (impl(A, B) = phi(B))) <=> ((~(bool(A) & (~bool(B)))) | (impl(A, B) = phi(B))))),
% 45.62/29.73 inference(bind,[status(th)],[])).
% 45.62/29.73 tff(1526,plain,
% 45.62/29.73 (![A: $i, B: $i] : ((bool(A) & (~bool(B))) => (impl(A, B) = phi(B))) <=> ![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (impl(A, B) = phi(B)))),
% 45.62/29.73 inference(quant_intro,[status(thm)],[1525])).
% 45.62/29.73 tff(1527,axiom,(![A: $i, B: $i] : ((bool(A) & (~bool(B))) => (impl(A, B) = phi(B)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','impl_axiom2')).
% 45.62/29.73 tff(1528,plain,
% 45.62/29.73 (![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (impl(A, B) = phi(B)))),
% 45.62/29.73 inference(modus_ponens,[status(thm)],[1527, 1526])).
% 45.62/29.73 tff(1529,plain,
% 45.62/29.73 (![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (impl(A, B) = phi(B)))),
% 45.62/29.73 inference(modus_ponens,[status(thm)],[1528, 1524])).
% 45.62/29.73 tff(1530,plain,(
% 45.62/29.73 ![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (impl(A, B) = phi(B)))),
% 45.62/29.73 inference(skolemize,[status(sab)],[1529])).
% 45.62/29.73 tff(1531,plain,
% 45.62/29.73 (![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))),
% 45.62/29.73 inference(modus_ponens,[status(thm)],[1530, 1523])).
% 45.62/29.73 tff(1532,plain,
% 45.62/29.73 (![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))),
% 45.62/29.73 inference(modus_ponens,[status(thm)],[1531, 1521])).
% 45.62/29.73 tff(1533,plain,
% 45.62/29.73 (((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | (bool(tptp_fun_R_5(P!7)) | (~bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))))) <=> ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | bool(tptp_fun_R_5(P!7)) | (~bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))))),
% 45.62/29.73 inference(rewrite,[status(thm)],[])).
% 45.62/29.73 tff(1534,plain,
% 45.62/29.73 ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | (bool(tptp_fun_R_5(P!7)) | (~bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))))),
% 45.62/29.73 inference(quant_inst,[status(thm)],[])).
% 45.62/29.73 tff(1535,plain,
% 45.62/29.73 ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | bool(tptp_fun_R_5(P!7)) | (~bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7)))),
% 45.62/29.73 inference(modus_ponens,[status(thm)],[1534, 1533])).
% 45.62/29.73 tff(1536,plain,
% 45.62/29.73 (bool(tptp_fun_R_5(P!7)) | (~bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7)))),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1535, 1532])).
% 45.62/29.73 tff(1537,plain,
% 45.62/29.73 (bool(tptp_fun_R_5(P!7))),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1536, 1519, 1453])).
% 45.62/29.73 tff(1538,plain,
% 45.62/29.73 (impl(false, tptp_fun_R_5(P!7)) = not1(false)),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1286, 1537])).
% 45.62/29.73 tff(1539,plain,
% 45.62/29.73 (bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) <=> ((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false)))),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1406, 249])).
% 45.62/29.73 tff(1540,plain,
% 45.62/29.73 ((~(bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) <=> ((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false))))) | ((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false)))),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1409, 1453])).
% 45.62/29.73 tff(1541,plain,
% 45.62/29.73 ((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false))),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1540, 1539])).
% 45.62/29.73 tff(1542,plain,
% 45.62/29.73 ((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = not1(false))),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1281, 1537])).
% 45.62/29.73 tff(1543,plain,
% 45.62/29.73 (impl(not1(false), tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1261, 1537])).
% 45.62/29.73 tff(1544,plain,
% 45.62/29.73 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1403, 1467, 1543, 1542, 1541, 1538])).
% 45.62/29.73 tff(1545,plain,
% 45.62/29.73 (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = not1(false)),
% 45.62/29.73 inference(transitivity,[status(thm)],[414, 1544])).
% 45.62/29.73 tff(1546,plain,
% 45.62/29.73 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = phi(not1(false))),
% 45.62/29.73 inference(monotonicity,[status(thm)],[1545])).
% 45.62/29.73 tff(1547,plain,
% 45.62/29.73 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false)),
% 45.62/29.73 inference(transitivity,[status(thm)],[1546, 48])).
% 45.62/29.73 tff(1548,plain,
% 45.62/29.73 ($false),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1462, 1547])).
% 45.62/29.73 tff(1549,plain,(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))), inference(lemma,lemma(discharge,[]))).
% 45.62/29.73 tff(1550,assumption,(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false)), introduced(assumption)).
% 45.62/29.73 tff(1551,assumption,(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))), introduced(assumption)).
% 45.62/29.73 tff(1552,plain,
% 45.62/29.73 (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.62/29.73 inference(symmetry,[status(thm)],[1551])).
% 45.62/29.73 tff(1553,plain,
% 45.62/29.73 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)),
% 45.62/29.73 inference(transitivity,[status(thm)],[415, 1552, 1550])).
% 45.62/29.73 tff(1554,plain,
% 45.62/29.73 ($false),
% 45.62/29.73 inference(unit_resolution,[status(thm)],[1374, 1553])).
% 45.62/29.73 tff(1555,plain,((~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false))) | (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))), inference(lemma,lemma(discharge,[]))).
% 45.62/29.74 tff(1556,plain,
% 45.62/29.74 ((~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false))) | (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))),
% 45.62/29.74 inference(unit_resolution,[status(thm)],[1555, 1549])).
% 45.62/29.74 tff(1557,plain,
% 45.62/29.74 (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false))),
% 45.62/29.74 inference(unit_resolution,[status(thm)],[1556, 1374])).
% 45.62/29.74 tff(1558,plain,
% 45.62/29.74 (~((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false)))),
% 45.62/29.74 inference(unit_resolution,[status(thm)],[1468, 1375, 1557])).
% 45.62/29.74 tff(1559,plain,
% 45.62/29.74 (~bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 45.62/29.74 inference(unit_resolution,[status(thm)],[1475, 1558])).
% 45.62/29.74 tff(1560,plain,
% 45.62/29.74 (~bool(f5(P!7, tptp_fun_R_5(P!7)))),
% 45.62/29.74 inference(unit_resolution,[status(thm)],[1481, 1559])).
% 45.62/29.74 tff(1561,plain,
% 45.62/29.74 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(f5(P!7, tptp_fun_R_5(P!7)))),
% 45.62/29.74 inference(unit_resolution,[status(thm)],[1486, 1560])).
% 45.62/29.74 tff(1562,assumption,(~bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))), introduced(assumption)).
% 45.62/29.74 tff(1563,plain,
% 45.62/29.74 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), err) = phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), err) = phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))),
% 45.62/29.74 inference(rewrite,[status(thm)],[])).
% 45.62/29.74 tff(1564,plain,
% 45.62/29.74 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), err) = phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))),
% 45.62/29.74 inference(quant_inst,[status(thm)],[])).
% 45.62/29.74 tff(1565,plain,
% 45.62/29.74 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), err) = phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))),
% 45.62/29.74 inference(modus_ponens,[status(thm)],[1564, 1563])).
% 45.62/29.74 tff(1566,plain,
% 45.62/29.74 (bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), err) = phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))),
% 45.62/29.74 inference(unit_resolution,[status(thm)],[1565, 358])).
% 45.62/29.74 tff(1567,plain,
% 45.62/29.74 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), err) = phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 45.62/29.74 inference(unit_resolution,[status(thm)],[1566, 1562])).
% 45.62/29.74 tff(1568,plain,
% 45.62/29.74 (phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), err)),
% 45.62/29.74 inference(symmetry,[status(thm)],[1567])).
% 45.62/29.74 tff(1569,plain,
% 45.62/29.74 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 45.62/29.74 inference(unit_resolution,[status(thm)],[1452, 1562])).
% 45.62/29.74 tff(1570,plain,
% 45.62/29.74 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 45.62/29.74 inference(quant_inst,[status(thm)],[])).
% 45.62/29.74 tff(1571,plain,
% 45.62/29.74 (lazy_impl(not1(false), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.62/29.74 inference(unit_resolution,[status(thm)],[1570, 33])).
% 45.62/29.74 tff(1572,plain,
% 45.62/29.74 (phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))),
% 45.62/29.74 inference(symmetry,[status(thm)],[1569])).
% 45.62/29.74 tff(1573,plain,
% 45.62/29.74 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), err) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))),
% 45.62/29.74 inference(transitivity,[status(thm)],[1567, 1572, 415])).
% 45.62/29.74 tff(1574,plain,
% 45.62/29.74 (phi(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), err)) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.62/29.74 inference(monotonicity,[status(thm)],[1573])).
% 45.62/29.74 tff(1575,plain,
% 45.62/29.74 (f5(P!7, tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), err)),
% 45.62/29.74 inference(transitivity,[status(thm)],[311, 1549, 414, 1569, 1568])).
% 45.62/29.74 tff(1576,plain,
% 45.62/29.74 (phi(f5(P!7, tptp_fun_R_5(P!7))) = phi(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), err))),
% 45.62/29.74 inference(monotonicity,[status(thm)],[1575])).
% 45.62/29.74 tff(1577,assumption,(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(f5(P!7, tptp_fun_R_5(P!7)))), introduced(assumption)).
% 45.62/29.74 tff(1578,plain,
% 45.62/29.74 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))),
% 45.62/29.74 inference(transitivity,[status(thm)],[1577, 1576, 1574, 1549])).
% 45.62/29.74 tff(1579,plain,
% 45.62/29.74 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(not1(false), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.62/29.74 inference(monotonicity,[status(thm)],[1290, 1578])).
% 45.62/29.74 tff(1580,plain,
% 45.62/29.74 (f6(P!7, tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), err)),
% 45.62/29.74 inference(transitivity,[status(thm)],[325, 1579, 1571, 1549, 414, 1569, 1568])).
% 45.62/29.74 tff(1581,plain,
% 45.62/29.74 (phi(f6(P!7, tptp_fun_R_5(P!7))) = phi(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), err))),
% 45.62/29.74 inference(monotonicity,[status(thm)],[1580])).
% 45.62/29.74 tff(1582,plain,
% 45.62/29.74 (phi(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), err)) = phi(f6(P!7, tptp_fun_R_5(P!7)))),
% 45.62/29.74 inference(symmetry,[status(thm)],[1581])).
% 45.62/29.74 tff(1583,plain,
% 45.62/29.74 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = phi(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), err))),
% 45.62/29.74 inference(symmetry,[status(thm)],[1574])).
% 45.62/29.74 tff(1584,plain,
% 45.62/29.74 (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.62/29.74 inference(symmetry,[status(thm)],[1549])).
% 45.62/29.74 tff(1585,plain,
% 45.62/29.74 (^[X1: $i, X2: $i] : refl((bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2))) <=> (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2))))),
% 45.62/29.74 inference(bind,[status(th)],[])).
% 45.62/29.74 tff(1586,plain,
% 45.62/29.74 (![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2))) <=> ![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))),
% 45.62/29.74 inference(quant_intro,[status(thm)],[1585])).
% 45.62/29.74 tff(1587,plain,
% 45.62/29.74 (^[X1: $i, X2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~bool(apply(P!7, X1))) & (~bool(apply(P!7, X2)))) <=> (~(bool(apply(P!7, X1)) | bool(apply(P!7, X2))))), ((~((~bool(apply(P!7, X1))) & (~bool(apply(P!7, X2))))) <=> (~(~(bool(apply(P!7, X1)) | bool(apply(P!7, X2))))))), rewrite((~(~(bool(apply(P!7, X1)) | bool(apply(P!7, X2))))) <=> (bool(apply(P!7, X1)) | bool(apply(P!7, X2)))), ((~((~bool(apply(P!7, X1))) & (~bool(apply(P!7, X2))))) <=> (bool(apply(P!7, X1)) | bool(apply(P!7, X2))))), (((~((~bool(apply(P!7, X1))) & (~bool(apply(P!7, X2))))) | (apply(P!7, X1) = apply(P!7, X2))) <=> ((bool(apply(P!7, X1)) | bool(apply(P!7, X2))) | (apply(P!7, X1) = apply(P!7, X2))))), rewrite(((bool(apply(P!7, X1)) | bool(apply(P!7, X2))) | (apply(P!7, X1) = apply(P!7, X2))) <=> (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))), (((~((~bool(apply(P!7, X1))) & (~bool(apply(P!7, X2))))) | (apply(P!7, X1) = apply(P!7, X2))) <=> (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))))),
% 45.62/29.74 inference(bind,[status(th)],[])).
% 45.62/29.74 tff(1588,plain,
% 45.62/29.74 (![X1: $i, X2: $i] : ((~((~bool(apply(P!7, X1))) & (~bool(apply(P!7, X2))))) | (apply(P!7, X1) = apply(P!7, X2))) <=> ![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))),
% 45.62/29.74 inference(quant_intro,[status(thm)],[1587])).
% 45.62/29.74 tff(1589,plain,
% 45.62/29.74 (![X1: $i, X2: $i] : ((~((~bool(apply(P!7, X1))) & (~bool(apply(P!7, X2))))) | (apply(P!7, X1) = apply(P!7, X2)))),
% 45.62/29.74 inference(and_elim,[status(thm)],[896])).
% 45.62/29.74 tff(1590,plain,
% 45.62/29.74 (![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))),
% 45.62/29.74 inference(modus_ponens,[status(thm)],[1589, 1588])).
% 45.62/29.74 tff(1591,plain,
% 45.62/29.74 (![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))),
% 45.62/29.74 inference(modus_ponens,[status(thm)],[1590, 1586])).
% 45.62/29.74 tff(1592,plain,
% 45.62/29.74 (((~![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))) | (bool(apply(P!7, tptp_fun_X_3(P!7))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = apply(P!7, tptp_fun_X_3(P!7))))) <=> ((~![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = apply(P!7, tptp_fun_X_3(P!7))))),
% 45.62/29.74 inference(rewrite,[status(thm)],[])).
% 45.62/29.74 tff(1593,plain,
% 45.62/29.74 ((bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = apply(P!7, tptp_fun_X_3(P!7)))) <=> (bool(apply(P!7, tptp_fun_X_3(P!7))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = apply(P!7, tptp_fun_X_3(P!7))))),
% 45.62/29.74 inference(rewrite,[status(thm)],[])).
% 45.62/29.74 tff(1594,plain,
% 45.62/29.74 (((~![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))) | (bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = apply(P!7, tptp_fun_X_3(P!7))))) <=> ((~![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))) | (bool(apply(P!7, tptp_fun_X_3(P!7))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = apply(P!7, tptp_fun_X_3(P!7)))))),
% 45.62/29.74 inference(monotonicity,[status(thm)],[1593])).
% 45.62/29.74 tff(1595,plain,
% 45.62/29.74 (((~![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))) | (bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = apply(P!7, tptp_fun_X_3(P!7))))) <=> ((~![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = apply(P!7, tptp_fun_X_3(P!7))))),
% 45.62/29.74 inference(transitivity,[status(thm)],[1594, 1592])).
% 45.62/29.74 tff(1596,plain,
% 45.62/29.74 ((~![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))) | (bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = apply(P!7, tptp_fun_X_3(P!7))))),
% 45.62/29.74 inference(quant_inst,[status(thm)],[])).
% 45.62/29.74 tff(1597,plain,
% 45.62/29.74 ((~![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = apply(P!7, tptp_fun_X_3(P!7)))),
% 45.62/29.74 inference(modus_ponens,[status(thm)],[1596, 1595])).
% 45.62/29.74 tff(1598,plain,
% 45.62/29.74 (bool(apply(P!7, tptp_fun_X_3(P!7))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = apply(P!7, tptp_fun_X_3(P!7)))),
% 45.62/29.74 inference(unit_resolution,[status(thm)],[1597, 1591])).
% 45.62/29.74 tff(1599,plain,
% 45.62/29.74 (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = apply(P!7, tptp_fun_X_3(P!7))),
% 45.62/29.74 inference(unit_resolution,[status(thm)],[1598, 348, 1562])).
% 45.62/29.74 tff(1600,plain,
% 45.62/29.74 (apply(P!7, tptp_fun_X_3(P!7)) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))),
% 45.62/29.74 inference(symmetry,[status(thm)],[1599])).
% 45.62/29.74 tff(1601,plain,
% 45.62/29.74 (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))),
% 45.62/29.74 inference(monotonicity,[status(thm)],[1600])).
% 45.62/29.74 tff(1602,plain,
% 45.62/29.74 (exists1(P!7) = exists2(P!7)),
% 45.62/29.74 inference(transitivity,[status(thm)],[346, 1300, 1601, 415, 1584, 1583, 1582, 1309])).
% 45.62/29.74 tff(1603,plain,
% 45.62/29.74 ($false),
% 45.62/29.74 inference(unit_resolution,[status(thm)],[897, 1602])).
% 45.62/29.74 tff(1604,plain,(bool(apply(P!7, tptp_fun_X_3(P!7))) | (~(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(f5(P!7, tptp_fun_R_5(P!7))))) | (~(prop(tptp_fun_R_5(P!7)) = not1(false))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))), inference(lemma,lemma(discharge,[]))).
% 45.62/29.74 tff(1605,plain,
% 45.62/29.74 (bool(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.62/29.74 inference(unit_resolution,[status(thm)],[1604, 1561, 1290, 1411])).
% 45.62/29.74 tff(1606,assumption,(bool(apply(P!7, tptp_fun_X_3(P!7)))), introduced(assumption)).
% 45.62/29.74 tff(1607,plain,
% 45.62/29.74 ((~((prop(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)) <=> bool(apply(P!7, tptp_fun_X_3(P!7))))) | (prop(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)) | (~bool(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.62/29.74 inference(tautology,[status(thm)],[])).
% 45.62/29.74 tff(1608,plain,
% 45.62/29.74 ((~((prop(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)) <=> bool(apply(P!7, tptp_fun_X_3(P!7))))) | (prop(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))),
% 45.62/29.74 inference(unit_resolution,[status(thm)],[1607, 1606])).
% 45.62/29.74 tff(1609,plain,
% 45.62/29.74 (prop(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)),
% 45.62/29.74 inference(unit_resolution,[status(thm)],[1608, 294])).
% 45.62/29.74 tff(1610,plain,
% 45.62/29.74 (lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))) = lazy_impl(not1(false), apply(P!7, tptp_fun_X_3(P!7)))),
% 45.62/29.74 inference(monotonicity,[status(thm)],[1609])).
% 45.62/29.74 tff(1611,plain,
% 45.62/29.74 (lazy_impl(not1(false), apply(P!7, tptp_fun_X_3(P!7))) = lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))),
% 45.62/29.74 inference(symmetry,[status(thm)],[1610])).
% 45.62/29.74 tff(1612,plain,
% 45.62/29.74 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), apply(P!7, tptp_fun_X_3(P!7))) = phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.62/29.74 inference(quant_inst,[status(thm)],[])).
% 45.62/29.74 tff(1613,plain,
% 45.62/29.74 (lazy_impl(not1(false), apply(P!7, tptp_fun_X_3(P!7))) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.62/29.74 inference(unit_resolution,[status(thm)],[1612, 33])).
% 45.62/29.74 tff(1614,plain,
% 45.62/29.74 (phi(apply(P!7, tptp_fun_X_3(P!7))) = lazy_impl(not1(false), apply(P!7, tptp_fun_X_3(P!7)))),
% 45.62/29.74 inference(symmetry,[status(thm)],[1613])).
% 45.62/29.74 tff(1615,assumption,(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))), introduced(assumption)).
% 45.62/29.74 tff(1616,plain,
% 45.62/29.74 (((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = not1(false))) | (~(Y = false))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = not1(false))) | (~(Y = false))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false))))))))),
% 45.62/29.74 inference(rewrite,[status(thm)],[])).
% 45.62/29.74 tff(1617,plain,
% 45.62/29.74 ((existsprefers(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~((~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false))) | (~(apply(P!7, tptp_fun_X_3(P!7)) = false)))))) <=> (existsprefers(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false)))))))),
% 45.62/29.74 inference(rewrite,[status(thm)],[])).
% 45.62/29.74 tff(1618,plain,
% 45.62/29.74 (((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = not1(false))) | (~(Y = false))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~((~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false))) | (~(apply(P!7, tptp_fun_X_3(P!7)) = false))))))) <=> ((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = not1(false))) | (~(Y = false))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false))))))))),
% 45.62/29.74 inference(monotonicity,[status(thm)],[1617])).
% 45.62/29.74 tff(1619,plain,
% 45.62/29.74 (((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = not1(false))) | (~(Y = false))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~((~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false))) | (~(apply(P!7, tptp_fun_X_3(P!7)) = false))))))) <=> ((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = not1(false))) | (~(Y = false))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false))))))))),
% 45.62/29.74 inference(transitivity,[status(thm)],[1618, 1616])).
% 45.62/29.74 tff(1620,plain,
% 45.62/29.74 ((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = not1(false))) | (~(Y = false))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~((~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false))) | (~(apply(P!7, tptp_fun_X_3(P!7)) = false))))))),
% 45.62/29.74 inference(quant_inst,[status(thm)],[])).
% 45.62/29.74 tff(1621,plain,
% 45.62/29.74 ((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = not1(false))) | (~(Y = false))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false)))))))),
% 45.62/29.74 inference(modus_ponens,[status(thm)],[1620, 1619])).
% 45.62/29.74 tff(1622,plain,
% 45.62/29.74 (existsprefers(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false))))))),
% 45.62/29.74 inference(unit_resolution,[status(thm)],[1621, 1224])).
% 45.62/29.74 tff(1623,plain,
% 45.62/29.74 ((~![X1: $i] : (~existsprefers(apply(P!7, X1), apply(P!7, tptp_fun_X_3(P!7))))) | (~existsprefers(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), apply(P!7, tptp_fun_X_3(P!7))))),
% 45.62/29.74 inference(quant_inst,[status(thm)],[])).
% 45.62/29.74 tff(1624,plain,
% 45.62/29.74 (~existsprefers(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), apply(P!7, tptp_fun_X_3(P!7)))),
% 45.62/29.74 inference(unit_resolution,[status(thm)],[1623, 1233])).
% 45.62/29.74 tff(1625,plain,
% 45.62/29.74 ((~(existsprefers(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false)))))))) | existsprefers(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), apply(P!7, tptp_fun_X_3(P!7))) | (~((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false)))))))),
% 45.62/29.74 inference(tautology,[status(thm)],[])).
% 45.62/29.74 tff(1626,plain,
% 45.62/29.74 ((~(existsprefers(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false)))))))) | (~((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false)))))))),
% 45.62/29.74 inference(unit_resolution,[status(thm)],[1625, 1624])).
% 45.62/29.74 tff(1627,plain,
% 45.62/29.74 (~((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false))))))),
% 45.62/29.74 inference(unit_resolution,[status(thm)],[1626, 1622])).
% 45.62/29.74 tff(1628,plain,
% 45.62/29.74 (((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false)))))) | ((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))),
% 45.62/29.74 inference(tautology,[status(thm)],[])).
% 45.62/29.74 tff(1629,plain,
% 45.62/29.74 ((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))),
% 45.62/29.74 inference(unit_resolution,[status(thm)],[1628, 1627])).
% 45.62/29.74 tff(1630,plain,
% 45.62/29.74 ((~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))),
% 45.62/29.74 inference(tautology,[status(thm)],[])).
% 45.62/29.74 tff(1631,plain,
% 45.62/29.74 ((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))),
% 45.62/29.74 inference(unit_resolution,[status(thm)],[1630, 1629])).
% 45.62/29.74 tff(1632,plain,
% 45.62/29.74 (~d(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.62/29.74 inference(unit_resolution,[status(thm)],[1631, 1606, 1562, 1615])).
% 45.62/29.74 tff(1633,plain,
% 45.62/29.74 ((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))))),
% 45.62/29.74 inference(unit_resolution,[status(thm)],[374, 1632])).
% 45.62/29.74 tff(1634,plain,
% 45.62/29.74 (~(d(apply(P!7, tptp_fun_X_3(P!7))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err)))),
% 45.62/29.74 inference(unit_resolution,[status(thm)],[383, 1633])).
% 45.62/29.74 tff(1635,plain,
% 45.62/29.74 (phi(apply(P!7, tptp_fun_X_3(P!7))) = err),
% 45.62/29.74 inference(unit_resolution,[status(thm)],[385, 1634])).
% 45.62/29.74 tff(1636,plain,
% 45.62/29.74 (err = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.62/29.74 inference(symmetry,[status(thm)],[1635])).
% 45.62/29.74 tff(1637,plain,
% 45.62/29.74 (err = f7(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.62/29.74 inference(transitivity,[status(thm)],[1636, 1614, 1611, 292])).
% 45.62/29.74 tff(1638,plain,
% 45.62/29.74 (forallprefers(err, false) <=> forallprefers(f7(apply(P!7, tptp_fun_X_3(P!7))), f7(P!6))),
% 45.62/29.74 inference(monotonicity,[status(thm)],[1637, 289])).
% 45.62/29.75 tff(1639,plain,
% 45.62/29.75 (forallprefers(f7(apply(P!7, tptp_fun_X_3(P!7))), f7(P!6)) <=> forallprefers(err, false)),
% 45.62/29.75 inference(symmetry,[status(thm)],[1638])).
% 45.62/29.75 tff(1640,plain,
% 45.62/29.75 ((~forallprefers(f7(apply(P!7, tptp_fun_X_3(P!7))), f7(P!6))) <=> (~forallprefers(err, false))),
% 45.62/29.75 inference(monotonicity,[status(thm)],[1639])).
% 45.62/29.75 tff(1641,plain,
% 45.62/29.75 ((~![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))) | (~forallprefers(f7(apply(P!7, tptp_fun_X_3(P!7))), f7(P!6)))),
% 45.62/29.75 inference(quant_inst,[status(thm)],[])).
% 45.62/29.75 tff(1642,plain,
% 45.62/29.75 (~forallprefers(f7(apply(P!7, tptp_fun_X_3(P!7))), f7(P!6))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[1641, 218])).
% 45.62/29.75 tff(1643,plain,
% 45.62/29.75 (~forallprefers(err, false)),
% 45.62/29.75 inference(modus_ponens,[status(thm)],[1642, 1640])).
% 45.62/29.75 tff(1644,plain,
% 45.62/29.75 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(err, false) <=> ((~(d(err) | (~d(false)))) | (~((~d(false)) | (~d(err)) | bool(err) | (~bool(false)))) | (~((~(err = false)) | (~(false = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(err, false) <=> ((~(d(err) | (~d(false)))) | (~((~d(false)) | (~d(err)) | bool(err) | (~bool(false)))) | (~((~(err = false)) | (~(false = not1(false))))))))),
% 45.62/29.75 inference(rewrite,[status(thm)],[])).
% 45.62/29.75 tff(1645,plain,
% 45.62/29.75 ((forallprefers(err, false) <=> ((~(d(err) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(err) | (~d(err)))) | (~((~(err = false)) | (~(false = not1(false))))))) <=> (forallprefers(err, false) <=> ((~(d(err) | (~d(false)))) | (~((~d(false)) | (~d(err)) | bool(err) | (~bool(false)))) | (~((~(err = false)) | (~(false = not1(false)))))))),
% 45.62/29.75 inference(rewrite,[status(thm)],[])).
% 45.62/29.75 tff(1646,plain,
% 45.62/29.75 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(err, false) <=> ((~(d(err) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(err) | (~d(err)))) | (~((~(err = false)) | (~(false = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(err, false) <=> ((~(d(err) | (~d(false)))) | (~((~d(false)) | (~d(err)) | bool(err) | (~bool(false)))) | (~((~(err = false)) | (~(false = not1(false))))))))),
% 45.62/29.75 inference(monotonicity,[status(thm)],[1645])).
% 45.62/29.75 tff(1647,plain,
% 45.62/29.75 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(err, false) <=> ((~(d(err) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(err) | (~d(err)))) | (~((~(err = false)) | (~(false = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(err, false) <=> ((~(d(err) | (~d(false)))) | (~((~d(false)) | (~d(err)) | bool(err) | (~bool(false)))) | (~((~(err = false)) | (~(false = not1(false))))))))),
% 45.62/29.75 inference(transitivity,[status(thm)],[1646, 1644])).
% 45.62/29.75 tff(1648,plain,
% 45.62/29.75 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(err, false) <=> ((~(d(err) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(err) | (~d(err)))) | (~((~(err = false)) | (~(false = not1(false)))))))),
% 45.62/29.75 inference(quant_inst,[status(thm)],[])).
% 45.62/29.75 tff(1649,plain,
% 45.62/29.75 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(err, false) <=> ((~(d(err) | (~d(false)))) | (~((~d(false)) | (~d(err)) | bool(err) | (~bool(false)))) | (~((~(err = false)) | (~(false = not1(false)))))))),
% 45.62/29.75 inference(modus_ponens,[status(thm)],[1648, 1647])).
% 45.62/29.75 tff(1650,plain,
% 45.62/29.75 (forallprefers(err, false) <=> ((~(d(err) | (~d(false)))) | (~((~d(false)) | (~d(err)) | bool(err) | (~bool(false)))) | (~((~(err = false)) | (~(false = not1(false))))))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[1649, 159])).
% 45.62/29.75 tff(1651,plain,
% 45.62/29.75 ((~((~d(false)) | (~d(err)) | bool(err) | (~bool(false)))) | (~d(false)) | (~d(err)) | bool(err) | (~bool(false))),
% 45.62/29.75 inference(tautology,[status(thm)],[])).
% 45.62/29.75 tff(1652,plain,
% 45.62/29.75 (~((~d(false)) | (~d(err)) | bool(err) | (~bool(false)))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[1651, 5, 396, 76, 571])).
% 45.62/29.75 tff(1653,plain,
% 45.62/29.75 (((~(d(err) | (~d(false)))) | (~((~d(false)) | (~d(err)) | bool(err) | (~bool(false)))) | (~((~(err = false)) | (~(false = not1(false)))))) | ((~d(false)) | (~d(err)) | bool(err) | (~bool(false)))),
% 45.62/29.75 inference(tautology,[status(thm)],[])).
% 45.62/29.75 tff(1654,plain,
% 45.62/29.75 ((~(d(err) | (~d(false)))) | (~((~d(false)) | (~d(err)) | bool(err) | (~bool(false)))) | (~((~(err = false)) | (~(false = not1(false)))))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[1653, 1652])).
% 45.62/29.75 tff(1655,plain,
% 45.62/29.75 ((~(forallprefers(err, false) <=> ((~(d(err) | (~d(false)))) | (~((~d(false)) | (~d(err)) | bool(err) | (~bool(false)))) | (~((~(err = false)) | (~(false = not1(false)))))))) | forallprefers(err, false) | (~((~(d(err) | (~d(false)))) | (~((~d(false)) | (~d(err)) | bool(err) | (~bool(false)))) | (~((~(err = false)) | (~(false = not1(false)))))))),
% 45.62/29.75 inference(tautology,[status(thm)],[])).
% 45.62/29.75 tff(1656,plain,
% 45.62/29.75 ((~(forallprefers(err, false) <=> ((~(d(err) | (~d(false)))) | (~((~d(false)) | (~d(err)) | bool(err) | (~bool(false)))) | (~((~(err = false)) | (~(false = not1(false)))))))) | forallprefers(err, false)),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[1655, 1654])).
% 45.62/29.75 tff(1657,plain,
% 45.62/29.75 (forallprefers(err, false)),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[1656, 1650])).
% 45.62/29.75 tff(1658,plain,
% 45.62/29.75 ($false),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[1657, 1643])).
% 45.62/29.75 tff(1659,plain,((~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))), inference(lemma,lemma(discharge,[]))).
% 45.62/29.75 tff(1660,plain,
% 45.62/29.75 (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[1659, 1605, 1411])).
% 45.62/29.75 tff(1661,plain,
% 45.62/29.75 (((~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))) | d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 45.62/29.75 inference(tautology,[status(thm)],[])).
% 45.62/29.75 tff(1662,plain,
% 45.62/29.75 ((~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[1661, 1660])).
% 45.62/29.75 tff(1663,plain,
% 45.62/29.75 (~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err)))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[1437, 1662])).
% 45.62/29.75 tff(1664,plain,
% 45.62/29.75 (phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[1432, 1663])).
% 45.62/29.75 tff(1665,plain,
% 45.62/29.75 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), err) = phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[1566, 1411])).
% 45.62/29.75 tff(1666,plain,
% 45.62/29.75 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), err) = err),
% 45.62/29.75 inference(transitivity,[status(thm)],[1665, 1664])).
% 45.62/29.75 tff(1667,plain,
% 45.62/29.75 (phi(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), err)) = phi(err)),
% 45.62/29.75 inference(monotonicity,[status(thm)],[1666])).
% 45.62/29.75 tff(1668,plain,
% 45.62/29.75 (phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), err)),
% 45.62/29.75 inference(symmetry,[status(thm)],[1665])).
% 45.62/29.75 tff(1669,plain,
% 45.62/29.75 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[1452, 1411])).
% 45.62/29.75 tff(1670,plain,
% 45.62/29.75 (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), err)),
% 45.62/29.75 inference(transitivity,[status(thm)],[414, 1669, 1668])).
% 45.62/29.75 tff(1671,plain,
% 45.62/29.75 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = phi(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), err))),
% 45.62/29.75 inference(monotonicity,[status(thm)],[1670])).
% 45.62/29.75 tff(1672,plain,
% 45.62/29.75 (f5(P!7, tptp_fun_R_5(P!7)) = err),
% 45.62/29.75 inference(transitivity,[status(thm)],[311, 1671, 1667, 429])).
% 45.62/29.75 tff(1673,plain,
% 45.62/29.75 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = impl(err, tptp_fun_R_5(P!7))),
% 45.62/29.75 inference(monotonicity,[status(thm)],[1672])).
% 45.62/29.75 tff(1674,plain,
% 45.62/29.75 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = err),
% 45.62/29.75 inference(transitivity,[status(thm)],[1673, 981, 429])).
% 45.62/29.75 tff(1675,plain,
% 45.62/29.75 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(not1(false), err)),
% 45.62/29.75 inference(monotonicity,[status(thm)],[1290, 1674])).
% 45.62/29.75 tff(1676,plain,
% 45.62/29.75 (f6(P!7, tptp_fun_R_5(P!7)) = err),
% 45.62/29.75 inference(transitivity,[status(thm)],[325, 1675, 431, 429])).
% 45.62/29.75 tff(1677,plain,
% 45.62/29.75 (phi(f6(P!7, tptp_fun_R_5(P!7))) = phi(err)),
% 45.62/29.75 inference(monotonicity,[status(thm)],[1676])).
% 45.62/29.75 tff(1678,plain,
% 45.62/29.75 (phi(f6(P!7, tptp_fun_R_5(P!7))) = err),
% 45.62/29.75 inference(transitivity,[status(thm)],[1677, 429])).
% 45.62/29.75 tff(1679,plain,
% 45.62/29.75 ((err = phi(f6(P!7, tptp_fun_R_5(P!7)))) <=> (phi(f6(P!7, tptp_fun_R_5(P!7))) = err)),
% 45.62/29.75 inference(commutativity,[status(thm)],[])).
% 45.62/29.75 tff(1680,plain,
% 45.62/29.75 (((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false)))))) | (d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))),
% 45.62/29.75 inference(tautology,[status(thm)],[])).
% 45.62/29.75 tff(1681,plain,
% 45.62/29.75 (d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[1680, 1627])).
% 45.62/29.75 tff(1682,plain,
% 45.62/29.75 ((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.62/29.75 inference(tautology,[status(thm)],[])).
% 45.62/29.75 tff(1683,plain,
% 45.62/29.75 (d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[1682, 1681])).
% 45.62/29.75 tff(1684,plain,
% 45.62/29.75 (~d(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[1683, 1660])).
% 45.62/29.75 tff(1685,plain,
% 45.62/29.75 ((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[374, 1684])).
% 45.62/29.75 tff(1686,plain,
% 45.62/29.75 (~(d(apply(P!7, tptp_fun_X_3(P!7))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err)))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[383, 1685])).
% 45.62/29.75 tff(1687,plain,
% 45.62/29.75 (phi(apply(P!7, tptp_fun_X_3(P!7))) = err),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[385, 1686])).
% 45.62/29.75 tff(1688,plain,
% 45.62/29.75 (exists1(P!7) = err),
% 45.62/29.75 inference(transitivity,[status(thm)],[346, 1687])).
% 45.62/29.75 tff(1689,plain,
% 45.62/29.75 ((exists1(P!7) = exists2(P!7)) <=> (err = phi(f6(P!7, tptp_fun_R_5(P!7))))),
% 45.62/29.75 inference(monotonicity,[status(thm)],[1688, 880])).
% 45.62/29.75 tff(1690,plain,
% 45.62/29.75 ((exists1(P!7) = exists2(P!7)) <=> (phi(f6(P!7, tptp_fun_R_5(P!7))) = err)),
% 45.62/29.75 inference(transitivity,[status(thm)],[1689, 1679])).
% 45.62/29.75 tff(1691,plain,
% 45.62/29.75 ((~(exists1(P!7) = exists2(P!7))) <=> (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = err))),
% 45.62/29.75 inference(monotonicity,[status(thm)],[1690])).
% 45.62/29.75 tff(1692,plain,
% 45.62/29.75 (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = err)),
% 45.62/29.75 inference(modus_ponens,[status(thm)],[897, 1691])).
% 45.62/29.75 tff(1693,plain,
% 45.62/29.75 ($false),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[1692, 1678])).
% 45.62/29.75 tff(1694,plain,((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (~(prop(tptp_fun_R_5(P!7)) = not1(false))) | (~(impl(not1(false), tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))) | (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)) | (~((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = not1(false)))) | (~(impl(false, tptp_fun_R_5(P!7)) = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 45.62/29.75 tff(1695,plain,
% 45.62/29.75 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[1694, 1373, 1290, 1328, 1327, 1326])).
% 45.62/29.75 tff(1696,plain,
% 45.62/29.75 (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = not1(false)),
% 45.62/29.75 inference(transitivity,[status(thm)],[414, 1695])).
% 45.62/29.75 tff(1697,plain,
% 45.62/29.75 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = phi(not1(false))),
% 45.62/29.75 inference(monotonicity,[status(thm)],[1696])).
% 45.62/29.75 tff(1698,plain,
% 45.62/29.75 (phi(not1(false)) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.62/29.75 inference(symmetry,[status(thm)],[1697])).
% 45.62/29.75 tff(1699,plain,
% 45.62/29.75 (not1(false) = f5(P!7, tptp_fun_R_5(P!7))),
% 45.62/29.75 inference(transitivity,[status(thm)],[603, 1698, 312])).
% 45.62/29.75 tff(1700,plain,
% 45.62/29.75 (impl(not1(false), tptp_fun_R_5(P!7)) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 45.62/29.75 inference(monotonicity,[status(thm)],[1699])).
% 45.62/29.75 tff(1701,plain,
% 45.62/29.75 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = impl(not1(false), tptp_fun_R_5(P!7))),
% 45.62/29.75 inference(symmetry,[status(thm)],[1700])).
% 45.62/29.75 tff(1702,assumption,(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))), introduced(assumption)).
% 45.62/29.75 tff(1703,plain,
% 45.62/29.75 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = tptp_fun_R_5(P!7)),
% 45.62/29.75 inference(transitivity,[status(thm)],[1333, 1331, 1702, 1701, 1328])).
% 45.62/29.75 tff(1704,plain,
% 45.62/29.75 (prop(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = prop(tptp_fun_R_5(P!7))),
% 45.62/29.75 inference(monotonicity,[status(thm)],[1703])).
% 45.62/29.75 tff(1705,plain,
% 45.62/29.75 (prop(tptp_fun_R_5(P!7)) = prop(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.62/29.75 inference(symmetry,[status(thm)],[1704])).
% 45.62/29.75 tff(1706,plain,
% 45.62/29.75 (not1(false) = false),
% 45.62/29.75 inference(transitivity,[status(thm)],[1291, 1705, 1356])).
% 45.62/29.75 tff(1707,plain,
% 45.62/29.75 ($false),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[60, 1706])).
% 45.62/29.75 tff(1708,plain,(bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(prop(tptp_fun_R_5(P!7)) = not1(false))) | (~(impl(not1(false), tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = not1(false)))) | (~(impl(false, tptp_fun_R_5(P!7)) = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 45.62/29.75 tff(1709,plain,
% 45.62/29.75 (bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[1708, 1350, 1328, 1290, 1327, 1326])).
% 45.62/29.75 tff(1710,plain,
% 45.62/29.75 (bool(lazy_impl(prop(false), impl(f5(P!7, false), false)))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[864, 1709, 1325, 1324])).
% 45.62/29.75 tff(1711,plain,
% 45.62/29.75 ((~(bool(lazy_impl(prop(false), impl(f5(P!7, false), false))) <=> ((lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false))))) | ((lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false)))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[866, 1710])).
% 45.62/29.75 tff(1712,plain,
% 45.62/29.75 ((lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[1711, 316])).
% 45.62/29.75 tff(1713,plain,
% 45.62/29.75 (~((~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~(phi(phi(apply(P!7, tptp_fun_X_3(P!7)))) = phi(apply(P!7, tptp_fun_X_3(P!7))))))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[952, 17, 949])).
% 45.62/29.75 tff(1714,plain,
% 45.62/29.75 (phi(phi(apply(P!7, tptp_fun_X_3(P!7)))) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[955, 1713])).
% 45.62/29.75 tff(1715,plain,
% 45.62/29.75 (~(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))) = not1(false))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[1127, 1092, 1714])).
% 45.62/29.75 tff(1716,plain,
% 45.62/29.75 (~bool(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[1132, 1715])).
% 45.62/29.75 tff(1717,plain,
% 45.62/29.75 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(phi(apply(P!7, tptp_fun_X_3(P!7)))) <=> ((phi(apply(P!7, tptp_fun_X_3(P!7))) = false) | (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))))),
% 45.62/29.75 inference(quant_inst,[status(thm)],[])).
% 45.62/29.75 tff(1718,plain,
% 45.62/29.75 (bool(phi(apply(P!7, tptp_fun_X_3(P!7)))) <=> ((phi(apply(P!7, tptp_fun_X_3(P!7))) = false) | (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[1717, 249])).
% 45.62/29.75 tff(1719,plain,
% 45.62/29.75 ((~(bool(phi(apply(P!7, tptp_fun_X_3(P!7)))) <=> ((phi(apply(P!7, tptp_fun_X_3(P!7))) = false) | (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))))) | bool(phi(apply(P!7, tptp_fun_X_3(P!7)))) | (~((phi(apply(P!7, tptp_fun_X_3(P!7))) = false) | (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))))),
% 45.62/29.75 inference(tautology,[status(thm)],[])).
% 45.62/29.75 tff(1720,plain,
% 45.62/29.75 (bool(phi(apply(P!7, tptp_fun_X_3(P!7)))) | (~((phi(apply(P!7, tptp_fun_X_3(P!7))) = false) | (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[1719, 1718])).
% 45.62/29.75 tff(1721,plain,
% 45.62/29.75 (~((phi(apply(P!7, tptp_fun_X_3(P!7))) = false) | (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[1720, 1716])).
% 45.62/29.75 tff(1722,plain,
% 45.62/29.75 (((phi(apply(P!7, tptp_fun_X_3(P!7))) = false) | (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)))),
% 45.62/29.75 inference(tautology,[status(thm)],[])).
% 45.62/29.75 tff(1723,plain,
% 45.62/29.75 (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[1722, 1721])).
% 45.62/29.75 tff(1724,plain,
% 45.62/29.75 (phi(f5(P!7, not1(false))) = impl(f5(P!7, not1(false)), not1(false))),
% 45.62/29.75 inference(symmetry,[status(thm)],[1307])).
% 45.62/29.75 tff(1725,plain,
% 45.62/29.75 (impl(f5(P!7, not1(false)), not1(false)) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))),
% 45.62/29.75 inference(transitivity,[status(thm)],[1307, 678, 644])).
% 45.62/29.75 tff(1726,plain,
% 45.62/29.75 (phi(impl(f5(P!7, not1(false)), not1(false))) = phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 45.62/29.75 inference(monotonicity,[status(thm)],[1725])).
% 45.62/29.75 tff(1727,plain,
% 45.62/29.75 (lazy_impl(prop(not1(false)), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))) = impl(f5(P!7, not1(false)), not1(false))),
% 45.62/29.75 inference(transitivity,[status(thm)],[713, 683, 682, 1726, 647, 1724])).
% 45.62/29.75 tff(1728,plain,
% 45.62/29.75 (bool(lazy_impl(prop(not1(false)), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)))) <=> bool(impl(f5(P!7, not1(false)), not1(false)))),
% 45.62/29.75 inference(monotonicity,[status(thm)],[1727])).
% 45.62/29.75 tff(1729,plain,
% 45.62/29.75 (bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) <=> bool(impl(f5(P!7, not1(false)), not1(false)))),
% 45.62/29.75 inference(transitivity,[status(thm)],[717, 1728])).
% 45.62/29.75 tff(1730,plain,
% 45.62/29.75 (bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[773, 1709, 730, 1324])).
% 45.62/29.75 tff(1731,plain,
% 45.62/29.75 (bool(impl(f5(P!7, not1(false)), not1(false)))),
% 45.62/29.75 inference(modus_ponens,[status(thm)],[1730, 1729])).
% 45.62/29.75 tff(1732,plain,
% 45.62/29.75 ((~(bool(impl(f5(P!7, not1(false)), not1(false))) <=> ((impl(f5(P!7, not1(false)), not1(false)) = false) | (impl(f5(P!7, not1(false)), not1(false)) = not1(false))))) | ((impl(f5(P!7, not1(false)), not1(false)) = false) | (impl(f5(P!7, not1(false)), not1(false)) = not1(false)))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[776, 1731])).
% 45.62/29.75 tff(1733,plain,
% 45.62/29.75 ((impl(f5(P!7, not1(false)), not1(false)) = false) | (impl(f5(P!7, not1(false)), not1(false)) = not1(false))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[1732, 710])).
% 45.62/29.75 tff(1734,plain,
% 45.62/29.75 (impl(f5(P!7, not1(false)), not1(false)) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))),
% 45.62/29.75 inference(transitivity,[status(thm)],[1307, 678, 644, 521])).
% 45.62/29.75 tff(1735,plain,
% 45.62/29.75 ((impl(f5(P!7, not1(false)), not1(false)) = false) <=> (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = false)),
% 45.62/29.75 inference(monotonicity,[status(thm)],[1734])).
% 45.62/29.75 tff(1736,plain,
% 45.62/29.75 ((impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = false) <=> (impl(f5(P!7, not1(false)), not1(false)) = false)),
% 45.62/29.75 inference(symmetry,[status(thm)],[1735])).
% 45.62/29.75 tff(1737,plain,
% 45.62/29.75 ((~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = false)) <=> (~(impl(f5(P!7, not1(false)), not1(false)) = false))),
% 45.62/29.75 inference(monotonicity,[status(thm)],[1736])).
% 45.62/29.75 tff(1738,plain,
% 45.62/29.75 (~(impl(f5(P!7, not1(false)), not1(false)) = false)),
% 45.62/29.75 inference(modus_ponens,[status(thm)],[1271, 1737])).
% 45.62/29.75 tff(1739,plain,
% 45.62/29.75 (impl(f5(P!7, not1(false)), not1(false)) = not1(false)),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[790, 1738, 1733])).
% 45.62/29.75 tff(1740,plain,
% 45.62/29.75 (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = impl(f5(P!7, not1(false)), impl(false, false))),
% 45.62/29.75 inference(transitivity,[status(thm)],[784, 524, 522, 645, 647, 1724, 810])).
% 45.62/29.75 tff(1741,plain,
% 45.62/29.75 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), false) = impl(impl(f5(P!7, not1(false)), impl(false, false)), false)),
% 45.62/29.75 inference(monotonicity,[status(thm)],[1740])).
% 45.62/29.75 tff(1742,plain,
% 45.62/29.75 (impl(impl(f5(P!7, not1(false)), impl(false, false)), false) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), false)),
% 45.62/29.75 inference(symmetry,[status(thm)],[1741])).
% 45.62/29.75 tff(1743,plain,
% 45.62/29.75 (impl(impl(f5(P!7, not1(false)), not1(false)), false2) = f4(P!7, tptp_fun_X_4(not1(false), P!7), false)),
% 45.62/29.75 inference(transitivity,[status(thm)],[817, 1742, 808])).
% 45.62/29.75 tff(1744,plain,
% 45.62/29.75 (forallprefers(impl(impl(f5(P!7, not1(false)), not1(false)), false2), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) <=> forallprefers(f4(P!7, tptp_fun_X_4(not1(false), P!7), false), f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 45.62/29.75 inference(monotonicity,[status(thm)],[1743, 805])).
% 45.62/29.75 tff(1745,plain,
% 45.62/29.75 (forallprefers(f4(P!7, tptp_fun_X_4(not1(false), P!7), false), f4(P!7, tptp_fun_X_4(false, P!7), false)) <=> forallprefers(impl(impl(f5(P!7, not1(false)), not1(false)), false2), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))),
% 45.62/29.75 inference(symmetry,[status(thm)],[1744])).
% 45.62/29.75 tff(1746,plain,
% 45.62/29.75 ((~forallprefers(f4(P!7, tptp_fun_X_4(not1(false), P!7), false), f4(P!7, tptp_fun_X_4(false, P!7), false))) <=> (~forallprefers(impl(impl(f5(P!7, not1(false)), not1(false)), false2), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)))),
% 45.62/29.75 inference(monotonicity,[status(thm)],[1745])).
% 45.62/29.75 tff(1747,plain,
% 45.62/29.75 (~forallprefers(impl(impl(f5(P!7, not1(false)), not1(false)), false2), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))),
% 45.62/29.75 inference(modus_ponens,[status(thm)],[827, 1746])).
% 45.62/29.75 tff(1748,plain,
% 45.62/29.75 (~((~(d(impl(impl(f5(P!7, not1(false)), not1(false)), false2)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~(bool(impl(impl(f5(P!7, not1(false)), not1(false)), false2)) | (~d(impl(impl(f5(P!7, not1(false)), not1(false)), false2))) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))) | (~(impl(impl(f5(P!7, not1(false)), not1(false)), false2) = false)))))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[829, 1747, 802])).
% 45.62/29.75 tff(1749,plain,
% 45.62/29.75 ((~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))) | (~(impl(impl(f5(P!7, not1(false)), not1(false)), false2) = false))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[831, 1748])).
% 45.62/29.75 tff(1750,plain,
% 45.62/29.75 (impl(f5(P!7, not1(false)), impl(false, false)) = not1(false)),
% 45.62/29.75 inference(transitivity,[status(thm)],[809, 1739])).
% 45.62/29.75 tff(1751,plain,
% 45.62/29.75 (impl(impl(f5(P!7, not1(false)), impl(false, false)), false) = impl(not1(false), false)),
% 45.62/29.75 inference(monotonicity,[status(thm)],[1750])).
% 45.62/29.75 tff(1752,plain,
% 45.62/29.75 (impl(impl(f5(P!7, not1(false)), not1(false)), false2) = false),
% 45.62/29.75 inference(transitivity,[status(thm)],[817, 1751, 114])).
% 45.62/29.75 tff(1753,plain,
% 45.62/29.75 (~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[836, 1752, 1749])).
% 45.62/29.75 tff(1754,plain,
% 45.62/29.75 (~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[1196, 1753, 348, 1739, 1723, 1307, 795])).
% 45.62/29.75 tff(1755,plain,
% 45.62/29.75 (lazy_impl(prop(false), impl(f5(P!7, false), false)) = false),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[875, 1754, 1712])).
% 45.62/29.75 tff(1756,plain,
% 45.62/29.75 (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[873, 1755])).
% 45.62/29.75 tff(1757,plain,
% 45.62/29.75 (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false)),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[1372, 1756, 1326, 1290])).
% 45.62/29.75 tff(1758,plain,
% 45.62/29.75 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[1694, 1757, 1290, 1328, 1327, 1326])).
% 45.62/29.75 tff(1759,assumption,(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = not1(false)), introduced(assumption)).
% 45.62/29.75 tff(1760,plain,
% 45.62/29.75 (d(false) <=> d(f7(P!6))),
% 45.62/29.75 inference(monotonicity,[status(thm)],[289])).
% 45.62/29.75 tff(1761,plain,
% 45.62/29.75 (d(false) <=> d(lazy_impl(prop(P!6), P!6))),
% 45.62/29.75 inference(transitivity,[status(thm)],[1760, 435])).
% 45.62/29.75 tff(1762,plain,
% 45.62/29.75 (d(lazy_impl(prop(P!6), P!6))),
% 45.62/29.75 inference(modus_ponens,[status(thm)],[5, 1761])).
% 45.62/29.75 tff(1763,plain,
% 45.62/29.75 (d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[462, 1762])).
% 45.62/29.75 tff(1764,plain,
% 45.62/29.75 (d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~(phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[464, 1763])).
% 45.62/29.75 tff(1765,plain,
% 45.62/29.75 (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[468, 17, 1764])).
% 45.62/29.75 tff(1766,plain,
% 45.62/29.75 (phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 45.62/29.75 inference(unit_resolution,[status(thm)],[470, 1765])).
% 45.62/29.75 tff(1767,plain,
% 45.62/29.75 (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.75 inference(symmetry,[status(thm)],[1766])).
% 45.62/29.75 tff(1768,plain,
% 45.62/29.75 (phi(tptp_fun_R_5(P!7)) = phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.75 inference(transitivity,[status(thm)],[1295, 1292, 1767])).
% 45.62/29.75 tff(1769,plain,
% 45.62/29.75 ((phi(tptp_fun_R_5(P!7)) = err) <=> (phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)),
% 45.62/29.75 inference(monotonicity,[status(thm)],[1768])).
% 45.62/29.75 tff(1770,plain,
% 45.62/29.75 ((phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err) <=> (phi(tptp_fun_R_5(P!7)) = err)),
% 45.62/29.75 inference(symmetry,[status(thm)],[1769])).
% 45.62/29.75 tff(1771,plain,
% 45.62/29.75 (err = impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))),
% 45.62/29.75 inference(transitivity,[status(thm)],[1093, 969])).
% 45.62/29.75 tff(1772,plain,
% 45.62/29.75 (phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = phi(tptp_fun_R_5(P!7))),
% 45.62/29.75 inference(transitivity,[status(thm)],[1766, 1302, 1294])).
% 45.62/29.75 tff(1773,plain,
% 45.62/29.75 ((phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err) <=> (phi(tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.75 inference(monotonicity,[status(thm)],[1772, 1771])).
% 45.62/29.75 tff(1774,plain,
% 45.62/29.75 ((phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err) <=> (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7)))),
% 45.62/29.76 inference(transitivity,[status(thm)],[1773, 1299])).
% 45.62/29.76 tff(1775,plain,
% 45.62/29.76 ((impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))) <=> (phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)),
% 45.62/29.76 inference(symmetry,[status(thm)],[1774])).
% 45.62/29.76 tff(1776,plain,
% 45.62/29.76 (phi(tptp_fun_R_5(P!7)) = not1(false)),
% 45.62/29.76 inference(transitivity,[status(thm)],[1295, 1292, 1759])).
% 45.62/29.76 tff(1777,plain,
% 45.62/29.76 ((impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))) <=> (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))),
% 45.62/29.76 inference(monotonicity,[status(thm)],[364, 1776])).
% 45.62/29.76 tff(1778,plain,
% 45.62/29.76 ((phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)) <=> (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7)))),
% 45.62/29.76 inference(symmetry,[status(thm)],[1777])).
% 45.62/29.76 tff(1779,plain,
% 45.62/29.76 ((phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)) <=> (phi(tptp_fun_R_5(P!7)) = err)),
% 45.62/29.76 inference(transitivity,[status(thm)],[1778, 1775, 1770])).
% 45.62/29.76 tff(1780,plain,
% 45.62/29.76 ((~(phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))) <=> (~(phi(tptp_fun_R_5(P!7)) = err))),
% 45.62/29.76 inference(monotonicity,[status(thm)],[1779])).
% 45.62/29.76 tff(1781,plain,
% 45.62/29.76 (d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.76 inference(unit_resolution,[status(thm)],[398, 364])).
% 45.62/29.76 tff(1782,plain,
% 45.62/29.76 (d(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.62/29.76 inference(modus_ponens,[status(thm)],[1781, 366])).
% 45.62/29.76 tff(1783,plain,
% 45.62/29.76 (d(phi(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(phi(apply(P!7, tptp_fun_X_3(P!7)))) = err))),
% 45.62/29.76 inference(unit_resolution,[status(thm)],[948, 1782])).
% 45.62/29.76 tff(1784,plain,
% 45.62/29.76 (~((~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~(phi(phi(apply(P!7, tptp_fun_X_3(P!7)))) = phi(apply(P!7, tptp_fun_X_3(P!7))))))),
% 45.62/29.76 inference(unit_resolution,[status(thm)],[952, 17, 1783])).
% 45.62/29.76 tff(1785,plain,
% 45.62/29.76 (phi(phi(apply(P!7, tptp_fun_X_3(P!7)))) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.62/29.76 inference(unit_resolution,[status(thm)],[955, 1784])).
% 45.62/29.76 tff(1786,plain,
% 45.62/29.76 (~(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))) = not1(false))),
% 45.62/29.76 inference(unit_resolution,[status(thm)],[1127, 1092, 1785])).
% 45.62/29.76 tff(1787,plain,
% 45.62/29.76 (~bool(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.62/29.76 inference(unit_resolution,[status(thm)],[1132, 1786])).
% 45.62/29.76 tff(1788,plain,
% 45.62/29.76 (~((phi(apply(P!7, tptp_fun_X_3(P!7))) = false) | (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)))),
% 45.62/29.76 inference(unit_resolution,[status(thm)],[1720, 1787])).
% 45.62/29.76 tff(1789,plain,
% 45.62/29.76 (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))),
% 45.62/29.76 inference(unit_resolution,[status(thm)],[1722, 1788])).
% 45.62/29.76 tff(1790,plain,
% 45.62/29.76 (~(phi(tptp_fun_R_5(P!7)) = err)),
% 45.62/29.76 inference(modus_ponens,[status(thm)],[1789, 1780])).
% 45.62/29.76 tff(1791,plain,
% 45.62/29.76 (d(tptp_fun_R_5(P!7)) | (~(phi(tptp_fun_R_5(P!7)) = err))),
% 45.62/29.76 inference(unit_resolution,[status(thm)],[1503, 1790])).
% 45.62/29.76 tff(1792,plain,
% 45.62/29.76 (~((~d(tptp_fun_R_5(P!7))) | (~(phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))))),
% 45.62/29.76 inference(unit_resolution,[status(thm)],[1508, 1791])).
% 45.62/29.76 tff(1793,plain,
% 45.62/29.76 (phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)),
% 45.62/29.76 inference(unit_resolution,[status(thm)],[1510, 1792])).
% 45.62/29.76 tff(1794,plain,
% 45.62/29.76 (tptp_fun_R_5(P!7) = phi(tptp_fun_R_5(P!7))),
% 45.62/29.76 inference(symmetry,[status(thm)],[1793])).
% 45.62/29.76 tff(1795,plain,
% 45.62/29.76 (tptp_fun_R_5(P!7) = not1(false)),
% 45.62/29.76 inference(transitivity,[status(thm)],[1794, 1295, 1292, 1759])).
% 45.62/29.76 tff(1796,plain,
% 45.62/29.76 (tptp_fun_X_4(tptp_fun_R_5(P!7), P!7) = tptp_fun_X_4(not1(false), P!7)),
% 45.62/29.76 inference(monotonicity,[status(thm)],[1795])).
% 45.62/29.76 tff(1797,plain,
% 45.62/29.76 (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))),
% 45.62/29.76 inference(monotonicity,[status(thm)],[1796, 1795])).
% 45.62/29.76 tff(1798,plain,
% 45.62/29.76 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))),
% 45.62/29.76 inference(transitivity,[status(thm)],[415, 1797, 521])).
% 45.62/29.76 tff(1799,plain,
% 45.62/29.76 ((impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)) <=> (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = not1(false))),
% 45.62/29.76 inference(monotonicity,[status(thm)],[1798])).
% 45.62/29.76 tff(1800,plain,
% 45.62/29.76 ((impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = not1(false)) <=> (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))),
% 45.62/29.76 inference(symmetry,[status(thm)],[1799])).
% 45.62/29.76 tff(1801,plain,
% 45.62/29.76 ((~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = not1(false))) <=> (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)))),
% 45.62/29.76 inference(monotonicity,[status(thm)],[1800])).
% 45.62/29.76 tff(1802,plain,
% 45.62/29.76 (impl(f5(P!7, not1(false)), not1(false)) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))),
% 45.62/29.76 inference(transitivity,[status(thm)],[957, 678, 644])).
% 45.62/29.76 tff(1803,plain,
% 45.62/29.76 (phi(impl(f5(P!7, not1(false)), not1(false))) = phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 45.62/29.76 inference(monotonicity,[status(thm)],[1802])).
% 45.62/29.76 tff(1804,plain,
% 45.62/29.76 (f6(P!7, tptp_fun_R_5(P!7)) = f6(P!7, not1(false))),
% 45.62/29.76 inference(monotonicity,[status(thm)],[1795])).
% 45.62/29.76 tff(1805,plain,
% 45.62/29.76 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))),
% 45.62/29.76 inference(transitivity,[status(thm)],[326, 1804, 743, 683, 682, 1803, 644, 521])).
% 45.62/29.76 tff(1806,plain,
% 45.62/29.76 ((lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false)) <=> (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = not1(false))),
% 45.62/29.76 inference(monotonicity,[status(thm)],[1805])).
% 45.62/29.76 tff(1807,plain,
% 45.62/29.76 ((~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))) <=> (~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = not1(false)))),
% 45.62/29.76 inference(monotonicity,[status(thm)],[1806])).
% 45.62/29.76 tff(1808,plain,
% 45.62/29.76 (~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = not1(false))),
% 45.62/29.76 inference(modus_ponens,[status(thm)],[1370, 1807])).
% 45.62/29.76 tff(1809,plain,
% 45.62/29.76 (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))),
% 45.62/29.76 inference(modus_ponens,[status(thm)],[1808, 1801])).
% 45.62/29.76 tff(1810,assumption,(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)), introduced(assumption)).
% 45.62/29.76 tff(1811,plain,
% 45.62/29.76 ($false),
% 45.62/29.76 inference(unit_resolution,[status(thm)],[1810, 1809])).
% 45.62/29.76 tff(1812,plain,((~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = not1(false))) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))) | (~(prop(tptp_fun_R_5(P!7)) = not1(false))) | (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false)) | (~(impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false))))) | (~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err))), inference(lemma,lemma(discharge,[]))).
% 45.62/29.76 tff(1813,plain,
% 45.62/29.76 (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = not1(false))),
% 45.62/29.76 inference(unit_resolution,[status(thm)],[1812, 1758, 1290, 1756, 1307, 363, 1092])).
% 45.62/29.76 tff(1814,plain,
% 45.62/29.76 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) <=> ((lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = not1(false))))),
% 45.62/29.76 inference(quant_inst,[status(thm)],[])).
% 45.62/29.76 tff(1815,plain,
% 45.62/29.76 (bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) <=> ((lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = not1(false)))),
% 45.62/29.76 inference(unit_resolution,[status(thm)],[1814, 249])).
% 45.62/29.76 tff(1816,plain,
% 45.62/29.76 (bool(lazy_impl(prop(P!6), P!6)) <=> bool(f7(P!6))),
% 45.62/29.76 inference(monotonicity,[status(thm)],[198])).
% 45.62/29.76 tff(1817,plain,
% 45.62/29.76 (bool(f7(P!6)) <=> bool(lazy_impl(prop(P!6), P!6))),
% 45.62/29.76 inference(symmetry,[status(thm)],[1816])).
% 45.62/29.76 tff(1818,plain,
% 45.62/29.76 (bool(f7(P!6)) <=> bool(false)),
% 45.62/29.76 inference(monotonicity,[status(thm)],[436])).
% 45.62/29.76 tff(1819,plain,
% 45.62/29.76 (bool(false) <=> bool(f7(P!6))),
% 45.62/29.76 inference(symmetry,[status(thm)],[1818])).
% 45.62/29.76 tff(1820,plain,
% 45.62/29.76 (bool(false) <=> bool(lazy_impl(prop(P!6), P!6))),
% 45.62/29.76 inference(transitivity,[status(thm)],[1819, 1817])).
% 45.62/29.76 tff(1821,plain,
% 45.62/29.76 (bool(lazy_impl(prop(P!6), P!6))),
% 45.62/29.76 inference(modus_ponens,[status(thm)],[76, 1820])).
% 45.62/29.76 tff(1822,plain,
% 45.62/29.76 (((~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~((~(lazy_impl(prop(P!6), P!6) = not1(false))) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false))))) | ((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 45.62/29.76 inference(tautology,[status(thm)],[])).
% 45.62/29.76 tff(1823,plain,
% 45.62/29.76 ((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.62/29.76 inference(unit_resolution,[status(thm)],[1822, 458])).
% 45.62/29.76 tff(1824,plain,
% 45.62/29.76 ((~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.62/29.76 inference(tautology,[status(thm)],[])).
% 45.62/29.76 tff(1825,plain,
% 45.62/29.76 ((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.62/29.76 inference(unit_resolution,[status(thm)],[1824, 1823])).
% 45.62/29.76 tff(1826,plain,
% 45.62/29.76 (bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.76 inference(unit_resolution,[status(thm)],[1825, 463, 1821, 440])).
% 45.62/29.76 tff(1827,plain,
% 45.62/29.76 ((~(bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) <=> ((lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = not1(false))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | ((lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = not1(false)))),
% 45.62/29.76 inference(tautology,[status(thm)],[])).
% 45.62/29.76 tff(1828,plain,
% 45.62/29.76 ((~(bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) <=> ((lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = not1(false))))) | ((lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = not1(false)))),
% 45.62/29.76 inference(unit_resolution,[status(thm)],[1827, 1826])).
% 45.62/29.76 tff(1829,plain,
% 45.62/29.76 ((lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = not1(false))),
% 45.62/29.76 inference(unit_resolution,[status(thm)],[1828, 1815])).
% 45.62/29.76 tff(1830,plain,
% 45.62/29.76 ((~((lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = not1(false)))) | (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = not1(false))),
% 45.62/29.76 inference(tautology,[status(thm)],[])).
% 45.62/29.76 tff(1831,plain,
% 45.62/29.76 ((lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = not1(false))),
% 45.62/29.76 inference(unit_resolution,[status(thm)],[1830, 1829])).
% 45.62/29.76 tff(1832,plain,
% 45.62/29.76 (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false),
% 45.62/29.76 inference(unit_resolution,[status(thm)],[1831, 1813])).
% 45.62/29.76 tff(1833,plain,
% 45.62/29.76 (phi(tptp_fun_R_5(P!7)) = false),
% 45.62/29.76 inference(transitivity,[status(thm)],[1295, 1292, 1832])).
% 45.62/29.76 tff(1834,plain,
% 45.62/29.76 ((impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))) <=> (phi(apply(P!7, tptp_fun_X_3(P!7))) = false)),
% 45.62/29.76 inference(monotonicity,[status(thm)],[363, 1833])).
% 45.62/29.76 tff(1835,plain,
% 45.62/29.76 ((phi(apply(P!7, tptp_fun_X_3(P!7))) = false) <=> (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7)))),
% 45.62/29.76 inference(symmetry,[status(thm)],[1834])).
% 45.62/29.76 tff(1836,plain,
% 45.62/29.76 ((phi(apply(P!7, tptp_fun_X_3(P!7))) = false) <=> (phi(tptp_fun_R_5(P!7)) = err)),
% 45.62/29.76 inference(transitivity,[status(thm)],[1835, 1306, 1298])).
% 45.62/29.76 tff(1837,plain,
% 45.62/29.76 ((~(phi(apply(P!7, tptp_fun_X_3(P!7))) = false)) <=> (~(phi(tptp_fun_R_5(P!7)) = err))),
% 45.62/29.76 inference(monotonicity,[status(thm)],[1836])).
% 45.62/29.76 tff(1838,plain,
% 45.62/29.76 (((phi(apply(P!7, tptp_fun_X_3(P!7))) = false) | (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = false))),
% 45.62/29.76 inference(tautology,[status(thm)],[])).
% 45.62/29.76 tff(1839,plain,
% 45.62/29.76 (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = false)),
% 45.62/29.76 inference(unit_resolution,[status(thm)],[1838, 1721])).
% 45.62/29.76 tff(1840,plain,
% 45.62/29.76 (~(phi(tptp_fun_R_5(P!7)) = err)),
% 45.62/29.76 inference(modus_ponens,[status(thm)],[1839, 1837])).
% 45.62/29.76 tff(1841,plain,
% 45.62/29.76 (d(tptp_fun_R_5(P!7)) | (~(phi(tptp_fun_R_5(P!7)) = err))),
% 45.62/29.76 inference(unit_resolution,[status(thm)],[1503, 1840])).
% 45.62/29.76 tff(1842,plain,
% 45.62/29.76 ((false = tptp_fun_R_5(P!7)) <=> (tptp_fun_R_5(P!7) = false)),
% 45.62/29.76 inference(commutativity,[status(thm)],[])).
% 45.62/29.76 tff(1843,plain,
% 45.62/29.76 ((phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)) <=> (false = tptp_fun_R_5(P!7))),
% 45.62/29.76 inference(monotonicity,[status(thm)],[1833])).
% 45.62/29.76 tff(1844,plain,
% 45.62/29.76 ((phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)) <=> (tptp_fun_R_5(P!7) = false)),
% 45.62/29.76 inference(transitivity,[status(thm)],[1843, 1842])).
% 45.62/29.76 tff(1845,plain,
% 45.62/29.76 ((tptp_fun_R_5(P!7) = false) <=> (phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))),
% 45.62/29.76 inference(symmetry,[status(thm)],[1844])).
% 45.62/29.76 tff(1846,plain,
% 45.62/29.76 ((~(tptp_fun_R_5(P!7) = false)) <=> (~(phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)))),
% 45.62/29.76 inference(monotonicity,[status(thm)],[1845])).
% 45.62/29.76 tff(1847,plain,
% 45.62/29.76 (impl(f5(P!7, not1(false)), impl(false, not1(false))) = impl(f5(P!7, not1(false)), not1(false))),
% 45.62/29.76 inference(monotonicity,[status(thm)],[421])).
% 45.62/29.76 tff(1848,plain,
% 45.62/29.76 (impl(f5(P!7, not1(false)), impl(false, not1(false))) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false)))),
% 45.62/29.76 inference(transitivity,[status(thm)],[1847, 1307, 678, 644, 521, 651])).
% 45.62/29.76 tff(1849,plain,
% 45.62/29.76 (impl(impl(f5(P!7, not1(false)), impl(false, not1(false))), not1(false)) = impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))),
% 45.62/29.76 inference(monotonicity,[status(thm)],[1848])).
% 45.62/29.76 tff(1850,plain,
% 45.62/29.76 (impl(f5(P!7, not1(false)), not1(false)) = impl(f5(P!7, not1(false)), impl(false, not1(false)))),
% 45.62/29.76 inference(symmetry,[status(thm)],[1847])).
% 45.62/29.76 tff(1851,plain,
% 45.62/29.76 (impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7))) = impl(impl(f5(P!7, not1(false)), impl(false, not1(false))), not1(false))),
% 45.62/29.76 inference(monotonicity,[status(thm)],[1850, 1326])).
% 45.62/29.76 tff(1852,plain,
% 45.62/29.76 (impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7))) = not1(false)),
% 45.62/29.76 inference(transitivity,[status(thm)],[1851, 1849, 712, 1739])).
% 45.62/29.76 tff(1853,plain,
% 45.62/29.76 (impl(impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = impl(not1(false), tptp_fun_R_5(P!7))),
% 45.62/29.76 inference(monotonicity,[status(thm)],[1852])).
% 45.62/29.76 tff(1854,plain,
% 45.62/29.76 (impl(impl(f5(P!7, not1(false)), impl(false, not1(false))), not1(false)) = impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7)))),
% 45.62/29.76 inference(symmetry,[status(thm)],[1851])).
% 45.62/29.76 tff(1855,plain,
% 45.62/29.76 (impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)) = impl(impl(f5(P!7, not1(false)), impl(false, not1(false))), not1(false))),
% 45.62/29.76 inference(symmetry,[status(thm)],[1849])).
% 45.62/29.76 tff(1856,plain,
% 45.62/29.76 (impl(f5(P!7, not1(false)), not1(false)) = impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))),
% 45.62/29.76 inference(symmetry,[status(thm)],[712])).
% 45.62/29.76 tff(1857,plain,
% 45.62/29.76 (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7)))),
% 45.62/29.76 inference(transitivity,[status(thm)],[784, 524, 522, 645, 647, 1724, 1856, 1855, 1854])).
% 45.62/29.76 tff(1858,plain,
% 45.62/29.76 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)) = impl(impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))),
% 45.62/29.76 inference(monotonicity,[status(thm)],[1857])).
% 45.62/29.76 tff(1859,plain,
% 45.62/29.76 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)),
% 45.62/29.76 inference(transitivity,[status(thm)],[1858, 1853, 1328])).
% 45.62/29.76 tff(1860,plain,
% 45.62/29.76 ((impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)) = false) <=> (tptp_fun_R_5(P!7) = false)),
% 45.62/29.76 inference(monotonicity,[status(thm)],[1859])).
% 45.62/29.76 tff(1861,plain,
% 45.62/29.76 ((~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)) = false)) <=> (~(tptp_fun_R_5(P!7) = false))),
% 45.62/29.76 inference(monotonicity,[status(thm)],[1860])).
% 45.62/29.76 tff(1862,plain,
% 45.62/29.76 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~(d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))) | (~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)) = false))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~(d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))) | (~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)) = false)))))))),
% 45.62/29.76 inference(rewrite,[status(thm)],[])).
% 45.62/29.76 tff(1863,plain,
% 45.62/29.76 ((forallprefers(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~(d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))))))) <=> (forallprefers(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~(d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))) | (~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)) = false))))))),
% 45.62/29.76 inference(rewrite,[status(thm)],[])).
% 45.62/29.76 tff(1864,plain,
% 45.62/29.76 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~(d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~(d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))) | (~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)) = false)))))))),
% 45.62/29.76 inference(monotonicity,[status(thm)],[1863])).
% 45.62/29.76 tff(1865,plain,
% 45.62/29.76 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~(d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~(d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))) | (~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)) = false)))))))),
% 45.62/29.76 inference(transitivity,[status(thm)],[1864, 1862])).
% 45.62/29.76 tff(1866,plain,
% 45.62/29.76 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~(d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)))))))),
% 45.62/29.76 inference(quant_inst,[status(thm)],[])).
% 45.62/29.76 tff(1867,plain,
% 45.62/29.76 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~(d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))) | (~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)) = false))))))),
% 45.62/29.76 inference(modus_ponens,[status(thm)],[1866, 1865])).
% 45.62/29.76 tff(1868,plain,
% 45.62/29.76 (forallprefers(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~(d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))) | (~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)) = false)))))),
% 45.62/29.76 inference(unit_resolution,[status(thm)],[1867, 159])).
% 45.62/29.76 tff(1869,plain,
% 45.62/29.76 ((~![P: $i, X: $i, R: $i] : (f4(P, X, R) = impl(apply(P, X), R))) | (f4(P!7, tptp_fun_X_4(not1(false), P!7), tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.77 inference(quant_inst,[status(thm)],[])).
% 45.62/29.77 tff(1870,plain,
% 45.62/29.77 (f4(P!7, tptp_fun_X_4(not1(false), P!7), tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))),
% 45.62/29.77 inference(unit_resolution,[status(thm)],[1869, 412])).
% 45.62/29.77 tff(1871,plain,
% 45.62/29.77 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)) = f4(P!7, tptp_fun_X_4(not1(false), P!7), tptp_fun_R_5(P!7))),
% 45.62/29.77 inference(symmetry,[status(thm)],[1870])).
% 45.62/29.77 tff(1872,plain,
% 45.62/29.77 (forallprefers(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> forallprefers(f4(P!7, tptp_fun_X_4(not1(false), P!7), tptp_fun_R_5(P!7)), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.62/29.77 inference(monotonicity,[status(thm)],[1871, 415])).
% 45.62/29.77 tff(1873,plain,
% 45.62/29.77 (forallprefers(f4(P!7, tptp_fun_X_4(not1(false), P!7), tptp_fun_R_5(P!7)), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) <=> forallprefers(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.77 inference(symmetry,[status(thm)],[1872])).
% 45.62/29.77 tff(1874,plain,
% 45.62/29.77 ((~forallprefers(f4(P!7, tptp_fun_X_4(not1(false), P!7), tptp_fun_R_5(P!7)), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) <=> (~forallprefers(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))))),
% 45.62/29.77 inference(monotonicity,[status(thm)],[1873])).
% 45.62/29.77 tff(1875,plain,
% 45.62/29.77 (((~(f5(P!7, tptp_fun_R_5(P!7)) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))) | (~![X1: $i] : (~forallprefers(f4(P!7, X1, tptp_fun_R_5(P!7)), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))))) | ![X1: $i] : (~forallprefers(f4(P!7, X1, tptp_fun_R_5(P!7)), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 45.62/29.77 inference(tautology,[status(thm)],[])).
% 45.62/29.77 tff(1876,plain,
% 45.62/29.77 (![X1: $i] : (~forallprefers(f4(P!7, X1, tptp_fun_R_5(P!7)), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 45.62/29.77 inference(unit_resolution,[status(thm)],[1875, 309])).
% 45.62/29.77 tff(1877,plain,
% 45.62/29.77 ((~![X1: $i] : (~forallprefers(f4(P!7, X1, tptp_fun_R_5(P!7)), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))) | (~forallprefers(f4(P!7, tptp_fun_X_4(not1(false), P!7), tptp_fun_R_5(P!7)), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 45.62/29.77 inference(quant_inst,[status(thm)],[])).
% 45.62/29.77 tff(1878,plain,
% 45.62/29.77 (~forallprefers(f4(P!7, tptp_fun_X_4(not1(false), P!7), tptp_fun_R_5(P!7)), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.62/29.77 inference(unit_resolution,[status(thm)],[1877, 1876])).
% 45.62/29.77 tff(1879,plain,
% 45.62/29.77 (~forallprefers(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.77 inference(modus_ponens,[status(thm)],[1878, 1874])).
% 45.62/29.77 tff(1880,plain,
% 45.62/29.77 ((~(forallprefers(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~(d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))) | (~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)) = false))))))) | forallprefers(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) | (~((~(d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))) | (~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)) = false))))))),
% 45.62/29.77 inference(tautology,[status(thm)],[])).
% 45.62/29.77 tff(1881,plain,
% 45.62/29.77 (~((~(d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))) | (~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)) = false)))))),
% 45.62/29.77 inference(unit_resolution,[status(thm)],[1880, 1879, 1868])).
% 45.62/29.77 tff(1882,plain,
% 45.62/29.77 (((~(d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))) | (~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)) = false))))) | ((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))) | (~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)) = false)))),
% 45.62/29.77 inference(tautology,[status(thm)],[])).
% 45.62/29.77 tff(1883,plain,
% 45.62/29.77 ((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))) | (~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)) = false))),
% 45.62/29.77 inference(unit_resolution,[status(thm)],[1882, 1881])).
% 45.62/29.77 tff(1884,plain,
% 45.62/29.77 ((~((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))) | (~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)) = false)))) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))) | (~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)) = false))),
% 45.62/29.77 inference(tautology,[status(thm)],[])).
% 45.62/29.77 tff(1885,plain,
% 45.62/29.77 (~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)) = false)),
% 45.62/29.77 inference(unit_resolution,[status(thm)],[1884, 1758, 1883])).
% 45.62/29.77 tff(1886,plain,
% 45.62/29.77 (~(tptp_fun_R_5(P!7) = false)),
% 45.62/29.77 inference(modus_ponens,[status(thm)],[1885, 1861])).
% 45.62/29.77 tff(1887,plain,
% 45.62/29.77 (~(phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))),
% 45.62/29.77 inference(modus_ponens,[status(thm)],[1886, 1846])).
% 45.62/29.77 tff(1888,plain,
% 45.62/29.77 ((~d(tptp_fun_R_5(P!7))) | (~(phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)))),
% 45.62/29.77 inference(unit_resolution,[status(thm)],[1510, 1887])).
% 45.62/29.77 tff(1889,plain,
% 45.62/29.77 ($false),
% 45.62/29.77 inference(unit_resolution,[status(thm)],[1508, 1888, 1841])).
% 45.62/29.77 tff(1890,plain,((~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err)) | (~(prop(tptp_fun_R_5(P!7)) = not1(false))) | (~(impl(not1(false), tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))) | (~(impl(false, tptp_fun_R_5(P!7)) = not1(false))) | (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = apply(P!7, tptp_fun_X_4(not1(false), P!7)))) | (~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))))) | (~((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = not1(false)))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (phi(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))) = err) | (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = false) | (~d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))))), inference(lemma,lemma(discharge,[]))).
% 45.62/29.77 tff(1891,plain,
% 45.62/29.77 (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err)),
% 45.62/29.77 inference(unit_resolution,[status(thm)],[1890, 348, 1288, 1287, 494, 523, 1282, 1277, 795, 1271, 730])).
% 45.62/29.77 tff(1892,plain,
% 45.62/29.77 (d(apply(P!7, tptp_fun_X_3(P!7))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err))),
% 45.62/29.77 inference(unit_resolution,[status(thm)],[385, 1891])).
% 45.62/29.77 tff(1893,plain,
% 45.62/29.77 (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))))),
% 45.62/29.77 inference(unit_resolution,[status(thm)],[383, 1892])).
% 45.62/29.77 tff(1894,plain,
% 45.62/29.77 (phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))),
% 45.62/29.77 inference(unit_resolution,[status(thm)],[369, 1893])).
% 45.62/29.77 tff(1895,plain,
% 45.62/29.77 (apply(P!7, tptp_fun_X_3(P!7)) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.62/29.77 inference(symmetry,[status(thm)],[1894])).
% 45.62/29.77 tff(1896,plain,
% 45.62/29.77 (bool(apply(P!7, tptp_fun_X_3(P!7))) <=> bool(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.62/29.77 inference(monotonicity,[status(thm)],[1895])).
% 45.62/29.77 tff(1897,plain,
% 45.62/29.77 (bool(apply(P!7, tptp_fun_X_3(P!7))) <=> bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.77 inference(transitivity,[status(thm)],[1896, 401])).
% 45.62/29.77 tff(1898,plain,
% 45.62/29.77 ((~bool(apply(P!7, tptp_fun_X_3(P!7)))) <=> (~bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))))),
% 45.62/29.77 inference(monotonicity,[status(thm)],[1897])).
% 45.62/29.77 tff(1899,plain,
% 45.62/29.77 (~bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.77 inference(modus_ponens,[status(thm)],[348, 1898])).
% 45.62/29.77 tff(1900,plain,
% 45.62/29.77 (d(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.62/29.77 inference(unit_resolution,[status(thm)],[374, 1893])).
% 45.62/29.77 tff(1901,plain,
% 45.62/29.77 (d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 45.62/29.77 inference(unit_resolution,[status(thm)],[1683, 1900])).
% 45.62/29.77 tff(1902,plain,
% 45.62/29.77 ((d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))),
% 45.62/29.77 inference(tautology,[status(thm)],[])).
% 45.62/29.77 tff(1903,plain,
% 45.62/29.77 (d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err))),
% 45.62/29.77 inference(unit_resolution,[status(thm)],[1902, 1901])).
% 45.62/29.77 tff(1904,plain,
% 45.62/29.77 (~((~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))),
% 45.62/29.77 inference(unit_resolution,[status(thm)],[1436, 17, 1903])).
% 45.62/29.77 tff(1905,plain,
% 45.62/29.77 (phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))),
% 45.62/29.77 inference(unit_resolution,[status(thm)],[1439, 1904])).
% 45.62/29.77 tff(1906,plain,
% 45.62/29.77 (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = apply(P!7, tptp_fun_X_3(P!7))),
% 45.62/29.77 inference(unit_resolution,[status(thm)],[1598, 1562, 348])).
% 45.62/29.77 tff(1907,assumption,(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))), introduced(assumption)).
% 45.62/29.77 tff(1908,plain,
% 45.62/29.77 (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))),
% 45.62/29.77 inference(transitivity,[status(thm)],[414, 1569, 1907])).
% 45.62/29.77 tff(1909,plain,
% 45.62/29.77 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 45.62/29.77 inference(monotonicity,[status(thm)],[1908])).
% 45.62/29.77 tff(1910,plain,
% 45.62/29.77 (f5(P!7, tptp_fun_R_5(P!7)) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.62/29.77 inference(transitivity,[status(thm)],[311, 1909, 1907, 1906, 1041])).
% 45.62/29.77 tff(1911,plain,
% 45.62/29.77 (bool(f5(P!7, tptp_fun_R_5(P!7))) <=> bool(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.62/29.77 inference(monotonicity,[status(thm)],[1910])).
% 45.62/29.77 tff(1912,plain,
% 45.62/29.77 (bool(phi(apply(P!7, tptp_fun_X_3(P!7)))) <=> bool(f5(P!7, tptp_fun_R_5(P!7)))),
% 45.62/29.77 inference(symmetry,[status(thm)],[1911])).
% 45.62/29.77 tff(1913,plain,
% 45.62/29.77 ((~bool(phi(apply(P!7, tptp_fun_X_3(P!7))))) <=> (~bool(f5(P!7, tptp_fun_R_5(P!7))))),
% 45.62/29.77 inference(monotonicity,[status(thm)],[1912])).
% 45.62/29.77 tff(1914,plain,
% 45.62/29.77 ((~bool(apply(P!7, tptp_fun_X_3(P!7)))) <=> (~bool(phi(apply(P!7, tptp_fun_X_3(P!7)))))),
% 45.62/29.77 inference(monotonicity,[status(thm)],[1042])).
% 45.62/29.77 tff(1915,plain,
% 45.62/29.77 (~bool(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.62/29.77 inference(modus_ponens,[status(thm)],[348, 1914])).
% 45.62/29.77 tff(1916,plain,
% 45.62/29.77 (~bool(f5(P!7, tptp_fun_R_5(P!7)))),
% 45.62/29.77 inference(modus_ponens,[status(thm)],[1915, 1913])).
% 45.62/29.77 tff(1917,plain,
% 45.62/29.77 (~(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(f5(P!7, tptp_fun_R_5(P!7))))),
% 45.62/29.77 inference(unit_resolution,[status(thm)],[1604, 1562, 1290, 348])).
% 45.62/29.77 tff(1918,plain,
% 45.62/29.77 (bool(f5(P!7, tptp_fun_R_5(P!7)))),
% 45.62/29.77 inference(unit_resolution,[status(thm)],[1486, 1917])).
% 45.62/29.77 tff(1919,plain,
% 45.62/29.77 ($false),
% 45.62/29.77 inference(unit_resolution,[status(thm)],[1918, 1916])).
% 45.62/29.77 tff(1920,plain,(bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))) | (~(prop(tptp_fun_R_5(P!7)) = not1(false))) | bool(apply(P!7, tptp_fun_X_3(P!7)))), inference(lemma,lemma(discharge,[]))).
% 45.62/29.77 tff(1921,plain,
% 45.62/29.77 (bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 45.62/29.77 inference(unit_resolution,[status(thm)],[1920, 1905, 1894, 1277, 348])).
% 45.62/29.77 tff(1922,plain,
% 45.62/29.77 ((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false))),
% 45.62/29.77 inference(unit_resolution,[status(thm)],[1410, 1921])).
% 45.62/29.77 tff(1923,plain,
% 45.62/29.77 (d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.62/29.77 inference(monotonicity,[status(thm)],[415])).
% 45.62/29.77 tff(1924,plain,
% 45.62/29.77 ((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) <=> (~d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 45.62/29.77 inference(monotonicity,[status(thm)],[1923])).
% 45.62/29.77 tff(1925,assumption,(d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))), introduced(assumption)).
% 45.62/29.77 tff(1926,assumption,(~bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))), introduced(assumption)).
% 45.62/29.77 tff(1927,plain,
% 45.62/29.77 (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false)),
% 45.62/29.77 inference(unit_resolution,[status(thm)],[1381, 1374, 1287])).
% 45.62/29.77 tff(1928,plain,
% 45.62/29.77 (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false)),
% 45.62/29.77 inference(unit_resolution,[status(thm)],[1383, 1927, 1376])).
% 45.62/29.77 tff(1929,plain,
% 45.62/29.77 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = impl(not1(false), tptp_fun_R_5(P!7))),
% 45.62/29.77 inference(monotonicity,[status(thm)],[1928])).
% 45.62/29.77 tff(1930,plain,
% 45.62/29.77 (impl(not1(false), tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))),
% 45.62/29.77 inference(symmetry,[status(thm)],[1929])).
% 45.62/29.77 tff(1931,plain,
% 45.62/29.77 (tptp_fun_R_5(P!7) = impl(not1(false), tptp_fun_R_5(P!7))),
% 45.62/29.77 inference(symmetry,[status(thm)],[1288])).
% 45.62/29.77 tff(1932,plain,
% 45.62/29.77 (tptp_fun_R_5(P!7) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))),
% 45.62/29.77 inference(transitivity,[status(thm)],[1931, 1930, 415])).
% 45.62/29.77 tff(1933,plain,
% 45.62/29.77 (bool(tptp_fun_R_5(P!7)) <=> bool(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.62/29.77 inference(monotonicity,[status(thm)],[1932])).
% 45.62/29.77 tff(1934,plain,
% 45.62/29.77 (bool(tptp_fun_R_5(P!7)) <=> bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.77 inference(transitivity,[status(thm)],[1933, 417])).
% 45.62/29.77 tff(1935,plain,
% 45.62/29.77 (bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.77 inference(modus_ponens,[status(thm)],[1272, 1934])).
% 45.62/29.77 tff(1936,plain,
% 45.62/29.77 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))))))))),
% 45.62/29.77 inference(rewrite,[status(thm)],[])).
% 45.62/29.77 tff(1937,plain,
% 45.62/29.77 ((forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))))) | (~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))))))) <=> (forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))))))))),
% 45.62/29.77 inference(rewrite,[status(thm)],[])).
% 45.62/29.77 tff(1938,plain,
% 45.62/29.77 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))))) | (~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))))))))),
% 45.62/29.77 inference(monotonicity,[status(thm)],[1937])).
% 45.62/29.77 tff(1939,plain,
% 45.62/29.77 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))))) | (~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))))))))),
% 45.62/29.77 inference(transitivity,[status(thm)],[1938, 1936])).
% 45.62/29.77 tff(1940,plain,
% 45.62/29.77 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))))) | (~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)))))))),
% 45.62/29.77 inference(quant_inst,[status(thm)],[])).
% 45.62/29.77 tff(1941,plain,
% 45.62/29.77 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))))))))),
% 45.62/29.77 inference(modus_ponens,[status(thm)],[1940, 1939])).
% 45.62/29.77 tff(1942,plain,
% 45.62/29.77 (forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))))))),
% 45.62/29.77 inference(unit_resolution,[status(thm)],[1941, 159])).
% 45.62/29.77 tff(1943,plain,
% 45.62/29.77 ((~![P: $i, X: $i, R: $i] : (f4(P, X, R) = impl(apply(P, X), R))) | (f4(P!7, tptp_fun_X_3(P!7), tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.77 inference(quant_inst,[status(thm)],[])).
% 45.62/29.77 tff(1944,plain,
% 45.62/29.77 (f4(P!7, tptp_fun_X_3(P!7), tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))),
% 45.62/29.77 inference(unit_resolution,[status(thm)],[1943, 412])).
% 45.62/29.77 tff(1945,plain,
% 45.62/29.77 (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = f4(P!7, tptp_fun_X_3(P!7), tptp_fun_R_5(P!7))),
% 45.62/29.77 inference(symmetry,[status(thm)],[1944])).
% 45.62/29.77 tff(1946,plain,
% 45.62/29.77 (forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> forallprefers(f4(P!7, tptp_fun_X_3(P!7), tptp_fun_R_5(P!7)), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.62/29.77 inference(monotonicity,[status(thm)],[1945, 415])).
% 45.62/29.77 tff(1947,plain,
% 45.62/29.77 (forallprefers(f4(P!7, tptp_fun_X_3(P!7), tptp_fun_R_5(P!7)), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) <=> forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.77 inference(symmetry,[status(thm)],[1946])).
% 45.62/29.77 tff(1948,plain,
% 45.62/29.77 ((~forallprefers(f4(P!7, tptp_fun_X_3(P!7), tptp_fun_R_5(P!7)), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) <=> (~forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))))),
% 45.62/29.77 inference(monotonicity,[status(thm)],[1947])).
% 45.62/29.77 tff(1949,plain,
% 45.62/29.77 ((~![X1: $i] : (~forallprefers(f4(P!7, X1, tptp_fun_R_5(P!7)), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))) | (~forallprefers(f4(P!7, tptp_fun_X_3(P!7), tptp_fun_R_5(P!7)), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 45.62/29.77 inference(quant_inst,[status(thm)],[])).
% 45.62/29.78 tff(1950,plain,
% 45.62/29.78 (~forallprefers(f4(P!7, tptp_fun_X_3(P!7), tptp_fun_R_5(P!7)), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1949, 1876])).
% 45.62/29.78 tff(1951,plain,
% 45.62/29.78 (~forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.78 inference(modus_ponens,[status(thm)],[1950, 1948])).
% 45.62/29.78 tff(1952,plain,
% 45.62/29.78 ((~(forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))))))))) | forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) | (~((~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))))))))),
% 45.62/29.78 inference(tautology,[status(thm)],[])).
% 45.62/29.78 tff(1953,plain,
% 45.62/29.78 (~((~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))))))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1952, 1951, 1942])).
% 45.62/29.78 tff(1954,plain,
% 45.62/29.78 (((~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))))))) | ((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))))),
% 45.62/29.78 inference(tautology,[status(thm)],[])).
% 45.62/29.78 tff(1955,plain,
% 45.62/29.78 ((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1954, 1953])).
% 45.62/29.78 tff(1956,plain,
% 45.62/29.78 ((~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))))),
% 45.62/29.78 inference(tautology,[status(thm)],[])).
% 45.62/29.78 tff(1957,plain,
% 45.62/29.78 ((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1956, 1955])).
% 45.62/29.78 tff(1958,plain,
% 45.62/29.78 (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1957, 1935, 1926, 1925])).
% 45.62/29.78 tff(1959,plain,
% 45.62/29.78 (~d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.62/29.78 inference(modus_ponens,[status(thm)],[1958, 1924])).
% 45.62/29.78 tff(1960,plain,
% 45.62/29.78 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1694, 1374, 1277, 1288, 1282, 1287])).
% 45.62/29.78 tff(1961,plain,
% 45.62/29.78 (phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false)),
% 45.62/29.78 inference(transitivity,[status(thm)],[1766, 1759])).
% 45.62/29.78 tff(1962,plain,
% 45.62/29.78 ((phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err) <=> (not1(false) = err)),
% 45.62/29.78 inference(monotonicity,[status(thm)],[1961])).
% 45.62/29.78 tff(1963,plain,
% 45.62/29.78 ((not1(false) = err) <=> (phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)),
% 45.62/29.78 inference(symmetry,[status(thm)],[1962])).
% 45.62/29.78 tff(1964,plain,
% 45.62/29.78 ((not1(false) = err) <=> (phi(tptp_fun_R_5(P!7)) = err)),
% 45.62/29.78 inference(transitivity,[status(thm)],[1963, 1770])).
% 45.62/29.78 tff(1965,plain,
% 45.62/29.78 ((~(not1(false) = err)) <=> (~(phi(tptp_fun_R_5(P!7)) = err))),
% 45.62/29.78 inference(monotonicity,[status(thm)],[1964])).
% 45.62/29.78 tff(1966,plain,
% 45.62/29.78 (~(phi(tptp_fun_R_5(P!7)) = err)),
% 45.62/29.78 inference(modus_ponens,[status(thm)],[564, 1965])).
% 45.62/29.78 tff(1967,plain,
% 45.62/29.78 (d(tptp_fun_R_5(P!7)) | (~(phi(tptp_fun_R_5(P!7)) = err))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1503, 1966])).
% 45.62/29.78 tff(1968,plain,
% 45.62/29.78 (~((~d(tptp_fun_R_5(P!7))) | (~(phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1508, 1967])).
% 45.62/29.78 tff(1969,plain,
% 45.62/29.78 (phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1510, 1968])).
% 45.62/29.78 tff(1970,plain,
% 45.62/29.78 (tptp_fun_R_5(P!7) = phi(tptp_fun_R_5(P!7))),
% 45.62/29.78 inference(symmetry,[status(thm)],[1969])).
% 45.62/29.78 tff(1971,plain,
% 45.62/29.78 (tptp_fun_R_5(P!7) = not1(false)),
% 45.62/29.78 inference(transitivity,[status(thm)],[1970, 1295, 1292, 1759])).
% 45.62/29.78 tff(1972,assumption,(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false)), introduced(assumption)).
% 45.62/29.78 tff(1973,plain,
% 45.62/29.78 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = impl(not1(false), not1(false))),
% 45.62/29.78 inference(monotonicity,[status(thm)],[1972, 1971])).
% 45.62/29.78 tff(1974,plain,
% 45.62/29.78 (impl(not1(false), not1(false)) = impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))),
% 45.62/29.78 inference(symmetry,[status(thm)],[1973])).
% 45.62/29.78 tff(1975,plain,
% 45.62/29.78 (not1(false) = false),
% 45.62/29.78 inference(transitivity,[status(thm)],[598, 1974, 415, 1584, 1364])).
% 45.62/29.78 tff(1976,plain,
% 45.62/29.78 ($false),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[60, 1975])).
% 45.62/29.78 tff(1977,plain,((~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = not1(false))) | (~(prop(tptp_fun_R_5(P!7)) = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 45.62/29.78 tff(1978,plain,
% 45.62/29.78 (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = not1(false))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1977, 1928, 1960, 1277])).
% 45.62/29.78 tff(1979,plain,
% 45.62/29.78 (bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1825, 1763, 1821, 1762])).
% 45.62/29.78 tff(1980,plain,
% 45.62/29.78 ((~(bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) <=> ((lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = not1(false))))) | ((lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = not1(false)))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1827, 1979])).
% 45.62/29.78 tff(1981,plain,
% 45.62/29.78 ((lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = not1(false))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1980, 1815])).
% 45.62/29.78 tff(1982,plain,
% 45.62/29.78 ((lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = not1(false))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1830, 1981])).
% 45.62/29.78 tff(1983,plain,
% 45.62/29.78 (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1982, 1978])).
% 45.62/29.78 tff(1984,plain,
% 45.62/29.78 (not1(false) = prop(tptp_fun_R_5(P!7))),
% 45.62/29.78 inference(symmetry,[status(thm)],[1277])).
% 45.62/29.78 tff(1985,plain,
% 45.62/29.78 (lazy_impl(not1(false), tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 45.62/29.78 inference(monotonicity,[status(thm)],[1984])).
% 45.62/29.78 tff(1986,plain,
% 45.62/29.78 (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)),
% 45.62/29.78 inference(transitivity,[status(thm)],[414, 1929, 1288])).
% 45.62/29.78 tff(1987,plain,
% 45.62/29.78 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = phi(tptp_fun_R_5(P!7))),
% 45.62/29.78 inference(monotonicity,[status(thm)],[1986])).
% 45.62/29.78 tff(1988,plain,
% 45.62/29.78 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false),
% 45.62/29.78 inference(transitivity,[status(thm)],[1987, 1295, 1985, 1983])).
% 45.62/29.78 tff(1989,plain,
% 45.62/29.78 ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = err) <=> (false = err)),
% 45.62/29.78 inference(monotonicity,[status(thm)],[1988])).
% 45.62/29.78 tff(1990,plain,
% 45.62/29.78 ((false = err) <=> (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = err)),
% 45.62/29.78 inference(symmetry,[status(thm)],[1989])).
% 45.62/29.78 tff(1991,plain,
% 45.62/29.78 ((~(false = err)) <=> (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = err))),
% 45.62/29.78 inference(monotonicity,[status(thm)],[1990])).
% 45.62/29.78 tff(1992,plain,
% 45.62/29.78 (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = err)),
% 45.62/29.78 inference(modus_ponens,[status(thm)],[556, 1991])).
% 45.62/29.78 tff(1993,plain,
% 45.62/29.78 (d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = err))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1423, 1992])).
% 45.62/29.78 tff(1994,plain,
% 45.62/29.78 (~((~d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1421, 1993])).
% 45.62/29.78 tff(1995,plain,
% 45.62/29.78 (((~d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))) | d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.62/29.78 inference(tautology,[status(thm)],[])).
% 45.62/29.78 tff(1996,plain,
% 45.62/29.78 (d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1995, 1994])).
% 45.62/29.78 tff(1997,plain,
% 45.62/29.78 ($false),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1996, 1959])).
% 45.62/29.78 tff(1998,plain,((impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))) | (~bool(tptp_fun_R_5(P!7))) | (~((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false))))), inference(lemma,lemma(discharge,[]))).
% 45.62/29.78 tff(1999,plain,
% 45.62/29.78 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1998, 1899, 399, 1272, 1922])).
% 45.62/29.78 tff(2000,plain,
% 45.62/29.78 (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = not1(false)),
% 45.62/29.78 inference(transitivity,[status(thm)],[414, 1999])).
% 45.62/29.78 tff(2001,plain,
% 45.62/29.78 (bool(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) <=> bool(not1(false))),
% 45.62/29.78 inference(monotonicity,[status(thm)],[2000])).
% 45.62/29.78 tff(2002,plain,
% 45.62/29.78 (bool(not1(false)) <=> bool(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.62/29.78 inference(symmetry,[status(thm)],[2001])).
% 45.62/29.78 tff(2003,plain,
% 45.62/29.78 (bool(not1(false)) <=> bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.78 inference(transitivity,[status(thm)],[2002, 417])).
% 45.62/29.78 tff(2004,plain,
% 45.62/29.78 (bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.78 inference(modus_ponens,[status(thm)],[272, 2003])).
% 45.62/29.78 tff(2005,plain,
% 45.62/29.78 (d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) <=> d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.78 inference(symmetry,[status(thm)],[1923])).
% 45.62/29.78 tff(2006,plain,
% 45.62/29.78 (d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) <=> d(not1(false))),
% 45.62/29.78 inference(monotonicity,[status(thm)],[2000])).
% 45.62/29.78 tff(2007,plain,
% 45.62/29.78 (d(not1(false)) <=> d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.62/29.78 inference(symmetry,[status(thm)],[2006])).
% 45.62/29.78 tff(2008,plain,
% 45.62/29.78 (d(not1(false)) <=> d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.78 inference(transitivity,[status(thm)],[2007, 2005])).
% 45.62/29.78 tff(2009,plain,
% 45.62/29.78 (d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.78 inference(modus_ponens,[status(thm)],[40, 2008])).
% 45.62/29.78 tff(2010,plain,
% 45.62/29.78 ($false),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1957, 2009, 2004, 1899, 399])).
% 45.62/29.78 tff(2011,plain,(bool(apply(P!7, tptp_fun_X_3(P!7))) | (~bool(tptp_fun_R_5(P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = apply(P!7, tptp_fun_X_4(not1(false), P!7)))) | (~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))))) | (phi(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))) = err) | (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = false) | (~d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))))), inference(lemma,lemma(discharge,[]))).
% 45.62/29.78 tff(2012,plain,
% 45.62/29.78 (bool(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[2011, 1257, 702, 519, 708, 1270, 695])).
% 45.62/29.78 tff(2013,plain,
% 45.62/29.78 ((~((prop(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)) <=> bool(apply(P!7, tptp_fun_X_3(P!7))))) | (prop(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1607, 2012])).
% 45.62/29.78 tff(2014,plain,
% 45.62/29.78 (prop(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[2013, 294])).
% 45.62/29.78 tff(2015,plain,
% 45.62/29.78 (lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))) = lazy_impl(not1(false), apply(P!7, tptp_fun_X_3(P!7)))),
% 45.62/29.78 inference(monotonicity,[status(thm)],[2014])).
% 45.62/29.78 tff(2016,plain,
% 45.62/29.78 (lazy_impl(not1(false), apply(P!7, tptp_fun_X_3(P!7))) = lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))),
% 45.62/29.78 inference(symmetry,[status(thm)],[2015])).
% 45.62/29.78 tff(2017,plain,
% 45.62/29.78 (phi(apply(P!7, tptp_fun_X_3(P!7))) = f7(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.62/29.78 inference(transitivity,[status(thm)],[1614, 2016, 292])).
% 45.62/29.78 tff(2018,plain,
% 45.62/29.78 (forallprefers(phi(apply(P!7, tptp_fun_X_3(P!7))), false) <=> forallprefers(f7(apply(P!7, tptp_fun_X_3(P!7))), f7(P!6))),
% 45.62/29.78 inference(monotonicity,[status(thm)],[2017, 289])).
% 45.62/29.78 tff(2019,plain,
% 45.62/29.78 (forallprefers(f7(apply(P!7, tptp_fun_X_3(P!7))), f7(P!6)) <=> forallprefers(phi(apply(P!7, tptp_fun_X_3(P!7))), false)),
% 45.62/29.78 inference(symmetry,[status(thm)],[2018])).
% 45.62/29.78 tff(2020,plain,
% 45.62/29.78 ((~forallprefers(f7(apply(P!7, tptp_fun_X_3(P!7))), f7(P!6))) <=> (~forallprefers(phi(apply(P!7, tptp_fun_X_3(P!7))), false))),
% 45.62/29.78 inference(monotonicity,[status(thm)],[2019])).
% 45.62/29.78 tff(2021,plain,
% 45.62/29.78 (~forallprefers(phi(apply(P!7, tptp_fun_X_3(P!7))), false)),
% 45.62/29.78 inference(modus_ponens,[status(thm)],[1642, 2020])).
% 45.62/29.78 tff(2022,plain,
% 45.62/29.78 ((~(forallprefers(phi(apply(P!7, tptp_fun_X_3(P!7))), false) <=> ((~((~d(false)) | d(phi(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(false = not1(false))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = false)))) | (~((~d(false)) | (~bool(false)) | (~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | bool(phi(apply(P!7, tptp_fun_X_3(P!7))))))))) | forallprefers(phi(apply(P!7, tptp_fun_X_3(P!7))), false) | (~((~((~d(false)) | d(phi(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(false = not1(false))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = false)))) | (~((~d(false)) | (~bool(false)) | (~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | bool(phi(apply(P!7, tptp_fun_X_3(P!7))))))))),
% 45.62/29.78 inference(tautology,[status(thm)],[])).
% 45.62/29.78 tff(2023,plain,
% 45.62/29.78 (~((~((~d(false)) | d(phi(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(false = not1(false))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = false)))) | (~((~d(false)) | (~bool(false)) | (~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | bool(phi(apply(P!7, tptp_fun_X_3(P!7)))))))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[2022, 2021, 166])).
% 45.62/29.78 tff(2024,plain,
% 45.62/29.78 (((~((~d(false)) | d(phi(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(false = not1(false))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = false)))) | (~((~d(false)) | (~bool(false)) | (~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | bool(phi(apply(P!7, tptp_fun_X_3(P!7))))))) | ((~d(false)) | (~bool(false)) | (~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | bool(phi(apply(P!7, tptp_fun_X_3(P!7)))))),
% 45.62/29.78 inference(tautology,[status(thm)],[])).
% 45.62/29.78 tff(2025,plain,
% 45.62/29.78 ((~d(false)) | (~bool(false)) | (~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | bool(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[2024, 2023])).
% 45.62/29.78 tff(2026,plain,
% 45.62/29.78 (((~((~d(false)) | d(phi(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(false = not1(false))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = false)))) | (~((~d(false)) | (~bool(false)) | (~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | bool(phi(apply(P!7, tptp_fun_X_3(P!7))))))) | ((~d(false)) | d(phi(apply(P!7, tptp_fun_X_3(P!7)))))),
% 45.62/29.78 inference(tautology,[status(thm)],[])).
% 45.62/29.78 tff(2027,plain,
% 45.62/29.78 ((~d(false)) | d(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[2026, 2023])).
% 45.62/29.78 tff(2028,plain,
% 45.62/29.78 ((~((~d(false)) | d(phi(apply(P!7, tptp_fun_X_3(P!7)))))) | (~d(false)) | d(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.62/29.78 inference(tautology,[status(thm)],[])).
% 45.62/29.78 tff(2029,plain,
% 45.62/29.78 ((~((~d(false)) | d(phi(apply(P!7, tptp_fun_X_3(P!7)))))) | d(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[2028, 5])).
% 45.62/29.78 tff(2030,plain,
% 45.62/29.78 (d(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[2029, 2027])).
% 45.62/29.78 tff(2031,plain,
% 45.62/29.78 ((~((~d(false)) | (~bool(false)) | (~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | bool(phi(apply(P!7, tptp_fun_X_3(P!7)))))) | (~d(false)) | (~bool(false)) | (~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | bool(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.62/29.78 inference(tautology,[status(thm)],[])).
% 45.62/29.78 tff(2032,plain,
% 45.62/29.78 ((~((~d(false)) | (~bool(false)) | (~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | bool(phi(apply(P!7, tptp_fun_X_3(P!7)))))) | (~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | bool(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[2031, 5, 76])).
% 45.62/29.78 tff(2033,plain,
% 45.62/29.78 (bool(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[2032, 2030, 2025])).
% 45.62/29.78 tff(2034,plain,
% 45.62/29.78 (prop(phi(apply(P!7, tptp_fun_X_3(P!7)))) = not1(false)),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1132, 2033])).
% 45.62/29.78 tff(2035,plain,
% 45.62/29.78 (d(phi(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(phi(apply(P!7, tptp_fun_X_3(P!7)))) = err))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[948, 2030])).
% 45.62/29.78 tff(2036,plain,
% 45.62/29.78 (~((~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~(phi(phi(apply(P!7, tptp_fun_X_3(P!7)))) = phi(apply(P!7, tptp_fun_X_3(P!7))))))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[952, 17, 2035])).
% 45.62/29.78 tff(2037,plain,
% 45.62/29.78 (phi(phi(apply(P!7, tptp_fun_X_3(P!7)))) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[955, 2036])).
% 45.62/29.78 tff(2038,plain,
% 45.62/29.78 (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err)),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1127, 2037, 2034])).
% 45.62/29.78 tff(2039,plain,
% 45.62/29.78 (d(apply(P!7, tptp_fun_X_3(P!7))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[385, 2038])).
% 45.62/29.78 tff(2040,plain,
% 45.62/29.78 (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[383, 2039])).
% 45.62/29.78 tff(2041,plain,
% 45.62/29.78 (d(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[374, 2040])).
% 45.62/29.78 tff(2042,plain,
% 45.62/29.78 (((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))))) | (~(d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_4(not1(false), P!7))))))) | ((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_4(not1(false), P!7)))))),
% 45.62/29.78 inference(tautology,[status(thm)],[])).
% 45.62/29.78 tff(2043,plain,
% 45.62/29.78 ((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_4(not1(false), P!7))))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[2042, 1238])).
% 45.62/29.78 tff(2044,plain,
% 45.62/29.78 ((~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_4(not1(false), P!7)))))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_4(not1(false), P!7))))),
% 45.62/29.78 inference(tautology,[status(thm)],[])).
% 45.62/29.78 tff(2045,plain,
% 45.62/29.78 ((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_4(not1(false), P!7))))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[2044, 2043])).
% 45.62/29.78 tff(2046,plain,
% 45.62/29.78 (bool(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[2045, 2041, 2012, 1266])).
% 45.62/29.78 tff(2047,plain,
% 45.62/29.78 (bool(impl(f5(P!7, not1(false)), not1(false)))),
% 45.62/29.78 inference(modus_ponens,[status(thm)],[2046, 1265])).
% 45.62/29.78 tff(2048,plain,
% 45.62/29.78 ((~(bool(impl(f5(P!7, not1(false)), not1(false))) <=> ((impl(f5(P!7, not1(false)), not1(false)) = false) | (impl(f5(P!7, not1(false)), not1(false)) = not1(false))))) | ((impl(f5(P!7, not1(false)), not1(false)) = false) | (impl(f5(P!7, not1(false)), not1(false)) = not1(false)))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[776, 2047])).
% 45.62/29.78 tff(2049,plain,
% 45.62/29.78 ((impl(f5(P!7, not1(false)), not1(false)) = false) | (impl(f5(P!7, not1(false)), not1(false)) = not1(false))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[2048, 710])).
% 45.62/29.78 tff(2050,plain,
% 45.62/29.78 (~(impl(f5(P!7, not1(false)), not1(false)) = false)),
% 45.62/29.78 inference(modus_ponens,[status(thm)],[1270, 782])).
% 45.62/29.78 tff(2051,plain,
% 45.62/29.78 (impl(f5(P!7, not1(false)), not1(false)) = not1(false)),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[790, 2050, 2049])).
% 45.62/29.78 tff(2052,plain,
% 45.62/29.78 (impl(f5(P!7, not1(false)), impl(false, not1(false))) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false)))),
% 45.62/29.78 inference(transitivity,[status(thm)],[1847, 676, 678, 644, 521, 651])).
% 45.62/29.78 tff(2053,plain,
% 45.62/29.78 (impl(impl(f5(P!7, not1(false)), impl(false, not1(false))), not1(false)) = impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))),
% 45.62/29.78 inference(monotonicity,[status(thm)],[2052])).
% 45.62/29.78 tff(2054,plain,
% 45.62/29.78 (impl(false, tptp_fun_R_5(P!7)) = not1(false)),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1286, 1257])).
% 45.62/29.78 tff(2055,plain,
% 45.62/29.78 (impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7))) = impl(impl(f5(P!7, not1(false)), impl(false, not1(false))), not1(false))),
% 45.62/29.78 inference(monotonicity,[status(thm)],[1850, 2054])).
% 45.62/29.78 tff(2056,plain,
% 45.62/29.78 (impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7))) = not1(false)),
% 45.62/29.78 inference(transitivity,[status(thm)],[2055, 2053, 712, 2051])).
% 45.62/29.78 tff(2057,plain,
% 45.62/29.78 (impl(impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = impl(not1(false), tptp_fun_R_5(P!7))),
% 45.62/29.78 inference(monotonicity,[status(thm)],[2056])).
% 45.62/29.78 tff(2058,plain,
% 45.62/29.78 (impl(impl(f5(P!7, not1(false)), impl(false, not1(false))), not1(false)) = impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7)))),
% 45.62/29.78 inference(symmetry,[status(thm)],[2055])).
% 45.62/29.78 tff(2059,plain,
% 45.62/29.78 (impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)) = impl(impl(f5(P!7, not1(false)), impl(false, not1(false))), not1(false))),
% 45.62/29.78 inference(symmetry,[status(thm)],[2053])).
% 45.62/29.78 tff(2060,plain,
% 45.62/29.78 (not1(false) = impl(f5(P!7, not1(false)), not1(false))),
% 45.62/29.78 inference(symmetry,[status(thm)],[2051])).
% 45.62/29.78 tff(2061,plain,
% 45.62/29.78 ((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = not1(false))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1281, 1257])).
% 45.62/29.78 tff(2062,plain,
% 45.62/29.78 (d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1683, 2041])).
% 45.62/29.78 tff(2063,plain,
% 45.62/29.78 (bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1659, 2062, 2012])).
% 45.62/29.78 tff(2064,plain,
% 45.62/29.78 ((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1410, 2063])).
% 45.62/29.78 tff(2065,plain,
% 45.62/29.78 (prop(tptp_fun_R_5(P!7)) = not1(false)),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1276, 1257])).
% 45.62/29.78 tff(2066,plain,
% 45.62/29.78 ((~(bool(apply(P!7, tptp_fun_X_3(P!7))) <=> ((apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = not1(false))))) | ((apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = not1(false)))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1198, 2012])).
% 45.62/29.78 tff(2067,plain,
% 45.62/29.78 ((apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = not1(false))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[2066, 794])).
% 45.62/29.78 tff(2068,plain,
% 45.62/29.78 ((apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1206, 2046])).
% 45.62/29.78 tff(2069,plain,
% 45.62/29.78 (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false)),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[484, 2068, 432])).
% 45.62/29.78 tff(2070,plain,
% 45.62/29.78 (~(apply(P!7, tptp_fun_X_3(P!7)) = false)),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1242, 2069])).
% 45.62/29.78 tff(2071,plain,
% 45.62/29.78 (apply(P!7, tptp_fun_X_3(P!7)) = not1(false)),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1244, 2070, 2067])).
% 45.62/29.78 tff(2072,plain,
% 45.62/29.78 (phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[369, 2040])).
% 45.62/29.78 tff(2073,plain,
% 45.62/29.78 (not1(false) = impl(f5(P!7, not1(false)), not1(false))),
% 45.62/29.78 inference(symmetry,[status(thm)],[958])).
% 45.62/29.78 tff(2074,plain,
% 45.62/29.78 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1694, 1374, 1290, 1328, 1327, 1326])).
% 45.62/29.78 tff(2075,plain,
% 45.62/29.78 (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = not1(false))),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1977, 1384, 2074, 1290])).
% 45.62/29.78 tff(2076,plain,
% 45.62/29.78 (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[1831, 2075])).
% 45.62/29.78 tff(2077,plain,
% 45.62/29.78 (impl(f5(P!7, not1(false)), impl(false, not1(false))) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false)))),
% 45.62/29.78 inference(transitivity,[status(thm)],[1847, 957, 678, 644, 521, 651])).
% 45.62/29.78 tff(2078,plain,
% 45.62/29.78 (impl(impl(f5(P!7, not1(false)), impl(false, not1(false))), not1(false)) = impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))),
% 45.62/29.78 inference(monotonicity,[status(thm)],[2077])).
% 45.62/29.78 tff(2079,plain,
% 45.62/29.78 (impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7))) = not1(false)),
% 45.62/29.78 inference(transitivity,[status(thm)],[1851, 2078, 712, 958])).
% 45.62/29.78 tff(2080,plain,
% 45.62/29.78 (impl(impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = impl(not1(false), tptp_fun_R_5(P!7))),
% 45.62/29.78 inference(monotonicity,[status(thm)],[2079])).
% 45.62/29.78 tff(2081,plain,
% 45.62/29.78 (impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)) = impl(impl(f5(P!7, not1(false)), impl(false, not1(false))), not1(false))),
% 45.62/29.78 inference(symmetry,[status(thm)],[2078])).
% 45.62/29.78 tff(2082,plain,
% 45.62/29.78 (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7)))),
% 45.62/29.78 inference(transitivity,[status(thm)],[1384, 2073, 1856, 2081, 1854])).
% 45.62/29.78 tff(2083,plain,
% 45.62/29.78 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = impl(impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))),
% 45.62/29.78 inference(monotonicity,[status(thm)],[2082])).
% 45.62/29.78 tff(2084,plain,
% 45.62/29.78 (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)),
% 45.62/29.78 inference(transitivity,[status(thm)],[414, 2083, 2080, 1328])).
% 45.62/29.78 tff(2085,plain,
% 45.62/29.78 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = phi(tptp_fun_R_5(P!7))),
% 45.62/29.78 inference(monotonicity,[status(thm)],[2084])).
% 45.62/29.78 tff(2086,plain,
% 45.62/29.78 (f5(P!7, tptp_fun_R_5(P!7)) = false),
% 45.62/29.78 inference(transitivity,[status(thm)],[311, 2085, 1295, 1292, 2076])).
% 45.62/29.78 tff(2087,plain,
% 45.62/29.78 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = impl(false, tptp_fun_R_5(P!7))),
% 45.62/29.78 inference(monotonicity,[status(thm)],[2086])).
% 45.62/29.78 tff(2088,plain,
% 45.62/29.78 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = not1(false)),
% 45.62/29.78 inference(transitivity,[status(thm)],[2087, 1326])).
% 45.62/29.78 tff(2089,plain,
% 45.62/29.78 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(not1(false), not1(false))),
% 45.62/29.78 inference(monotonicity,[status(thm)],[1290, 2088])).
% 45.62/29.78 tff(2090,plain,
% 45.62/29.78 (f6(P!7, tptp_fun_R_5(P!7)) = impl(f5(P!7, not1(false)), not1(false))),
% 45.62/29.78 inference(transitivity,[status(thm)],[325, 2089, 50, 48, 2073])).
% 45.62/29.78 tff(2091,plain,
% 45.62/29.78 (phi(f6(P!7, tptp_fun_R_5(P!7))) = phi(impl(f5(P!7, not1(false)), not1(false)))),
% 45.62/29.78 inference(monotonicity,[status(thm)],[2090])).
% 45.62/29.78 tff(2092,plain,
% 45.62/29.78 (phi(impl(f5(P!7, not1(false)), not1(false))) = phi(f6(P!7, tptp_fun_R_5(P!7)))),
% 45.62/29.78 inference(symmetry,[status(thm)],[2091])).
% 45.62/29.78 tff(2093,plain,
% 45.62/29.78 (phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = phi(impl(f5(P!7, not1(false)), not1(false)))),
% 45.62/29.78 inference(symmetry,[status(thm)],[1803])).
% 45.62/29.78 tff(2094,assumption,(apply(P!7, tptp_fun_X_3(P!7)) = not1(false)), introduced(assumption)).
% 45.62/29.78 tff(2095,plain,
% 45.62/29.78 (exists1(P!7) = exists2(P!7)),
% 45.62/29.78 inference(transitivity,[status(thm)],[346, 961, 2094, 2073, 957, 678, 2093, 2092, 1309])).
% 45.62/29.78 tff(2096,plain,
% 45.62/29.78 ($false),
% 45.62/29.78 inference(unit_resolution,[status(thm)],[897, 2095])).
% 45.62/29.78 tff(2097,plain,((impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))) | (~(apply(P!7, tptp_fun_X_3(P!7)) = not1(false))) | (~(impl(f5(P!7, not1(false)), not1(false)) = not1(false))) | (~(impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false))))) | (~(impl(false, tptp_fun_R_5(P!7)) = not1(false))) | (~(impl(not1(false), tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))) | (~(prop(tptp_fun_R_5(P!7)) = not1(false))) | (~((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false)))) | (~((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = not1(false))))), inference(lemma,lemma(discharge,[]))).
% 45.62/29.79 tff(2098,plain,
% 45.62/29.79 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)),
% 45.62/29.79 inference(unit_resolution,[status(thm)],[2097, 2072, 2071, 2051, 676, 2054, 1262, 2065, 2064, 2061])).
% 45.62/29.79 tff(2099,plain,
% 45.62/29.79 (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = impl(f5(P!7, not1(false)), not1(false))),
% 45.62/29.79 inference(transitivity,[status(thm)],[414, 2098, 2060])).
% 45.62/29.79 tff(2100,plain,
% 45.62/29.79 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = phi(impl(f5(P!7, not1(false)), not1(false)))),
% 45.62/29.79 inference(monotonicity,[status(thm)],[2099])).
% 45.62/29.79 tff(2101,plain,
% 45.62/29.79 (f5(P!7, tptp_fun_R_5(P!7)) = impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7)))),
% 45.62/29.79 inference(transitivity,[status(thm)],[311, 2100, 680, 647, 677, 1856, 2059, 2058])).
% 45.62/29.79 tff(2102,plain,
% 45.62/29.79 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = impl(impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))),
% 45.62/29.79 inference(monotonicity,[status(thm)],[2101])).
% 45.62/29.79 tff(2103,plain,
% 45.62/29.79 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)),
% 45.62/29.79 inference(transitivity,[status(thm)],[2102, 2057, 1262])).
% 45.62/29.79 tff(2104,plain,
% 45.62/29.79 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 45.62/29.79 inference(monotonicity,[status(thm)],[2103])).
% 45.62/29.79 tff(2105,plain,
% 45.62/29.79 (f6(P!7, tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 45.62/29.79 inference(transitivity,[status(thm)],[325, 2104])).
% 45.62/29.79 tff(2106,plain,
% 45.62/29.79 (phi(f6(P!7, tptp_fun_R_5(P!7))) = phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.79 inference(monotonicity,[status(thm)],[2105])).
% 45.62/29.79 tff(2107,plain,
% 45.62/29.79 (exists2(P!7) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 45.62/29.79 inference(transitivity,[status(thm)],[880, 2106, 471])).
% 45.62/29.79 tff(2108,plain,
% 45.62/29.79 (exists1(P!7) = not1(false)),
% 45.62/29.79 inference(transitivity,[status(thm)],[346, 2072, 2071])).
% 45.62/29.79 tff(2109,plain,
% 45.62/29.79 ((exists1(P!7) = exists2(P!7)) <=> (not1(false) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.79 inference(monotonicity,[status(thm)],[2108, 2107])).
% 45.62/29.79 tff(2110,plain,
% 45.62/29.79 ((exists1(P!7) = exists2(P!7)) <=> (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = not1(false))),
% 45.62/29.79 inference(transitivity,[status(thm)],[2109, 433])).
% 45.62/29.79 tff(2111,plain,
% 45.62/29.79 ((~(exists1(P!7) = exists2(P!7))) <=> (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = not1(false)))),
% 45.62/29.79 inference(monotonicity,[status(thm)],[2110])).
% 45.62/29.79 tff(2112,plain,
% 45.62/29.79 (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = not1(false))),
% 45.62/29.79 inference(modus_ponens,[status(thm)],[897, 2111])).
% 45.62/29.79 tff(2113,plain,
% 45.62/29.79 (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false),
% 45.62/29.79 inference(unit_resolution,[status(thm)],[1831, 2112])).
% 45.62/29.79 tff(2114,plain,
% 45.62/29.79 (impl(not1(false), impl(false, tptp_fun_R_5(P!7))) = impl(not1(false), not1(false))),
% 45.62/29.79 inference(monotonicity,[status(thm)],[2054])).
% 45.62/29.79 tff(2115,plain,
% 45.62/29.79 (impl(not1(false), impl(false, tptp_fun_R_5(P!7))) = not1(false)),
% 45.62/29.79 inference(transitivity,[status(thm)],[2114, 501])).
% 45.62/29.79 tff(2116,plain,
% 45.62/29.79 (impl(impl(not1(false), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = impl(not1(false), tptp_fun_R_5(P!7))),
% 45.62/29.79 inference(monotonicity,[status(thm)],[2115])).
% 45.62/29.79 tff(2117,plain,
% 45.62/29.79 (impl(not1(false), tptp_fun_R_5(P!7)) = impl(impl(not1(false), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))),
% 45.62/29.79 inference(symmetry,[status(thm)],[2116])).
% 45.62/29.79 tff(2118,plain,
% 45.62/29.79 (tptp_fun_R_5(P!7) = impl(not1(false), tptp_fun_R_5(P!7))),
% 45.62/29.79 inference(symmetry,[status(thm)],[1262])).
% 45.62/29.79 tff(2119,plain,
% 45.62/29.79 (tptp_fun_R_5(P!7) = impl(impl(not1(false), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))),
% 45.62/29.79 inference(transitivity,[status(thm)],[2118, 2117])).
% 45.62/29.79 tff(2120,plain,
% 45.62/29.79 (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(impl(not1(false), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 45.62/29.79 inference(monotonicity,[status(thm)],[2119])).
% 45.62/29.79 tff(2121,plain,
% 45.62/29.79 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(impl(not1(false), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 45.62/29.79 inference(symmetry,[status(thm)],[2120])).
% 45.62/29.79 tff(2122,plain,
% 45.62/29.79 (^[P: $i, Q: $i, R: $i] : refl((f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R))) <=> (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R))))),
% 45.62/29.79 inference(bind,[status(th)],[])).
% 45.62/29.79 tff(2123,plain,
% 45.62/29.79 (![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R))) <=> ![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))),
% 45.62/29.79 inference(quant_intro,[status(thm)],[2122])).
% 45.62/29.79 tff(2124,plain,
% 45.62/29.79 (![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R))) <=> ![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))),
% 45.62/29.79 inference(rewrite,[status(thm)],[])).
% 45.62/29.79 tff(2125,axiom,(![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','def_f1')).
% 45.62/29.79 tff(2126,plain,
% 45.62/29.79 (![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))),
% 45.62/29.79 inference(modus_ponens,[status(thm)],[2125, 2124])).
% 45.62/29.79 tff(2127,plain,(
% 45.62/29.79 ![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))),
% 45.62/29.79 inference(skolemize,[status(sab)],[2126])).
% 45.62/29.79 tff(2128,plain,
% 45.62/29.79 (![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))),
% 45.62/29.79 inference(modus_ponens,[status(thm)],[2127, 2123])).
% 45.62/29.79 tff(2129,plain,
% 45.62/29.79 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(not1(false), false, tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(impl(not1(false), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))))),
% 45.62/29.79 inference(quant_inst,[status(thm)],[])).
% 45.62/29.79 tff(2130,plain,
% 45.62/29.79 (f1(not1(false), false, tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(impl(not1(false), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 45.62/29.79 inference(unit_resolution,[status(thm)],[2129, 2128])).
% 45.62/29.79 tff(2131,plain,
% 45.62/29.79 (f1(not1(false), false, tptp_fun_R_5(P!7)) = f1(impl(f5(P!7, not1(false)), not1(false)), false, tptp_fun_R_5(P!7))),
% 45.62/29.79 inference(monotonicity,[status(thm)],[2060])).
% 45.62/29.79 tff(2132,plain,
% 45.62/29.79 (f1(impl(f5(P!7, not1(false)), not1(false)), false, tptp_fun_R_5(P!7)) = f1(not1(false), false, tptp_fun_R_5(P!7))),
% 45.62/29.79 inference(symmetry,[status(thm)],[2131])).
% 45.62/29.79 tff(2133,plain,
% 45.62/29.79 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(impl(f5(P!7, not1(false)), not1(false)), false, tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))))),
% 45.62/29.79 inference(quant_inst,[status(thm)],[])).
% 45.62/29.79 tff(2134,plain,
% 45.62/29.79 (f1(impl(f5(P!7, not1(false)), not1(false)), false, tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 45.62/29.79 inference(unit_resolution,[status(thm)],[2133, 2128])).
% 45.62/29.79 tff(2135,plain,
% 45.62/29.79 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = f1(impl(f5(P!7, not1(false)), not1(false)), false, tptp_fun_R_5(P!7))),
% 45.62/29.79 inference(symmetry,[status(thm)],[2134])).
% 45.62/29.79 tff(2136,plain,
% 45.62/29.79 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = lazy_impl(not1(false), impl(impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 45.62/29.79 inference(monotonicity,[status(thm)],[2065])).
% 45.62/29.79 tff(2137,plain,
% 45.62/29.79 (lazy_impl(not1(false), impl(impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 45.62/29.79 inference(symmetry,[status(thm)],[2136])).
% 45.62/29.79 tff(2138,plain,
% 45.62/29.79 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), impl(impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = phi(impl(impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))))),
% 45.62/29.79 inference(quant_inst,[status(thm)],[])).
% 45.62/29.79 tff(2139,plain,
% 45.62/29.79 (lazy_impl(not1(false), impl(impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = phi(impl(impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 45.62/29.79 inference(unit_resolution,[status(thm)],[2138, 33])).
% 45.62/29.79 tff(2140,plain,
% 45.62/29.79 (phi(impl(impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = lazy_impl(not1(false), impl(impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 45.62/29.79 inference(symmetry,[status(thm)],[2139])).
% 45.62/29.79 tff(2141,plain,
% 45.62/29.79 (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7)))),
% 45.62/29.79 inference(transitivity,[status(thm)],[1263, 783, 522, 645, 647, 677, 1856, 2059, 2058])).
% 45.62/29.79 tff(2142,plain,
% 45.62/29.79 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)) = impl(impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))),
% 45.62/29.79 inference(monotonicity,[status(thm)],[2141])).
% 45.62/29.79 tff(2143,plain,
% 45.62/29.79 (impl(impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))),
% 45.62/29.79 inference(symmetry,[status(thm)],[2142])).
% 45.62/29.79 tff(2144,plain,
% 45.62/29.79 (phi(impl(impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = phi(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)))),
% 45.62/29.79 inference(monotonicity,[status(thm)],[2143])).
% 45.62/29.79 tff(2145,plain,
% 45.62/29.79 (phi(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) = phi(impl(impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 45.62/29.79 inference(symmetry,[status(thm)],[2144])).
% 45.62/29.79 tff(2146,plain,
% 45.62/29.79 (((~(d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))) | (~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)) = false))))) | (d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))),
% 45.62/29.79 inference(tautology,[status(thm)],[])).
% 45.62/29.79 tff(2147,plain,
% 45.62/29.79 (d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))))),
% 45.62/29.79 inference(unit_resolution,[status(thm)],[2146, 1881])).
% 45.62/29.79 tff(2148,plain,
% 45.62/29.79 (d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) <=> d(impl(f5(P!7, not1(false)), not1(false)))),
% 45.62/29.79 inference(monotonicity,[status(thm)],[2099])).
% 45.62/29.79 tff(2149,plain,
% 45.62/29.79 (d(impl(f5(P!7, not1(false)), not1(false))) <=> d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.62/29.79 inference(symmetry,[status(thm)],[2148])).
% 45.70/29.79 tff(2150,plain,
% 45.70/29.79 (d(impl(f5(P!7, not1(false)), not1(false))) <=> d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.79 inference(transitivity,[status(thm)],[2149, 2005])).
% 45.70/29.79 tff(2151,plain,
% 45.70/29.79 (d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.79 inference(modus_ponens,[status(thm)],[694, 2150])).
% 45.70/29.79 tff(2152,plain,
% 45.70/29.79 ((~(d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.79 inference(tautology,[status(thm)],[])).
% 45.70/29.79 tff(2153,plain,
% 45.70/29.79 (d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.79 inference(unit_resolution,[status(thm)],[2152, 2151, 2147])).
% 45.70/29.79 tff(2154,plain,
% 45.70/29.79 ((d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) | (~(phi(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) = err))) | (~d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.79 inference(tautology,[status(thm)],[])).
% 45.70/29.79 tff(2155,plain,
% 45.70/29.79 (d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) | (~(phi(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) = err))),
% 45.70/29.79 inference(unit_resolution,[status(thm)],[2154, 2153])).
% 45.70/29.79 tff(2156,plain,
% 45.70/29.79 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)))) | (~(phi(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)))))) | (~(d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) | (~(phi(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)))) | (~(phi(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)))))) | (~(d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) | (~(phi(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) = err)))))),
% 45.70/29.79 inference(rewrite,[status(thm)],[])).
% 45.70/29.79 tff(2157,plain,
% 45.70/29.79 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)))) | (~(phi(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)))))) | (~(d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) | (~(phi(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) = err)))))),
% 45.70/29.79 inference(quant_inst,[status(thm)],[])).
% 45.70/29.79 tff(2158,plain,
% 45.70/29.79 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)))) | (~(phi(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)))))) | (~(d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) | (~(phi(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) = err))))),
% 45.70/29.79 inference(modus_ponens,[status(thm)],[2157, 2156])).
% 45.70/29.79 tff(2159,plain,
% 45.70/29.79 ((~((~d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)))) | (~(phi(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)))))) | (~(d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) | (~(phi(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) = err))))),
% 45.70/29.79 inference(unit_resolution,[status(thm)],[2158, 17])).
% 45.70/29.79 tff(2160,plain,
% 45.70/29.79 (~((~d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)))) | (~(phi(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)))))),
% 45.70/29.79 inference(unit_resolution,[status(thm)],[2159, 2155])).
% 45.70/29.79 tff(2161,plain,
% 45.70/29.79 (((~d(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)))) | (~(phi(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))))) | (phi(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.79 inference(tautology,[status(thm)],[])).
% 45.70/29.79 tff(2162,plain,
% 45.70/29.79 (phi(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7))),
% 45.70/29.79 inference(unit_resolution,[status(thm)],[2161, 2160])).
% 45.70/29.79 tff(2163,plain,
% 45.70/29.79 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)) = phi(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.79 inference(symmetry,[status(thm)],[2162])).
% 45.70/29.79 tff(2164,plain,
% 45.70/29.79 (impl(not1(false), tptp_fun_R_5(P!7)) = impl(impl(impl(f5(P!7, not1(false)), not1(false)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))),
% 45.70/29.79 inference(symmetry,[status(thm)],[2057])).
% 45.70/29.79 tff(2165,plain,
% 45.70/29.79 (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = impl(not1(false), tptp_fun_R_5(P!7))),
% 45.70/29.79 inference(monotonicity,[status(thm)],[2071])).
% 45.70/29.79 tff(2166,plain,
% 45.70/29.79 (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)),
% 45.70/29.79 inference(transitivity,[status(thm)],[2165, 1262])).
% 45.70/29.79 tff(2167,plain,
% 45.70/29.79 ((impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false) <=> (tptp_fun_R_5(P!7) = false)),
% 45.70/29.79 inference(monotonicity,[status(thm)],[2166])).
% 45.70/29.79 tff(2168,plain,
% 45.70/29.79 ((~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false)) <=> (~(tptp_fun_R_5(P!7) = false))),
% 45.70/29.79 inference(monotonicity,[status(thm)],[2167])).
% 45.70/29.79 tff(2169,plain,
% 45.70/29.79 (((~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))))))) | ((~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))))),
% 45.70/29.79 inference(tautology,[status(thm)],[])).
% 45.70/29.79 tff(2170,plain,
% 45.70/29.79 ((~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)))),
% 45.70/29.79 inference(unit_resolution,[status(thm)],[2169, 1953])).
% 45.70/29.79 tff(2171,plain,
% 45.70/29.79 ((~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))))) | (~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)))),
% 45.70/29.79 inference(tautology,[status(thm)],[])).
% 45.70/29.79 tff(2172,plain,
% 45.70/29.79 ((~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)))),
% 45.70/29.79 inference(unit_resolution,[status(thm)],[2171, 2170])).
% 45.70/29.79 tff(2173,plain,
% 45.70/29.79 (~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false)),
% 45.70/29.79 inference(unit_resolution,[status(thm)],[2172, 2098])).
% 45.70/29.79 tff(2174,plain,
% 45.70/29.79 (~(tptp_fun_R_5(P!7) = false)),
% 45.70/29.79 inference(modus_ponens,[status(thm)],[2173, 2168])).
% 45.70/29.79 tff(2175,plain,
% 45.70/29.79 (tptp_fun_R_5(P!7) = not1(false)),
% 45.70/29.79 inference(unit_resolution,[status(thm)],[1393, 2174, 2061])).
% 45.70/29.79 tff(2176,plain,
% 45.70/29.79 (not1(false) = tptp_fun_R_5(P!7)),
% 45.70/29.79 inference(symmetry,[status(thm)],[2175])).
% 45.70/29.79 tff(2177,plain,
% 45.70/29.79 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = false),
% 45.70/29.79 inference(transitivity,[status(thm)],[522, 645, 647, 677, 2051, 2176, 2118, 2164, 2143, 2163, 2145, 2140, 2137, 2135, 2132, 2130, 2121, 2113])).
% 45.70/29.79 tff(2178,plain,
% 45.70/29.79 ($false),
% 45.70/29.79 inference(unit_resolution,[status(thm)],[1270, 2177])).
% 45.70/29.79 tff(2179,plain,((phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false)), inference(lemma,lemma(discharge,[]))).
% 45.70/29.79 tff(2180,plain,
% 45.70/29.79 (phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err),
% 45.70/29.79 inference(unit_resolution,[status(thm)],[2179, 432])).
% 45.70/29.79 tff(2181,plain,
% 45.70/29.79 (f5(P!7, not1(false)) = err),
% 45.70/29.79 inference(transitivity,[status(thm)],[529, 2180])).
% 45.70/29.79 tff(2182,plain,
% 45.70/29.79 (phi(f5(P!7, not1(false))) = phi(err)),
% 45.70/29.79 inference(monotonicity,[status(thm)],[2181])).
% 45.70/29.79 tff(2183,plain,
% 45.70/29.79 (impl(f5(P!7, not1(false)), not1(false)) = err),
% 45.70/29.79 inference(transitivity,[status(thm)],[676, 2182, 429])).
% 45.70/29.79 tff(2184,plain,
% 45.70/29.79 (lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = lazy_impl(not1(false), err)),
% 45.70/29.79 inference(monotonicity,[status(thm)],[275, 2183])).
% 45.70/29.79 tff(2185,plain,
% 45.70/29.79 (lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = err),
% 45.70/29.79 inference(transitivity,[status(thm)],[2184, 431, 429])).
% 45.70/29.79 tff(2186,plain,
% 45.70/29.79 (bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) <=> bool(err)),
% 45.70/29.79 inference(monotonicity,[status(thm)],[2185])).
% 45.70/29.79 tff(2187,plain,
% 45.70/29.79 (bool(err) <=> bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))),
% 45.70/29.79 inference(symmetry,[status(thm)],[2186])).
% 45.70/29.79 tff(2188,plain,
% 45.70/29.79 ((~bool(err)) <=> (~bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))))),
% 45.70/29.79 inference(monotonicity,[status(thm)],[2187])).
% 45.70/29.79 tff(2189,plain,
% 45.70/29.79 (~bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))),
% 45.70/29.79 inference(modus_ponens,[status(thm)],[571, 2188])).
% 45.70/29.79 tff(2190,plain,
% 45.70/29.79 (d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) <=> d(err)),
% 45.70/29.79 inference(monotonicity,[status(thm)],[2185])).
% 45.70/29.79 tff(2191,plain,
% 45.70/29.79 (d(err) <=> d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))),
% 45.70/29.79 inference(symmetry,[status(thm)],[2190])).
% 45.70/29.79 tff(2192,plain,
% 45.70/29.79 (d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))),
% 45.70/29.79 inference(modus_ponens,[status(thm)],[396, 2191])).
% 45.70/29.79 tff(2193,assumption,(~bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))), introduced(assumption)).
% 45.70/29.79 tff(2194,plain,
% 45.70/29.79 ($false),
% 45.70/29.79 inference(unit_resolution,[status(thm)],[773, 734, 729, 730, 2193])).
% 45.70/29.79 tff(2195,plain,((~(prop(tptp_fun_R_5(P!7)) = false)) | (~d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))) | bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))), inference(lemma,lemma(discharge,[]))).
% 45.70/29.79 tff(2196,plain,
% 45.70/29.79 (~(prop(tptp_fun_R_5(P!7)) = false)),
% 45.70/29.79 inference(unit_resolution,[status(thm)],[2195, 2192, 2189])).
% 45.70/29.79 tff(2197,plain,
% 45.70/29.79 (bool(tptp_fun_R_5(P!7))),
% 45.70/29.79 inference(unit_resolution,[status(thm)],[1256, 2196])).
% 45.70/29.79 tff(2198,plain,
% 45.70/29.79 (impl(false, tptp_fun_R_5(P!7)) = not1(false)),
% 45.70/29.79 inference(unit_resolution,[status(thm)],[1286, 2197])).
% 45.70/29.79 tff(2199,plain,
% 45.70/29.79 ((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = not1(false))),
% 45.70/29.79 inference(unit_resolution,[status(thm)],[1281, 2197])).
% 45.70/29.79 tff(2200,plain,
% 45.70/29.79 (prop(tptp_fun_R_5(P!7)) = not1(false)),
% 45.70/29.79 inference(unit_resolution,[status(thm)],[1276, 2197])).
% 45.70/29.79 tff(2201,plain,
% 45.70/29.79 (impl(not1(false), tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)),
% 45.70/29.79 inference(unit_resolution,[status(thm)],[1261, 2197])).
% 45.70/29.79 tff(2202,plain,
% 45.70/29.79 (lazy_impl(not1(false), impl(f5(P!7, not1(false)), not1(false))) = lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))),
% 45.70/29.79 inference(monotonicity,[status(thm)],[600])).
% 45.70/29.79 tff(2203,plain,
% 45.70/29.79 (phi(impl(f5(P!7, not1(false)), not1(false))) = lazy_impl(not1(false), impl(f5(P!7, not1(false)), not1(false)))),
% 45.70/29.79 inference(symmetry,[status(thm)],[682])).
% 45.70/29.79 tff(2204,plain,
% 45.70/29.79 (phi(impl(f5(P!7, not1(false)), not1(false))) = err),
% 45.70/29.79 inference(transitivity,[status(thm)],[2203, 2202, 2184, 431, 429])).
% 45.70/29.79 tff(2205,assumption,(phi(impl(f5(P!7, not1(false)), not1(false))) = err), introduced(assumption)).
% 45.70/29.79 tff(2206,plain,
% 45.70/29.79 (lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = lazy_impl(not1(false), impl(f5(P!7, not1(false)), not1(false)))),
% 45.70/29.79 inference(symmetry,[status(thm)],[2202])).
% 45.70/29.79 tff(2207,assumption,(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))), introduced(assumption)).
% 45.70/29.79 tff(2208,plain,
% 45.70/29.79 (f5(P!7, not1(false)) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false)))),
% 45.70/29.79 inference(transitivity,[status(thm)],[529, 2207, 521, 651])).
% 45.70/29.79 tff(2209,plain,
% 45.70/29.79 (impl(f5(P!7, not1(false)), not1(false)) = impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))),
% 45.70/29.79 inference(monotonicity,[status(thm)],[2208])).
% 45.70/29.79 tff(2210,plain,
% 45.70/29.79 (lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = lazy_impl(prop(not1(false)), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)))),
% 45.70/29.79 inference(monotonicity,[status(thm)],[2209])).
% 45.70/29.79 tff(2211,plain,
% 45.70/29.79 (lazy_impl(prop(not1(false)), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))) = lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))),
% 45.70/29.79 inference(symmetry,[status(thm)],[2210])).
% 45.70/29.79 tff(2212,plain,
% 45.70/29.79 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(apply(P!7, tptp_fun_X_4(not1(false), P!7)), false, not1(false)) = lazy_impl(prop(not1(false)), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))))),
% 45.70/29.79 inference(quant_inst,[status(thm)],[])).
% 45.70/29.79 tff(2213,plain,
% 45.70/29.79 (f1(apply(P!7, tptp_fun_X_4(not1(false), P!7)), false, not1(false)) = lazy_impl(prop(not1(false)), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)))),
% 45.70/29.79 inference(unit_resolution,[status(thm)],[2212, 2128])).
% 45.70/29.79 tff(2214,assumption,(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false)), introduced(assumption)).
% 45.70/29.79 tff(2215,plain,
% 45.70/29.79 (f1(apply(P!7, tptp_fun_X_4(not1(false), P!7)), false, not1(false)) = f1(not1(false), false, not1(false))),
% 45.70/29.79 inference(monotonicity,[status(thm)],[2214])).
% 45.70/29.79 tff(2216,plain,
% 45.70/29.79 (f1(not1(false), false, not1(false)) = f1(apply(P!7, tptp_fun_X_4(not1(false), P!7)), false, not1(false))),
% 45.70/29.79 inference(symmetry,[status(thm)],[2215])).
% 45.70/29.79 tff(2217,plain,
% 45.70/29.79 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(not1(false), false, not1(false)) = lazy_impl(prop(not1(false)), impl(impl(not1(false), impl(false, not1(false))), not1(false))))),
% 45.70/29.79 inference(quant_inst,[status(thm)],[])).
% 45.70/29.79 tff(2218,plain,
% 45.70/29.79 (f1(not1(false), false, not1(false)) = lazy_impl(prop(not1(false)), impl(impl(not1(false), impl(false, not1(false))), not1(false)))),
% 45.70/29.79 inference(unit_resolution,[status(thm)],[2217, 2128])).
% 45.70/29.79 tff(2219,plain,
% 45.70/29.79 (lazy_impl(prop(not1(false)), impl(impl(not1(false), impl(false, not1(false))), not1(false))) = f1(not1(false), false, not1(false))),
% 45.70/29.79 inference(symmetry,[status(thm)],[2218])).
% 45.70/29.79 tff(2220,plain,
% 45.70/29.79 (impl(not1(false), impl(false, not1(false))) = impl(not1(false), not1(false))),
% 45.70/29.79 inference(monotonicity,[status(thm)],[421])).
% 45.70/29.79 tff(2221,plain,
% 45.70/29.79 (impl(not1(false), impl(false, not1(false))) = not1(false)),
% 45.70/29.79 inference(transitivity,[status(thm)],[2220, 501])).
% 45.70/29.79 tff(2222,plain,
% 45.70/29.79 (impl(impl(not1(false), impl(false, not1(false))), not1(false)) = impl(not1(false), not1(false))),
% 45.70/29.79 inference(monotonicity,[status(thm)],[2221])).
% 45.70/29.79 tff(2223,plain,
% 45.70/29.79 (impl(impl(not1(false), impl(false, not1(false))), not1(false)) = not1(false)),
% 45.70/29.79 inference(transitivity,[status(thm)],[2222, 501])).
% 45.70/29.80 tff(2224,plain,
% 45.70/29.80 (lazy_impl(prop(not1(false)), impl(impl(not1(false), impl(false, not1(false))), not1(false))) = lazy_impl(not1(false), not1(false))),
% 45.70/29.80 inference(monotonicity,[status(thm)],[275, 2223])).
% 45.70/29.80 tff(2225,plain,
% 45.70/29.80 (lazy_impl(not1(false), not1(false)) = lazy_impl(prop(not1(false)), impl(impl(not1(false), impl(false, not1(false))), not1(false)))),
% 45.70/29.80 inference(symmetry,[status(thm)],[2224])).
% 45.70/29.80 tff(2226,plain,
% 45.70/29.80 (not1(false) = err),
% 45.70/29.80 inference(transitivity,[status(thm)],[603, 602, 2225, 2219, 2216, 2213, 2211, 2206, 682, 2205])).
% 45.70/29.80 tff(2227,plain,
% 45.70/29.80 ($false),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[564, 2226])).
% 45.70/29.80 tff(2228,plain,((~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))) | (~(phi(impl(f5(P!7, not1(false)), not1(false))) = err)) | (~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))))), inference(lemma,lemma(discharge,[]))).
% 45.70/29.80 tff(2229,plain,
% 45.70/29.80 ((~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))) | (~(phi(impl(f5(P!7, not1(false)), not1(false))) = err))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[2228, 644])).
% 45.70/29.80 tff(2230,plain,
% 45.70/29.80 (~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[2229, 2204])).
% 45.70/29.80 tff(2231,plain,
% 45.70/29.80 (~((apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false)))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[484, 2230, 432])).
% 45.70/29.80 tff(2232,plain,
% 45.70/29.80 (~bool(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[1206, 2231])).
% 45.70/29.80 tff(2233,assumption,(~bool(apply(P!7, tptp_fun_X_4(not1(false), P!7)))), introduced(assumption)).
% 45.70/29.80 tff(2234,plain,
% 45.70/29.80 (phi(apply(P!7, tptp_fun_X_3(P!7))) = f7(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.70/29.80 inference(transitivity,[status(thm)],[1614, 1611, 292])).
% 45.70/29.80 tff(2235,plain,
% 45.70/29.80 (forallprefers(phi(apply(P!7, tptp_fun_X_3(P!7))), false) <=> forallprefers(f7(apply(P!7, tptp_fun_X_3(P!7))), f7(P!6))),
% 45.70/29.80 inference(monotonicity,[status(thm)],[2234, 289])).
% 45.70/29.80 tff(2236,plain,
% 45.70/29.80 (forallprefers(f7(apply(P!7, tptp_fun_X_3(P!7))), f7(P!6)) <=> forallprefers(phi(apply(P!7, tptp_fun_X_3(P!7))), false)),
% 45.70/29.80 inference(symmetry,[status(thm)],[2235])).
% 45.70/29.80 tff(2237,plain,
% 45.70/29.80 ((~forallprefers(f7(apply(P!7, tptp_fun_X_3(P!7))), f7(P!6))) <=> (~forallprefers(phi(apply(P!7, tptp_fun_X_3(P!7))), false))),
% 45.70/29.80 inference(monotonicity,[status(thm)],[2236])).
% 45.70/29.80 tff(2238,plain,
% 45.70/29.80 (~forallprefers(phi(apply(P!7, tptp_fun_X_3(P!7))), false)),
% 45.70/29.80 inference(modus_ponens,[status(thm)],[1642, 2237])).
% 45.70/29.80 tff(2239,plain,
% 45.70/29.80 (~((~((~d(false)) | d(phi(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(false = not1(false))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = false)))) | (~((~d(false)) | (~bool(false)) | (~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | bool(phi(apply(P!7, tptp_fun_X_3(P!7)))))))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[2022, 2238, 166])).
% 45.70/29.80 tff(2240,plain,
% 45.70/29.80 ((~d(false)) | (~bool(false)) | (~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | bool(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[2024, 2239])).
% 45.70/29.80 tff(2241,plain,
% 45.70/29.80 ((~d(false)) | d(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[2026, 2239])).
% 45.70/29.80 tff(2242,plain,
% 45.70/29.80 (d(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[2029, 2241])).
% 45.70/29.80 tff(2243,plain,
% 45.70/29.80 (bool(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[2032, 2242, 2240])).
% 45.70/29.80 tff(2244,plain,
% 45.70/29.80 (prop(phi(apply(P!7, tptp_fun_X_3(P!7)))) = not1(false)),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[1132, 2243])).
% 45.70/29.80 tff(2245,plain,
% 45.70/29.80 (d(phi(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(phi(apply(P!7, tptp_fun_X_3(P!7)))) = err))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[948, 2242])).
% 45.70/29.80 tff(2246,plain,
% 45.70/29.80 (~((~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~(phi(phi(apply(P!7, tptp_fun_X_3(P!7)))) = phi(apply(P!7, tptp_fun_X_3(P!7))))))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[952, 17, 2245])).
% 45.70/29.80 tff(2247,plain,
% 45.70/29.80 (phi(phi(apply(P!7, tptp_fun_X_3(P!7)))) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[955, 2246])).
% 45.70/29.80 tff(2248,plain,
% 45.70/29.80 (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err)),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[1127, 2247, 2244])).
% 45.70/29.80 tff(2249,plain,
% 45.70/29.80 (d(apply(P!7, tptp_fun_X_3(P!7))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[385, 2248])).
% 45.70/29.80 tff(2250,plain,
% 45.70/29.80 (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[383, 2249])).
% 45.70/29.80 tff(2251,plain,
% 45.70/29.80 (d(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[374, 2250])).
% 45.70/29.80 tff(2252,plain,
% 45.70/29.80 (((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))))) | (~(d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_4(not1(false), P!7))))))) | (d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))),
% 45.70/29.80 inference(tautology,[status(thm)],[])).
% 45.70/29.80 tff(2253,plain,
% 45.70/29.80 (d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[2252, 1238])).
% 45.70/29.80 tff(2254,plain,
% 45.70/29.80 ((~(d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.70/29.80 inference(tautology,[status(thm)],[])).
% 45.70/29.80 tff(2255,plain,
% 45.70/29.80 (d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[2254, 2253])).
% 45.70/29.80 tff(2256,plain,
% 45.70/29.80 (d(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[2255, 2251])).
% 45.70/29.80 tff(2257,plain,
% 45.70/29.80 ($false),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[2045, 2256, 2251, 2233, 1606])).
% 45.70/29.80 tff(2258,plain,((~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(not1(false), P!7)))), inference(lemma,lemma(discharge,[]))).
% 45.70/29.80 tff(2259,plain,
% 45.70/29.80 (~bool(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[2258, 2232])).
% 45.70/29.80 tff(2260,plain,
% 45.70/29.80 (((~![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))) | (bool(apply(P!7, tptp_fun_X_3(P!7))) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = apply(P!7, tptp_fun_X_3(P!7))) | bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))))) <=> ((~![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = apply(P!7, tptp_fun_X_3(P!7))) | bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))))),
% 45.70/29.80 inference(rewrite,[status(thm)],[])).
% 45.70/29.80 tff(2261,plain,
% 45.70/29.80 ((bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = apply(P!7, tptp_fun_X_3(P!7)))) <=> (bool(apply(P!7, tptp_fun_X_3(P!7))) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = apply(P!7, tptp_fun_X_3(P!7))) | bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))))),
% 45.70/29.80 inference(rewrite,[status(thm)],[])).
% 45.70/29.80 tff(2262,plain,
% 45.70/29.80 (((~![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))) | (bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = apply(P!7, tptp_fun_X_3(P!7))))) <=> ((~![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))) | (bool(apply(P!7, tptp_fun_X_3(P!7))) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = apply(P!7, tptp_fun_X_3(P!7))) | bool(apply(P!7, tptp_fun_X_4(not1(false), P!7)))))),
% 45.70/29.80 inference(monotonicity,[status(thm)],[2261])).
% 45.70/29.80 tff(2263,plain,
% 45.70/29.80 (((~![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))) | (bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = apply(P!7, tptp_fun_X_3(P!7))))) <=> ((~![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = apply(P!7, tptp_fun_X_3(P!7))) | bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))))),
% 45.70/29.80 inference(transitivity,[status(thm)],[2262, 2260])).
% 45.70/29.80 tff(2264,plain,
% 45.70/29.80 ((~![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))) | (bool(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = apply(P!7, tptp_fun_X_3(P!7))))),
% 45.70/29.80 inference(quant_inst,[status(thm)],[])).
% 45.70/29.80 tff(2265,plain,
% 45.70/29.80 ((~![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = apply(P!7, tptp_fun_X_3(P!7))) | bool(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.70/29.80 inference(modus_ponens,[status(thm)],[2264, 2263])).
% 45.70/29.80 tff(2266,plain,
% 45.70/29.80 (bool(apply(P!7, tptp_fun_X_3(P!7))) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = apply(P!7, tptp_fun_X_3(P!7))) | bool(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[2265, 1591])).
% 45.70/29.80 tff(2267,plain,
% 45.70/29.80 (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = apply(P!7, tptp_fun_X_3(P!7))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[2266, 2259, 2232])).
% 45.70/29.80 tff(2268,plain,
% 45.70/29.80 (apply(P!7, tptp_fun_X_3(P!7)) = apply(P!7, tptp_fun_X_4(not1(false), P!7))),
% 45.70/29.80 inference(symmetry,[status(thm)],[2267])).
% 45.70/29.80 tff(2269,plain,
% 45.70/29.80 (phi(apply(P!7, tptp_fun_X_3(P!7))) = phi(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.70/29.80 inference(monotonicity,[status(thm)],[2268])).
% 45.70/29.80 tff(2270,plain,
% 45.70/29.80 (exists1(P!7) = err),
% 45.70/29.80 inference(transitivity,[status(thm)],[346, 2269, 783, 522, 645, 2180])).
% 45.70/29.80 tff(2271,plain,
% 45.70/29.80 ((exists1(P!7) = exists2(P!7)) <=> (err = phi(f6(P!7, tptp_fun_R_5(P!7))))),
% 45.70/29.80 inference(monotonicity,[status(thm)],[2270, 880])).
% 45.70/29.80 tff(2272,plain,
% 45.70/29.80 ((exists1(P!7) = exists2(P!7)) <=> (phi(f6(P!7, tptp_fun_R_5(P!7))) = err)),
% 45.70/29.80 inference(transitivity,[status(thm)],[2271, 1679])).
% 45.70/29.80 tff(2273,plain,
% 45.70/29.80 ((~(exists1(P!7) = exists2(P!7))) <=> (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = err))),
% 45.70/29.80 inference(monotonicity,[status(thm)],[2272])).
% 45.70/29.80 tff(2274,plain,
% 45.70/29.80 (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = err)),
% 45.70/29.80 inference(modus_ponens,[status(thm)],[897, 2273])).
% 45.70/29.80 tff(2275,plain,
% 45.70/29.80 (d(f6(P!7, tptp_fun_R_5(P!7))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = err))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[1315, 2274])).
% 45.70/29.80 tff(2276,plain,
% 45.70/29.80 (~((~d(f6(P!7, tptp_fun_R_5(P!7)))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = f6(P!7, tptp_fun_R_5(P!7)))))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[1320, 2275])).
% 45.70/29.80 tff(2277,plain,
% 45.70/29.80 (d(f6(P!7, tptp_fun_R_5(P!7)))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[1322, 2276])).
% 45.70/29.80 tff(2278,plain,
% 45.70/29.80 (d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.80 inference(modus_ponens,[status(thm)],[2277, 328])).
% 45.70/29.80 tff(2279,plain,
% 45.70/29.80 (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[773, 2278, 2192, 2189])).
% 45.70/29.80 tff(2280,plain,
% 45.70/29.80 (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[1708, 2279, 2201, 2200, 2199, 2198])).
% 45.70/29.80 tff(2281,plain,
% 45.70/29.80 (phi(f6(P!7, tptp_fun_R_5(P!7))) = f6(P!7, tptp_fun_R_5(P!7))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[1334, 2276])).
% 45.70/29.80 tff(2282,plain,
% 45.70/29.80 (f6(P!7, tptp_fun_R_5(P!7)) = phi(f6(P!7, tptp_fun_R_5(P!7)))),
% 45.70/29.80 inference(symmetry,[status(thm)],[2281])).
% 45.70/29.80 tff(2283,plain,
% 45.70/29.80 (not1(false) = prop(tptp_fun_R_5(P!7))),
% 45.70/29.80 inference(symmetry,[status(thm)],[2200])).
% 45.70/29.80 tff(2284,plain,
% 45.70/29.80 (lazy_impl(not1(false), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.80 inference(monotonicity,[status(thm)],[2283])).
% 45.70/29.80 tff(2285,plain,
% 45.70/29.80 (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(not1(false), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.80 inference(symmetry,[status(thm)],[1331])).
% 45.70/29.80 tff(2286,plain,
% 45.70/29.80 (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = phi(f6(P!7, tptp_fun_R_5(P!7)))),
% 45.70/29.80 inference(transitivity,[status(thm)],[2285, 2284, 326, 2282])).
% 45.70/29.80 tff(2287,plain,
% 45.70/29.80 ((phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err) <=> (phi(f6(P!7, tptp_fun_R_5(P!7))) = err)),
% 45.70/29.80 inference(monotonicity,[status(thm)],[2286])).
% 45.70/29.80 tff(2288,plain,
% 45.70/29.80 ((phi(f6(P!7, tptp_fun_R_5(P!7))) = err) <=> (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)),
% 45.70/29.80 inference(symmetry,[status(thm)],[2287])).
% 45.70/29.80 tff(2289,plain,
% 45.70/29.80 ((~(phi(f6(P!7, tptp_fun_R_5(P!7))) = err)) <=> (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err))),
% 45.70/29.80 inference(monotonicity,[status(thm)],[2288])).
% 45.70/29.80 tff(2290,plain,
% 45.70/29.80 (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)),
% 45.70/29.80 inference(modus_ponens,[status(thm)],[2274, 2289])).
% 45.70/29.80 tff(2291,plain,
% 45.70/29.80 (d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[1342, 2290])).
% 45.70/29.80 tff(2292,plain,
% 45.70/29.80 (~((~d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[1347, 2291])).
% 45.70/29.80 tff(2293,plain,
% 45.70/29.80 ($false),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[1349, 2292, 2280])).
% 45.70/29.80 tff(2294,plain,(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false), inference(lemma,lemma(discharge,[]))).
% 45.70/29.80 tff(2295,plain,
% 45.70/29.80 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = impl(false, not1(false))),
% 45.70/29.80 inference(monotonicity,[status(thm)],[2294])).
% 45.70/29.80 tff(2296,plain,
% 45.70/29.80 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(apply(P!7, tptp_fun_X_4(false, P!7))) <=> ((apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))))),
% 45.70/29.80 inference(quant_inst,[status(thm)],[])).
% 45.70/29.80 tff(2297,plain,
% 45.70/29.80 (bool(apply(P!7, tptp_fun_X_4(false, P!7))) <=> ((apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false)))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[2296, 249])).
% 45.70/29.80 tff(2298,plain,
% 45.70/29.80 (phi(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))) = phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 45.70/29.80 inference(monotonicity,[status(thm)],[522])).
% 45.70/29.80 tff(2299,plain,
% 45.70/29.80 (phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = phi(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)))),
% 45.70/29.80 inference(symmetry,[status(thm)],[2298])).
% 45.70/29.80 tff(2300,plain,
% 45.70/29.80 (f5(P!7, not1(false)) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))),
% 45.70/29.80 inference(transitivity,[status(thm)],[529, 644])).
% 45.70/29.80 tff(2301,plain,
% 45.70/29.80 (phi(f5(P!7, not1(false))) = phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 45.70/29.80 inference(monotonicity,[status(thm)],[2300])).
% 45.70/29.80 tff(2302,plain,
% 45.70/29.80 (phi(f5(P!7, not1(false))) = phi(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)))),
% 45.70/29.80 inference(transitivity,[status(thm)],[2301, 2299])).
% 45.70/29.80 tff(2303,plain,
% 45.70/29.80 (impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), not1(false)) = impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))),
% 45.70/29.80 inference(monotonicity,[status(thm)],[651])).
% 45.70/29.80 tff(2304,plain,
% 45.70/29.80 (impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)) = impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), not1(false))),
% 45.70/29.80 inference(symmetry,[status(thm)],[2303])).
% 45.70/29.80 tff(2305,plain,
% 45.70/29.80 (impl(f5(P!7, not1(false)), not1(false)) = impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), not1(false))),
% 45.70/29.80 inference(transitivity,[status(thm)],[1856, 2304])).
% 45.70/29.80 tff(2306,plain,
% 45.70/29.80 ((impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false)))) <=> (impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), not1(false)) = phi(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))))),
% 45.70/29.80 inference(monotonicity,[status(thm)],[2305, 2302])).
% 45.70/29.80 tff(2307,plain,
% 45.70/29.80 ((impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), not1(false)) = phi(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)))) <=> (impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false))))),
% 45.70/29.80 inference(symmetry,[status(thm)],[2306])).
% 45.70/29.80 tff(2308,plain,
% 45.70/29.80 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = impl(false, not1(false))),
% 45.70/29.80 inference(monotonicity,[status(thm)],[588])).
% 45.70/29.80 tff(2309,plain,
% 45.70/29.80 (impl(false, not1(false)) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))),
% 45.70/29.80 inference(symmetry,[status(thm)],[2308])).
% 45.70/29.80 tff(2310,plain,
% 45.70/29.80 (not1(false) = impl(false, not1(false))),
% 45.70/29.80 inference(symmetry,[status(thm)],[421])).
% 45.70/29.80 tff(2311,plain,
% 45.70/29.80 (not1(false) = phi(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)))),
% 45.70/29.80 inference(transitivity,[status(thm)],[2310, 2309, 522, 645, 2299])).
% 45.70/29.80 tff(2312,assumption,(~(phi(impl(f5(P!7, not1(false)), not1(false))) = impl(f5(P!7, not1(false)), not1(false)))), introduced(assumption)).
% 45.70/29.80 tff(2313,plain,
% 45.70/29.80 ((impl(f5(P!7, not1(false)), not1(false)) = phi(impl(f5(P!7, not1(false)), not1(false)))) <=> (phi(impl(f5(P!7, not1(false)), not1(false))) = impl(f5(P!7, not1(false)), not1(false)))),
% 45.70/29.80 inference(commutativity,[status(thm)],[])).
% 45.70/29.80 tff(2314,plain,
% 45.70/29.80 (((~d(impl(f5(P!7, not1(false)), not1(false)))) | (~(phi(impl(f5(P!7, not1(false)), not1(false))) = impl(f5(P!7, not1(false)), not1(false))))) | (phi(impl(f5(P!7, not1(false)), not1(false))) = impl(f5(P!7, not1(false)), not1(false)))),
% 45.70/29.80 inference(tautology,[status(thm)],[])).
% 45.70/29.80 tff(2315,plain,
% 45.70/29.80 ((~d(impl(f5(P!7, not1(false)), not1(false)))) | (~(phi(impl(f5(P!7, not1(false)), not1(false))) = impl(f5(P!7, not1(false)), not1(false))))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[2314, 2312])).
% 45.70/29.80 tff(2316,plain,
% 45.70/29.80 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(f5(P!7, not1(false)), not1(false)))) | (~(phi(impl(f5(P!7, not1(false)), not1(false))) = impl(f5(P!7, not1(false)), not1(false)))))) | (~(d(impl(f5(P!7, not1(false)), not1(false))) | (~(phi(impl(f5(P!7, not1(false)), not1(false))) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(impl(f5(P!7, not1(false)), not1(false)))) | (~(phi(impl(f5(P!7, not1(false)), not1(false))) = impl(f5(P!7, not1(false)), not1(false)))))) | (~(d(impl(f5(P!7, not1(false)), not1(false))) | (~(phi(impl(f5(P!7, not1(false)), not1(false))) = err)))))),
% 45.70/29.80 inference(rewrite,[status(thm)],[])).
% 45.70/29.80 tff(2317,plain,
% 45.70/29.80 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(f5(P!7, not1(false)), not1(false)))) | (~(phi(impl(f5(P!7, not1(false)), not1(false))) = impl(f5(P!7, not1(false)), not1(false)))))) | (~(d(impl(f5(P!7, not1(false)), not1(false))) | (~(phi(impl(f5(P!7, not1(false)), not1(false))) = err)))))),
% 45.70/29.80 inference(quant_inst,[status(thm)],[])).
% 45.70/29.80 tff(2318,plain,
% 45.70/29.80 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(impl(f5(P!7, not1(false)), not1(false)))) | (~(phi(impl(f5(P!7, not1(false)), not1(false))) = impl(f5(P!7, not1(false)), not1(false)))))) | (~(d(impl(f5(P!7, not1(false)), not1(false))) | (~(phi(impl(f5(P!7, not1(false)), not1(false))) = err))))),
% 45.70/29.80 inference(modus_ponens,[status(thm)],[2317, 2316])).
% 45.70/29.80 tff(2319,plain,
% 45.70/29.80 ((~((~d(impl(f5(P!7, not1(false)), not1(false)))) | (~(phi(impl(f5(P!7, not1(false)), not1(false))) = impl(f5(P!7, not1(false)), not1(false)))))) | (~(d(impl(f5(P!7, not1(false)), not1(false))) | (~(phi(impl(f5(P!7, not1(false)), not1(false))) = err))))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[2318, 17])).
% 45.70/29.80 tff(2320,plain,
% 45.70/29.80 (~(d(impl(f5(P!7, not1(false)), not1(false))) | (~(phi(impl(f5(P!7, not1(false)), not1(false))) = err)))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[2319, 2315])).
% 45.70/29.80 tff(2321,plain,
% 45.70/29.80 ((d(impl(f5(P!7, not1(false)), not1(false))) | (~(phi(impl(f5(P!7, not1(false)), not1(false))) = err))) | (phi(impl(f5(P!7, not1(false)), not1(false))) = err)),
% 45.70/29.80 inference(tautology,[status(thm)],[])).
% 45.70/29.80 tff(2322,plain,
% 45.70/29.80 (phi(impl(f5(P!7, not1(false)), not1(false))) = err),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[2321, 2320])).
% 45.70/29.80 tff(2323,plain,
% 45.70/29.80 (err = phi(impl(f5(P!7, not1(false)), not1(false)))),
% 45.70/29.80 inference(symmetry,[status(thm)],[2322])).
% 45.70/29.80 tff(2324,plain,
% 45.70/29.80 (phi(f5(P!7, not1(false))) = phi(impl(f5(P!7, not1(false)), not1(false)))),
% 45.70/29.80 inference(transitivity,[status(thm)],[543, 429, 2323])).
% 45.70/29.80 tff(2325,plain,
% 45.70/29.80 ((impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false)))) <=> (impl(f5(P!7, not1(false)), not1(false)) = phi(impl(f5(P!7, not1(false)), not1(false))))),
% 45.70/29.80 inference(monotonicity,[status(thm)],[2324])).
% 45.70/29.80 tff(2326,plain,
% 45.70/29.80 ((impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false)))) <=> (phi(impl(f5(P!7, not1(false)), not1(false))) = impl(f5(P!7, not1(false)), not1(false)))),
% 45.70/29.80 inference(transitivity,[status(thm)],[2325, 2313])).
% 45.70/29.80 tff(2327,plain,
% 45.70/29.80 ((phi(impl(f5(P!7, not1(false)), not1(false))) = impl(f5(P!7, not1(false)), not1(false))) <=> (impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false))))),
% 45.70/29.80 inference(symmetry,[status(thm)],[2326])).
% 45.70/29.80 tff(2328,plain,
% 45.70/29.80 ((~(phi(impl(f5(P!7, not1(false)), not1(false))) = impl(f5(P!7, not1(false)), not1(false)))) <=> (~(impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false)))))),
% 45.70/29.80 inference(monotonicity,[status(thm)],[2327])).
% 45.70/29.80 tff(2329,plain,
% 45.70/29.80 (~(impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false))))),
% 45.70/29.80 inference(modus_ponens,[status(thm)],[2312, 2328])).
% 45.70/29.80 tff(2330,plain,
% 45.70/29.80 ($false),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[576, 2329, 572])).
% 45.70/29.80 tff(2331,plain,((~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err)) | (phi(impl(f5(P!7, not1(false)), not1(false))) = impl(f5(P!7, not1(false)), not1(false)))), inference(lemma,lemma(discharge,[]))).
% 45.70/29.80 tff(2332,plain,
% 45.70/29.80 (~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err)),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[2331, 2312])).
% 45.70/29.80 tff(2333,plain,
% 45.70/29.80 (d(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) | (~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[539, 2332])).
% 45.70/29.80 tff(2334,plain,
% 45.70/29.80 (~((~d(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))) | (~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[537, 2333])).
% 45.70/29.80 tff(2335,plain,
% 45.70/29.80 (phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[532, 2334])).
% 45.70/29.80 tff(2336,plain,
% 45.70/29.80 (f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)) = phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 45.70/29.80 inference(symmetry,[status(thm)],[2335])).
% 45.70/29.80 tff(2337,plain,
% 45.70/29.80 (f1(apply(P!7, tptp_fun_X_4(not1(false), P!7)), false, not1(false)) = f1(false, false, not1(false))),
% 45.70/29.80 inference(monotonicity,[status(thm)],[588])).
% 45.70/29.80 tff(2338,plain,
% 45.70/29.80 (f1(false, false, not1(false)) = f1(apply(P!7, tptp_fun_X_4(not1(false), P!7)), false, not1(false))),
% 45.70/29.80 inference(symmetry,[status(thm)],[2337])).
% 45.70/29.80 tff(2339,plain,
% 45.70/29.80 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(false, false, not1(false)) = lazy_impl(prop(not1(false)), impl(impl(false, impl(false, not1(false))), not1(false))))),
% 45.70/29.80 inference(quant_inst,[status(thm)],[])).
% 45.70/29.80 tff(2340,plain,
% 45.70/29.80 (f1(false, false, not1(false)) = lazy_impl(prop(not1(false)), impl(impl(false, impl(false, not1(false))), not1(false)))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[2339, 2128])).
% 45.70/29.80 tff(2341,plain,
% 45.70/29.80 (lazy_impl(prop(not1(false)), impl(impl(false, impl(false, not1(false))), not1(false))) = f1(false, false, not1(false))),
% 45.70/29.80 inference(symmetry,[status(thm)],[2340])).
% 45.70/29.80 tff(2342,plain,
% 45.70/29.80 (impl(false, impl(false, not1(false))) = impl(false, not1(false))),
% 45.70/29.80 inference(monotonicity,[status(thm)],[421])).
% 45.70/29.80 tff(2343,plain,
% 45.70/29.80 (impl(false, impl(false, not1(false))) = not1(false)),
% 45.70/29.80 inference(transitivity,[status(thm)],[2342, 421])).
% 45.70/29.80 tff(2344,plain,
% 45.70/29.80 (impl(impl(false, impl(false, not1(false))), not1(false)) = impl(not1(false), not1(false))),
% 45.70/29.80 inference(monotonicity,[status(thm)],[2343])).
% 45.70/29.80 tff(2345,plain,
% 45.70/29.80 (impl(impl(false, impl(false, not1(false))), not1(false)) = not1(false)),
% 45.70/29.80 inference(transitivity,[status(thm)],[2344, 501])).
% 45.70/29.80 tff(2346,plain,
% 45.70/29.80 (lazy_impl(prop(not1(false)), impl(impl(false, impl(false, not1(false))), not1(false))) = lazy_impl(not1(false), not1(false))),
% 45.70/29.80 inference(monotonicity,[status(thm)],[275, 2345])).
% 45.70/29.80 tff(2347,plain,
% 45.70/29.80 (lazy_impl(not1(false), not1(false)) = lazy_impl(prop(not1(false)), impl(impl(false, impl(false, not1(false))), not1(false)))),
% 45.70/29.80 inference(symmetry,[status(thm)],[2346])).
% 45.70/29.80 tff(2348,plain,
% 45.70/29.80 (not1(false) = err),
% 45.70/29.80 inference(transitivity,[status(thm)],[603, 602, 2347, 2341, 2338, 2213, 2211, 2206, 682, 2205])).
% 45.70/29.80 tff(2349,plain,
% 45.70/29.80 ($false),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[564, 2348])).
% 45.70/29.80 tff(2350,plain,((~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false)) | (~(phi(impl(f5(P!7, not1(false)), not1(false))) = err)) | (~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))))), inference(lemma,lemma(discharge,[]))).
% 45.70/29.80 tff(2351,plain,
% 45.70/29.80 (~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false)),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[2350, 2335, 2322])).
% 45.70/29.80 tff(2352,plain,
% 45.70/29.80 (~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[2228, 2335, 2322])).
% 45.70/29.80 tff(2353,plain,
% 45.70/29.80 (~((apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false) | (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false)))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[484, 2352, 2351])).
% 45.70/29.80 tff(2354,plain,
% 45.70/29.80 (~bool(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[482, 2353, 475])).
% 45.70/29.80 tff(2355,plain,
% 45.70/29.80 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = phi(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[480, 2354])).
% 45.70/29.80 tff(2356,plain,
% 45.70/29.80 (phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))),
% 45.70/29.80 inference(symmetry,[status(thm)],[2355])).
% 45.70/29.80 tff(2357,plain,
% 45.70/29.80 (phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 45.70/29.80 inference(transitivity,[status(thm)],[2356, 522, 2336])).
% 45.70/29.80 tff(2358,plain,
% 45.70/29.80 ((phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err) <=> (phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err)),
% 45.70/29.80 inference(monotonicity,[status(thm)],[2357])).
% 45.70/29.80 tff(2359,plain,
% 45.70/29.80 ((phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err) <=> (phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err)),
% 45.70/29.80 inference(symmetry,[status(thm)],[2358])).
% 45.70/29.80 tff(2360,plain,
% 45.70/29.80 ((~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err)) <=> (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err))),
% 45.70/29.80 inference(monotonicity,[status(thm)],[2359])).
% 45.70/29.80 tff(2361,plain,
% 45.70/29.80 (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err)),
% 45.70/29.80 inference(modus_ponens,[status(thm)],[2332, 2360])).
% 45.70/29.80 tff(2362,plain,
% 45.70/29.80 (d(apply(P!7, tptp_fun_X_4(not1(false), P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[616, 2361])).
% 45.70/29.80 tff(2363,plain,
% 45.70/29.80 (~((~d(apply(P!7, tptp_fun_X_4(not1(false), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = apply(P!7, tptp_fun_X_4(not1(false), P!7)))))),
% 45.70/29.80 inference(unit_resolution,[status(thm)],[513, 2362])).
% 45.70/29.81 tff(2364,plain,
% 45.70/29.81 (phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = apply(P!7, tptp_fun_X_4(not1(false), P!7))),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[508, 2363])).
% 45.70/29.81 tff(2365,plain,
% 45.70/29.81 (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = phi(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 45.70/29.81 inference(symmetry,[status(thm)],[2364])).
% 45.70/29.81 tff(2366,plain,
% 45.70/29.81 (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false)))),
% 45.70/29.81 inference(transitivity,[status(thm)],[2365, 2356, 651])).
% 45.70/29.81 tff(2367,plain,
% 45.70/29.81 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))),
% 45.70/29.81 inference(monotonicity,[status(thm)],[2366])).
% 45.70/29.81 tff(2368,plain,
% 45.70/29.81 (impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))),
% 45.70/29.81 inference(symmetry,[status(thm)],[2367])).
% 45.70/29.81 tff(2369,plain,
% 45.70/29.81 (impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), not1(false)) = phi(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)))),
% 45.70/29.81 inference(transitivity,[status(thm)],[2303, 2368, 522, 2336, 2299])).
% 45.70/29.81 tff(2370,plain,
% 45.70/29.81 (f5(P!7, not1(false)) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))),
% 45.70/29.81 inference(transitivity,[status(thm)],[529, 2335])).
% 45.70/29.81 tff(2371,plain,
% 45.70/29.81 (phi(f5(P!7, not1(false))) = phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 45.70/29.81 inference(monotonicity,[status(thm)],[2370])).
% 45.70/29.81 tff(2372,plain,
% 45.70/29.81 (phi(f5(P!7, not1(false))) = phi(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)))),
% 45.70/29.81 inference(transitivity,[status(thm)],[2371, 2299])).
% 45.70/29.81 tff(2373,plain,
% 45.70/29.81 (f5(P!7, not1(false)) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false)))),
% 45.70/29.81 inference(transitivity,[status(thm)],[529, 2335, 521, 651])).
% 45.70/29.81 tff(2374,plain,
% 45.70/29.81 (impl(f5(P!7, not1(false)), not1(false)) = impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))),
% 45.70/29.81 inference(monotonicity,[status(thm)],[2373])).
% 45.70/29.81 tff(2375,plain,
% 45.70/29.81 (impl(f5(P!7, not1(false)), not1(false)) = impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), not1(false))),
% 45.70/29.81 inference(transitivity,[status(thm)],[2374, 2304])).
% 45.70/29.81 tff(2376,plain,
% 45.70/29.81 ((impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false)))) <=> (impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), not1(false)) = phi(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))))),
% 45.70/29.81 inference(monotonicity,[status(thm)],[2375, 2372])).
% 45.70/29.81 tff(2377,plain,
% 45.70/29.81 ((~(impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false))))) <=> (~(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), not1(false)) = phi(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)))))),
% 45.70/29.81 inference(monotonicity,[status(thm)],[2376])).
% 45.70/29.81 tff(2378,plain,
% 45.70/29.81 (f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)) = f5(P!7, not1(false))),
% 45.70/29.81 inference(transitivity,[status(thm)],[2336, 530])).
% 45.70/29.81 tff(2379,plain,
% 45.70/29.81 (phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = phi(f5(P!7, not1(false)))),
% 45.70/29.81 inference(monotonicity,[status(thm)],[2378])).
% 45.70/29.81 tff(2380,plain,
% 45.70/29.81 (phi(f5(P!7, not1(false))) = phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 45.70/29.81 inference(symmetry,[status(thm)],[2379])).
% 45.70/29.81 tff(2381,plain,
% 45.70/29.81 (impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)) = impl(f5(P!7, not1(false)), not1(false))),
% 45.70/29.81 inference(symmetry,[status(thm)],[2374])).
% 45.70/29.81 tff(2382,plain,
% 45.70/29.81 (impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))),
% 45.70/29.81 inference(transitivity,[status(thm)],[2381, 957, 2380, 2335])).
% 45.70/29.81 tff(2383,plain,
% 45.70/29.81 (phi(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))) = phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 45.70/29.81 inference(monotonicity,[status(thm)],[2382])).
% 45.70/29.81 tff(2384,plain,
% 45.70/29.81 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))) = phi(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))))),
% 45.70/29.81 inference(quant_inst,[status(thm)],[])).
% 45.70/29.81 tff(2385,plain,
% 45.70/29.81 (lazy_impl(not1(false), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))) = phi(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)))),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[2384, 33])).
% 45.70/29.81 tff(2386,plain,
% 45.70/29.81 (lazy_impl(prop(not1(false)), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))) = lazy_impl(not1(false), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)))),
% 45.70/29.81 inference(monotonicity,[status(thm)],[275])).
% 45.70/29.81 tff(2387,plain,
% 45.70/29.81 (lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = lazy_impl(prop(not1(false)), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)))),
% 45.70/29.81 inference(monotonicity,[status(thm)],[2374])).
% 45.70/29.81 tff(2388,plain,
% 45.70/29.81 (phi(impl(f5(P!7, not1(false)), not1(false))) = impl(f5(P!7, not1(false)), not1(false))),
% 45.70/29.81 inference(transitivity,[status(thm)],[2203, 2202, 2387, 2386, 2385, 2383, 2379, 1011])).
% 45.70/29.81 tff(2389,plain,
% 45.70/29.81 ($false),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[2312, 2388])).
% 45.70/29.81 tff(2390,plain,((~(impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false))))) | (phi(impl(f5(P!7, not1(false)), not1(false))) = impl(f5(P!7, not1(false)), not1(false)))), inference(lemma,lemma(discharge,[]))).
% 45.70/29.81 tff(2391,plain,
% 45.70/29.81 (~(impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false))))),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[2390, 2312])).
% 45.70/29.81 tff(2392,plain,
% 45.70/29.81 (~(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), not1(false)) = phi(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))))),
% 45.70/29.81 inference(modus_ponens,[status(thm)],[2391, 2377])).
% 45.70/29.81 tff(2393,plain,
% 45.70/29.81 ($false),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[2392, 2369])).
% 45.70/29.81 tff(2394,plain,(phi(impl(f5(P!7, not1(false)), not1(false))) = impl(f5(P!7, not1(false)), not1(false))), inference(lemma,lemma(discharge,[]))).
% 45.70/29.81 tff(2395,plain,
% 45.70/29.81 (lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), not1(false))),
% 45.70/29.81 inference(transitivity,[status(thm)],[2206, 682, 2394, 1856, 2304])).
% 45.70/29.81 tff(2396,plain,
% 45.70/29.81 ((lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = not1(false)) <=> (impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), not1(false)) = phi(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))))),
% 45.70/29.81 inference(monotonicity,[status(thm)],[2395, 2311])).
% 45.70/29.81 tff(2397,plain,
% 45.70/29.81 ((lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = not1(false)) <=> (impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false))))),
% 45.70/29.81 inference(transitivity,[status(thm)],[2396, 2307])).
% 45.70/29.81 tff(2398,plain,
% 45.70/29.81 (lazy_impl(prop(not1(false)), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))) = f1(apply(P!7, tptp_fun_X_4(not1(false), P!7)), false, not1(false))),
% 45.70/29.81 inference(symmetry,[status(thm)],[2213])).
% 45.70/29.81 tff(2399,plain,
% 45.70/29.81 (lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = lazy_impl(prop(not1(false)), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)))),
% 45.70/29.81 inference(monotonicity,[status(thm)],[1856])).
% 45.70/29.81 tff(2400,plain,
% 45.70/29.81 (lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = not1(false)),
% 45.70/29.81 inference(transitivity,[status(thm)],[2399, 2398, 2337, 2340, 2346, 50, 48])).
% 45.70/29.81 tff(2401,plain,
% 45.70/29.81 (impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false)))),
% 45.70/29.81 inference(modus_ponens,[status(thm)],[2400, 2397])).
% 45.70/29.81 tff(2402,plain,
% 45.70/29.81 ($false),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[525, 2401])).
% 45.70/29.81 tff(2403,plain,((~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false)) | (impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false))))), inference(lemma,lemma(discharge,[]))).
% 45.70/29.81 tff(2404,plain,
% 45.70/29.81 (impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false)))),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[2403, 2294])).
% 45.70/29.81 tff(2405,plain,
% 45.70/29.81 (impl(lazy_impl(not1(false), impl(false, not1(false))), not1(false)) = not1(false)),
% 45.70/29.81 inference(transitivity,[status(thm)],[596, 501])).
% 45.70/29.81 tff(2406,plain,
% 45.70/29.81 (lazy_impl(prop(not1(false)), impl(lazy_impl(not1(false), impl(false, not1(false))), not1(false))) = lazy_impl(not1(false), not1(false))),
% 45.70/29.81 inference(monotonicity,[status(thm)],[275, 2405])).
% 45.70/29.81 tff(2407,plain,
% 45.70/29.81 (f2(not1(false), apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = f2(not1(false), false, not1(false))),
% 45.70/29.81 inference(monotonicity,[status(thm)],[2294])).
% 45.70/29.81 tff(2408,plain,
% 45.70/29.81 (lazy_impl(prop(not1(false)), impl(lazy_impl(not1(false), impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))), not1(false))) = f2(not1(false), apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))),
% 45.70/29.81 inference(symmetry,[status(thm)],[587])).
% 45.70/29.81 tff(2409,plain,
% 45.70/29.81 (impl(f5(P!7, not1(false)), not1(false)) = impl(lazy_impl(not1(false), impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))), not1(false))),
% 45.70/29.81 inference(symmetry,[status(thm)],[584])).
% 45.70/29.81 tff(2410,plain,
% 45.70/29.81 (lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = lazy_impl(prop(not1(false)), impl(lazy_impl(not1(false), impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))), not1(false)))),
% 45.70/29.81 inference(monotonicity,[status(thm)],[2409])).
% 45.70/29.81 tff(2411,plain,
% 45.70/29.81 (impl(f5(P!7, not1(false)), not1(false)) = phi(impl(f5(P!7, not1(false)), not1(false)))),
% 45.70/29.81 inference(symmetry,[status(thm)],[2394])).
% 45.70/29.81 tff(2412,plain,
% 45.70/29.81 (impl(f5(P!7, not1(false)), not1(false)) = not1(false)),
% 45.70/29.81 inference(transitivity,[status(thm)],[2411, 2203, 2202, 2410, 2408, 2407, 592, 2406, 50, 48])).
% 45.70/29.81 tff(2413,plain,
% 45.70/29.81 (phi(f5(P!7, not1(false))) = impl(f5(P!7, not1(false)), not1(false))),
% 45.70/29.81 inference(symmetry,[status(thm)],[2404])).
% 45.70/29.81 tff(2414,plain,
% 45.70/29.81 (phi(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))) = phi(impl(f5(P!7, not1(false)), not1(false)))),
% 45.70/29.81 inference(transitivity,[status(thm)],[703, 2413, 2411])).
% 45.70/29.81 tff(2415,plain,
% 45.70/29.81 ((phi(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))) = err) <=> (phi(impl(f5(P!7, not1(false)), not1(false))) = err)),
% 45.70/29.81 inference(monotonicity,[status(thm)],[2414])).
% 45.70/29.81 tff(2416,plain,
% 45.70/29.81 ((phi(impl(f5(P!7, not1(false)), not1(false))) = err) <=> (phi(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))) = err)),
% 45.70/29.81 inference(symmetry,[status(thm)],[2415])).
% 45.70/29.81 tff(2417,plain,
% 45.70/29.81 ((~(phi(impl(f5(P!7, not1(false)), not1(false))) = err)) <=> (~(phi(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))) = err))),
% 45.70/29.81 inference(monotonicity,[status(thm)],[2416])).
% 45.70/29.81 tff(2418,plain,
% 45.70/29.81 ((~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false)) | (~(phi(impl(f5(P!7, not1(false)), not1(false))) = err))),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[2350, 644])).
% 45.70/29.81 tff(2419,plain,
% 45.70/29.81 (~(phi(impl(f5(P!7, not1(false)), not1(false))) = err)),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[2418, 2294])).
% 45.70/29.81 tff(2420,plain,
% 45.70/29.81 (~(phi(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))) = err)),
% 45.70/29.81 inference(modus_ponens,[status(thm)],[2419, 2417])).
% 45.70/29.81 tff(2421,plain,
% 45.70/29.81 (bool(apply(P!7, tptp_fun_X_3(P!7))) | (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)) | (~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false))) | (impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[1196, 2420, 2412, 2404])).
% 45.70/29.81 tff(2422,plain,
% 45.70/29.81 (impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false)),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[2421, 348, 899, 1194])).
% 45.70/29.81 tff(2423,plain,
% 45.70/29.81 (f4(P!7, tptp_fun_X_4(false, P!7), false) = not1(false)),
% 45.70/29.81 inference(transitivity,[status(thm)],[804, 2422])).
% 45.70/29.81 tff(2424,plain,
% 45.70/29.81 (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = phi(not1(false))),
% 45.70/29.81 inference(monotonicity,[status(thm)],[2423])).
% 45.70/29.81 tff(2425,plain,
% 45.70/29.81 ((impl(apply(P!7, tptp_fun_X_3(P!7)), false) = false) <=> (phi(apply(P!7, tptp_fun_X_3(P!7))) = false)),
% 45.70/29.81 inference(monotonicity,[status(thm)],[938])).
% 45.70/29.81 tff(2426,plain,
% 45.70/29.81 ((~(impl(apply(P!7, tptp_fun_X_3(P!7)), false) = false)) <=> (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = false))),
% 45.70/29.81 inference(monotonicity,[status(thm)],[2425])).
% 45.70/29.81 tff(2427,plain,
% 45.70/29.81 (((~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))))) | (~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), false) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))))) | (~(bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)))))) | ((~(impl(apply(P!7, tptp_fun_X_3(P!7)), false) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))))),
% 45.70/29.81 inference(tautology,[status(thm)],[])).
% 45.70/29.81 tff(2428,plain,
% 45.70/29.81 ((~(impl(apply(P!7, tptp_fun_X_3(P!7)), false) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false)))),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[2427, 1068])).
% 45.70/29.81 tff(2429,plain,
% 45.70/29.81 ((~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), false) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))))) | (~(impl(apply(P!7, tptp_fun_X_3(P!7)), false) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false)))),
% 45.70/29.81 inference(tautology,[status(thm)],[])).
% 45.70/29.81 tff(2430,plain,
% 45.70/29.81 ((~(impl(apply(P!7, tptp_fun_X_3(P!7)), false) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false)))),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[2429, 2428])).
% 45.70/29.81 tff(2431,plain,
% 45.70/29.81 (~(impl(apply(P!7, tptp_fun_X_3(P!7)), false) = false)),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[2430, 2422])).
% 45.70/29.81 tff(2432,plain,
% 45.70/29.81 (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = false)),
% 45.70/29.81 inference(modus_ponens,[status(thm)],[2431, 2426])).
% 45.70/29.81 tff(2433,plain,
% 45.70/29.81 ((~((phi(apply(P!7, tptp_fun_X_3(P!7))) = false) | (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)))) | (phi(apply(P!7, tptp_fun_X_3(P!7))) = false) | (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))),
% 45.70/29.81 inference(tautology,[status(thm)],[])).
% 45.70/29.81 tff(2434,plain,
% 45.70/29.81 (~((phi(apply(P!7, tptp_fun_X_3(P!7))) = false) | (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)))),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[2433, 2432, 1194])).
% 45.70/29.81 tff(2435,plain,
% 45.70/29.81 ((~(bool(phi(apply(P!7, tptp_fun_X_3(P!7)))) <=> ((phi(apply(P!7, tptp_fun_X_3(P!7))) = false) | (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))))) | (~bool(phi(apply(P!7, tptp_fun_X_3(P!7))))) | ((phi(apply(P!7, tptp_fun_X_3(P!7))) = false) | (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)))),
% 45.70/29.81 inference(tautology,[status(thm)],[])).
% 45.70/29.81 tff(2436,plain,
% 45.70/29.81 ((~bool(phi(apply(P!7, tptp_fun_X_3(P!7))))) | ((phi(apply(P!7, tptp_fun_X_3(P!7))) = false) | (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)))),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[2435, 1718])).
% 45.70/29.81 tff(2437,plain,
% 45.70/29.81 (~bool(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[2436, 2434])).
% 45.70/29.81 tff(2438,plain,
% 45.70/29.81 (~bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false))),
% 45.70/29.81 inference(modus_ponens,[status(thm)],[2437, 946])).
% 45.70/29.81 tff(2439,plain,
% 45.70/29.81 (bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) <=> bool(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 45.70/29.81 inference(monotonicity,[status(thm)],[805])).
% 45.70/29.81 tff(2440,plain,
% 45.70/29.81 (bool(f4(P!7, tptp_fun_X_4(false, P!7), false)) <=> bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))),
% 45.70/29.81 inference(symmetry,[status(thm)],[2439])).
% 45.70/29.81 tff(2441,plain,
% 45.70/29.81 (bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) <=> bool(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 45.70/29.81 inference(monotonicity,[status(thm)],[1136])).
% 45.70/29.81 tff(2442,plain,
% 45.70/29.81 (bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) <=> bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))),
% 45.70/29.81 inference(transitivity,[status(thm)],[2441, 2440])).
% 45.70/29.81 tff(2443,assumption,(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false)), introduced(assumption)).
% 45.70/29.81 tff(2444,plain,
% 45.70/29.81 (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false)),
% 45.70/29.81 inference(modus_ponens,[status(thm)],[2443, 1146])).
% 45.70/29.81 tff(2445,plain,
% 45.70/29.81 (((phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = false) | (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false))) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false)))),
% 45.70/29.81 inference(tautology,[status(thm)],[])).
% 45.70/29.81 tff(2446,plain,
% 45.70/29.81 ((phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = false) | (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false))),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[2445, 2444])).
% 45.70/29.81 tff(2447,assumption,(~(bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) <=> ((phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = false) | (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false))))), introduced(assumption)).
% 45.70/29.81 tff(2448,plain,
% 45.70/29.81 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) <=> ((phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = false) | (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false))))),
% 45.70/29.81 inference(quant_inst,[status(thm)],[])).
% 45.70/29.81 tff(2449,plain,
% 45.70/29.81 ($false),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[2448, 249, 2447])).
% 45.70/29.81 tff(2450,plain,(bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) <=> ((phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = false) | (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 45.70/29.81 tff(2451,plain,
% 45.70/29.81 ((~(bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) <=> ((phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = false) | (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false))))) | bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~((phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = false) | (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false))))),
% 45.70/29.81 inference(tautology,[status(thm)],[])).
% 45.70/29.81 tff(2452,plain,
% 45.70/29.81 (bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~((phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = false) | (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false))))),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[2451, 2450])).
% 45.70/29.81 tff(2453,plain,
% 45.70/29.81 (bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[2452, 2446])).
% 45.70/29.81 tff(2454,plain,
% 45.70/29.81 (bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))),
% 45.70/29.81 inference(modus_ponens,[status(thm)],[2453, 2442])).
% 45.70/29.81 tff(2455,plain,
% 45.70/29.81 ($false),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[1154, 2454])).
% 45.70/29.81 tff(2456,plain,(((~d(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false)))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false))) | (~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 45.70/29.81 tff(2457,plain,
% 45.70/29.81 ((~d(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[2456, 2438, 943, 2422])).
% 45.70/29.81 tff(2458,plain,
% 45.70/29.81 (~(d(f4(P!7, tptp_fun_X_4(false, P!7), false)) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err)))),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[1021, 2457])).
% 45.70/29.81 tff(2459,plain,
% 45.70/29.81 (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[1016, 2458])).
% 45.70/29.81 tff(2460,plain,
% 45.70/29.81 (err = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 45.70/29.81 inference(symmetry,[status(thm)],[2459])).
% 45.70/29.81 tff(2461,plain,
% 45.70/29.81 ((~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err)) | (~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false))) | (~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~(impl(apply(P!7, tptp_fun_X_3(P!7)), false) = phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))))),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[1014, 2412, 2404, 2420])).
% 45.70/29.81 tff(2462,plain,
% 45.70/29.81 (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[2461, 2459, 899, 363, 938])).
% 45.70/29.81 tff(2463,plain,
% 45.70/29.81 ((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))))),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[369, 2462])).
% 45.70/29.81 tff(2464,plain,
% 45.70/29.81 (~(d(apply(P!7, tptp_fun_X_3(P!7))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err)))),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[383, 2463])).
% 45.70/29.81 tff(2465,plain,
% 45.70/29.81 (phi(apply(P!7, tptp_fun_X_3(P!7))) = err),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[385, 2464])).
% 45.70/29.81 tff(2466,plain,
% 45.70/29.81 (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)),
% 45.70/29.81 inference(transitivity,[status(thm)],[2465, 2460, 2424, 48])).
% 45.70/29.81 tff(2467,plain,
% 45.70/29.81 ($false),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[1194, 2466])).
% 45.70/29.81 tff(2468,plain,(bool(apply(P!7, tptp_fun_X_3(P!7))) | (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)) | (~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 45.70/29.81 tff(2469,plain,
% 45.70/29.81 (bool(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[2468, 898, 877])).
% 45.70/29.81 tff(2470,plain,
% 45.70/29.81 ((~((prop(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)) <=> bool(apply(P!7, tptp_fun_X_3(P!7))))) | (prop(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[1607, 2469])).
% 45.70/29.81 tff(2471,plain,
% 45.70/29.81 (prop(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[2470, 294])).
% 45.70/29.81 tff(2472,plain,
% 45.70/29.81 (lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))) = lazy_impl(not1(false), apply(P!7, tptp_fun_X_3(P!7)))),
% 45.70/29.81 inference(monotonicity,[status(thm)],[2471])).
% 45.70/29.81 tff(2473,plain,
% 45.70/29.81 (lazy_impl(not1(false), apply(P!7, tptp_fun_X_3(P!7))) = lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))),
% 45.70/29.81 inference(symmetry,[status(thm)],[2472])).
% 45.70/29.81 tff(2474,plain,
% 45.70/29.81 (phi(apply(P!7, tptp_fun_X_3(P!7))) = f7(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.70/29.81 inference(transitivity,[status(thm)],[1614, 2473, 292])).
% 45.70/29.81 tff(2475,plain,
% 45.70/29.81 (forallprefers(phi(apply(P!7, tptp_fun_X_3(P!7))), false) <=> forallprefers(f7(apply(P!7, tptp_fun_X_3(P!7))), f7(P!6))),
% 45.70/29.81 inference(monotonicity,[status(thm)],[2474, 289])).
% 45.70/29.81 tff(2476,plain,
% 45.70/29.81 (forallprefers(f7(apply(P!7, tptp_fun_X_3(P!7))), f7(P!6)) <=> forallprefers(phi(apply(P!7, tptp_fun_X_3(P!7))), false)),
% 45.70/29.81 inference(symmetry,[status(thm)],[2475])).
% 45.70/29.81 tff(2477,plain,
% 45.70/29.81 ((~forallprefers(f7(apply(P!7, tptp_fun_X_3(P!7))), f7(P!6))) <=> (~forallprefers(phi(apply(P!7, tptp_fun_X_3(P!7))), false))),
% 45.70/29.81 inference(monotonicity,[status(thm)],[2476])).
% 45.70/29.81 tff(2478,plain,
% 45.70/29.81 (~forallprefers(phi(apply(P!7, tptp_fun_X_3(P!7))), false)),
% 45.70/29.81 inference(modus_ponens,[status(thm)],[1642, 2477])).
% 45.70/29.81 tff(2479,plain,
% 45.70/29.81 (~((~((~d(false)) | d(phi(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(false = not1(false))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = false)))) | (~((~d(false)) | (~bool(false)) | (~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | bool(phi(apply(P!7, tptp_fun_X_3(P!7)))))))),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[2022, 2478, 166])).
% 45.70/29.81 tff(2480,plain,
% 45.70/29.81 ((~d(false)) | (~bool(false)) | (~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | bool(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[2024, 2479])).
% 45.70/29.81 tff(2481,plain,
% 45.70/29.81 ((~d(false)) | d(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[2026, 2479])).
% 45.70/29.81 tff(2482,plain,
% 45.70/29.81 (d(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[2029, 2481])).
% 45.70/29.81 tff(2483,plain,
% 45.70/29.81 (bool(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[2032, 2482, 2480])).
% 45.70/29.81 tff(2484,plain,
% 45.70/29.81 ((phi(apply(P!7, tptp_fun_X_3(P!7))) = false) | (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[2436, 2483])).
% 45.70/29.81 tff(2485,plain,
% 45.70/29.81 (phi(apply(P!7, tptp_fun_X_3(P!7))) = false),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[2433, 2484, 898])).
% 45.70/29.81 tff(2486,plain,
% 45.70/29.81 ((phi(apply(P!7, tptp_fun_X_3(P!7))) = err) <=> (false = err)),
% 45.70/29.81 inference(monotonicity,[status(thm)],[2485])).
% 45.70/29.81 tff(2487,plain,
% 45.70/29.81 ((false = err) <=> (phi(apply(P!7, tptp_fun_X_3(P!7))) = err)),
% 45.70/29.81 inference(symmetry,[status(thm)],[2486])).
% 45.70/29.81 tff(2488,plain,
% 45.70/29.81 ((~(false = err)) <=> (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err))),
% 45.70/29.81 inference(monotonicity,[status(thm)],[2487])).
% 45.70/29.81 tff(2489,plain,
% 45.70/29.81 (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err)),
% 45.70/29.81 inference(modus_ponens,[status(thm)],[556, 2488])).
% 45.70/29.81 tff(2490,plain,
% 45.70/29.81 (d(apply(P!7, tptp_fun_X_3(P!7))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err))),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[385, 2489])).
% 45.70/29.81 tff(2491,plain,
% 45.70/29.81 (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))))),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[383, 2490])).
% 45.70/29.81 tff(2492,plain,
% 45.70/29.81 (d(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.70/29.81 inference(unit_resolution,[status(thm)],[374, 2491])).
% 45.70/29.81 tff(2493,plain,
% 45.70/29.81 (((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = not1(false))) | (~(Y = false))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(false, P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))))) | (~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7))))))))) <=> ((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = not1(false))) | (~(Y = false))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(false, P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))))) | (~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))))))))),
% 45.70/29.81 inference(rewrite,[status(thm)],[])).
% 45.70/29.81 tff(2494,plain,
% 45.70/29.81 ((existsprefers(apply(P!7, tptp_fun_X_4(false, P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))))) | (~((~(apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))) | (~(apply(P!7, tptp_fun_X_3(P!7)) = false)))))) <=> (existsprefers(apply(P!7, tptp_fun_X_4(false, P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))))) | (~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7))))))))),
% 45.70/29.81 inference(rewrite,[status(thm)],[])).
% 45.70/29.81 tff(2495,plain,
% 45.70/29.81 (((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = not1(false))) | (~(Y = false))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(false, P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))))) | (~((~(apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))) | (~(apply(P!7, tptp_fun_X_3(P!7)) = false))))))) <=> ((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = not1(false))) | (~(Y = false))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(false, P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))))) | (~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))))))))),
% 45.70/29.82 inference(monotonicity,[status(thm)],[2494])).
% 45.70/29.82 tff(2496,plain,
% 45.70/29.82 (((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = not1(false))) | (~(Y = false))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(false, P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))))) | (~((~(apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))) | (~(apply(P!7, tptp_fun_X_3(P!7)) = false))))))) <=> ((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = not1(false))) | (~(Y = false))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(false, P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))))) | (~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))))))))),
% 45.70/29.82 inference(transitivity,[status(thm)],[2495, 2493])).
% 45.70/29.82 tff(2497,plain,
% 45.70/29.82 ((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = not1(false))) | (~(Y = false))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(false, P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))))) | (~((~(apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))) | (~(apply(P!7, tptp_fun_X_3(P!7)) = false))))))),
% 45.70/29.82 inference(quant_inst,[status(thm)],[])).
% 45.70/29.82 tff(2498,plain,
% 45.70/29.82 ((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = not1(false))) | (~(Y = false))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(false, P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))))) | (~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7))))))))),
% 45.70/29.82 inference(modus_ponens,[status(thm)],[2497, 2496])).
% 45.70/29.82 tff(2499,plain,
% 45.70/29.82 (existsprefers(apply(P!7, tptp_fun_X_4(false, P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))))) | (~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))))))),
% 45.70/29.82 inference(unit_resolution,[status(thm)],[2498, 1224])).
% 45.70/29.82 tff(2500,plain,
% 45.70/29.82 ((~![X1: $i] : (~existsprefers(apply(P!7, X1), apply(P!7, tptp_fun_X_3(P!7))))) | (~existsprefers(apply(P!7, tptp_fun_X_4(false, P!7)), apply(P!7, tptp_fun_X_3(P!7))))),
% 45.70/29.82 inference(quant_inst,[status(thm)],[])).
% 45.70/29.82 tff(2501,plain,
% 45.70/29.82 (~existsprefers(apply(P!7, tptp_fun_X_4(false, P!7)), apply(P!7, tptp_fun_X_3(P!7)))),
% 45.70/29.82 inference(unit_resolution,[status(thm)],[2500, 1233])).
% 45.70/29.82 tff(2502,plain,
% 45.70/29.82 ((~(existsprefers(apply(P!7, tptp_fun_X_4(false, P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))))) | (~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7))))))))) | existsprefers(apply(P!7, tptp_fun_X_4(false, P!7)), apply(P!7, tptp_fun_X_3(P!7))) | (~((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))))) | (~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7))))))))),
% 45.70/29.82 inference(tautology,[status(thm)],[])).
% 45.70/29.82 tff(2503,plain,
% 45.70/29.82 ((~(existsprefers(apply(P!7, tptp_fun_X_4(false, P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))))) | (~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7))))))))) | (~((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))))) | (~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7))))))))),
% 45.70/29.82 inference(unit_resolution,[status(thm)],[2502, 2501])).
% 45.70/29.82 tff(2504,plain,
% 45.70/29.82 (~((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))))) | (~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))))))),
% 45.70/29.82 inference(unit_resolution,[status(thm)],[2503, 2499])).
% 45.70/29.82 tff(2505,plain,
% 45.70/29.82 (((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))))) | (~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7))))))) | (d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))),
% 45.70/29.82 inference(tautology,[status(thm)],[])).
% 45.70/29.82 tff(2506,plain,
% 45.70/29.82 (d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.70/29.82 inference(unit_resolution,[status(thm)],[2505, 2504])).
% 45.70/29.82 tff(2507,plain,
% 45.70/29.82 ((~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.70/29.82 inference(tautology,[status(thm)],[])).
% 45.70/29.82 tff(2508,plain,
% 45.70/29.82 (d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.70/29.82 inference(unit_resolution,[status(thm)],[2507, 2506])).
% 45.70/29.82 tff(2509,plain,
% 45.70/29.82 (d(apply(P!7, tptp_fun_X_4(false, P!7)))),
% 45.70/29.82 inference(unit_resolution,[status(thm)],[2508, 2492])).
% 45.70/29.82 tff(2510,plain,
% 45.70/29.82 (((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))))) | (~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7))))))) | ((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))))),
% 45.70/29.82 inference(tautology,[status(thm)],[])).
% 45.70/29.82 tff(2511,plain,
% 45.70/29.82 ((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7))))),
% 45.70/29.82 inference(unit_resolution,[status(thm)],[2510, 2504])).
% 45.70/29.82 tff(2512,plain,
% 45.70/29.82 ((~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7))))),
% 45.70/29.82 inference(tautology,[status(thm)],[])).
% 45.70/29.82 tff(2513,plain,
% 45.70/29.82 ((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7))))),
% 45.70/29.82 inference(unit_resolution,[status(thm)],[2512, 2511])).
% 45.70/29.82 tff(2514,plain,
% 45.70/29.82 (bool(apply(P!7, tptp_fun_X_4(false, P!7)))),
% 45.70/29.82 inference(unit_resolution,[status(thm)],[2513, 2492, 2469, 2509])).
% 45.70/29.82 tff(2515,plain,
% 45.70/29.82 ((~(bool(apply(P!7, tptp_fun_X_4(false, P!7))) <=> ((apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))))) | (~bool(apply(P!7, tptp_fun_X_4(false, P!7)))) | ((apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false)))),
% 45.70/29.82 inference(tautology,[status(thm)],[])).
% 45.70/29.82 tff(2516,plain,
% 45.70/29.82 ((~(bool(apply(P!7, tptp_fun_X_4(false, P!7))) <=> ((apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))))) | ((apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false)))),
% 45.70/29.82 inference(unit_resolution,[status(thm)],[2515, 2514])).
% 45.70/29.82 tff(2517,plain,
% 45.70/29.82 ((apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))),
% 45.70/29.82 inference(unit_resolution,[status(thm)],[2516, 2297])).
% 45.70/29.82 tff(2518,plain,
% 45.70/29.82 ((false = apply(P!7, tptp_fun_X_3(P!7))) <=> (apply(P!7, tptp_fun_X_3(P!7)) = false)),
% 45.70/29.82 inference(commutativity,[status(thm)],[])).
% 45.70/29.82 tff(2519,plain,
% 45.70/29.82 ((phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))) <=> (false = apply(P!7, tptp_fun_X_3(P!7)))),
% 45.70/29.82 inference(monotonicity,[status(thm)],[2485])).
% 45.70/29.82 tff(2520,plain,
% 45.70/29.82 ((phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))) <=> (apply(P!7, tptp_fun_X_3(P!7)) = false)),
% 45.70/29.82 inference(transitivity,[status(thm)],[2519, 2518])).
% 45.70/29.82 tff(2521,plain,
% 45.70/29.82 (phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))),
% 45.70/29.82 inference(unit_resolution,[status(thm)],[369, 2491])).
% 45.70/29.82 tff(2522,plain,
% 45.70/29.82 (apply(P!7, tptp_fun_X_3(P!7)) = false),
% 45.70/29.82 inference(modus_ponens,[status(thm)],[2521, 2520])).
% 45.70/29.82 tff(2523,plain,
% 45.70/29.82 (((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))))) | (~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7))))))) | ((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))))),
% 45.70/29.82 inference(tautology,[status(thm)],[])).
% 45.70/29.82 tff(2524,plain,
% 45.70/29.82 ((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false)))),
% 45.70/29.82 inference(unit_resolution,[status(thm)],[2523, 2504])).
% 45.70/29.82 tff(2525,plain,
% 45.70/29.82 ((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))))) | (~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false)))),
% 45.70/29.82 inference(tautology,[status(thm)],[])).
% 45.70/29.82 tff(2526,plain,
% 45.70/29.82 ((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false)))),
% 45.70/29.82 inference(unit_resolution,[status(thm)],[2525, 2524])).
% 45.70/29.82 tff(2527,plain,
% 45.70/29.82 (~(apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))),
% 45.70/29.82 inference(unit_resolution,[status(thm)],[2526, 2522])).
% 45.70/29.82 tff(2528,plain,
% 45.70/29.82 ((~((apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false)))) | (apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))),
% 45.70/29.82 inference(tautology,[status(thm)],[])).
% 45.70/29.82 tff(2529,plain,
% 45.70/29.82 (apply(P!7, tptp_fun_X_4(false, P!7)) = false),
% 45.70/29.82 inference(unit_resolution,[status(thm)],[2528, 2527, 2517])).
% 45.70/29.82 tff(2530,plain,
% 45.70/29.82 (false = apply(P!7, tptp_fun_X_4(false, P!7))),
% 45.70/29.82 inference(symmetry,[status(thm)],[2529])).
% 45.70/29.82 tff(2531,plain,
% 45.70/29.82 (f2(not1(false), false, false) = f2(not1(false), apply(P!7, tptp_fun_X_4(false, P!7)), false)),
% 45.70/29.82 inference(monotonicity,[status(thm)],[2530])).
% 45.70/29.82 tff(2532,plain,
% 45.70/29.82 (f2(not1(false), apply(P!7, tptp_fun_X_4(false, P!7)), false) = f2(not1(false), false, false)),
% 45.70/29.82 inference(symmetry,[status(thm)],[2531])).
% 45.70/29.82 tff(2533,plain,
% 45.70/29.82 ((~![P: $i, Q: $i, R: $i] : (f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R)))) | (f2(not1(false), apply(P!7, tptp_fun_X_4(false, P!7)), false) = lazy_impl(prop(false), impl(lazy_impl(not1(false), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)), false)))),
% 45.70/29.82 inference(quant_inst,[status(thm)],[])).
% 45.70/29.82 tff(2534,plain,
% 45.70/29.82 (f2(not1(false), apply(P!7, tptp_fun_X_4(false, P!7)), false) = lazy_impl(prop(false), impl(lazy_impl(not1(false), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)), false))),
% 45.70/29.82 inference(unit_resolution,[status(thm)],[2533, 141])).
% 45.70/29.82 tff(2535,plain,
% 45.70/29.82 (lazy_impl(prop(false), impl(lazy_impl(not1(false), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)), false)) = f2(not1(false), apply(P!7, tptp_fun_X_4(false, P!7)), false)),
% 45.70/29.82 inference(symmetry,[status(thm)],[2534])).
% 45.70/29.82 tff(2536,plain,
% 45.70/29.82 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), f4(P!7, tptp_fun_X_4(false, P!7), false)) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 45.70/29.82 inference(quant_inst,[status(thm)],[])).
% 45.70/29.82 tff(2537,plain,
% 45.70/29.82 (lazy_impl(not1(false), f4(P!7, tptp_fun_X_4(false, P!7), false)) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 45.70/29.82 inference(unit_resolution,[status(thm)],[2536, 33])).
% 45.70/29.82 tff(2538,plain,
% 45.70/29.82 (lazy_impl(not1(false), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) = lazy_impl(not1(false), f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 45.70/29.82 inference(monotonicity,[status(thm)],[805])).
% 45.70/29.82 tff(2539,plain,
% 45.70/29.82 (lazy_impl(not1(false), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) = f5(P!7, false)),
% 45.70/29.82 inference(transitivity,[status(thm)],[2538, 2537, 932])).
% 45.70/29.82 tff(2540,plain,
% 45.70/29.82 (impl(lazy_impl(not1(false), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)), false) = impl(f5(P!7, false), false)),
% 45.70/29.82 inference(monotonicity,[status(thm)],[2539])).
% 45.70/29.82 tff(2541,plain,
% 45.70/29.82 (lazy_impl(prop(false), impl(lazy_impl(not1(false), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)), false)) = lazy_impl(prop(false), impl(f5(P!7, false), false))),
% 45.70/29.82 inference(monotonicity,[status(thm)],[2540])).
% 45.70/29.82 tff(2542,plain,
% 45.70/29.82 (lazy_impl(prop(false), impl(f5(P!7, false), false)) = lazy_impl(prop(false), impl(lazy_impl(not1(false), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)), false))),
% 45.70/29.82 inference(symmetry,[status(thm)],[2541])).
% 45.70/29.82 tff(2543,plain,
% 45.70/29.82 (not1(false) = lazy_impl(prop(false), impl(f5(P!7, false), false))),
% 45.70/29.82 inference(symmetry,[status(thm)],[877])).
% 45.70/29.82 tff(2544,plain,
% 45.70/29.82 (not1(false) = false),
% 45.70/29.82 inference(transitivity,[status(thm)],[2543, 2542, 2535, 2532, 143, 134, 35, 23])).
% 45.70/29.82 tff(2545,plain,
% 45.70/29.82 ($false),
% 45.70/29.82 inference(unit_resolution,[status(thm)],[60, 2544])).
% 45.70/29.82 tff(2546,plain,(~(prop(tptp_fun_R_5(P!7)) = false)), inference(lemma,lemma(discharge,[]))).
% 45.70/29.82 tff(2547,plain,
% 45.70/29.82 (bool(tptp_fun_R_5(P!7))),
% 45.70/29.82 inference(unit_resolution,[status(thm)],[1256, 2546])).
% 45.70/29.82 tff(2548,plain,
% 45.70/29.82 (impl(false, tptp_fun_R_5(P!7)) = not1(false)),
% 45.70/29.82 inference(unit_resolution,[status(thm)],[1286, 2547])).
% 45.70/29.82 tff(2549,plain,
% 45.70/29.82 ((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = not1(false))),
% 45.70/29.82 inference(unit_resolution,[status(thm)],[1281, 2547])).
% 45.70/29.82 tff(2550,plain,
% 45.70/29.82 (impl(not1(false), tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)),
% 45.70/29.82 inference(unit_resolution,[status(thm)],[1261, 2547])).
% 45.70/29.82 tff(2551,plain,
% 45.70/29.82 (prop(tptp_fun_R_5(P!7)) = not1(false)),
% 45.70/29.82 inference(unit_resolution,[status(thm)],[1276, 2547])).
% 45.70/29.82 tff(2552,plain,
% 45.70/29.82 (~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err)),
% 45.70/29.82 inference(unit_resolution,[status(thm)],[606, 2294])).
% 45.70/29.82 tff(2553,assumption,(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false), introduced(assumption)).
% 45.70/29.82 tff(2554,plain,
% 45.70/29.82 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = phi(impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 45.70/29.82 inference(quant_inst,[status(thm)],[])).
% 45.70/29.82 tff(2555,plain,
% 45.70/29.82 (lazy_impl(not1(false), impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = phi(impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.82 inference(unit_resolution,[status(thm)],[2554, 33])).
% 45.70/29.82 tff(2556,plain,
% 45.70/29.82 ((~![X: $i] : ((prop(X) = not1(false)) <=> bool(X))) | ((prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false)) <=> bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.82 inference(quant_inst,[status(thm)],[])).
% 45.70/29.82 tff(2557,plain,
% 45.70/29.82 ((prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false)) <=> bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.82 inference(unit_resolution,[status(thm)],[2556, 126])).
% 45.70/29.82 tff(2558,plain,
% 45.70/29.82 ((~((prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false)) <=> bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false)) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.82 inference(tautology,[status(thm)],[])).
% 45.70/29.82 tff(2559,plain,
% 45.70/29.82 ((~((prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false)) <=> bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))),
% 45.70/29.82 inference(unit_resolution,[status(thm)],[2558, 1826])).
% 45.70/29.82 tff(2560,plain,
% 45.70/29.82 (prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false)),
% 45.70/29.82 inference(unit_resolution,[status(thm)],[2559, 2557])).
% 45.70/29.82 tff(2561,plain,
% 45.70/29.82 (not1(false) = prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.82 inference(symmetry,[status(thm)],[2560])).
% 45.70/29.82 tff(2562,plain,
% 45.70/29.82 (lazy_impl(not1(false), impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = lazy_impl(prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))), impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.82 inference(monotonicity,[status(thm)],[2561])).
% 45.70/29.82 tff(2563,plain,
% 45.70/29.82 (lazy_impl(prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))), impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = lazy_impl(not1(false), impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.82 inference(symmetry,[status(thm)],[2562])).
% 45.70/29.82 tff(2564,plain,
% 45.70/29.82 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))), impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 45.70/29.82 inference(quant_inst,[status(thm)],[])).
% 45.70/29.82 tff(2565,plain,
% 45.70/29.82 (f1(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))), impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.82 inference(unit_resolution,[status(thm)],[2564, 2128])).
% 45.70/29.82 tff(2566,plain,
% 45.70/29.82 (impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false)))),
% 45.70/29.82 inference(unit_resolution,[status(thm)],[2403, 588])).
% 45.70/29.82 tff(2567,plain,
% 45.70/29.82 (impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)) = impl(f5(P!7, not1(false)), not1(false))),
% 45.70/29.82 inference(symmetry,[status(thm)],[653])).
% 45.70/29.82 tff(2568,plain,
% 45.70/29.82 (impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))),
% 45.70/29.82 inference(transitivity,[status(thm)],[2567, 2566, 678, 644, 521])).
% 45.70/29.82 tff(2569,plain,
% 45.70/29.82 (f1(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = f1(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.82 inference(monotonicity,[status(thm)],[2568])).
% 45.70/29.82 tff(2570,plain,
% 45.70/29.82 (f1(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = f1(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.82 inference(symmetry,[status(thm)],[2569])).
% 45.70/29.82 tff(2571,plain,
% 45.70/29.82 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))), impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 45.70/29.82 inference(quant_inst,[status(thm)],[])).
% 45.70/29.82 tff(2572,plain,
% 45.70/29.82 (f1(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))), impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.82 inference(unit_resolution,[status(thm)],[2571, 2128])).
% 45.70/29.83 tff(2573,plain,
% 45.70/29.83 (lazy_impl(prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))), impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = f1(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.83 inference(symmetry,[status(thm)],[2572])).
% 45.70/29.83 tff(2574,plain,
% 45.70/29.83 (((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | ((~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false)))) <=> ((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false)))),
% 45.70/29.83 inference(rewrite,[status(thm)],[])).
% 45.70/29.83 tff(2575,plain,
% 45.70/29.83 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | ((~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false)))),
% 45.70/29.83 inference(quant_inst,[status(thm)],[])).
% 45.70/29.83 tff(2576,plain,
% 45.70/29.83 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))),
% 45.70/29.83 inference(modus_ponens,[status(thm)],[2575, 2574])).
% 45.70/29.83 tff(2577,plain,
% 45.70/29.83 (impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false)),
% 45.70/29.83 inference(unit_resolution,[status(thm)],[2576, 89, 1826])).
% 45.70/29.83 tff(2578,plain,
% 45.70/29.83 (impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))),
% 45.70/29.83 inference(monotonicity,[status(thm)],[651, 2577])).
% 45.70/29.83 tff(2579,plain,
% 45.70/29.83 (impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)) = impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.83 inference(symmetry,[status(thm)],[2578])).
% 45.70/29.83 tff(2580,plain,
% 45.70/29.83 (phi(f5(P!7, not1(false))) = impl(f5(P!7, not1(false)), not1(false))),
% 45.70/29.83 inference(symmetry,[status(thm)],[2566])).
% 45.70/29.83 tff(2581,plain,
% 45.70/29.83 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))),
% 45.70/29.83 inference(monotonicity,[status(thm)],[2577])).
% 45.70/29.83 tff(2582,plain,
% 45.70/29.83 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.83 inference(transitivity,[status(thm)],[2581, 522, 645, 647, 2580, 653, 2579])).
% 45.70/29.83 tff(2583,plain,
% 45.70/29.83 (impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.83 inference(monotonicity,[status(thm)],[2582])).
% 45.70/29.83 tff(2584,plain,
% 45.70/29.83 (impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.83 inference(symmetry,[status(thm)],[2583])).
% 45.70/29.83 tff(2585,plain,
% 45.70/29.83 (lazy_impl(prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))), impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = lazy_impl(prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.83 inference(monotonicity,[status(thm)],[2584])).
% 45.70/29.83 tff(2586,plain,
% 45.70/29.83 (lazy_impl(prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = lazy_impl(prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))), impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.83 inference(symmetry,[status(thm)],[2585])).
% 45.70/29.83 tff(2587,plain,
% 45.70/29.83 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(apply(P!7, tptp_fun_X_4(not1(false), P!7)), false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 45.70/29.83 inference(quant_inst,[status(thm)],[])).
% 45.70/29.83 tff(2588,plain,
% 45.70/29.83 (f1(apply(P!7, tptp_fun_X_4(not1(false), P!7)), false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.83 inference(unit_resolution,[status(thm)],[2587, 2128])).
% 45.70/29.83 tff(2589,plain,
% 45.70/29.83 (f1(apply(P!7, tptp_fun_X_4(not1(false), P!7)), false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = f1(false, false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.83 inference(monotonicity,[status(thm)],[588])).
% 45.70/29.83 tff(2590,plain,
% 45.70/29.83 (f1(false, false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = f1(apply(P!7, tptp_fun_X_4(not1(false), P!7)), false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.83 inference(symmetry,[status(thm)],[2589])).
% 45.70/29.83 tff(2591,plain,
% 45.70/29.83 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(false, false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))), impl(impl(false, impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 45.70/29.83 inference(quant_inst,[status(thm)],[])).
% 45.70/29.83 tff(2592,plain,
% 45.70/29.83 (f1(false, false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))), impl(impl(false, impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.83 inference(unit_resolution,[status(thm)],[2591, 2128])).
% 45.70/29.83 tff(2593,plain,
% 45.70/29.83 (lazy_impl(prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))), impl(impl(false, impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = f1(false, false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.83 inference(symmetry,[status(thm)],[2592])).
% 45.70/29.83 tff(2594,plain,
% 45.70/29.83 (((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | ((~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (impl(not1(false), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) <=> ((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (impl(not1(false), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.83 inference(rewrite,[status(thm)],[])).
% 45.70/29.83 tff(2595,plain,
% 45.70/29.83 ((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | ((~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (impl(not1(false), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.83 inference(quant_inst,[status(thm)],[])).
% 45.70/29.83 tff(2596,plain,
% 45.70/29.83 ((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (impl(not1(false), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.83 inference(modus_ponens,[status(thm)],[2595, 2594])).
% 45.70/29.83 tff(2597,plain,
% 45.70/29.83 (impl(not1(false), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 45.70/29.83 inference(unit_resolution,[status(thm)],[2596, 110, 1826])).
% 45.70/29.83 tff(2598,plain,
% 45.70/29.83 (impl(false, impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = impl(false, not1(false))),
% 45.70/29.83 inference(monotonicity,[status(thm)],[2577])).
% 45.70/29.83 tff(2599,plain,
% 45.70/29.83 (impl(false, impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = not1(false)),
% 45.70/29.83 inference(transitivity,[status(thm)],[2598, 421])).
% 45.70/29.83 tff(2600,plain,
% 45.70/29.83 (impl(impl(false, impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(not1(false), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.83 inference(monotonicity,[status(thm)],[2599])).
% 45.70/29.83 tff(2601,plain,
% 45.70/29.83 (impl(impl(false, impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 45.70/29.83 inference(transitivity,[status(thm)],[2600, 2597])).
% 45.70/29.83 tff(2602,plain,
% 45.70/29.83 (lazy_impl(prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))), impl(impl(false, impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = lazy_impl(not1(false), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.83 inference(monotonicity,[status(thm)],[2560, 2601])).
% 45.70/29.83 tff(2603,plain,
% 45.70/29.83 (lazy_impl(not1(false), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))), impl(impl(false, impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.83 inference(symmetry,[status(thm)],[2602])).
% 45.70/29.83 tff(2604,plain,
% 45.70/29.83 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.83 inference(quant_inst,[status(thm)],[])).
% 45.70/29.83 tff(2605,plain,
% 45.70/29.83 (lazy_impl(not1(false), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.83 inference(unit_resolution,[status(thm)],[2604, 33])).
% 45.70/29.83 tff(2606,plain,
% 45.70/29.83 (phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(not1(false), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.83 inference(symmetry,[status(thm)],[2605])).
% 45.70/29.83 tff(2607,plain,
% 45.70/29.83 (phi(tptp_fun_R_5(P!7)) = phi(impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.83 inference(transitivity,[status(thm)],[1295, 1292, 1289, 2606, 2603, 2593, 2590, 2588, 2586, 2573, 2570, 2565, 2563, 2555])).
% 45.70/29.83 tff(2608,plain,
% 45.70/29.83 ((phi(tptp_fun_R_5(P!7)) = err) <=> (phi(impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = err)),
% 45.70/29.83 inference(monotonicity,[status(thm)],[2607])).
% 45.70/29.83 tff(2609,plain,
% 45.70/29.83 ((phi(impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = err) <=> (phi(tptp_fun_R_5(P!7)) = err)),
% 45.70/29.83 inference(symmetry,[status(thm)],[2608])).
% 45.70/29.83 tff(2610,plain,
% 45.70/29.83 (impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, not1(false))) = impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))),
% 45.70/29.83 inference(monotonicity,[status(thm)],[651, 421])).
% 45.70/29.83 tff(2611,plain,
% 45.70/29.83 (impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)) = impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, not1(false)))),
% 45.70/29.83 inference(symmetry,[status(thm)],[2610])).
% 45.70/29.83 tff(2612,plain,
% 45.70/29.83 (impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), impl(false, false)) = impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, not1(false))), not1(false))),
% 45.70/29.83 inference(monotonicity,[status(thm)],[2611, 93])).
% 45.70/29.83 tff(2613,plain,
% 45.70/29.83 (impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, not1(false))), not1(false)) = impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), impl(false, false))),
% 45.70/29.83 inference(symmetry,[status(thm)],[2612])).
% 45.70/29.83 tff(2614,plain,
% 45.70/29.83 (impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, not1(false))), not1(false)), false2) = impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), impl(false, false)), false)),
% 45.70/29.83 inference(monotonicity,[status(thm)],[2613, 816])).
% 45.70/29.83 tff(2615,plain,
% 45.70/29.83 (phi(impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, not1(false))), not1(false)), false2)) = phi(impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), impl(false, false)), false))),
% 45.70/29.83 inference(monotonicity,[status(thm)],[2614])).
% 45.70/29.83 tff(2616,plain,
% 45.70/29.83 (phi(impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), impl(false, false)), false)) = phi(impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, not1(false))), not1(false)), false2))),
% 45.70/29.83 inference(symmetry,[status(thm)],[2615])).
% 45.70/29.83 tff(2617,plain,
% 45.70/29.83 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), impl(false, false)), false)) = phi(impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), impl(false, false)), false)))),
% 45.70/29.83 inference(quant_inst,[status(thm)],[])).
% 45.70/29.83 tff(2618,plain,
% 45.70/29.83 (lazy_impl(not1(false), impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), impl(false, false)), false)) = phi(impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), impl(false, false)), false))),
% 45.70/29.83 inference(unit_resolution,[status(thm)],[2617, 33])).
% 45.70/29.83 tff(2619,plain,
% 45.70/29.83 (lazy_impl(not1(false), impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), impl(false, false)), false)) = lazy_impl(prop(false), impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), impl(false, false)), false))),
% 45.70/29.83 inference(monotonicity,[status(thm)],[132])).
% 45.70/29.83 tff(2620,plain,
% 45.70/29.83 (lazy_impl(prop(false), impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), impl(false, false)), false)) = lazy_impl(not1(false), impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), impl(false, false)), false))),
% 45.70/29.83 inference(symmetry,[status(thm)],[2619])).
% 45.70/29.83 tff(2621,plain,
% 45.70/29.83 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), false, false) = lazy_impl(prop(false), impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), impl(false, false)), false)))),
% 45.70/29.83 inference(quant_inst,[status(thm)],[])).
% 45.70/29.83 tff(2622,plain,
% 45.70/29.83 (f1(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), false, false) = lazy_impl(prop(false), impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), impl(false, false)), false))),
% 45.70/29.83 inference(unit_resolution,[status(thm)],[2621, 2128])).
% 45.70/29.83 tff(2623,plain,
% 45.70/29.83 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))),
% 45.70/29.83 inference(transitivity,[status(thm)],[522, 645, 647, 2580, 653])).
% 45.70/29.83 tff(2624,plain,
% 45.70/29.83 (f1(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), false, false) = f1(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), false, false)),
% 45.70/29.83 inference(monotonicity,[status(thm)],[2623])).
% 45.70/29.83 tff(2625,plain,
% 45.70/29.83 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), false, false) = lazy_impl(prop(false), impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, false)), false)))),
% 45.70/29.83 inference(quant_inst,[status(thm)],[])).
% 45.70/29.83 tff(2626,plain,
% 45.70/29.83 (f1(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), false, false) = lazy_impl(prop(false), impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, false)), false))),
% 45.70/29.83 inference(unit_resolution,[status(thm)],[2625, 2128])).
% 45.70/29.83 tff(2627,plain,
% 45.70/29.83 (lazy_impl(prop(false), impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, false)), false)) = f1(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), false, false)),
% 45.70/29.83 inference(symmetry,[status(thm)],[2626])).
% 45.70/29.83 tff(2628,plain,
% 45.70/29.83 (impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, false)) = impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))),
% 45.70/29.83 inference(monotonicity,[status(thm)],[651, 93])).
% 45.70/29.83 tff(2629,plain,
% 45.70/29.83 (impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)) = impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, false))),
% 45.70/29.83 inference(symmetry,[status(thm)],[2628])).
% 45.70/29.83 tff(2630,plain,
% 45.70/29.83 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, false)) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))),
% 45.70/29.83 inference(monotonicity,[status(thm)],[93])).
% 45.70/29.83 tff(2631,plain,
% 45.70/29.83 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, false)) = impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, false))),
% 45.70/29.83 inference(transitivity,[status(thm)],[2630, 522, 645, 647, 2580, 653, 2629])).
% 45.70/29.83 tff(2632,plain,
% 45.70/29.83 (impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, false)), false) = impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, false)), false)),
% 45.70/29.83 inference(monotonicity,[status(thm)],[2631])).
% 45.70/29.83 tff(2633,plain,
% 45.70/29.83 (lazy_impl(prop(false), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, false)), false)) = lazy_impl(prop(false), impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, false)), false))),
% 45.70/29.83 inference(monotonicity,[status(thm)],[2632])).
% 45.70/29.83 tff(2634,plain,
% 45.70/29.83 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(apply(P!7, tptp_fun_X_4(not1(false), P!7)), false, false) = lazy_impl(prop(false), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, false)), false)))),
% 45.70/29.83 inference(quant_inst,[status(thm)],[])).
% 45.70/29.83 tff(2635,plain,
% 45.70/29.83 (f1(apply(P!7, tptp_fun_X_4(not1(false), P!7)), false, false) = lazy_impl(prop(false), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, false)), false))),
% 45.70/29.83 inference(unit_resolution,[status(thm)],[2634, 2128])).
% 45.70/29.83 tff(2636,plain,
% 45.70/29.83 (f1(false, false, false) = f1(apply(P!7, tptp_fun_X_4(not1(false), P!7)), false, false)),
% 45.70/29.83 inference(monotonicity,[status(thm)],[589])).
% 45.70/29.83 tff(2637,plain,
% 45.70/29.83 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(false, false, false) = lazy_impl(prop(false), impl(impl(false, impl(false, false)), false)))),
% 45.70/29.83 inference(quant_inst,[status(thm)],[])).
% 45.70/29.83 tff(2638,plain,
% 45.70/29.83 (f1(false, false, false) = lazy_impl(prop(false), impl(impl(false, impl(false, false)), false))),
% 45.70/29.83 inference(unit_resolution,[status(thm)],[2637, 2128])).
% 45.70/29.83 tff(2639,plain,
% 45.70/29.83 (lazy_impl(prop(false), impl(impl(false, impl(false, false)), false)) = f1(false, false, false)),
% 45.70/29.83 inference(symmetry,[status(thm)],[2638])).
% 45.70/29.83 tff(2640,plain,
% 45.70/29.83 (impl(false, impl(false, false)) = impl(false, not1(false))),
% 45.70/29.83 inference(monotonicity,[status(thm)],[93])).
% 45.70/29.83 tff(2641,plain,
% 45.70/29.83 (impl(false, impl(false, false)) = not1(false)),
% 45.70/29.83 inference(transitivity,[status(thm)],[2640, 421])).
% 45.70/29.83 tff(2642,plain,
% 45.70/29.83 (impl(impl(false, impl(false, false)), false) = impl(not1(false), false)),
% 45.70/29.83 inference(monotonicity,[status(thm)],[2641])).
% 45.70/29.83 tff(2643,plain,
% 45.70/29.83 (impl(not1(false), false) = impl(impl(false, impl(false, false)), false)),
% 45.70/29.83 inference(symmetry,[status(thm)],[2642])).
% 45.70/29.83 tff(2644,plain,
% 45.70/29.83 (false = impl(impl(false, impl(false, false)), false)),
% 45.70/29.83 inference(transitivity,[status(thm)],[115, 2643])).
% 45.70/29.83 tff(2645,plain,
% 45.70/29.83 (lazy_impl(not1(false), false) = lazy_impl(prop(false), impl(impl(false, impl(false, false)), false))),
% 45.70/29.83 inference(monotonicity,[status(thm)],[132, 2644])).
% 45.70/29.83 tff(2646,plain,
% 45.70/29.83 (lazy_impl(prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = f1(apply(P!7, tptp_fun_X_4(not1(false), P!7)), false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.83 inference(symmetry,[status(thm)],[2588])).
% 45.70/29.83 tff(2647,plain,
% 45.70/29.83 (lazy_impl(prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))), impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = f1(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.83 inference(symmetry,[status(thm)],[2565])).
% 45.70/29.83 tff(2648,plain,
% 45.70/29.83 (phi(impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = lazy_impl(not1(false), impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.83 inference(symmetry,[status(thm)],[2555])).
% 45.70/29.83 tff(2649,plain,
% 45.70/29.83 (phi(impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = phi(impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, not1(false))), not1(false)), false2))),
% 45.70/29.83 inference(transitivity,[status(thm)],[2648, 2562, 2647, 2569, 2572, 2585, 2646, 2589, 2592, 2602, 2605, 471, 2553, 205, 204, 2645, 2639, 2636, 2635, 2633, 2627, 2624, 2622, 2620, 2618, 2616])).
% 45.70/29.83 tff(2650,plain,
% 45.70/29.83 ((phi(impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = err) <=> (phi(impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, not1(false))), not1(false)), false2)) = err)),
% 45.70/29.83 inference(monotonicity,[status(thm)],[2649])).
% 45.70/29.83 tff(2651,plain,
% 45.70/29.83 ((phi(impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, not1(false))), not1(false)), false2)) = err) <=> (phi(impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = err)),
% 45.70/29.83 inference(symmetry,[status(thm)],[2650])).
% 45.70/29.83 tff(2652,plain,
% 45.70/29.83 ((phi(impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, not1(false))), not1(false)), false2)) = err) <=> (phi(tptp_fun_R_5(P!7)) = err)),
% 45.70/29.83 inference(transitivity,[status(thm)],[2651, 2609])).
% 45.70/29.83 tff(2653,plain,
% 45.70/29.83 ((~(phi(impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, not1(false))), not1(false)), false2)) = err)) <=> (~(phi(tptp_fun_R_5(P!7)) = err))),
% 45.70/29.83 inference(monotonicity,[status(thm)],[2652])).
% 45.70/29.83 tff(2654,plain,
% 45.70/29.83 (false = phi(impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, not1(false))), not1(false)), false2))),
% 45.70/29.83 inference(transitivity,[status(thm)],[205, 204, 2645, 2639, 2636, 2635, 2633, 2627, 2624, 2622, 2620, 2618, 2616])).
% 45.70/29.83 tff(2655,plain,
% 45.70/29.83 ((false = err) <=> (phi(impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, not1(false))), not1(false)), false2)) = err)),
% 45.70/29.83 inference(monotonicity,[status(thm)],[2654])).
% 45.70/29.83 tff(2656,plain,
% 45.70/29.83 ((~(false = err)) <=> (~(phi(impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, not1(false))), not1(false)), false2)) = err))),
% 45.70/29.83 inference(monotonicity,[status(thm)],[2655])).
% 45.70/29.83 tff(2657,plain,
% 45.70/29.83 (~(phi(impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, not1(false))), not1(false)), false2)) = err)),
% 45.70/29.83 inference(modus_ponens,[status(thm)],[556, 2656])).
% 45.70/29.83 tff(2658,plain,
% 45.70/29.83 (~(phi(tptp_fun_R_5(P!7)) = err)),
% 45.70/29.83 inference(modus_ponens,[status(thm)],[2657, 2653])).
% 45.70/29.83 tff(2659,plain,
% 45.70/29.83 (d(tptp_fun_R_5(P!7)) | (~(phi(tptp_fun_R_5(P!7)) = err))),
% 45.70/29.83 inference(unit_resolution,[status(thm)],[1503, 2658])).
% 45.70/29.83 tff(2660,plain,
% 45.70/29.83 (~((~d(tptp_fun_R_5(P!7))) | (~(phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))))),
% 45.70/29.83 inference(unit_resolution,[status(thm)],[1508, 2659])).
% 45.70/29.83 tff(2661,plain,
% 45.70/29.83 (phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)),
% 45.70/29.83 inference(unit_resolution,[status(thm)],[1510, 2660])).
% 45.70/29.83 tff(2662,plain,
% 45.70/29.83 (tptp_fun_R_5(P!7) = phi(tptp_fun_R_5(P!7))),
% 45.70/29.83 inference(symmetry,[status(thm)],[2661])).
% 45.70/29.83 tff(2663,plain,
% 45.70/29.83 (tptp_fun_R_5(P!7) = false),
% 45.70/29.83 inference(transitivity,[status(thm)],[2662, 1295, 1292, 2553])).
% 45.70/29.83 tff(2664,plain,
% 45.70/29.83 (f5(P!7, tptp_fun_R_5(P!7)) = f5(P!7, false)),
% 45.70/29.83 inference(monotonicity,[status(thm)],[2663])).
% 45.70/29.83 tff(2665,plain,
% 45.70/29.83 (f5(P!7, false) = f5(P!7, tptp_fun_R_5(P!7))),
% 45.70/29.83 inference(symmetry,[status(thm)],[2664])).
% 45.70/29.83 tff(2666,plain,
% 45.70/29.83 (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.70/29.83 inference(transitivity,[status(thm)],[932, 2665, 311])).
% 45.70/29.83 tff(2667,plain,
% 45.70/29.83 ((phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = false) <=> (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false)),
% 45.70/29.83 inference(monotonicity,[status(thm)],[2666])).
% 45.70/29.83 tff(2668,plain,
% 45.70/29.83 ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) <=> (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = false)),
% 45.70/29.83 inference(symmetry,[status(thm)],[2667])).
% 45.70/29.83 tff(2669,plain,
% 45.70/29.84 ((phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false)) <=> (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false))),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2666])).
% 45.70/29.84 tff(2670,plain,
% 45.70/29.84 ((~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false))) <=> (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false)))),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2669])).
% 45.70/29.84 tff(2671,plain,
% 45.70/29.84 (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_3(P!7)), false)),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2663])).
% 45.70/29.84 tff(2672,plain,
% 45.70/29.84 (d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) <=> d(impl(apply(P!7, tptp_fun_X_3(P!7)), false))),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2671])).
% 45.70/29.84 tff(2673,plain,
% 45.70/29.84 (d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) <=> d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.84 inference(symmetry,[status(thm)],[2672])).
% 45.70/29.84 tff(2674,plain,
% 45.70/29.84 (d(apply(P!7, tptp_fun_X_3(P!7))) <=> d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.84 inference(transitivity,[status(thm)],[372, 940, 2673])).
% 45.70/29.84 tff(2675,plain,
% 45.70/29.84 (d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.84 inference(modus_ponens,[status(thm)],[375, 2674])).
% 45.70/29.84 tff(2676,plain,
% 45.70/29.84 (bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) <=> bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false))),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2671])).
% 45.70/29.84 tff(2677,plain,
% 45.70/29.84 (bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) <=> bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.84 inference(symmetry,[status(thm)],[2676])).
% 45.70/29.84 tff(2678,plain,
% 45.70/29.84 (bool(apply(P!7, tptp_fun_X_3(P!7))) <=> bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.84 inference(transitivity,[status(thm)],[402, 945, 2677])).
% 45.70/29.84 tff(2679,plain,
% 45.70/29.84 ((~bool(apply(P!7, tptp_fun_X_3(P!7)))) <=> (~bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2678])).
% 45.70/29.84 tff(2680,plain,
% 45.70/29.84 (~bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.84 inference(modus_ponens,[status(thm)],[348, 2679])).
% 45.70/29.84 tff(2681,plain,
% 45.70/29.84 (tptp_fun_X_4(tptp_fun_R_5(P!7), P!7) = tptp_fun_X_4(false, P!7)),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2663])).
% 45.70/29.84 tff(2682,plain,
% 45.70/29.84 (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = f4(P!7, tptp_fun_X_4(false, P!7), false)),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2681, 2663])).
% 45.70/29.84 tff(2683,plain,
% 45.70/29.84 (d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) <=> d(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2682])).
% 45.70/29.84 tff(2684,plain,
% 45.70/29.84 (d(f4(P!7, tptp_fun_X_4(false, P!7), false)) <=> d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.70/29.84 inference(symmetry,[status(thm)],[2683])).
% 45.70/29.84 tff(2685,plain,
% 45.70/29.84 (d(f4(P!7, tptp_fun_X_4(false, P!7), false)) <=> d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.84 inference(transitivity,[status(thm)],[2684, 2005])).
% 45.70/29.84 tff(2686,plain,
% 45.70/29.84 (impl(false, not1(false)) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))),
% 45.70/29.84 inference(monotonicity,[status(thm)],[589])).
% 45.70/29.84 tff(2687,assumption,(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false)), introduced(assumption)).
% 45.70/29.84 tff(2688,plain,
% 45.70/29.84 (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 45.70/29.84 inference(transitivity,[status(thm)],[2687, 2310, 2686, 522, 645])).
% 45.70/29.84 tff(2689,plain,
% 45.70/29.84 ((phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err) <=> (phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err)),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2688])).
% 45.70/29.84 tff(2690,plain,
% 45.70/29.84 ((phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err) <=> (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err)),
% 45.70/29.84 inference(symmetry,[status(thm)],[2689])).
% 45.70/29.84 tff(2691,plain,
% 45.70/29.84 ((~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err)) <=> (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err))),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2690])).
% 45.70/29.84 tff(2692,plain,
% 45.70/29.84 (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err)),
% 45.70/29.84 inference(modus_ponens,[status(thm)],[689, 2691])).
% 45.70/29.84 tff(2693,plain,
% 45.70/29.84 (d(f4(P!7, tptp_fun_X_4(false, P!7), false)) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err))),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[1016, 2692])).
% 45.70/29.84 tff(2694,plain,
% 45.70/29.84 (~((~d(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[1021, 2693])).
% 45.70/29.84 tff(2695,plain,
% 45.70/29.84 (d(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[1048, 2694])).
% 45.70/29.84 tff(2696,plain,
% 45.70/29.84 (d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.84 inference(modus_ponens,[status(thm)],[2695, 2685])).
% 45.70/29.84 tff(2697,plain,
% 45.70/29.84 (bool(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) <=> bool(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2682])).
% 45.70/29.84 tff(2698,plain,
% 45.70/29.84 (bool(f4(P!7, tptp_fun_X_4(false, P!7), false)) <=> bool(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.70/29.84 inference(symmetry,[status(thm)],[2697])).
% 45.70/29.84 tff(2699,plain,
% 45.70/29.84 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 45.70/29.84 inference(transitivity,[status(thm)],[312, 2664, 908])).
% 45.70/29.84 tff(2700,plain,
% 45.70/29.84 ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) <=> (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2699, 2682])).
% 45.70/29.84 tff(2701,plain,
% 45.70/29.84 (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false)),
% 45.70/29.84 inference(modus_ponens,[status(thm)],[1549, 2700])).
% 45.70/29.84 tff(2702,plain,
% 45.70/29.84 (f4(P!7, tptp_fun_X_4(false, P!7), false) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 45.70/29.84 inference(symmetry,[status(thm)],[2701])).
% 45.70/29.84 tff(2703,plain,
% 45.70/29.84 (f4(P!7, tptp_fun_X_4(false, P!7), false) = impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))),
% 45.70/29.84 inference(transitivity,[status(thm)],[2702, 2687, 2310, 2686, 522, 645, 647, 2580, 653])).
% 45.70/29.84 tff(2704,plain,
% 45.70/29.84 (bool(f4(P!7, tptp_fun_X_4(false, P!7), false)) <=> bool(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)))),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2703])).
% 45.70/29.84 tff(2705,plain,
% 45.70/29.84 (bool(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))) <=> bool(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 45.70/29.84 inference(symmetry,[status(thm)],[2704])).
% 45.70/29.84 tff(2706,plain,
% 45.70/29.84 (bool(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))) <=> bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.84 inference(transitivity,[status(thm)],[2705, 2698, 417])).
% 45.70/29.84 tff(2707,plain,
% 45.70/29.84 (not1(false) = impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))),
% 45.70/29.84 inference(transitivity,[status(thm)],[2310, 2686, 522, 645, 647, 2580, 653])).
% 45.70/29.84 tff(2708,plain,
% 45.70/29.84 (bool(not1(false)) <=> bool(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)))),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2707])).
% 45.70/29.84 tff(2709,plain,
% 45.70/29.84 (bool(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)))),
% 45.70/29.84 inference(modus_ponens,[status(thm)],[272, 2708])).
% 45.70/29.84 tff(2710,plain,
% 45.70/29.84 (bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.84 inference(modus_ponens,[status(thm)],[2709, 2706])).
% 45.70/29.84 tff(2711,plain,
% 45.70/29.84 ($false),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[1957, 2710, 2696, 1926, 1925])).
% 45.70/29.84 tff(2712,plain,((~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))) | (~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(prop(tptp_fun_R_5(P!7)) = not1(false))) | (phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err)), inference(lemma,lemma(discharge,[]))).
% 45.70/29.84 tff(2713,plain,
% 45.70/29.84 (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false))),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[2712, 2680, 2675, 588, 2553, 1290, 689])).
% 45.70/29.84 tff(2714,plain,
% 45.70/29.84 (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false))),
% 45.70/29.84 inference(modus_ponens,[status(thm)],[2713, 2670])).
% 45.70/29.84 tff(2715,assumption,(phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)), introduced(assumption)).
% 45.70/29.84 tff(2716,plain,
% 45.70/29.84 (false = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 45.70/29.84 inference(symmetry,[status(thm)],[2553])).
% 45.70/29.84 tff(2717,plain,
% 45.70/29.84 (false = tptp_fun_R_5(P!7)),
% 45.70/29.84 inference(transitivity,[status(thm)],[2716, 1302, 1294, 2715])).
% 45.70/29.84 tff(2718,plain,
% 45.70/29.84 (tptp_fun_R_5(P!7) = phi(tptp_fun_R_5(P!7))),
% 45.70/29.84 inference(symmetry,[status(thm)],[2715])).
% 45.70/29.84 tff(2719,plain,
% 45.70/29.84 (tptp_fun_R_5(P!7) = false),
% 45.70/29.84 inference(transitivity,[status(thm)],[2718, 1295, 1292, 2553])).
% 45.70/29.84 tff(2720,plain,
% 45.70/29.84 (tptp_fun_X_4(tptp_fun_R_5(P!7), P!7) = tptp_fun_X_4(false, P!7)),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2719])).
% 45.70/29.84 tff(2721,plain,
% 45.70/29.84 (tptp_fun_X_4(false, P!7) = tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)),
% 45.70/29.84 inference(symmetry,[status(thm)],[2720])).
% 45.70/29.84 tff(2722,plain,
% 45.70/29.84 (f4(P!7, tptp_fun_X_4(false, P!7), false) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2721, 2717])).
% 45.70/29.84 tff(2723,plain,
% 45.70/29.84 (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = f4(P!7, tptp_fun_X_4(false, P!7), false)),
% 45.70/29.84 inference(symmetry,[status(thm)],[2722])).
% 45.70/29.84 tff(2724,plain,
% 45.70/29.84 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)),
% 45.70/29.84 inference(transitivity,[status(thm)],[415, 2723, 804])).
% 45.70/29.84 tff(2725,plain,
% 45.70/29.84 ((impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)) <=> (impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2724])).
% 45.70/29.84 tff(2726,plain,
% 45.70/29.84 ((impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false)) <=> (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))),
% 45.70/29.84 inference(symmetry,[status(thm)],[2725])).
% 45.70/29.84 tff(2727,plain,
% 45.70/29.84 (impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.70/29.84 inference(transitivity,[status(thm)],[805, 2722, 1584])).
% 45.70/29.84 tff(2728,plain,
% 45.70/29.84 ((impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false)) <=> (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false))),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2727])).
% 45.70/29.84 tff(2729,plain,
% 45.70/29.84 ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false)) <=> (impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))),
% 45.70/29.84 inference(symmetry,[status(thm)],[2728])).
% 45.70/29.84 tff(2730,plain,
% 45.70/29.84 ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false)) <=> (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))),
% 45.70/29.84 inference(transitivity,[status(thm)],[2729, 2726])).
% 45.70/29.84 tff(2731,plain,
% 45.70/29.84 ((~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false))) <=> (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)))),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2730])).
% 45.70/29.84 tff(2732,assumption,(~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false))), introduced(assumption)).
% 45.70/29.84 tff(2733,plain,
% 45.70/29.84 (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))),
% 45.70/29.84 inference(modus_ponens,[status(thm)],[2732, 2731])).
% 45.70/29.84 tff(2734,plain,
% 45.70/29.84 ($false),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[1810, 2733])).
% 45.70/29.84 tff(2735,plain,((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false)) | (~(phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(prop(tptp_fun_R_5(P!7)) = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 45.70/29.84 tff(2736,plain,
% 45.70/29.84 (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[2735, 2714, 2661, 2553, 1290])).
% 45.70/29.84 tff(2737,plain,
% 45.70/29.84 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[1694, 2736, 1328, 1290, 1327, 1326])).
% 45.70/29.84 tff(2738,plain,
% 45.70/29.84 (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = false),
% 45.70/29.84 inference(modus_ponens,[status(thm)],[2737, 2668])).
% 45.70/29.84 tff(2739,assumption,(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = false), introduced(assumption)).
% 45.70/29.84 tff(2740,plain,
% 45.70/29.84 (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = phi(impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, not1(false))), not1(false)), false2))),
% 45.70/29.84 inference(transitivity,[status(thm)],[2739, 205, 204, 2645, 2639, 2636, 2635, 2633, 2627, 2624, 2622, 2620, 2618, 2616])).
% 45.70/29.84 tff(2741,plain,
% 45.70/29.84 ((phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err) <=> (phi(impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, not1(false))), not1(false)), false2)) = err)),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2740])).
% 45.70/29.84 tff(2742,plain,
% 45.70/29.84 ((phi(impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, not1(false))), not1(false)), false2)) = err) <=> (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err)),
% 45.70/29.84 inference(symmetry,[status(thm)],[2741])).
% 45.70/29.84 tff(2743,plain,
% 45.70/29.84 ((~(phi(impl(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, not1(false))), not1(false)), false2)) = err)) <=> (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err))),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2742])).
% 45.70/29.84 tff(2744,plain,
% 45.70/29.84 (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err)),
% 45.70/29.84 inference(modus_ponens,[status(thm)],[2657, 2743])).
% 45.70/29.84 tff(2745,plain,
% 45.70/29.84 (d(f4(P!7, tptp_fun_X_4(false, P!7), false)) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err))),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[1016, 2744])).
% 45.70/29.84 tff(2746,plain,
% 45.70/29.84 (~((~d(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[1021, 2745])).
% 45.70/29.84 tff(2747,plain,
% 45.70/29.84 (d(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[1048, 2746])).
% 45.70/29.84 tff(2748,plain,
% 45.70/29.84 (d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.84 inference(modus_ponens,[status(thm)],[2747, 2685])).
% 45.70/29.84 tff(2749,plain,
% 45.70/29.84 (f4(P!7, tptp_fun_X_4(false, P!7), false) = false),
% 45.70/29.84 inference(transitivity,[status(thm)],[2702, 2739])).
% 45.70/29.84 tff(2750,plain,
% 45.70/29.84 (bool(f4(P!7, tptp_fun_X_4(false, P!7), false)) <=> bool(false)),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2749])).
% 45.70/29.84 tff(2751,plain,
% 45.70/29.84 (bool(false) <=> bool(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 45.70/29.84 inference(symmetry,[status(thm)],[2750])).
% 45.70/29.84 tff(2752,plain,
% 45.70/29.84 (bool(false) <=> bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.84 inference(transitivity,[status(thm)],[2751, 2698, 417])).
% 45.70/29.84 tff(2753,plain,
% 45.70/29.84 (bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.84 inference(modus_ponens,[status(thm)],[76, 2752])).
% 45.70/29.84 tff(2754,plain,
% 45.70/29.84 ($false),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[1957, 2753, 2748, 1926, 1925])).
% 45.70/29.84 tff(2755,plain,((~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = false)) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(prop(tptp_fun_R_5(P!7)) = not1(false))) | (~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false))), inference(lemma,lemma(discharge,[]))).
% 45.70/29.84 tff(2756,plain,
% 45.70/29.84 (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = false)),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[2755, 2680, 2675, 2553, 1290, 588])).
% 45.70/29.84 tff(2757,plain,
% 45.70/29.84 ($false),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[2756, 2738])).
% 45.70/29.84 tff(2758,plain,(((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))))) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(prop(tptp_fun_R_5(P!7)) = not1(false))) | (~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false)) | (~(impl(not1(false), tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))) | (~((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = not1(false)))) | (~(impl(false, tptp_fun_R_5(P!7)) = not1(false))) | (phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err) | bool(apply(P!7, tptp_fun_X_3(P!7)))), inference(lemma,lemma(discharge,[]))).
% 45.70/29.84 tff(2759,plain,
% 45.70/29.84 (((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))))) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(prop(tptp_fun_R_5(P!7)) = not1(false))) | (~(impl(not1(false), tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))) | (~((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = not1(false)))) | (~(impl(false, tptp_fun_R_5(P!7)) = not1(false))) | bool(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[2758, 2294, 2552])).
% 45.70/29.84 tff(2760,plain,
% 45.70/29.84 (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false)),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[2759, 368, 2551, 2550, 2549, 2548, 348])).
% 45.70/29.84 tff(2761,plain,
% 45.70/29.84 (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = not1(false)),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[1982, 2760])).
% 45.70/29.84 tff(2762,plain,
% 45.70/29.84 (not1(false) = prop(tptp_fun_R_5(P!7))),
% 45.70/29.84 inference(symmetry,[status(thm)],[2551])).
% 45.70/29.84 tff(2763,plain,
% 45.70/29.84 (lazy_impl(not1(false), tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2762])).
% 45.70/29.84 tff(2764,plain,
% 45.70/29.84 (phi(tptp_fun_R_5(P!7)) = phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.84 inference(transitivity,[status(thm)],[1295, 2763, 1767])).
% 45.70/29.84 tff(2765,plain,
% 45.70/29.84 ((phi(tptp_fun_R_5(P!7)) = err) <=> (phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2764])).
% 45.70/29.84 tff(2766,plain,
% 45.70/29.84 ((phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err) <=> (phi(tptp_fun_R_5(P!7)) = err)),
% 45.70/29.84 inference(symmetry,[status(thm)],[2765])).
% 45.70/29.84 tff(2767,plain,
% 45.70/29.84 (phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false)),
% 45.70/29.84 inference(transitivity,[status(thm)],[1766, 2761])).
% 45.70/29.84 tff(2768,plain,
% 45.70/29.84 ((phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err) <=> (not1(false) = err)),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2767])).
% 45.70/29.84 tff(2769,plain,
% 45.70/29.84 ((not1(false) = err) <=> (phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)),
% 45.70/29.84 inference(symmetry,[status(thm)],[2768])).
% 45.70/29.84 tff(2770,plain,
% 45.70/29.84 ((not1(false) = err) <=> (phi(tptp_fun_R_5(P!7)) = err)),
% 45.70/29.84 inference(transitivity,[status(thm)],[2769, 2766])).
% 45.70/29.84 tff(2771,plain,
% 45.70/29.84 ((~(not1(false) = err)) <=> (~(phi(tptp_fun_R_5(P!7)) = err))),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2770])).
% 45.70/29.84 tff(2772,plain,
% 45.70/29.84 (~(phi(tptp_fun_R_5(P!7)) = err)),
% 45.70/29.84 inference(modus_ponens,[status(thm)],[564, 2771])).
% 45.70/29.84 tff(2773,plain,
% 45.70/29.84 (d(tptp_fun_R_5(P!7)) | (~(phi(tptp_fun_R_5(P!7)) = err))),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[1503, 2772])).
% 45.70/29.84 tff(2774,plain,
% 45.70/29.84 (~((~d(tptp_fun_R_5(P!7))) | (~(phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))))),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[1508, 2773])).
% 45.70/29.84 tff(2775,plain,
% 45.70/29.84 (phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[1510, 2774])).
% 45.70/29.84 tff(2776,plain,
% 45.70/29.84 (tptp_fun_R_5(P!7) = phi(tptp_fun_R_5(P!7))),
% 45.70/29.84 inference(symmetry,[status(thm)],[2775])).
% 45.70/29.84 tff(2777,plain,
% 45.70/29.84 (tptp_fun_R_5(P!7) = not1(false)),
% 45.70/29.84 inference(transitivity,[status(thm)],[2776, 1295, 2763, 2761])).
% 45.70/29.84 tff(2778,plain,
% 45.70/29.84 (tptp_fun_X_4(tptp_fun_R_5(P!7), P!7) = tptp_fun_X_4(not1(false), P!7)),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2777])).
% 45.70/29.84 tff(2779,plain,
% 45.70/29.84 (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2778, 2777])).
% 45.70/29.84 tff(2780,plain,
% 45.70/29.84 (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = not1(false)),
% 45.70/29.84 inference(transitivity,[status(thm)],[2779, 521, 2295, 421])).
% 45.70/29.84 tff(2781,plain,
% 45.70/29.84 (bool(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) <=> bool(not1(false))),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2780])).
% 45.70/29.84 tff(2782,plain,
% 45.70/29.84 (bool(not1(false)) <=> bool(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.70/29.84 inference(symmetry,[status(thm)],[2781])).
% 45.70/29.84 tff(2783,plain,
% 45.70/29.84 (bool(not1(false)) <=> bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.84 inference(transitivity,[status(thm)],[2782, 417])).
% 45.70/29.84 tff(2784,plain,
% 45.70/29.84 (bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.84 inference(modus_ponens,[status(thm)],[272, 2783])).
% 45.70/29.84 tff(2785,plain,
% 45.70/29.84 (d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) <=> d(not1(false))),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2780])).
% 45.70/29.84 tff(2786,plain,
% 45.70/29.84 (d(not1(false)) <=> d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.70/29.84 inference(symmetry,[status(thm)],[2785])).
% 45.70/29.84 tff(2787,plain,
% 45.70/29.84 (d(not1(false)) <=> d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.84 inference(transitivity,[status(thm)],[2786, 2005])).
% 45.70/29.84 tff(2788,plain,
% 45.70/29.84 (d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.84 inference(modus_ponens,[status(thm)],[40, 2787])).
% 45.70/29.84 tff(2789,plain,
% 45.70/29.84 ($false),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[1957, 2788, 2784, 405, 399])).
% 45.70/29.84 tff(2790,plain,(((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))))) | bool(apply(P!7, tptp_fun_X_3(P!7)))), inference(lemma,lemma(discharge,[]))).
% 45.70/29.84 tff(2791,plain,
% 45.70/29.84 ((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))))),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[2790, 348])).
% 45.70/29.84 tff(2792,plain,
% 45.70/29.84 (~(d(apply(P!7, tptp_fun_X_3(P!7))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err)))),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[383, 2791])).
% 45.70/29.84 tff(2793,plain,
% 45.70/29.84 (phi(apply(P!7, tptp_fun_X_3(P!7))) = err),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[385, 2792])).
% 45.70/29.84 tff(2794,plain,
% 45.70/29.84 (err = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.70/29.84 inference(symmetry,[status(thm)],[2793])).
% 45.70/29.84 tff(2795,plain,
% 45.70/29.84 (err = exists1(P!7)),
% 45.70/29.84 inference(transitivity,[status(thm)],[2794, 347])).
% 45.70/29.84 tff(2796,plain,
% 45.70/29.84 ((phi(f6(P!7, tptp_fun_R_5(P!7))) = err) <=> (exists2(P!7) = exists1(P!7))),
% 45.70/29.84 inference(monotonicity,[status(thm)],[1309, 2795])).
% 45.70/29.84 tff(2797,plain,
% 45.70/29.84 ((phi(f6(P!7, tptp_fun_R_5(P!7))) = err) <=> (exists1(P!7) = exists2(P!7))),
% 45.70/29.84 inference(transitivity,[status(thm)],[2796, 329])).
% 45.70/29.84 tff(2798,plain,
% 45.70/29.84 ((exists1(P!7) = exists2(P!7)) <=> (phi(f6(P!7, tptp_fun_R_5(P!7))) = err)),
% 45.70/29.84 inference(symmetry,[status(thm)],[2797])).
% 45.70/29.84 tff(2799,plain,
% 45.70/29.84 ((~(exists1(P!7) = exists2(P!7))) <=> (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = err))),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2798])).
% 45.70/29.84 tff(2800,plain,
% 45.70/29.84 (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = err)),
% 45.70/29.84 inference(modus_ponens,[status(thm)],[897, 2799])).
% 45.70/29.84 tff(2801,plain,
% 45.70/29.84 (d(f6(P!7, tptp_fun_R_5(P!7))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = err))),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[1315, 2800])).
% 45.70/29.84 tff(2802,plain,
% 45.70/29.84 (~((~d(f6(P!7, tptp_fun_R_5(P!7)))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = f6(P!7, tptp_fun_R_5(P!7)))))),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[1320, 2801])).
% 45.70/29.84 tff(2803,plain,
% 45.70/29.84 (d(f6(P!7, tptp_fun_R_5(P!7)))),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[1322, 2802])).
% 45.70/29.84 tff(2804,plain,
% 45.70/29.84 (d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.84 inference(modus_ponens,[status(thm)],[2803, 328])).
% 45.70/29.84 tff(2805,plain,
% 45.70/29.84 (d(lazy_impl(prop(false), impl(f5(P!7, false), false)))),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[859, 2804])).
% 45.70/29.84 tff(2806,plain,
% 45.70/29.84 (lazy_impl(not1(false), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2762])).
% 45.70/29.84 tff(2807,plain,
% 45.70/29.84 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(not1(false), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.84 inference(symmetry,[status(thm)],[2806])).
% 45.70/29.84 tff(2808,plain,
% 45.70/29.84 (phi(f6(P!7, tptp_fun_R_5(P!7))) = f6(P!7, tptp_fun_R_5(P!7))),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[1334, 2802])).
% 45.70/29.84 tff(2809,plain,
% 45.70/29.84 (exists2(P!7) = phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.84 inference(transitivity,[status(thm)],[880, 2808, 325, 2807, 1331])).
% 45.70/29.84 tff(2810,plain,
% 45.70/29.84 (exists1(P!7) = err),
% 45.70/29.84 inference(transitivity,[status(thm)],[346, 2793])).
% 45.70/29.84 tff(2811,plain,
% 45.70/29.84 ((exists1(P!7) = exists2(P!7)) <=> (err = phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2810, 2809])).
% 45.70/29.84 tff(2812,plain,
% 45.70/29.84 ((exists1(P!7) = exists2(P!7)) <=> (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)),
% 45.70/29.84 inference(transitivity,[status(thm)],[2811, 1329])).
% 45.70/29.84 tff(2813,plain,
% 45.70/29.84 ((~(exists1(P!7) = exists2(P!7))) <=> (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err))),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2812])).
% 45.70/29.84 tff(2814,plain,
% 45.70/29.84 (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)),
% 45.70/29.84 inference(modus_ponens,[status(thm)],[897, 2813])).
% 45.70/29.84 tff(2815,plain,
% 45.70/29.84 (d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err))),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[1342, 2814])).
% 45.70/29.84 tff(2816,plain,
% 45.70/29.84 (~((~d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[1347, 2815])).
% 45.70/29.84 tff(2817,plain,
% 45.70/29.84 (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[1349, 2816])).
% 45.70/29.84 tff(2818,plain,
% 45.70/29.84 (bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[1708, 2817, 2550, 2551, 2549, 2548])).
% 45.70/29.84 tff(2819,plain,
% 45.70/29.84 (bool(lazy_impl(prop(false), impl(f5(P!7, false), false)))),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[864, 2818, 2805, 2804])).
% 45.70/29.84 tff(2820,plain,
% 45.70/29.84 ((~(bool(lazy_impl(prop(false), impl(f5(P!7, false), false))) <=> ((lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false))))) | ((lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false)))),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[866, 2819])).
% 45.70/29.84 tff(2821,plain,
% 45.70/29.84 ((lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false))),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[2820, 316])).
% 45.70/29.84 tff(2822,plain,
% 45.70/29.84 ((impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = not1(false)) <=> (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))),
% 45.70/29.84 inference(monotonicity,[status(thm)],[363])).
% 45.70/29.84 tff(2823,plain,
% 45.70/29.84 ((~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = not1(false))) <=> (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)))),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2822])).
% 45.70/29.84 tff(2824,plain,
% 45.70/29.84 ((not1(false) = apply(P!7, tptp_fun_X_3(P!7))) <=> (apply(P!7, tptp_fun_X_3(P!7)) = not1(false))),
% 45.70/29.84 inference(commutativity,[status(thm)],[])).
% 45.70/29.84 tff(2825,assumption,(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = not1(false)), introduced(assumption)).
% 45.70/29.84 tff(2826,plain,
% 45.70/29.84 (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)),
% 45.70/29.84 inference(transitivity,[status(thm)],[1300, 2825])).
% 45.70/29.84 tff(2827,plain,
% 45.70/29.84 ((phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))) <=> (not1(false) = apply(P!7, tptp_fun_X_3(P!7)))),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2826])).
% 45.70/29.84 tff(2828,plain,
% 45.70/29.84 ((phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))) <=> (apply(P!7, tptp_fun_X_3(P!7)) = not1(false))),
% 45.70/29.84 inference(transitivity,[status(thm)],[2827, 2824])).
% 45.70/29.84 tff(2829,plain,
% 45.70/29.84 ((apply(P!7, tptp_fun_X_3(P!7)) = not1(false)) <=> (phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))),
% 45.70/29.84 inference(symmetry,[status(thm)],[2828])).
% 45.70/29.84 tff(2830,plain,
% 45.70/29.84 ((~(apply(P!7, tptp_fun_X_3(P!7)) = not1(false))) <=> (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))))),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2829])).
% 45.70/29.84 tff(2831,plain,
% 45.70/29.84 ((~(bool(apply(P!7, tptp_fun_X_3(P!7))) <=> ((apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = not1(false))))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (~((apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = not1(false))))),
% 45.70/29.84 inference(tautology,[status(thm)],[])).
% 45.70/29.84 tff(2832,plain,
% 45.70/29.84 ((~(bool(apply(P!7, tptp_fun_X_3(P!7))) <=> ((apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = not1(false))))) | (~((apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = not1(false))))),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[2831, 348])).
% 45.70/29.84 tff(2833,plain,
% 45.70/29.84 (~((apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = not1(false)))),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[2832, 794])).
% 45.70/29.84 tff(2834,plain,
% 45.70/29.84 (((apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = not1(false))) | (~(apply(P!7, tptp_fun_X_3(P!7)) = not1(false)))),
% 45.70/29.84 inference(tautology,[status(thm)],[])).
% 45.70/29.84 tff(2835,plain,
% 45.70/29.84 (~(apply(P!7, tptp_fun_X_3(P!7)) = not1(false))),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[2834, 2833])).
% 45.70/29.84 tff(2836,plain,
% 45.70/29.84 (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))),
% 45.70/29.84 inference(modus_ponens,[status(thm)],[2835, 2830])).
% 45.70/29.84 tff(2837,plain,
% 45.70/29.84 (phi(apply(P!7, tptp_fun_X_3(P!7))) = phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 45.70/29.84 inference(transitivity,[status(thm)],[1300, 2825, 2310, 2686, 522, 645])).
% 45.70/29.84 tff(2838,plain,
% 45.70/29.84 ((phi(apply(P!7, tptp_fun_X_3(P!7))) = err) <=> (phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err)),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2837])).
% 45.70/29.84 tff(2839,plain,
% 45.70/29.84 ((phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err) <=> (phi(apply(P!7, tptp_fun_X_3(P!7))) = err)),
% 45.70/29.84 inference(symmetry,[status(thm)],[2838])).
% 45.70/29.84 tff(2840,plain,
% 45.70/29.84 ((~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err)) <=> (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err))),
% 45.70/29.84 inference(monotonicity,[status(thm)],[2839])).
% 45.70/29.84 tff(2841,plain,
% 45.70/29.84 (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err)),
% 45.70/29.84 inference(modus_ponens,[status(thm)],[689, 2840])).
% 45.70/29.84 tff(2842,plain,
% 45.70/29.84 (d(apply(P!7, tptp_fun_X_3(P!7))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err))),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[385, 2841])).
% 45.70/29.84 tff(2843,plain,
% 45.70/29.84 (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))))),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[383, 2842])).
% 45.70/29.84 tff(2844,plain,
% 45.70/29.84 (phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[369, 2843])).
% 45.70/29.84 tff(2845,plain,
% 45.70/29.84 ($false),
% 45.70/29.84 inference(unit_resolution,[status(thm)],[2844, 2836])).
% 45.70/29.84 tff(2846,plain,(bool(apply(P!7, tptp_fun_X_3(P!7))) | (~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = not1(false))) | (phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err) | (~(apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false))), inference(lemma,lemma(discharge,[]))).
% 45.70/29.85 tff(2847,plain,
% 45.70/29.85 (bool(apply(P!7, tptp_fun_X_3(P!7))) | (~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = not1(false)))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2846, 2552, 2294])).
% 45.70/29.85 tff(2848,plain,
% 45.70/29.85 (~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = not1(false))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2847, 348])).
% 45.70/29.85 tff(2849,plain,
% 45.70/29.85 (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))),
% 45.70/29.85 inference(modus_ponens,[status(thm)],[2848, 2823])).
% 45.70/29.85 tff(2850,plain,
% 45.70/29.85 (~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2468, 2849, 348])).
% 45.70/29.85 tff(2851,plain,
% 45.70/29.85 ((~((lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false)))) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[875, 2850])).
% 45.70/29.85 tff(2852,plain,
% 45.70/29.85 (lazy_impl(prop(false), impl(f5(P!7, false), false)) = false),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2851, 2821])).
% 45.70/29.85 tff(2853,plain,
% 45.70/29.85 (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[873, 2852])).
% 45.70/29.85 tff(2854,plain,
% 45.70/29.85 (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false)),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[1372, 2853, 2548, 2551])).
% 45.70/29.85 tff(2855,plain,
% 45.70/29.85 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[1694, 2854, 2551, 2550, 2549, 2548])).
% 45.70/29.85 tff(2856,plain,
% 45.70/29.85 ((~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = not1(false))) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))) | (~(prop(tptp_fun_R_5(P!7)) = not1(false))) | (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false)) | (~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[1812, 2404])).
% 45.70/29.85 tff(2857,plain,
% 45.70/29.85 (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = not1(false))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2856, 2855, 2551, 2793, 363, 2853])).
% 45.70/29.85 tff(2858,plain,
% 45.70/29.85 (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[1982, 2857])).
% 45.70/29.85 tff(2859,plain,
% 45.70/29.85 (err = impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))),
% 45.70/29.85 inference(transitivity,[status(thm)],[2794, 1300])).
% 45.70/29.85 tff(2860,plain,
% 45.70/29.85 (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = lazy_impl(not1(false), tptp_fun_R_5(P!7))),
% 45.70/29.85 inference(symmetry,[status(thm)],[2763])).
% 45.70/29.85 tff(2861,plain,
% 45.70/29.85 (phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = phi(tptp_fun_R_5(P!7))),
% 45.70/29.85 inference(transitivity,[status(thm)],[1766, 2860, 1294])).
% 45.70/29.85 tff(2862,plain,
% 45.70/29.85 ((phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err) <=> (phi(tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.85 inference(monotonicity,[status(thm)],[2861, 2859])).
% 45.70/29.85 tff(2863,plain,
% 45.70/29.85 ((phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err) <=> (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7)))),
% 45.70/29.85 inference(transitivity,[status(thm)],[2862, 1299])).
% 45.70/29.85 tff(2864,plain,
% 45.70/29.85 ((impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))) <=> (phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)),
% 45.70/29.85 inference(symmetry,[status(thm)],[2863])).
% 45.70/29.85 tff(2865,plain,
% 45.70/29.85 (phi(tptp_fun_R_5(P!7)) = false),
% 45.70/29.85 inference(transitivity,[status(thm)],[1295, 2763, 2858])).
% 45.70/29.85 tff(2866,plain,
% 45.70/29.85 ((impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))) <=> (phi(apply(P!7, tptp_fun_X_3(P!7))) = false)),
% 45.70/29.85 inference(monotonicity,[status(thm)],[363, 2865])).
% 45.70/29.85 tff(2867,plain,
% 45.70/29.85 ((phi(apply(P!7, tptp_fun_X_3(P!7))) = false) <=> (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7)))),
% 45.70/29.85 inference(symmetry,[status(thm)],[2866])).
% 45.70/29.85 tff(2868,plain,
% 45.70/29.85 ((phi(apply(P!7, tptp_fun_X_3(P!7))) = false) <=> (phi(tptp_fun_R_5(P!7)) = err)),
% 45.70/29.85 inference(transitivity,[status(thm)],[2867, 2864, 2766])).
% 45.70/29.85 tff(2869,plain,
% 45.70/29.85 ((~(phi(apply(P!7, tptp_fun_X_3(P!7))) = false)) <=> (~(phi(tptp_fun_R_5(P!7)) = err))),
% 45.70/29.85 inference(monotonicity,[status(thm)],[2868])).
% 45.70/29.85 tff(2870,plain,
% 45.70/29.85 (~(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))) = not1(false))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[1127, 2793, 1714])).
% 45.70/29.85 tff(2871,plain,
% 45.70/29.85 (~bool(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[1132, 2870])).
% 45.70/29.85 tff(2872,plain,
% 45.70/29.85 (~((phi(apply(P!7, tptp_fun_X_3(P!7))) = false) | (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[1720, 2871])).
% 45.70/29.85 tff(2873,plain,
% 45.70/29.85 (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = false)),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[1838, 2872])).
% 45.70/29.85 tff(2874,plain,
% 45.70/29.85 (~(phi(tptp_fun_R_5(P!7)) = err)),
% 45.70/29.85 inference(modus_ponens,[status(thm)],[2873, 2869])).
% 45.70/29.85 tff(2875,plain,
% 45.70/29.85 (d(tptp_fun_R_5(P!7)) | (~(phi(tptp_fun_R_5(P!7)) = err))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[1503, 2874])).
% 45.70/29.85 tff(2876,plain,
% 45.70/29.85 (~((~d(tptp_fun_R_5(P!7))) | (~(phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[1508, 2875])).
% 45.70/29.85 tff(2877,plain,
% 45.70/29.85 (phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[1510, 2876])).
% 45.70/29.85 tff(2878,plain,
% 45.70/29.85 (tptp_fun_R_5(P!7) = phi(tptp_fun_R_5(P!7))),
% 45.70/29.85 inference(symmetry,[status(thm)],[2877])).
% 45.70/29.85 tff(2879,plain,
% 45.70/29.85 (tptp_fun_R_5(P!7) = false),
% 45.70/29.85 inference(transitivity,[status(thm)],[2878, 1295, 2763, 2858])).
% 45.70/29.85 tff(2880,plain,
% 45.70/29.85 (f5(P!7, tptp_fun_R_5(P!7)) = f5(P!7, false)),
% 45.70/29.85 inference(monotonicity,[status(thm)],[2879])).
% 45.70/29.85 tff(2881,plain,
% 45.70/29.85 (f5(P!7, false) = f5(P!7, tptp_fun_R_5(P!7))),
% 45.70/29.85 inference(symmetry,[status(thm)],[2880])).
% 45.70/29.85 tff(2882,plain,
% 45.70/29.85 (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f5(P!7, tptp_fun_R_5(P!7))),
% 45.70/29.85 inference(transitivity,[status(thm)],[932, 2881])).
% 45.70/29.85 tff(2883,plain,
% 45.70/29.85 (bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) <=> bool(f5(P!7, tptp_fun_R_5(P!7)))),
% 45.70/29.85 inference(monotonicity,[status(thm)],[2882])).
% 45.70/29.85 tff(2884,plain,
% 45.70/29.85 (bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) <=> bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 45.70/29.85 inference(transitivity,[status(thm)],[2883, 314])).
% 45.70/29.85 tff(2885,plain,
% 45.70/29.85 ((~bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) <=> (~bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))))),
% 45.70/29.85 inference(monotonicity,[status(thm)],[2884])).
% 45.70/29.85 tff(2886,plain,
% 45.70/29.85 ((~bool(phi(apply(P!7, tptp_fun_X_3(P!7))))) <=> (~bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.85 inference(monotonicity,[status(thm)],[401])).
% 45.70/29.85 tff(2887,plain,
% 45.70/29.85 (~bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.85 inference(modus_ponens,[status(thm)],[2871, 2886])).
% 45.70/29.85 tff(2888,plain,
% 45.70/29.85 ((~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = false)) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(prop(tptp_fun_R_5(P!7)) = not1(false)))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2755, 2294])).
% 45.70/29.85 tff(2889,plain,
% 45.70/29.85 (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = false)),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2888, 2858, 399, 2551, 2887])).
% 45.70/29.85 tff(2890,plain,
% 45.70/29.85 ((~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(prop(tptp_fun_R_5(P!7)) = not1(false)))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2712, 2552, 2294])).
% 45.70/29.85 tff(2891,plain,
% 45.70/29.85 (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2890, 2858, 399, 2551, 2887])).
% 45.70/29.85 tff(2892,plain,
% 45.70/29.85 ((~((phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = false) | (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false)))) | (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = false) | (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false))),
% 45.70/29.85 inference(tautology,[status(thm)],[])).
% 45.70/29.85 tff(2893,plain,
% 45.70/29.85 (~((phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = false) | (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false)))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2892, 2891, 2889])).
% 45.70/29.85 tff(2894,plain,
% 45.70/29.85 ((~(bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) <=> ((phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = false) | (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false))))) | (~bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | ((phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = false) | (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false)))),
% 45.70/29.85 inference(tautology,[status(thm)],[])).
% 45.70/29.85 tff(2895,plain,
% 45.70/29.85 ((~bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | ((phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = false) | (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false)))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2894, 2450])).
% 45.70/29.85 tff(2896,plain,
% 45.70/29.85 (~bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2895, 2893])).
% 45.70/29.85 tff(2897,plain,
% 45.70/29.85 (~bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 45.70/29.85 inference(modus_ponens,[status(thm)],[2896, 2885])).
% 45.70/29.85 tff(2898,plain,
% 45.70/29.85 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false)),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2735, 2877, 2551, 2858, 2855])).
% 45.70/29.85 tff(2899,plain,
% 45.70/29.85 (((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false)))),
% 45.70/29.85 inference(tautology,[status(thm)],[])).
% 45.70/29.85 tff(2900,plain,
% 45.70/29.85 ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2899, 2898])).
% 45.70/29.85 tff(2901,plain,
% 45.70/29.85 ((~(bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) <=> ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false))))) | bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) | (~((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false))))),
% 45.70/29.85 inference(tautology,[status(thm)],[])).
% 45.70/29.85 tff(2902,plain,
% 45.70/29.85 (bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) | (~((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false))))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2901, 1473])).
% 45.70/29.85 tff(2903,plain,
% 45.70/29.85 (bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2902, 2900])).
% 45.70/29.85 tff(2904,plain,
% 45.70/29.85 ($false),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2903, 2897])).
% 45.70/29.85 tff(2905,plain,(bool(apply(P!7, tptp_fun_X_3(P!7)))), inference(lemma,lemma(discharge,[]))).
% 45.70/29.85 tff(2906,plain,
% 45.70/29.85 ((~((prop(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)) <=> bool(apply(P!7, tptp_fun_X_3(P!7))))) | (prop(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[1607, 2905])).
% 45.70/29.85 tff(2907,plain,
% 45.70/29.85 (prop(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2906, 294])).
% 45.70/29.85 tff(2908,plain,
% 45.70/29.85 (lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))) = lazy_impl(not1(false), apply(P!7, tptp_fun_X_3(P!7)))),
% 45.70/29.85 inference(monotonicity,[status(thm)],[2907])).
% 45.70/29.85 tff(2909,plain,
% 45.70/29.85 (lazy_impl(not1(false), apply(P!7, tptp_fun_X_3(P!7))) = lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))),
% 45.70/29.85 inference(symmetry,[status(thm)],[2908])).
% 45.70/29.85 tff(2910,plain,
% 45.70/29.85 (phi(apply(P!7, tptp_fun_X_3(P!7))) = f7(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.70/29.85 inference(transitivity,[status(thm)],[1614, 2909, 292])).
% 45.70/29.85 tff(2911,plain,
% 45.70/29.85 (forallprefers(phi(apply(P!7, tptp_fun_X_3(P!7))), false) <=> forallprefers(f7(apply(P!7, tptp_fun_X_3(P!7))), f7(P!6))),
% 45.70/29.85 inference(monotonicity,[status(thm)],[2910, 289])).
% 45.70/29.85 tff(2912,plain,
% 45.70/29.85 (forallprefers(f7(apply(P!7, tptp_fun_X_3(P!7))), f7(P!6)) <=> forallprefers(phi(apply(P!7, tptp_fun_X_3(P!7))), false)),
% 45.70/29.85 inference(symmetry,[status(thm)],[2911])).
% 45.70/29.85 tff(2913,plain,
% 45.70/29.85 ((~forallprefers(f7(apply(P!7, tptp_fun_X_3(P!7))), f7(P!6))) <=> (~forallprefers(phi(apply(P!7, tptp_fun_X_3(P!7))), false))),
% 45.70/29.85 inference(monotonicity,[status(thm)],[2912])).
% 45.70/29.85 tff(2914,plain,
% 45.70/29.85 (~forallprefers(phi(apply(P!7, tptp_fun_X_3(P!7))), false)),
% 45.70/29.85 inference(modus_ponens,[status(thm)],[1642, 2913])).
% 45.70/29.85 tff(2915,plain,
% 45.70/29.85 (~((~((~d(false)) | d(phi(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(false = not1(false))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = false)))) | (~((~d(false)) | (~bool(false)) | (~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | bool(phi(apply(P!7, tptp_fun_X_3(P!7)))))))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2022, 2914, 166])).
% 45.70/29.85 tff(2916,plain,
% 45.70/29.85 ((~d(false)) | (~bool(false)) | (~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | bool(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2024, 2915])).
% 45.70/29.85 tff(2917,plain,
% 45.70/29.85 ((~d(false)) | d(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2026, 2915])).
% 45.70/29.85 tff(2918,plain,
% 45.70/29.85 (d(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2029, 2917])).
% 45.70/29.85 tff(2919,plain,
% 45.70/29.85 (bool(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2032, 2918, 2916])).
% 45.70/29.85 tff(2920,plain,
% 45.70/29.85 (prop(phi(apply(P!7, tptp_fun_X_3(P!7)))) = not1(false)),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[1132, 2919])).
% 45.70/29.85 tff(2921,plain,
% 45.70/29.85 (d(phi(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(phi(apply(P!7, tptp_fun_X_3(P!7)))) = err))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[948, 2918])).
% 45.70/29.85 tff(2922,plain,
% 45.70/29.85 (~((~d(phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~(phi(phi(apply(P!7, tptp_fun_X_3(P!7)))) = phi(apply(P!7, tptp_fun_X_3(P!7))))))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[952, 17, 2921])).
% 45.70/29.85 tff(2923,plain,
% 45.70/29.85 (phi(phi(apply(P!7, tptp_fun_X_3(P!7)))) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[955, 2922])).
% 45.70/29.85 tff(2924,plain,
% 45.70/29.85 (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err)),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[1127, 2923, 2920])).
% 45.70/29.85 tff(2925,plain,
% 45.70/29.85 (d(apply(P!7, tptp_fun_X_3(P!7))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[385, 2924])).
% 45.70/29.85 tff(2926,plain,
% 45.70/29.85 (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[383, 2925])).
% 45.70/29.85 tff(2927,plain,
% 45.70/29.85 (phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[369, 2926])).
% 45.70/29.85 tff(2928,plain,
% 45.70/29.85 (apply(P!7, tptp_fun_X_3(P!7)) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.70/29.85 inference(symmetry,[status(thm)],[2927])).
% 45.70/29.85 tff(2929,plain,
% 45.70/29.85 ((apply(P!7, tptp_fun_X_3(P!7)) = not1(false)) <=> (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))),
% 45.70/29.85 inference(monotonicity,[status(thm)],[2928])).
% 45.70/29.85 tff(2930,plain,
% 45.70/29.85 ((phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)) <=> (apply(P!7, tptp_fun_X_3(P!7)) = not1(false))),
% 45.70/29.85 inference(symmetry,[status(thm)],[2929])).
% 45.70/29.85 tff(2931,plain,
% 45.70/29.85 (not1(false) = prop(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.70/29.85 inference(symmetry,[status(thm)],[2920])).
% 45.70/29.85 tff(2932,plain,
% 45.70/29.85 (lazy_impl(not1(false), phi(apply(P!7, tptp_fun_X_3(P!7)))) = lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.70/29.85 inference(monotonicity,[status(thm)],[2931])).
% 45.70/29.85 tff(2933,plain,
% 45.70/29.85 (phi(apply(P!7, tptp_fun_X_3(P!7))) = phi(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.70/29.85 inference(symmetry,[status(thm)],[2923])).
% 45.70/29.85 tff(2934,plain,
% 45.70/29.85 (phi(apply(P!7, tptp_fun_X_3(P!7))) = lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.70/29.85 inference(transitivity,[status(thm)],[2933, 1089, 2932])).
% 45.70/29.85 tff(2935,plain,
% 45.70/29.85 ((phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)) <=> (lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = not1(false))),
% 45.70/29.85 inference(monotonicity,[status(thm)],[2934])).
% 45.70/29.85 tff(2936,plain,
% 45.70/29.85 ((lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = not1(false)) <=> (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))),
% 45.70/29.85 inference(symmetry,[status(thm)],[2935])).
% 45.70/29.85 tff(2937,plain,
% 45.70/29.85 (lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = lazy_impl(not1(false), phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.70/29.85 inference(symmetry,[status(thm)],[2932])).
% 45.70/29.85 tff(2938,plain,
% 45.70/29.85 (phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = false),
% 45.70/29.85 inference(transitivity,[status(thm)],[1766, 2553])).
% 45.70/29.85 tff(2939,plain,
% 45.70/29.85 ((phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err) <=> (false = err)),
% 45.70/29.85 inference(monotonicity,[status(thm)],[2938])).
% 45.70/29.85 tff(2940,plain,
% 45.70/29.85 ((false = err) <=> (phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)),
% 45.70/29.85 inference(symmetry,[status(thm)],[2939])).
% 45.70/29.85 tff(2941,plain,
% 45.70/29.85 ((false = err) <=> (phi(tptp_fun_R_5(P!7)) = err)),
% 45.70/29.85 inference(transitivity,[status(thm)],[2940, 2766])).
% 45.70/29.85 tff(2942,plain,
% 45.70/29.85 ((~(false = err)) <=> (~(phi(tptp_fun_R_5(P!7)) = err))),
% 45.70/29.85 inference(monotonicity,[status(thm)],[2941])).
% 45.70/29.85 tff(2943,plain,
% 45.70/29.85 (~(phi(tptp_fun_R_5(P!7)) = err)),
% 45.70/29.85 inference(modus_ponens,[status(thm)],[556, 2942])).
% 45.70/29.85 tff(2944,plain,
% 45.70/29.85 (d(tptp_fun_R_5(P!7)) | (~(phi(tptp_fun_R_5(P!7)) = err))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[1503, 2943])).
% 45.70/29.85 tff(2945,plain,
% 45.70/29.85 (~((~d(tptp_fun_R_5(P!7))) | (~(phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[1508, 2944])).
% 45.70/29.85 tff(2946,plain,
% 45.70/29.85 (phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[1510, 2945])).
% 45.70/29.85 tff(2947,plain,
% 45.70/29.85 (tptp_fun_R_5(P!7) = phi(tptp_fun_R_5(P!7))),
% 45.70/29.85 inference(symmetry,[status(thm)],[2946])).
% 45.70/29.85 tff(2948,plain,
% 45.70/29.85 (tptp_fun_R_5(P!7) = false),
% 45.70/29.85 inference(transitivity,[status(thm)],[2947, 1295, 2763, 2553])).
% 45.70/29.85 tff(2949,plain,
% 45.70/29.85 (d(apply(P!7, tptp_fun_X_3(P!7)))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[374, 2926])).
% 45.70/29.85 tff(2950,plain,
% 45.70/29.85 (d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[1683, 2949])).
% 45.70/29.85 tff(2951,plain,
% 45.70/29.85 (bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[1659, 2950, 2905])).
% 45.70/29.85 tff(2952,plain,
% 45.70/29.85 ((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[1410, 2951])).
% 45.70/29.85 tff(2953,plain,
% 45.70/29.85 ((impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))) | (~(apply(P!7, tptp_fun_X_3(P!7)) = not1(false))) | (~(impl(false, tptp_fun_R_5(P!7)) = not1(false))) | (~(impl(not1(false), tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))) | (~(prop(tptp_fun_R_5(P!7)) = not1(false))) | (~((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false)))) | (~((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = not1(false))))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2097, 2412, 2404])).
% 45.70/29.85 tff(2954,plain,
% 45.70/29.85 ((impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)) | (~(apply(P!7, tptp_fun_X_3(P!7)) = not1(false)))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2953, 2549, 2548, 2550, 2551, 2952, 2927])).
% 45.70/29.85 tff(2955,plain,
% 45.70/29.85 (~(apply(P!7, tptp_fun_X_3(P!7)) = not1(false))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2954, 1374])).
% 45.70/29.85 tff(2956,plain,
% 45.70/29.85 ((~(bool(apply(P!7, tptp_fun_X_3(P!7))) <=> ((apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = not1(false))))) | ((apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = not1(false)))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[1198, 2905])).
% 45.70/29.85 tff(2957,plain,
% 45.70/29.85 ((apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = not1(false))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2956, 794])).
% 45.70/29.85 tff(2958,plain,
% 45.70/29.85 ((apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = not1(false))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[1244, 2957])).
% 45.70/29.85 tff(2959,plain,
% 45.70/29.85 (apply(P!7, tptp_fun_X_3(P!7)) = false),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2958, 2955])).
% 45.70/29.85 tff(2960,plain,
% 45.70/29.85 ((~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false)) | (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[1381, 2548])).
% 45.70/29.85 tff(2961,plain,
% 45.70/29.85 (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false)),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2960, 1374])).
% 45.70/29.85 tff(2962,plain,
% 45.70/29.85 ((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[1383, 2952])).
% 45.70/29.85 tff(2963,plain,
% 45.70/29.85 (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false)),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2962, 2961])).
% 45.70/29.85 tff(2964,plain,
% 45.70/29.85 (((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false)))))) | ((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false))))),
% 45.70/29.85 inference(tautology,[status(thm)],[])).
% 45.70/29.85 tff(2965,plain,
% 45.70/29.85 ((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false)))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2964, 1627])).
% 45.70/29.85 tff(2966,plain,
% 45.70/29.85 ((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false))))) | (~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false)))),
% 45.70/29.85 inference(tautology,[status(thm)],[])).
% 45.70/29.85 tff(2967,plain,
% 45.70/29.85 ((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false)))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2966, 2965])).
% 45.70/29.85 tff(2968,plain,
% 45.70/29.85 ($false),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2967, 2963, 2959])).
% 45.70/29.85 tff(2969,plain,(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)), inference(lemma,lemma(discharge,[]))).
% 45.70/29.85 tff(2970,plain,
% 45.70/29.85 ((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false)) | (~(phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2735, 2551])).
% 45.70/29.85 tff(2971,plain,
% 45.70/29.85 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false)),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2970, 2946, 2553, 2969])).
% 45.70/29.85 tff(2972,plain,
% 45.70/29.85 (f5(P!7, tptp_fun_R_5(P!7)) = not1(false)),
% 45.70/29.85 inference(transitivity,[status(thm)],[311, 2971])).
% 45.70/29.85 tff(2973,plain,
% 45.70/29.85 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = impl(not1(false), false)),
% 45.70/29.85 inference(monotonicity,[status(thm)],[2972, 2948])).
% 45.70/29.85 tff(2974,assumption,(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err), introduced(assumption)).
% 45.70/29.85 tff(2975,plain,
% 45.70/29.85 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(not1(false), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.85 inference(monotonicity,[status(thm)],[2551])).
% 45.70/29.85 tff(2976,plain,
% 45.70/29.85 (impl(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 45.70/29.85 inference(monotonicity,[status(thm)],[312])).
% 45.70/29.85 tff(2977,plain,
% 45.70/29.85 (lazy_impl(not1(false), impl(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.85 inference(monotonicity,[status(thm)],[2762, 2976])).
% 45.70/29.85 tff(2978,plain,
% 45.70/29.85 (lazy_impl(not1(false), impl(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = err),
% 45.70/29.85 inference(transitivity,[status(thm)],[2977, 2975, 1331, 2974])).
% 45.70/29.85 tff(2979,plain,
% 45.70/29.85 (impl(lazy_impl(not1(false), impl(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = impl(err, tptp_fun_R_5(P!7))),
% 45.70/29.85 inference(monotonicity,[status(thm)],[2978])).
% 45.70/29.85 tff(2980,plain,
% 45.70/29.85 (impl(err, tptp_fun_R_5(P!7)) = impl(lazy_impl(not1(false), impl(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))),
% 45.70/29.85 inference(symmetry,[status(thm)],[2979])).
% 45.70/29.85 tff(2981,plain,
% 45.70/29.85 (err = impl(lazy_impl(not1(false), impl(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))),
% 45.70/29.85 inference(transitivity,[status(thm)],[983, 982, 2980])).
% 45.70/29.85 tff(2982,plain,
% 45.70/29.85 (lazy_impl(not1(false), err) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(lazy_impl(not1(false), impl(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 45.70/29.85 inference(monotonicity,[status(thm)],[2762, 2981])).
% 45.70/29.85 tff(2983,plain,
% 45.70/29.85 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(lazy_impl(not1(false), impl(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = lazy_impl(not1(false), err)),
% 45.70/29.85 inference(symmetry,[status(thm)],[2982])).
% 45.70/29.85 tff(2984,plain,
% 45.70/29.85 ((~![P: $i, Q: $i, R: $i] : (f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R)))) | (f2(not1(false), phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(lazy_impl(not1(false), impl(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))))),
% 45.70/29.85 inference(quant_inst,[status(thm)],[])).
% 45.70/29.85 tff(2985,plain,
% 45.70/29.85 (f2(not1(false), phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(lazy_impl(not1(false), impl(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2984, 141])).
% 45.70/29.85 tff(2986,plain,
% 45.70/29.85 ((not1(false) = err) <=> (phi(tptp_fun_R_5(P!7)) = err)),
% 45.70/29.85 inference(transitivity,[status(thm)],[1963, 2766])).
% 45.70/29.85 tff(2987,plain,
% 45.70/29.85 ((~(not1(false) = err)) <=> (~(phi(tptp_fun_R_5(P!7)) = err))),
% 45.70/29.85 inference(monotonicity,[status(thm)],[2986])).
% 45.70/29.85 tff(2988,plain,
% 45.70/29.85 (~(phi(tptp_fun_R_5(P!7)) = err)),
% 45.70/29.85 inference(modus_ponens,[status(thm)],[564, 2987])).
% 45.70/29.85 tff(2989,plain,
% 45.70/29.85 (d(tptp_fun_R_5(P!7)) | (~(phi(tptp_fun_R_5(P!7)) = err))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[1503, 2988])).
% 45.70/29.85 tff(2990,plain,
% 45.70/29.85 (~((~d(tptp_fun_R_5(P!7))) | (~(phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[1508, 2989])).
% 45.70/29.85 tff(2991,plain,
% 45.70/29.85 (phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[1510, 2990])).
% 45.70/29.85 tff(2992,plain,
% 45.70/29.85 (tptp_fun_R_5(P!7) = phi(tptp_fun_R_5(P!7))),
% 45.70/29.85 inference(symmetry,[status(thm)],[2991])).
% 45.70/29.85 tff(2993,plain,
% 45.70/29.85 (tptp_fun_R_5(P!7) = not1(false)),
% 45.70/29.85 inference(transitivity,[status(thm)],[2992, 1295, 2763, 1759])).
% 45.70/29.85 tff(2994,plain,
% 45.70/29.85 (f6(P!7, tptp_fun_R_5(P!7)) = f6(P!7, not1(false))),
% 45.70/29.85 inference(monotonicity,[status(thm)],[2993])).
% 45.70/29.85 tff(2995,plain,
% 45.70/29.85 (f6(P!7, not1(false)) = f6(P!7, tptp_fun_R_5(P!7))),
% 45.70/29.85 inference(symmetry,[status(thm)],[2994])).
% 45.70/29.85 tff(2996,plain,
% 45.70/29.85 (lazy_impl(prop(not1(false)), impl(lazy_impl(not1(false), impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))), not1(false))) = lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))),
% 45.70/29.85 inference(symmetry,[status(thm)],[2410])).
% 45.70/29.85 tff(2997,plain,
% 45.70/29.85 (f2(not1(false), false, not1(false)) = f2(not1(false), apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))),
% 45.70/29.85 inference(symmetry,[status(thm)],[2407])).
% 45.70/29.85 tff(2998,plain,
% 45.70/29.85 (lazy_impl(not1(false), not1(false)) = lazy_impl(prop(not1(false)), impl(lazy_impl(not1(false), impl(false, not1(false))), not1(false)))),
% 45.70/29.85 inference(symmetry,[status(thm)],[2406])).
% 45.70/29.85 tff(2999,plain,
% 45.70/29.85 (not1(false) = err),
% 45.70/29.85 inference(transitivity,[status(thm)],[603, 602, 2998, 593, 2997, 587, 2996, 744, 2995, 325, 2807, 1331, 2974])).
% 45.70/29.85 tff(3000,plain,
% 45.70/29.85 ($false),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[564, 2999])).
% 45.70/29.85 tff(3001,plain,((~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = not1(false))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err))), inference(lemma,lemma(discharge,[]))).
% 45.70/29.85 tff(3002,plain,
% 45.70/29.85 (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = not1(false))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[3001, 2974])).
% 45.70/29.85 tff(3003,plain,
% 45.70/29.85 (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[1982, 3002])).
% 45.70/29.85 tff(3004,plain,
% 45.70/29.85 (phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = false),
% 45.70/29.85 inference(transitivity,[status(thm)],[1766, 3003])).
% 45.70/29.85 tff(3005,plain,
% 45.70/29.85 ((phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err) <=> (false = err)),
% 45.70/29.85 inference(monotonicity,[status(thm)],[3004])).
% 45.70/29.85 tff(3006,plain,
% 45.70/29.85 ((false = err) <=> (phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)),
% 45.70/29.85 inference(symmetry,[status(thm)],[3005])).
% 45.70/29.85 tff(3007,plain,
% 45.70/29.85 ((false = err) <=> (phi(tptp_fun_R_5(P!7)) = err)),
% 45.70/29.85 inference(transitivity,[status(thm)],[3006, 2766])).
% 45.70/29.85 tff(3008,plain,
% 45.70/29.85 ((~(false = err)) <=> (~(phi(tptp_fun_R_5(P!7)) = err))),
% 45.70/29.85 inference(monotonicity,[status(thm)],[3007])).
% 45.70/29.85 tff(3009,plain,
% 45.70/29.85 (~(phi(tptp_fun_R_5(P!7)) = err)),
% 45.70/29.85 inference(modus_ponens,[status(thm)],[556, 3008])).
% 45.70/29.85 tff(3010,plain,
% 45.70/29.85 (d(tptp_fun_R_5(P!7)) | (~(phi(tptp_fun_R_5(P!7)) = err))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[1503, 3009])).
% 45.70/29.85 tff(3011,plain,
% 45.70/29.85 (~((~d(tptp_fun_R_5(P!7))) | (~(phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[1508, 3010])).
% 45.70/29.85 tff(3012,plain,
% 45.70/29.85 (phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[1510, 3011])).
% 45.70/29.85 tff(3013,plain,
% 45.70/29.85 (tptp_fun_R_5(P!7) = phi(tptp_fun_R_5(P!7))),
% 45.70/29.85 inference(symmetry,[status(thm)],[3012])).
% 45.70/29.85 tff(3014,plain,
% 45.70/29.85 (tptp_fun_R_5(P!7) = false),
% 45.70/29.85 inference(transitivity,[status(thm)],[3013, 1295, 2763, 3003])).
% 45.70/29.85 tff(3015,plain,
% 45.70/29.85 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false)),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[2970, 3012, 3003, 2969])).
% 45.70/29.85 tff(3016,plain,
% 45.70/29.85 (f2(not1(false), phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = f2(not1(false), not1(false), false)),
% 45.70/29.85 inference(monotonicity,[status(thm)],[3015, 3014])).
% 45.70/29.85 tff(3017,plain,
% 45.70/29.85 (f2(not1(false), not1(false), false) = f2(not1(false), phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))),
% 45.70/29.85 inference(symmetry,[status(thm)],[3016])).
% 45.70/29.85 tff(3018,plain,
% 45.70/29.85 ((~![P: $i, Q: $i, R: $i] : (f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R)))) | (f2(not1(false), not1(false), false) = lazy_impl(prop(false), impl(lazy_impl(not1(false), impl(not1(false), false)), false)))),
% 45.70/29.85 inference(quant_inst,[status(thm)],[])).
% 45.70/29.85 tff(3019,plain,
% 45.70/29.85 (f2(not1(false), not1(false), false) = lazy_impl(prop(false), impl(lazy_impl(not1(false), impl(not1(false), false)), false))),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[3018, 141])).
% 45.70/29.85 tff(3020,plain,
% 45.70/29.85 (lazy_impl(prop(false), impl(lazy_impl(not1(false), impl(not1(false), false)), false)) = f2(not1(false), not1(false), false)),
% 45.70/29.85 inference(symmetry,[status(thm)],[3019])).
% 45.70/29.85 tff(3021,plain,
% 45.70/29.85 (lazy_impl(not1(false), impl(not1(false), false)) = lazy_impl(not1(false), false)),
% 45.70/29.85 inference(monotonicity,[status(thm)],[114])).
% 45.70/29.85 tff(3022,plain,
% 45.70/29.85 (lazy_impl(not1(false), impl(not1(false), false)) = false),
% 45.70/29.85 inference(transitivity,[status(thm)],[3021, 35, 23])).
% 45.70/29.85 tff(3023,plain,
% 45.70/29.85 (impl(lazy_impl(not1(false), impl(not1(false), false)), false) = impl(false, false)),
% 45.70/29.85 inference(monotonicity,[status(thm)],[3022])).
% 45.70/29.85 tff(3024,plain,
% 45.70/29.85 (impl(lazy_impl(not1(false), impl(not1(false), false)), false) = not1(false)),
% 45.70/29.85 inference(transitivity,[status(thm)],[3023, 93])).
% 45.70/29.85 tff(3025,plain,
% 45.70/29.85 (lazy_impl(prop(false), impl(lazy_impl(not1(false), impl(not1(false), false)), false)) = lazy_impl(not1(false), not1(false))),
% 45.70/29.85 inference(monotonicity,[status(thm)],[131, 3024])).
% 45.70/29.85 tff(3026,plain,
% 45.70/29.85 (lazy_impl(not1(false), not1(false)) = lazy_impl(prop(false), impl(lazy_impl(not1(false), impl(not1(false), false)), false))),
% 45.70/29.85 inference(symmetry,[status(thm)],[3025])).
% 45.70/29.85 tff(3027,plain,
% 45.70/29.85 (not1(false) = err),
% 45.70/29.85 inference(transitivity,[status(thm)],[603, 602, 3026, 3020, 3017, 2985, 2983, 431, 429])).
% 45.70/29.85 tff(3028,plain,
% 45.70/29.85 ($false),
% 45.70/29.85 inference(unit_resolution,[status(thm)],[564, 3027])).
% 45.70/29.85 tff(3029,plain,(~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)), inference(lemma,lemma(discharge,[]))).
% 45.70/29.85 tff(3030,plain,
% 45.70/29.85 (d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err))),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[1342, 3029])).
% 45.70/29.86 tff(3031,plain,
% 45.70/29.86 (~((~d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[1347, 3030])).
% 45.70/29.86 tff(3032,plain,
% 45.70/29.86 (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[1349, 3031])).
% 45.70/29.86 tff(3033,plain,
% 45.70/29.86 (f6(P!7, tptp_fun_R_5(P!7)) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 45.70/29.86 inference(transitivity,[status(thm)],[325, 2975, 1331, 3032])).
% 45.70/29.86 tff(3034,plain,
% 45.70/29.86 (lazy_impl(not1(false), f6(P!7, tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.86 inference(monotonicity,[status(thm)],[2762, 3033])).
% 45.70/29.86 tff(3035,plain,
% 45.70/29.86 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), f6(P!7, tptp_fun_R_5(P!7))) = phi(f6(P!7, tptp_fun_R_5(P!7))))),
% 45.70/29.86 inference(quant_inst,[status(thm)],[])).
% 45.70/29.86 tff(3036,plain,
% 45.70/29.86 (lazy_impl(not1(false), f6(P!7, tptp_fun_R_5(P!7))) = phi(f6(P!7, tptp_fun_R_5(P!7)))),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[3035, 33])).
% 45.70/29.86 tff(3037,plain,
% 45.70/29.86 (phi(f6(P!7, tptp_fun_R_5(P!7))) = lazy_impl(not1(false), f6(P!7, tptp_fun_R_5(P!7)))),
% 45.70/29.86 inference(symmetry,[status(thm)],[3036])).
% 45.70/29.86 tff(3038,plain,
% 45.70/29.86 (exists2(P!7) = false),
% 45.70/29.86 inference(transitivity,[status(thm)],[880, 3037, 3034, 2975, 1331, 3032, 2973, 114])).
% 45.70/29.86 tff(3039,plain,
% 45.70/29.86 (exists1(P!7) = lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.70/29.86 inference(transitivity,[status(thm)],[346, 2933, 1089, 2932])).
% 45.70/29.86 tff(3040,plain,
% 45.70/29.86 ((exists1(P!7) = exists2(P!7)) <=> (lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = false)),
% 45.70/29.86 inference(monotonicity,[status(thm)],[3039, 3038])).
% 45.70/29.86 tff(3041,plain,
% 45.70/29.86 ((~(exists1(P!7) = exists2(P!7))) <=> (~(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = false))),
% 45.70/29.86 inference(monotonicity,[status(thm)],[3040])).
% 45.70/29.86 tff(3042,plain,
% 45.70/29.86 (~(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = false)),
% 45.70/29.86 inference(modus_ponens,[status(thm)],[897, 3041])).
% 45.70/29.86 tff(3043,plain,
% 45.70/29.86 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))) <=> ((lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = false) | (lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = not1(false))))),
% 45.70/29.86 inference(quant_inst,[status(thm)],[])).
% 45.70/29.86 tff(3044,plain,
% 45.70/29.86 (bool(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))) <=> ((lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = false) | (lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = not1(false)))),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[3043, 249])).
% 45.70/29.86 tff(3045,plain,
% 45.70/29.86 ((~(bool(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))) <=> ((lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = false) | (lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = not1(false))))) | (~bool(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))))) | ((lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = false) | (lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = not1(false)))),
% 45.70/29.86 inference(tautology,[status(thm)],[])).
% 45.70/29.86 tff(3046,plain,
% 45.70/29.86 ((~(bool(lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))) <=> ((lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = false) | (lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = not1(false))))) | ((lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = false) | (lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = not1(false)))),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[3045, 1124])).
% 45.70/29.86 tff(3047,plain,
% 45.70/29.86 ((lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = false) | (lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = not1(false))),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[3046, 3044])).
% 45.70/29.86 tff(3048,plain,
% 45.70/29.86 ((~((lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = false) | (lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = not1(false)))) | (lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = false) | (lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = not1(false))),
% 45.70/29.86 inference(tautology,[status(thm)],[])).
% 45.70/29.86 tff(3049,plain,
% 45.70/29.86 ((lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = false) | (lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = not1(false))),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[3048, 3047])).
% 45.70/29.86 tff(3050,plain,
% 45.70/29.86 (lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = not1(false)),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[3049, 3042])).
% 45.70/29.86 tff(3051,plain,
% 45.70/29.86 (not1(false) = lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 45.70/29.86 inference(symmetry,[status(thm)],[3050])).
% 45.70/29.86 tff(3052,plain,
% 45.70/29.86 (not1(false) = apply(P!7, tptp_fun_X_3(P!7))),
% 45.70/29.86 inference(transitivity,[status(thm)],[3051, 2937, 1088, 2923, 2927])).
% 45.70/29.86 tff(3053,plain,
% 45.70/29.86 (impl(not1(false), false) = impl(apply(P!7, tptp_fun_X_3(P!7)), false)),
% 45.70/29.86 inference(monotonicity,[status(thm)],[3052])).
% 45.70/29.86 tff(3054,plain,
% 45.70/29.86 (impl(apply(P!7, tptp_fun_X_3(P!7)), false) = impl(not1(false), false)),
% 45.70/29.86 inference(symmetry,[status(thm)],[3053])).
% 45.70/29.86 tff(3055,plain,
% 45.70/29.86 (false = tptp_fun_R_5(P!7)),
% 45.70/29.86 inference(transitivity,[status(thm)],[2716, 2860, 1294, 2946])).
% 45.70/29.86 tff(3056,plain,
% 45.70/29.86 (impl(apply(P!7, tptp_fun_X_3(P!7)), false) = impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))),
% 45.70/29.86 inference(monotonicity,[status(thm)],[3055])).
% 45.70/29.86 tff(3057,plain,
% 45.70/29.86 (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_3(P!7)), false)),
% 45.70/29.86 inference(symmetry,[status(thm)],[3056])).
% 45.70/29.86 tff(3058,plain,
% 45.70/29.86 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) <=> ((impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false) | (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = not1(false))))),
% 45.70/29.86 inference(quant_inst,[status(thm)],[])).
% 45.70/29.86 tff(3059,plain,
% 45.70/29.86 (bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) <=> ((impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false) | (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = not1(false)))),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[3058, 249])).
% 45.70/29.86 tff(3060,assumption,(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = err), introduced(assumption)).
% 45.70/29.86 tff(3061,plain,
% 45.70/29.86 (f5(P!7, tptp_fun_R_5(P!7)) = err),
% 45.70/29.86 inference(transitivity,[status(thm)],[311, 3060])).
% 45.70/29.86 tff(3062,plain,
% 45.70/29.86 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = impl(err, tptp_fun_R_5(P!7))),
% 45.70/29.86 inference(monotonicity,[status(thm)],[3061])).
% 45.70/29.86 tff(3063,plain,
% 45.70/29.86 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = err),
% 45.70/29.86 inference(transitivity,[status(thm)],[3062, 981, 429])).
% 45.70/29.86 tff(3064,plain,
% 45.70/29.86 ((phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) <=> (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)),
% 45.70/29.86 inference(monotonicity,[status(thm)],[3063])).
% 45.70/29.86 tff(3065,plain,
% 45.70/29.86 ((phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err) <=> (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.86 inference(symmetry,[status(thm)],[3064])).
% 45.70/29.86 tff(3066,plain,
% 45.70/29.86 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(not1(false), err)),
% 45.70/29.86 inference(monotonicity,[status(thm)],[2551, 3063])).
% 45.70/29.86 tff(3067,plain,
% 45.70/29.86 (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err),
% 45.70/29.86 inference(transitivity,[status(thm)],[2285, 2806, 3066, 431, 429])).
% 45.70/29.86 tff(3068,plain,
% 45.70/29.86 (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 45.70/29.86 inference(modus_ponens,[status(thm)],[3067, 3065])).
% 45.70/29.86 tff(3069,plain,
% 45.70/29.86 (f6(P!7, tptp_fun_R_5(P!7)) = err),
% 45.70/29.86 inference(transitivity,[status(thm)],[325, 3066, 431, 429])).
% 45.70/29.86 tff(3070,plain,
% 45.70/29.86 (bool(f6(P!7, tptp_fun_R_5(P!7))) <=> bool(err)),
% 45.70/29.86 inference(monotonicity,[status(thm)],[3069])).
% 45.70/29.86 tff(3071,plain,
% 45.70/29.86 (bool(err) <=> bool(f6(P!7, tptp_fun_R_5(P!7)))),
% 45.70/29.86 inference(symmetry,[status(thm)],[3070])).
% 45.70/29.86 tff(3072,plain,
% 45.70/29.86 (bool(err) <=> bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.86 inference(transitivity,[status(thm)],[3071, 720])).
% 45.70/29.86 tff(3073,plain,
% 45.70/29.86 ((~bool(err)) <=> (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 45.70/29.86 inference(monotonicity,[status(thm)],[3072])).
% 45.70/29.86 tff(3074,plain,
% 45.70/29.86 (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.86 inference(modus_ponens,[status(thm)],[571, 3073])).
% 45.70/29.86 tff(3075,plain,
% 45.70/29.86 (bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[1708, 2550, 2551, 2549, 2548])).
% 45.70/29.86 tff(3076,plain,
% 45.70/29.86 ($false),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[3075, 3074, 3068])).
% 45.70/29.86 tff(3077,plain,(~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = err)), inference(lemma,lemma(discharge,[]))).
% 45.70/29.86 tff(3078,plain,
% 45.70/29.86 (d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = err))),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[1423, 3077])).
% 45.70/29.86 tff(3079,plain,
% 45.70/29.86 (~((~d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))))),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[1421, 3078])).
% 45.70/29.86 tff(3080,plain,
% 45.70/29.86 (d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[1995, 3079])).
% 45.70/29.86 tff(3081,plain,
% 45.70/29.86 (d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.86 inference(modus_ponens,[status(thm)],[3080, 2005])).
% 45.70/29.86 tff(3082,plain,
% 45.70/29.86 (((~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))))))) | (d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))),
% 45.70/29.86 inference(tautology,[status(thm)],[])).
% 45.70/29.86 tff(3083,plain,
% 45.70/29.86 (d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[3082, 1953])).
% 45.70/29.86 tff(3084,plain,
% 45.70/29.86 ((~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.86 inference(tautology,[status(thm)],[])).
% 45.70/29.86 tff(3085,plain,
% 45.70/29.86 (d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[3084, 3083])).
% 45.70/29.86 tff(3086,plain,
% 45.70/29.86 (d(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[3085, 3081])).
% 45.70/29.86 tff(3087,plain,
% 45.70/29.86 (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = f5(P!7, tptp_fun_R_5(P!7))),
% 45.70/29.86 inference(transitivity,[status(thm)],[1584, 312])).
% 45.70/29.86 tff(3088,plain,
% 45.70/29.86 (bool(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) <=> bool(f5(P!7, tptp_fun_R_5(P!7)))),
% 45.70/29.86 inference(monotonicity,[status(thm)],[3087])).
% 45.70/29.86 tff(3089,plain,
% 45.70/29.86 (bool(f5(P!7, tptp_fun_R_5(P!7))) <=> bool(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 45.70/29.86 inference(symmetry,[status(thm)],[3088])).
% 45.70/29.86 tff(3090,plain,
% 45.70/29.86 (bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) <=> bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.86 inference(transitivity,[status(thm)],[313, 3089, 417])).
% 45.70/29.86 tff(3091,plain,
% 45.70/29.86 ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = not1(false))),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[2899, 2971])).
% 45.70/29.86 tff(3092,plain,
% 45.70/29.86 (bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[2902, 3091])).
% 45.70/29.86 tff(3093,plain,
% 45.70/29.86 (bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.86 inference(modus_ponens,[status(thm)],[3092, 3090])).
% 45.70/29.86 tff(3094,plain,
% 45.70/29.86 (bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[1957, 3093, 3081, 3086])).
% 45.70/29.86 tff(3095,plain,
% 45.70/29.86 ((~(bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) <=> ((impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false) | (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = not1(false))))) | (~bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))) | ((impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false) | (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = not1(false)))),
% 45.70/29.86 inference(tautology,[status(thm)],[])).
% 45.70/29.86 tff(3096,plain,
% 45.70/29.86 ((~(bool(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))) <=> ((impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false) | (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = not1(false))))) | ((impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false) | (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = not1(false)))),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[3095, 3094])).
% 45.70/29.86 tff(3097,plain,
% 45.70/29.86 ((impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false) | (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = not1(false))),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[3096, 3059])).
% 45.70/29.86 tff(3098,plain,
% 45.70/29.86 (~(impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false)),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[2172, 2969])).
% 45.70/29.86 tff(3099,plain,
% 45.70/29.86 ((~((impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false) | (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = not1(false)))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false) | (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = not1(false))),
% 45.70/29.86 inference(tautology,[status(thm)],[])).
% 45.70/29.86 tff(3100,plain,
% 45.70/29.86 ((~((impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = false) | (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = not1(false)))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = not1(false))),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[3099, 3098])).
% 45.70/29.86 tff(3101,plain,
% 45.70/29.86 (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = not1(false)),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[3100, 3097])).
% 45.70/29.86 tff(3102,plain,
% 45.70/29.86 (not1(false) = impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))),
% 45.70/29.86 inference(symmetry,[status(thm)],[3101])).
% 45.70/29.86 tff(3103,plain,
% 45.70/29.86 (not1(false) = false),
% 45.70/29.86 inference(transitivity,[status(thm)],[3102, 3057, 3054, 114])).
% 45.70/29.86 tff(3104,plain,
% 45.70/29.86 ($false),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[60, 3103])).
% 45.70/29.86 tff(3105,plain,(~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false)), inference(lemma,lemma(discharge,[]))).
% 45.70/29.86 tff(3106,plain,
% 45.70/29.86 (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = not1(false)),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[1982, 3105])).
% 45.70/29.86 tff(3107,plain,
% 45.70/29.86 (phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false)),
% 45.70/29.86 inference(transitivity,[status(thm)],[1766, 3106])).
% 45.70/29.86 tff(3108,plain,
% 45.70/29.86 ((phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err) <=> (not1(false) = err)),
% 45.70/29.86 inference(monotonicity,[status(thm)],[3107])).
% 45.70/29.86 tff(3109,plain,
% 45.70/29.86 ((not1(false) = err) <=> (phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)),
% 45.70/29.86 inference(symmetry,[status(thm)],[3108])).
% 45.70/29.86 tff(3110,plain,
% 45.70/29.86 ((not1(false) = err) <=> (phi(tptp_fun_R_5(P!7)) = err)),
% 45.70/29.86 inference(transitivity,[status(thm)],[3109, 2766])).
% 45.70/29.86 tff(3111,plain,
% 45.70/29.86 ((~(not1(false) = err)) <=> (~(phi(tptp_fun_R_5(P!7)) = err))),
% 45.70/29.86 inference(monotonicity,[status(thm)],[3110])).
% 45.70/29.86 tff(3112,plain,
% 45.70/29.86 (~(phi(tptp_fun_R_5(P!7)) = err)),
% 45.70/29.86 inference(modus_ponens,[status(thm)],[564, 3111])).
% 45.70/29.86 tff(3113,plain,
% 45.70/29.86 (d(tptp_fun_R_5(P!7)) | (~(phi(tptp_fun_R_5(P!7)) = err))),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[1503, 3112])).
% 45.70/29.86 tff(3114,plain,
% 45.70/29.86 (~((~d(tptp_fun_R_5(P!7))) | (~(phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))))),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[1508, 3113])).
% 45.70/29.86 tff(3115,plain,
% 45.70/29.86 (phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[1510, 3114])).
% 45.70/29.86 tff(3116,plain,
% 45.70/29.86 (tptp_fun_R_5(P!7) = phi(tptp_fun_R_5(P!7))),
% 45.70/29.86 inference(symmetry,[status(thm)],[3115])).
% 45.70/29.86 tff(3117,plain,
% 45.70/29.86 (tptp_fun_R_5(P!7) = not1(false)),
% 45.70/29.86 inference(transitivity,[status(thm)],[3116, 1295, 2763, 3106])).
% 45.70/29.86 tff(3118,plain,
% 45.70/29.86 (f6(P!7, tptp_fun_R_5(P!7)) = f6(P!7, not1(false))),
% 45.70/29.86 inference(monotonicity,[status(thm)],[3117])).
% 45.70/29.86 tff(3119,plain,
% 45.70/29.86 (f6(P!7, tptp_fun_R_5(P!7)) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 45.70/29.86 inference(transitivity,[status(thm)],[325, 2807, 1331, 3032])).
% 45.70/29.86 tff(3120,plain,
% 45.70/29.86 (lazy_impl(not1(false), f6(P!7, tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.86 inference(monotonicity,[status(thm)],[2762, 3119])).
% 45.70/29.86 tff(3121,plain,
% 45.70/29.86 (exists2(P!7) = not1(false)),
% 45.70/29.86 inference(transitivity,[status(thm)],[880, 3037, 3120, 326, 3118, 743, 2410, 2408, 2407, 592, 2406, 50, 48])).
% 45.70/29.86 tff(3122,plain,
% 45.70/29.86 ((exists1(P!7) = exists2(P!7)) <=> (lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = not1(false))),
% 45.70/29.86 inference(monotonicity,[status(thm)],[3039, 3121])).
% 45.70/29.86 tff(3123,plain,
% 45.70/29.86 ((exists1(P!7) = exists2(P!7)) <=> (apply(P!7, tptp_fun_X_3(P!7)) = not1(false))),
% 45.70/29.86 inference(transitivity,[status(thm)],[3122, 2936, 2930])).
% 45.70/29.86 tff(3124,plain,
% 45.70/29.86 ((~(exists1(P!7) = exists2(P!7))) <=> (~(apply(P!7, tptp_fun_X_3(P!7)) = not1(false)))),
% 45.70/29.86 inference(monotonicity,[status(thm)],[3123])).
% 45.70/29.86 tff(3125,plain,
% 45.70/29.86 (~(apply(P!7, tptp_fun_X_3(P!7)) = not1(false))),
% 45.70/29.86 inference(modus_ponens,[status(thm)],[897, 3124])).
% 45.70/29.86 tff(3126,plain,
% 45.70/29.86 (apply(P!7, tptp_fun_X_3(P!7)) = false),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[2958, 3125])).
% 45.70/29.86 tff(3127,plain,
% 45.70/29.86 (~(apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[2526, 3126])).
% 45.70/29.86 tff(3128,plain,
% 45.70/29.86 (d(apply(P!7, tptp_fun_X_4(false, P!7)))),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[2508, 2949])).
% 45.70/29.86 tff(3129,plain,
% 45.70/29.86 (bool(apply(P!7, tptp_fun_X_4(false, P!7)))),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[2513, 2949, 2905, 3128])).
% 45.70/29.86 tff(3130,plain,
% 45.70/29.86 ((~(bool(apply(P!7, tptp_fun_X_4(false, P!7))) <=> ((apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))))) | ((apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false)))),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[2515, 3129])).
% 45.70/29.86 tff(3131,plain,
% 45.70/29.86 ((apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[3130, 2297])).
% 45.70/29.86 tff(3132,plain,
% 45.70/29.86 ((apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[2528, 3131])).
% 45.70/29.86 tff(3133,plain,
% 45.70/29.86 (apply(P!7, tptp_fun_X_4(false, P!7)) = false),
% 45.70/29.86 inference(unit_resolution,[status(thm)],[3132, 3127])).
% 45.70/29.86 tff(3134,plain,
% 45.70/29.86 (false = apply(P!7, tptp_fun_X_4(false, P!7))),
% 45.70/29.86 inference(symmetry,[status(thm)],[3133])).
% 45.70/29.86 tff(3135,plain,
% 45.70/29.86 (f2(not1(false), false, false) = f2(not1(false), apply(P!7, tptp_fun_X_4(false, P!7)), false)),
% 45.70/29.86 inference(monotonicity,[status(thm)],[3134])).
% 45.70/29.86 tff(3136,plain,
% 45.70/29.86 (f2(not1(false), apply(P!7, tptp_fun_X_4(false, P!7)), false) = f2(not1(false), false, false)),
% 45.70/29.86 inference(symmetry,[status(thm)],[3135])).
% 45.70/29.86 tff(3137,plain,
% 45.70/29.86 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.86 inference(symmetry,[status(thm)],[3032])).
% 45.70/29.86 tff(3138,plain,
% 45.70/29.86 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = f6(P!7, tptp_fun_R_5(P!7))),
% 45.70/29.86 inference(transitivity,[status(thm)],[3137, 2285, 2806, 326])).
% 45.70/29.86 tff(3139,plain,
% 45.70/29.86 (d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) <=> d(f6(P!7, tptp_fun_R_5(P!7)))),
% 45.70/29.87 inference(monotonicity,[status(thm)],[3138])).
% 45.70/29.87 tff(3140,plain,
% 45.70/29.87 (d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) <=> d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.87 inference(transitivity,[status(thm)],[3139, 328])).
% 45.70/29.87 tff(3141,plain,
% 45.70/29.87 (((~d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.87 inference(tautology,[status(thm)],[])).
% 45.70/29.87 tff(3142,plain,
% 45.70/29.87 (d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 45.70/29.87 inference(unit_resolution,[status(thm)],[3141, 3031])).
% 45.70/29.87 tff(3143,plain,
% 45.70/29.87 (d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.87 inference(modus_ponens,[status(thm)],[3142, 3140])).
% 45.70/29.87 tff(3144,plain,
% 45.70/29.87 (bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 45.70/29.87 inference(unit_resolution,[status(thm)],[3075, 3032])).
% 45.70/29.87 tff(3145,plain,
% 45.70/29.87 (d(lazy_impl(prop(false), impl(f5(P!7, false), false)))),
% 45.70/29.87 inference(unit_resolution,[status(thm)],[859, 3143])).
% 45.70/29.87 tff(3146,plain,
% 45.70/29.87 (bool(lazy_impl(prop(false), impl(f5(P!7, false), false)))),
% 45.70/29.87 inference(unit_resolution,[status(thm)],[864, 3145, 3144, 3143])).
% 45.70/29.87 tff(3147,plain,
% 45.70/29.87 ((~(bool(lazy_impl(prop(false), impl(f5(P!7, false), false))) <=> ((lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false))))) | ((lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false)))),
% 45.70/29.87 inference(unit_resolution,[status(thm)],[866, 3146])).
% 45.70/29.87 tff(3148,plain,
% 45.70/29.87 ((lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false))),
% 45.70/29.87 inference(unit_resolution,[status(thm)],[3147, 316])).
% 45.70/29.87 tff(3149,plain,
% 45.70/29.87 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false)),
% 45.70/29.87 inference(transitivity,[status(thm)],[326, 3118, 743, 2410, 2408, 2407, 592, 2406, 50, 48])).
% 45.70/29.87 tff(3150,plain,
% 45.70/29.87 (~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)),
% 45.70/29.87 inference(unit_resolution,[status(thm)],[873, 3149])).
% 45.70/29.87 tff(3151,plain,
% 45.70/29.87 (lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false)),
% 45.70/29.87 inference(unit_resolution,[status(thm)],[875, 3150, 3148])).
% 45.70/29.87 tff(3152,plain,
% 45.70/29.87 (not1(false) = lazy_impl(prop(false), impl(f5(P!7, false), false))),
% 45.70/29.87 inference(symmetry,[status(thm)],[3151])).
% 45.70/29.87 tff(3153,plain,
% 45.70/29.87 (not1(false) = false),
% 45.70/29.87 inference(transitivity,[status(thm)],[3152, 2542, 2535, 3136, 143, 134, 35, 23])).
% 45.70/29.87 tff(3154,plain,
% 45.70/29.87 ($false),
% 45.70/29.87 inference(unit_resolution,[status(thm)],[60, 3153])).
% 45.70/29.87 % SZS output end Proof
%------------------------------------------------------------------------------