TSTP Solution File: SWW099+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW099+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 42.88s 27.90s
% Output : Proof 43.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWW099+1 : TPTP v8.1.0. Released v5.2.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Sep 4 12:08:10 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 42.88/27.90 % SZS status Theorem
% 42.88/27.90 % SZS output start Proof
% 42.88/27.90 tff(false_type, type, (
% 42.88/27.90 false: $i)).
% 42.88/27.90 tff(impl_type, type, (
% 42.88/27.90 impl: ( $i * $i ) > $i)).
% 42.88/27.90 tff(not1_type, type, (
% 42.88/27.90 not1: $i > $i)).
% 42.88/27.90 tff(apply_type, type, (
% 42.88/27.90 apply: ( $i * $i ) > $i)).
% 42.88/27.90 tff(tptp_fun_X_4_type, type, (
% 42.88/27.90 tptp_fun_X_4: ( $i * $i ) > $i)).
% 42.88/27.90 tff(tptp_fun_P_7_type, type, (
% 42.88/27.90 tptp_fun_P_7: $i)).
% 42.88/27.90 tff(phi_type, type, (
% 42.88/27.90 phi: $i > $i)).
% 42.88/27.90 tff(d_type, type, (
% 42.88/27.90 d: $i > $o)).
% 42.88/27.90 tff(err_type, type, (
% 42.88/27.90 err: $i)).
% 42.88/27.90 tff(true_type, type, (
% 42.88/27.90 true: $i)).
% 42.88/27.90 tff(lazy_impl_type, type, (
% 42.88/27.90 lazy_impl: ( $i * $i ) > $i)).
% 42.88/27.90 tff(prop_type, type, (
% 42.88/27.90 prop: $i > $i)).
% 42.88/27.90 tff(bool_type, type, (
% 42.88/27.90 bool: $i > $o)).
% 42.88/27.90 tff(f1_type, type, (
% 42.88/27.90 f1: ( $i * $i * $i ) > $i)).
% 42.88/27.90 tff(tptp_fun_X_3_type, type, (
% 42.88/27.90 tptp_fun_X_3: $i > $i)).
% 42.88/27.90 tff(exists2_type, type, (
% 42.88/27.90 exists2: $i > $i)).
% 42.88/27.90 tff(exists1_type, type, (
% 42.88/27.90 exists1: $i > $i)).
% 42.88/27.90 tff(f5_type, type, (
% 42.88/27.90 f5: ( $i * $i ) > $i)).
% 42.88/27.90 tff(f4_type, type, (
% 42.88/27.90 f4: ( $i * $i * $i ) > $i)).
% 42.88/27.90 tff(tptp_fun_R_5_type, type, (
% 42.88/27.90 tptp_fun_R_5: $i > $i)).
% 42.88/27.90 tff(f6_type, type, (
% 42.88/27.90 f6: ( $i * $i ) > $i)).
% 42.88/27.90 tff(forallprefers_type, type, (
% 42.88/27.90 forallprefers: ( $i * $i ) > $o)).
% 42.88/27.90 tff(tptp_fun_P_6_type, type, (
% 42.88/27.90 tptp_fun_P_6: $i)).
% 42.88/27.90 tff(f7_type, type, (
% 42.88/27.90 f7: $i > $i)).
% 42.88/27.90 tff(false2_type, type, (
% 42.88/27.90 false2: $i)).
% 42.88/27.90 tff(f2_type, type, (
% 42.88/27.90 f2: ( $i * $i * $i ) > $i)).
% 42.88/27.90 tff(existsprefers_type, type, (
% 42.88/27.90 existsprefers: ( $i * $i ) > $o)).
% 42.88/27.90 tff(1,plain,
% 42.88/27.90 (d(false) <=> d(false)),
% 42.88/27.90 inference(rewrite,[status(thm)],[])).
% 42.88/27.90 tff(2,axiom,((d(true) & d(false)) & d(err)), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','false_true_err_in_d')).
% 42.88/27.90 tff(3,plain,
% 42.88/27.90 (d(true) & d(false)),
% 42.88/27.90 inference(and_elim,[status(thm)],[2])).
% 42.88/27.90 tff(4,plain,
% 42.88/27.90 (d(false)),
% 42.88/27.90 inference(and_elim,[status(thm)],[3])).
% 42.88/27.90 tff(5,plain,
% 42.88/27.90 (d(false)),
% 42.88/27.90 inference(modus_ponens,[status(thm)],[4, 1])).
% 42.88/27.90 tff(6,plain,
% 42.88/27.90 ((d(false) | (~(phi(false) = err))) | (~d(false))),
% 42.88/27.90 inference(tautology,[status(thm)],[])).
% 42.88/27.90 tff(7,plain,
% 42.88/27.90 (d(false) | (~(phi(false) = err))),
% 42.88/27.90 inference(unit_resolution,[status(thm)],[6, 5])).
% 42.88/27.90 tff(8,plain,
% 42.88/27.90 (^[X: $i] : refl(((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err))))) <=> ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err))))))),
% 42.88/27.90 inference(bind,[status(th)],[])).
% 42.88/27.90 tff(9,plain,
% 42.88/27.90 (![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err))))) <=> ![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 42.88/27.90 inference(quant_intro,[status(thm)],[8])).
% 42.88/27.90 tff(10,plain,
% 42.88/27.90 (^[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)))))))),
% 42.88/27.90 inference(bind,[status(th)],[])).
% 42.88/27.90 tff(11,plain,
% 42.88/27.90 (![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err))) <=> ![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 42.88/27.90 inference(quant_intro,[status(thm)],[10])).
% 42.88/27.90 tff(12,plain,
% 42.88/27.90 (![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err))) <=> ![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err)))),
% 42.88/27.90 inference(rewrite,[status(thm)],[])).
% 42.88/27.90 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')).
% 42.88/27.90 tff(14,plain,
% 42.88/27.90 (![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err)))),
% 42.88/27.90 inference(modus_ponens,[status(thm)],[13, 12])).
% 42.88/27.90 tff(15,plain,(
% 42.88/27.90 ![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err)))),
% 42.88/27.90 inference(skolemize,[status(sab)],[14])).
% 42.88/27.90 tff(16,plain,
% 42.88/27.90 (![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 42.88/27.90 inference(modus_ponens,[status(thm)],[15, 11])).
% 42.88/27.90 tff(17,plain,
% 42.88/27.90 (![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 42.88/27.90 inference(modus_ponens,[status(thm)],[16, 9])).
% 42.88/27.90 tff(18,plain,
% 42.88/27.90 (((~![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)))))),
% 42.88/27.90 inference(rewrite,[status(thm)],[])).
% 42.88/27.90 tff(19,plain,
% 42.88/27.90 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(false)) | (~(phi(false) = false)))) | (~(d(false) | (~(phi(false) = err)))))),
% 42.88/27.90 inference(quant_inst,[status(thm)],[])).
% 42.88/27.90 tff(20,plain,
% 42.88/27.90 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(false)) | (~(phi(false) = false)))) | (~(d(false) | (~(phi(false) = err))))),
% 42.88/27.90 inference(modus_ponens,[status(thm)],[19, 18])).
% 42.88/27.90 tff(21,plain,
% 42.88/27.90 (~((~d(false)) | (~(phi(false) = false)))),
% 42.88/27.90 inference(unit_resolution,[status(thm)],[20, 17, 7])).
% 42.88/27.90 tff(22,plain,
% 42.88/27.90 (((~d(false)) | (~(phi(false) = false))) | (phi(false) = false)),
% 42.88/27.90 inference(tautology,[status(thm)],[])).
% 42.88/27.90 tff(23,plain,
% 42.88/27.90 (phi(false) = false),
% 42.88/27.90 inference(unit_resolution,[status(thm)],[22, 21])).
% 42.88/27.90 tff(24,plain,
% 42.88/27.90 (^[B: $i] : refl((lazy_impl(not1(false), B) = phi(B)) <=> (lazy_impl(not1(false), B) = phi(B)))),
% 42.88/27.90 inference(bind,[status(th)],[])).
% 42.88/27.90 tff(25,plain,
% 42.88/27.90 (![B: $i] : (lazy_impl(not1(false), B) = phi(B)) <=> ![B: $i] : (lazy_impl(not1(false), B) = phi(B))),
% 42.88/27.90 inference(quant_intro,[status(thm)],[24])).
% 42.88/27.90 tff(26,plain,
% 42.88/27.90 (^[B: $i] : rewrite((lazy_impl(true, B) = phi(B)) <=> (lazy_impl(not1(false), B) = phi(B)))),
% 42.88/27.90 inference(bind,[status(th)],[])).
% 42.88/27.90 tff(27,plain,
% 42.88/27.90 (![B: $i] : (lazy_impl(true, B) = phi(B)) <=> ![B: $i] : (lazy_impl(not1(false), B) = phi(B))),
% 42.88/27.90 inference(quant_intro,[status(thm)],[26])).
% 42.88/27.90 tff(28,plain,
% 42.88/27.90 (![B: $i] : (lazy_impl(true, B) = phi(B)) <=> ![B: $i] : (lazy_impl(true, B) = phi(B))),
% 42.88/27.90 inference(rewrite,[status(thm)],[])).
% 42.88/27.90 tff(29,axiom,(![B: $i] : (lazy_impl(true, B) = phi(B))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','lazy_impl_axiom3')).
% 42.88/27.90 tff(30,plain,
% 42.88/27.90 (![B: $i] : (lazy_impl(true, B) = phi(B))),
% 42.88/27.90 inference(modus_ponens,[status(thm)],[29, 28])).
% 42.88/27.90 tff(31,plain,
% 42.88/27.90 (![B: $i] : (lazy_impl(not1(false), B) = phi(B))),
% 42.88/27.90 inference(modus_ponens,[status(thm)],[30, 27])).
% 42.88/27.90 tff(32,plain,(
% 42.88/27.90 ![B: $i] : (lazy_impl(not1(false), B) = phi(B))),
% 42.88/27.90 inference(skolemize,[status(sab)],[31])).
% 42.88/27.90 tff(33,plain,
% 42.88/27.90 (![B: $i] : (lazy_impl(not1(false), B) = phi(B))),
% 42.88/27.90 inference(modus_ponens,[status(thm)],[32, 25])).
% 42.88/27.90 tff(34,plain,
% 42.88/27.90 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), false) = phi(false))),
% 42.88/27.90 inference(quant_inst,[status(thm)],[])).
% 42.88/27.90 tff(35,plain,
% 42.88/27.90 (lazy_impl(not1(false), false) = phi(false)),
% 42.88/27.90 inference(unit_resolution,[status(thm)],[34, 33])).
% 42.88/27.90 tff(36,plain,
% 42.88/27.90 ((not1(false) = phi(false)) <=> (not1(false) = false)),
% 42.88/27.90 inference(monotonicity,[status(thm)],[23])).
% 42.88/27.90 tff(37,plain,
% 42.88/27.90 ((not1(false) = false) <=> (not1(false) = phi(false))),
% 42.88/27.90 inference(symmetry,[status(thm)],[36])).
% 42.88/27.90 tff(38,plain,
% 42.88/27.90 ((~(not1(false) = false)) <=> (~(not1(false) = phi(false)))),
% 42.88/27.90 inference(monotonicity,[status(thm)],[37])).
% 42.88/27.90 tff(39,plain,
% 42.88/27.90 ((~(true = false)) <=> (~(not1(false) = false))),
% 42.88/27.90 inference(rewrite,[status(thm)],[])).
% 42.88/27.90 tff(40,plain,
% 42.88/27.90 ((~(true = false)) <=> (~(true = false))),
% 42.88/27.90 inference(rewrite,[status(thm)],[])).
% 42.88/27.90 tff(41,axiom,(((~(true = false)) & (~(true = err))) & (~(false = err))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','distinct_false_true_err')).
% 42.88/27.90 tff(42,plain,
% 42.88/27.90 ((~(true = false)) & (~(true = err))),
% 42.88/27.90 inference(and_elim,[status(thm)],[41])).
% 42.88/27.90 tff(43,plain,
% 42.88/27.90 (~(true = false)),
% 42.88/27.90 inference(and_elim,[status(thm)],[42])).
% 42.88/27.90 tff(44,plain,
% 42.88/27.90 (~(true = false)),
% 42.88/27.90 inference(modus_ponens,[status(thm)],[43, 40])).
% 42.88/27.90 tff(45,plain,
% 42.88/27.90 (~(not1(false) = false)),
% 42.88/27.90 inference(modus_ponens,[status(thm)],[44, 39])).
% 42.88/27.90 tff(46,plain,
% 42.88/27.90 (~(not1(false) = phi(false))),
% 42.88/27.90 inference(modus_ponens,[status(thm)],[45, 38])).
% 42.88/27.90 tff(47,plain,
% 42.88/27.90 (^[A: $i] : refl((bool(A) | (not1(A) = phi(A))) <=> (bool(A) | (not1(A) = phi(A))))),
% 42.88/27.90 inference(bind,[status(th)],[])).
% 42.88/27.90 tff(48,plain,
% 42.88/27.90 (![A: $i] : (bool(A) | (not1(A) = phi(A))) <=> ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 42.88/27.90 inference(quant_intro,[status(thm)],[47])).
% 42.88/27.90 tff(49,plain,
% 42.88/27.90 (![A: $i] : (bool(A) | (not1(A) = phi(A))) <=> ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 42.88/27.90 inference(rewrite,[status(thm)],[])).
% 42.88/27.90 tff(50,plain,
% 42.88/27.90 (^[A: $i] : rewrite(((~bool(A)) => (not1(A) = phi(A))) <=> (bool(A) | (not1(A) = phi(A))))),
% 42.88/27.90 inference(bind,[status(th)],[])).
% 42.88/27.90 tff(51,plain,
% 42.88/27.90 (![A: $i] : ((~bool(A)) => (not1(A) = phi(A))) <=> ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 42.88/27.90 inference(quant_intro,[status(thm)],[50])).
% 42.88/27.90 tff(52,axiom,(![A: $i] : ((~bool(A)) => (not1(A) = phi(A)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','not1_axiom1')).
% 42.88/27.90 tff(53,plain,
% 42.88/27.90 (![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 42.88/27.90 inference(modus_ponens,[status(thm)],[52, 51])).
% 42.88/27.90 tff(54,plain,
% 42.88/27.90 (![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 42.88/27.90 inference(modus_ponens,[status(thm)],[53, 49])).
% 42.88/27.90 tff(55,plain,(
% 42.88/27.90 ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 42.88/27.90 inference(skolemize,[status(sab)],[54])).
% 42.88/27.90 tff(56,plain,
% 42.88/27.90 (![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 42.88/27.90 inference(modus_ponens,[status(thm)],[55, 48])).
% 42.88/27.90 tff(57,plain,
% 42.88/27.90 (((~![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)))),
% 42.88/27.90 inference(rewrite,[status(thm)],[])).
% 42.88/27.90 tff(58,plain,
% 42.88/27.90 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | (bool(false) | (not1(false) = phi(false)))),
% 42.88/27.90 inference(quant_inst,[status(thm)],[])).
% 42.88/27.90 tff(59,plain,
% 42.88/27.90 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | bool(false) | (not1(false) = phi(false))),
% 42.88/27.90 inference(modus_ponens,[status(thm)],[58, 57])).
% 42.88/27.90 tff(60,plain,
% 42.88/27.90 (bool(false) | (not1(false) = phi(false))),
% 42.88/27.90 inference(unit_resolution,[status(thm)],[59, 56])).
% 42.88/27.90 tff(61,plain,
% 42.88/27.90 (bool(false)),
% 42.88/27.90 inference(unit_resolution,[status(thm)],[60, 46])).
% 42.88/27.90 tff(62,plain,
% 42.88/27.90 (^[B: $i] : refl(((~bool(B)) | (impl(false, B) = not1(false))) <=> ((~bool(B)) | (impl(false, B) = not1(false))))),
% 42.88/27.90 inference(bind,[status(th)],[])).
% 42.88/27.90 tff(63,plain,
% 42.88/27.90 (![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false))) <=> ![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))),
% 42.88/27.90 inference(quant_intro,[status(thm)],[62])).
% 42.88/27.90 tff(64,plain,
% 42.88/27.90 (^[B: $i] : rewrite(((~bool(B)) | (impl(false, B) = true)) <=> ((~bool(B)) | (impl(false, B) = not1(false))))),
% 42.88/27.90 inference(bind,[status(th)],[])).
% 42.88/27.90 tff(65,plain,
% 42.88/27.90 (![B: $i] : ((~bool(B)) | (impl(false, B) = true)) <=> ![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))),
% 42.88/27.90 inference(quant_intro,[status(thm)],[64])).
% 42.88/27.90 tff(66,plain,
% 42.88/27.90 (![B: $i] : ((~bool(B)) | (impl(false, B) = true)) <=> ![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 42.88/27.90 inference(rewrite,[status(thm)],[])).
% 42.88/27.90 tff(67,plain,
% 42.88/27.90 (^[B: $i] : rewrite((bool(B) => (impl(false, B) = true)) <=> ((~bool(B)) | (impl(false, B) = true)))),
% 42.88/27.90 inference(bind,[status(th)],[])).
% 42.88/27.90 tff(68,plain,
% 42.88/27.90 (![B: $i] : (bool(B) => (impl(false, B) = true)) <=> ![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 42.88/27.90 inference(quant_intro,[status(thm)],[67])).
% 42.88/27.90 tff(69,axiom,(![B: $i] : (bool(B) => (impl(false, B) = true))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','impl_axiom3')).
% 42.88/27.90 tff(70,plain,
% 42.88/27.90 (![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 42.88/27.90 inference(modus_ponens,[status(thm)],[69, 68])).
% 42.88/27.90 tff(71,plain,
% 42.88/27.90 (![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 42.88/27.90 inference(modus_ponens,[status(thm)],[70, 66])).
% 42.88/27.90 tff(72,plain,
% 42.88/27.90 (![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))),
% 42.88/27.90 inference(modus_ponens,[status(thm)],[71, 65])).
% 42.88/27.90 tff(73,plain,(
% 42.88/27.90 ![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))),
% 42.88/27.90 inference(skolemize,[status(sab)],[72])).
% 42.88/27.90 tff(74,plain,
% 42.88/27.90 (![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))),
% 42.88/27.90 inference(modus_ponens,[status(thm)],[73, 63])).
% 42.88/27.90 tff(75,plain,
% 42.88/27.90 (((~![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)))),
% 42.88/27.90 inference(rewrite,[status(thm)],[])).
% 42.88/27.90 tff(76,plain,
% 42.88/27.90 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | ((~bool(false)) | (impl(false, false) = not1(false)))),
% 42.88/27.90 inference(quant_inst,[status(thm)],[])).
% 42.88/27.90 tff(77,plain,
% 42.88/27.90 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | (~bool(false)) | (impl(false, false) = not1(false))),
% 42.88/27.90 inference(modus_ponens,[status(thm)],[76, 75])).
% 42.88/27.90 tff(78,plain,
% 42.88/27.90 (impl(false, false) = not1(false)),
% 42.88/27.90 inference(unit_resolution,[status(thm)],[77, 74, 61])).
% 42.88/27.90 tff(79,plain,
% 42.88/27.90 (^[B: $i] : refl(((~bool(B)) | (impl(not1(false), B) = B)) <=> ((~bool(B)) | (impl(not1(false), B) = B)))),
% 42.88/27.90 inference(bind,[status(th)],[])).
% 42.88/27.90 tff(80,plain,
% 42.88/27.90 (![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B)) <=> ![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))),
% 42.88/27.90 inference(quant_intro,[status(thm)],[79])).
% 42.88/27.90 tff(81,plain,
% 42.88/27.90 (^[B: $i] : rewrite(((~bool(B)) | (impl(true, B) = B)) <=> ((~bool(B)) | (impl(not1(false), B) = B)))),
% 42.88/27.90 inference(bind,[status(th)],[])).
% 42.88/27.90 tff(82,plain,
% 42.88/27.90 (![B: $i] : ((~bool(B)) | (impl(true, B) = B)) <=> ![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))),
% 42.88/27.90 inference(quant_intro,[status(thm)],[81])).
% 42.88/27.90 tff(83,plain,
% 42.88/27.90 (![B: $i] : ((~bool(B)) | (impl(true, B) = B)) <=> ![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 42.88/27.90 inference(rewrite,[status(thm)],[])).
% 42.88/27.90 tff(84,plain,
% 42.88/27.90 (^[B: $i] : rewrite((bool(B) => (impl(true, B) = B)) <=> ((~bool(B)) | (impl(true, B) = B)))),
% 42.88/27.90 inference(bind,[status(th)],[])).
% 42.88/27.90 tff(85,plain,
% 42.88/27.90 (![B: $i] : (bool(B) => (impl(true, B) = B)) <=> ![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 42.88/27.90 inference(quant_intro,[status(thm)],[84])).
% 42.88/27.90 tff(86,axiom,(![B: $i] : (bool(B) => (impl(true, B) = B))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','impl_axiom4')).
% 42.88/27.90 tff(87,plain,
% 42.88/27.90 (![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 42.88/27.90 inference(modus_ponens,[status(thm)],[86, 85])).
% 42.88/27.90 tff(88,plain,
% 42.88/27.90 (![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 42.88/27.90 inference(modus_ponens,[status(thm)],[87, 83])).
% 42.88/27.90 tff(89,plain,
% 42.88/27.90 (![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))),
% 42.88/27.90 inference(modus_ponens,[status(thm)],[88, 82])).
% 42.88/27.90 tff(90,plain,(
% 42.88/27.90 ![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))),
% 42.88/27.90 inference(skolemize,[status(sab)],[89])).
% 42.88/27.90 tff(91,plain,
% 42.88/27.90 (![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))),
% 42.88/27.90 inference(modus_ponens,[status(thm)],[90, 80])).
% 42.88/27.90 tff(92,plain,
% 42.88/27.90 (((~![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))),
% 42.88/27.91 inference(rewrite,[status(thm)],[])).
% 42.88/27.91 tff(93,plain,
% 42.88/27.91 ((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | ((~bool(false)) | (impl(not1(false), false) = false))),
% 42.88/27.91 inference(quant_inst,[status(thm)],[])).
% 42.88/27.91 tff(94,plain,
% 42.88/27.91 ((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | (~bool(false)) | (impl(not1(false), false) = false)),
% 42.88/27.91 inference(modus_ponens,[status(thm)],[93, 92])).
% 42.88/27.91 tff(95,plain,
% 42.88/27.91 (impl(not1(false), false) = false),
% 42.88/27.91 inference(unit_resolution,[status(thm)],[94, 91, 61])).
% 42.88/27.91 tff(96,plain,
% 42.88/27.91 (impl(false, impl(not1(false), false)) = impl(false, false)),
% 42.88/27.91 inference(monotonicity,[status(thm)],[95])).
% 42.88/27.91 tff(97,plain,
% 42.88/27.91 (impl(false, impl(not1(false), false)) = not1(false)),
% 42.88/27.91 inference(transitivity,[status(thm)],[96, 78])).
% 42.88/27.91 tff(98,plain,
% 42.88/27.91 (impl(impl(false, impl(not1(false), false)), false) = impl(not1(false), false)),
% 42.88/27.91 inference(monotonicity,[status(thm)],[97])).
% 42.88/27.91 tff(99,plain,
% 42.88/27.91 (impl(not1(false), false) = impl(impl(false, impl(not1(false), false)), false)),
% 42.88/27.91 inference(symmetry,[status(thm)],[98])).
% 42.88/27.91 tff(100,plain,
% 42.88/27.91 (false = impl(not1(false), false)),
% 42.88/27.91 inference(symmetry,[status(thm)],[95])).
% 42.88/27.91 tff(101,plain,
% 42.88/27.91 (false = impl(impl(false, impl(not1(false), false)), false)),
% 42.88/27.91 inference(transitivity,[status(thm)],[100, 99])).
% 42.88/27.91 tff(102,plain,
% 42.88/27.91 (^[X: $i] : refl(((prop(X) = not1(false)) <=> bool(X)) <=> ((prop(X) = not1(false)) <=> bool(X)))),
% 42.88/27.91 inference(bind,[status(th)],[])).
% 42.88/27.91 tff(103,plain,
% 42.88/27.91 (![X: $i] : ((prop(X) = not1(false)) <=> bool(X)) <=> ![X: $i] : ((prop(X) = not1(false)) <=> bool(X))),
% 42.88/27.91 inference(quant_intro,[status(thm)],[102])).
% 42.88/27.91 tff(104,plain,
% 42.88/27.91 (^[X: $i] : rewrite(((prop(X) = true) <=> bool(X)) <=> ((prop(X) = not1(false)) <=> bool(X)))),
% 42.88/27.91 inference(bind,[status(th)],[])).
% 42.88/27.91 tff(105,plain,
% 42.88/27.91 (![X: $i] : ((prop(X) = true) <=> bool(X)) <=> ![X: $i] : ((prop(X) = not1(false)) <=> bool(X))),
% 42.88/27.91 inference(quant_intro,[status(thm)],[104])).
% 42.88/27.91 tff(106,plain,
% 42.88/27.91 (![X: $i] : ((prop(X) = true) <=> bool(X)) <=> ![X: $i] : ((prop(X) = true) <=> bool(X))),
% 42.88/27.91 inference(rewrite,[status(thm)],[])).
% 42.88/27.91 tff(107,axiom,(![X: $i] : ((prop(X) = true) <=> bool(X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','prop_true')).
% 42.88/27.91 tff(108,plain,
% 42.88/27.91 (![X: $i] : ((prop(X) = true) <=> bool(X))),
% 42.88/27.91 inference(modus_ponens,[status(thm)],[107, 106])).
% 42.88/27.91 tff(109,plain,
% 42.88/27.91 (![X: $i] : ((prop(X) = not1(false)) <=> bool(X))),
% 42.88/27.91 inference(modus_ponens,[status(thm)],[108, 105])).
% 42.88/27.91 tff(110,plain,(
% 42.88/27.91 ![X: $i] : ((prop(X) = not1(false)) <=> bool(X))),
% 42.88/27.91 inference(skolemize,[status(sab)],[109])).
% 42.88/27.91 tff(111,plain,
% 42.88/27.91 (![X: $i] : ((prop(X) = not1(false)) <=> bool(X))),
% 42.88/27.91 inference(modus_ponens,[status(thm)],[110, 103])).
% 42.88/27.91 tff(112,plain,
% 42.88/27.91 ((~![X: $i] : ((prop(X) = not1(false)) <=> bool(X))) | ((prop(false) = not1(false)) <=> bool(false))),
% 42.88/27.91 inference(quant_inst,[status(thm)],[])).
% 42.88/27.91 tff(113,plain,
% 42.88/27.91 ((prop(false) = not1(false)) <=> bool(false)),
% 42.88/27.91 inference(unit_resolution,[status(thm)],[112, 111])).
% 42.88/27.91 tff(114,plain,
% 42.88/27.91 ((~((prop(false) = not1(false)) <=> bool(false))) | (prop(false) = not1(false)) | (~bool(false))),
% 42.88/27.91 inference(tautology,[status(thm)],[])).
% 42.88/27.91 tff(115,plain,
% 42.88/27.91 ((~((prop(false) = not1(false)) <=> bool(false))) | (prop(false) = not1(false))),
% 42.88/27.91 inference(unit_resolution,[status(thm)],[114, 61])).
% 42.88/27.91 tff(116,plain,
% 42.88/27.91 (prop(false) = not1(false)),
% 42.88/27.91 inference(unit_resolution,[status(thm)],[115, 113])).
% 42.88/27.91 tff(117,plain,
% 42.88/27.91 (not1(false) = prop(false)),
% 42.88/27.91 inference(symmetry,[status(thm)],[116])).
% 42.88/27.91 tff(118,plain,
% 42.88/27.91 (lazy_impl(not1(false), false) = lazy_impl(prop(false), impl(impl(false, impl(not1(false), false)), false))),
% 42.88/27.91 inference(monotonicity,[status(thm)],[117, 101])).
% 42.88/27.91 tff(119,plain,
% 42.88/27.91 (lazy_impl(prop(false), impl(impl(false, impl(not1(false), false)), false)) = lazy_impl(not1(false), false)),
% 42.88/27.91 inference(symmetry,[status(thm)],[118])).
% 42.88/27.91 tff(120,plain,
% 42.88/27.91 (^[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))))),
% 42.88/27.91 inference(bind,[status(th)],[])).
% 42.88/27.91 tff(121,plain,
% 42.88/27.91 (![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)))),
% 42.88/27.91 inference(quant_intro,[status(thm)],[120])).
% 42.88/27.91 tff(122,plain,
% 42.88/27.91 (![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)))),
% 42.88/27.91 inference(rewrite,[status(thm)],[])).
% 42.88/27.91 tff(123,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')).
% 42.88/27.91 tff(124,plain,
% 42.88/27.91 (![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))),
% 42.88/27.91 inference(modus_ponens,[status(thm)],[123, 122])).
% 42.88/27.91 tff(125,plain,(
% 42.88/27.91 ![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))),
% 42.88/27.91 inference(skolemize,[status(sab)],[124])).
% 42.88/27.91 tff(126,plain,
% 42.88/27.91 (![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))),
% 42.88/27.91 inference(modus_ponens,[status(thm)],[125, 121])).
% 42.88/27.91 tff(127,plain,
% 42.88/27.91 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(false, not1(false), false) = lazy_impl(prop(false), impl(impl(false, impl(not1(false), false)), false)))),
% 42.88/27.91 inference(quant_inst,[status(thm)],[])).
% 42.88/27.91 tff(128,plain,
% 42.88/27.91 (f1(false, not1(false), false) = lazy_impl(prop(false), impl(impl(false, impl(not1(false), false)), false))),
% 42.88/27.91 inference(unit_resolution,[status(thm)],[127, 126])).
% 42.88/27.91 tff(129,plain,
% 42.88/27.91 ((false = not1(false)) <=> (not1(false) = false)),
% 42.88/27.91 inference(commutativity,[status(thm)],[])).
% 42.88/27.91 tff(130,plain,
% 42.88/27.91 (d(true) <=> d(not1(false))),
% 42.88/27.91 inference(rewrite,[status(thm)],[])).
% 42.88/27.91 tff(131,plain,
% 42.88/27.91 (d(true) <=> d(true)),
% 42.88/27.91 inference(rewrite,[status(thm)],[])).
% 42.88/27.91 tff(132,plain,
% 42.88/27.91 (d(true)),
% 42.88/27.91 inference(and_elim,[status(thm)],[3])).
% 42.88/27.91 tff(133,plain,
% 42.88/27.91 (d(true)),
% 42.88/27.91 inference(modus_ponens,[status(thm)],[132, 131])).
% 42.88/27.91 tff(134,plain,
% 42.88/27.91 (d(not1(false))),
% 42.88/27.91 inference(modus_ponens,[status(thm)],[133, 130])).
% 42.88/27.91 tff(135,plain,
% 42.88/27.91 ((d(not1(false)) | (~(phi(not1(false)) = err))) | (~d(not1(false)))),
% 42.88/27.91 inference(tautology,[status(thm)],[])).
% 42.88/27.91 tff(136,plain,
% 42.88/27.91 (d(not1(false)) | (~(phi(not1(false)) = err))),
% 42.88/27.91 inference(unit_resolution,[status(thm)],[135, 134])).
% 42.88/27.91 tff(137,plain,
% 42.88/27.91 (((~![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)))))),
% 42.88/27.91 inference(rewrite,[status(thm)],[])).
% 42.88/27.91 tff(138,plain,
% 42.88/27.91 ((~![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)))))),
% 42.88/27.91 inference(quant_inst,[status(thm)],[])).
% 42.88/27.91 tff(139,plain,
% 42.88/27.91 ((~![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))))),
% 42.88/27.91 inference(modus_ponens,[status(thm)],[138, 137])).
% 42.88/27.91 tff(140,plain,
% 42.88/27.91 (~((~d(not1(false))) | (~(phi(not1(false)) = not1(false))))),
% 42.88/27.91 inference(unit_resolution,[status(thm)],[139, 17, 136])).
% 42.88/27.91 tff(141,plain,
% 42.88/27.91 (((~d(not1(false))) | (~(phi(not1(false)) = not1(false)))) | (phi(not1(false)) = not1(false))),
% 42.88/27.91 inference(tautology,[status(thm)],[])).
% 42.88/27.91 tff(142,plain,
% 42.88/27.91 (phi(not1(false)) = not1(false)),
% 42.88/27.91 inference(unit_resolution,[status(thm)],[141, 140])).
% 42.88/27.91 tff(143,plain,
% 42.88/27.91 ((not1(true) = false) <=> (not1(not1(false)) = false)),
% 42.88/27.91 inference(rewrite,[status(thm)],[])).
% 42.88/27.91 tff(144,plain,
% 42.88/27.91 ((not1(true) = false) <=> (not1(true) = false)),
% 42.88/27.91 inference(rewrite,[status(thm)],[])).
% 42.88/27.91 tff(145,axiom,(not1(true) = false), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','not1_axiom3')).
% 42.88/27.91 tff(146,plain,
% 42.88/27.91 (not1(true) = false),
% 42.88/27.91 inference(modus_ponens,[status(thm)],[145, 144])).
% 42.88/27.91 tff(147,plain,
% 42.88/27.91 (not1(not1(false)) = false),
% 42.88/27.91 inference(modus_ponens,[status(thm)],[146, 143])).
% 42.88/27.91 tff(148,plain,
% 42.88/27.91 ((not1(not1(false)) = phi(not1(false))) <=> (false = not1(false))),
% 42.88/27.91 inference(monotonicity,[status(thm)],[147, 142])).
% 42.88/27.91 tff(149,plain,
% 42.88/27.91 ((not1(not1(false)) = phi(not1(false))) <=> (not1(false) = false)),
% 42.88/27.91 inference(transitivity,[status(thm)],[148, 129])).
% 42.88/27.91 tff(150,plain,
% 42.88/27.91 ((not1(false) = false) <=> (not1(not1(false)) = phi(not1(false)))),
% 42.88/27.91 inference(symmetry,[status(thm)],[149])).
% 42.88/27.91 tff(151,plain,
% 42.88/27.91 ((~(not1(false) = false)) <=> (~(not1(not1(false)) = phi(not1(false))))),
% 42.88/27.91 inference(monotonicity,[status(thm)],[150])).
% 42.88/27.91 tff(152,plain,
% 42.88/27.91 (~(not1(not1(false)) = phi(not1(false)))),
% 42.88/27.91 inference(modus_ponens,[status(thm)],[45, 151])).
% 42.88/27.91 tff(153,plain,
% 42.88/27.91 (((~![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))))),
% 42.88/27.91 inference(rewrite,[status(thm)],[])).
% 42.88/27.91 tff(154,plain,
% 42.88/27.91 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | (bool(not1(false)) | (not1(not1(false)) = phi(not1(false))))),
% 42.88/27.91 inference(quant_inst,[status(thm)],[])).
% 42.88/27.91 tff(155,plain,
% 42.88/27.91 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | bool(not1(false)) | (not1(not1(false)) = phi(not1(false)))),
% 42.88/27.91 inference(modus_ponens,[status(thm)],[154, 153])).
% 42.88/27.91 tff(156,plain,
% 42.88/27.91 (bool(not1(false)) | (not1(not1(false)) = phi(not1(false)))),
% 42.88/27.91 inference(unit_resolution,[status(thm)],[155, 56])).
% 42.88/27.91 tff(157,plain,
% 42.88/27.91 (bool(not1(false))),
% 42.88/27.91 inference(unit_resolution,[status(thm)],[156, 152])).
% 42.88/27.91 tff(158,plain,
% 42.88/27.91 (((~![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)))),
% 42.88/27.91 inference(rewrite,[status(thm)],[])).
% 42.88/27.91 tff(159,plain,
% 42.88/27.91 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | ((~bool(not1(false))) | (impl(false, not1(false)) = not1(false)))),
% 42.88/27.91 inference(quant_inst,[status(thm)],[])).
% 42.88/27.91 tff(160,plain,
% 42.88/27.91 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | (~bool(not1(false))) | (impl(false, not1(false)) = not1(false))),
% 42.88/27.91 inference(modus_ponens,[status(thm)],[159, 158])).
% 42.88/27.91 tff(161,plain,
% 42.88/27.91 (impl(false, not1(false)) = not1(false)),
% 42.88/27.91 inference(unit_resolution,[status(thm)],[160, 74, 157])).
% 42.88/27.91 tff(162,plain,
% 42.88/27.91 (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))),
% 42.88/27.91 inference(monotonicity,[status(thm)],[161])).
% 42.88/27.91 tff(163,plain,
% 42.88/27.91 (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)))),
% 42.88/27.91 inference(symmetry,[status(thm)],[162])).
% 42.88/27.91 tff(164,plain,
% 42.88/27.91 (^[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)))),
% 42.88/27.91 inference(bind,[status(th)],[])).
% 42.88/27.91 tff(165,plain,
% 42.88/27.91 (![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))),
% 42.88/27.91 inference(quant_intro,[status(thm)],[164])).
% 42.88/27.91 tff(166,plain,
% 42.88/27.91 (![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))),
% 42.88/27.91 inference(rewrite,[status(thm)],[])).
% 42.88/27.91 tff(167,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')).
% 42.88/27.91 tff(168,plain,
% 42.88/27.91 (![P: $i, X: $i, R: $i] : (f4(P, X, R) = impl(apply(P, X), R))),
% 42.88/27.91 inference(modus_ponens,[status(thm)],[167, 166])).
% 42.88/27.91 tff(169,plain,(
% 42.88/27.91 ![P: $i, X: $i, R: $i] : (f4(P, X, R) = impl(apply(P, X), R))),
% 42.92/27.91 inference(skolemize,[status(sab)],[168])).
% 42.92/27.91 tff(170,plain,
% 42.92/27.91 (![P: $i, X: $i, R: $i] : (f4(P, X, R) = impl(apply(P, X), R))),
% 42.92/27.91 inference(modus_ponens,[status(thm)],[169, 165])).
% 42.92/27.91 tff(171,plain,
% 42.92/27.91 ((~![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)))),
% 42.92/27.91 inference(quant_inst,[status(thm)],[])).
% 42.92/27.91 tff(172,plain,
% 42.92/27.91 (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))),
% 42.92/27.91 inference(unit_resolution,[status(thm)],[171, 170])).
% 42.92/27.91 tff(173,assumption,(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err), introduced(assumption)).
% 42.92/27.91 tff(174,plain,
% 42.92/27.91 (d(err) <=> d(err)),
% 42.92/27.91 inference(rewrite,[status(thm)],[])).
% 42.92/27.91 tff(175,plain,
% 42.92/27.91 (d(err)),
% 42.92/27.91 inference(and_elim,[status(thm)],[2])).
% 42.92/27.91 tff(176,plain,
% 42.92/27.91 (d(err)),
% 42.92/27.91 inference(modus_ponens,[status(thm)],[175, 174])).
% 42.92/27.91 tff(177,plain,
% 42.92/27.91 ((d(err) | (~(phi(err) = err))) | (~d(err))),
% 42.92/27.91 inference(tautology,[status(thm)],[])).
% 42.92/27.91 tff(178,plain,
% 42.92/27.91 (d(err) | (~(phi(err) = err))),
% 42.92/27.91 inference(unit_resolution,[status(thm)],[177, 176])).
% 42.92/27.91 tff(179,plain,
% 42.92/27.91 (((~![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)))))),
% 42.92/27.91 inference(rewrite,[status(thm)],[])).
% 42.92/27.91 tff(180,plain,
% 42.92/27.91 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(err)) | (~(phi(err) = err)))) | (~(d(err) | (~(phi(err) = err)))))),
% 42.92/27.91 inference(quant_inst,[status(thm)],[])).
% 42.92/27.91 tff(181,plain,
% 42.92/27.91 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(err)) | (~(phi(err) = err)))) | (~(d(err) | (~(phi(err) = err))))),
% 42.92/27.91 inference(modus_ponens,[status(thm)],[180, 179])).
% 42.92/27.91 tff(182,plain,
% 42.92/27.91 (~((~d(err)) | (~(phi(err) = err)))),
% 42.92/27.91 inference(unit_resolution,[status(thm)],[181, 17, 178])).
% 42.92/27.91 tff(183,plain,
% 42.92/27.91 (((~d(err)) | (~(phi(err) = err))) | (phi(err) = err)),
% 42.92/27.91 inference(tautology,[status(thm)],[])).
% 42.92/27.91 tff(184,plain,
% 42.92/27.91 (phi(err) = err),
% 42.92/27.91 inference(unit_resolution,[status(thm)],[183, 182])).
% 42.92/27.91 tff(185,plain,
% 42.92/27.91 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), err) = phi(err))),
% 42.92/27.91 inference(quant_inst,[status(thm)],[])).
% 42.92/27.91 tff(186,plain,
% 42.92/27.91 (lazy_impl(not1(false), err) = phi(err)),
% 42.92/27.91 inference(unit_resolution,[status(thm)],[185, 33])).
% 42.92/27.91 tff(187,plain,
% 42.92/27.91 (^[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)))))))),
% 42.92/27.91 inference(bind,[status(th)],[])).
% 42.92/27.91 tff(188,plain,
% 42.92/27.91 (![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))))))),
% 42.92/27.91 inference(quant_intro,[status(thm)],[187])).
% 42.92/27.91 tff(189,plain,
% 42.92/27.91 (^[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)))))))),
% 42.92/27.91 inference(bind,[status(th)],[])).
% 42.92/27.91 tff(190,plain,
% 42.92/27.91 (![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))))))),
% 42.92/27.91 inference(quant_intro,[status(thm)],[189])).
% 42.92/27.91 tff(191,plain,
% 42.92/27.91 (![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))))))),
% 42.92/27.91 inference(transitivity,[status(thm)],[190, 188])).
% 42.92/27.91 tff(192,plain,
% 42.92/27.91 (^[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)))))))),
% 42.92/27.91 inference(bind,[status(th)],[])).
% 42.92/27.91 tff(193,plain,
% 42.92/27.91 (![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))))))),
% 42.92/27.91 inference(quant_intro,[status(thm)],[192])).
% 42.92/27.91 tff(194,plain,
% 42.92/27.91 (![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))))),
% 42.92/27.91 inference(rewrite,[status(thm)],[])).
% 42.92/27.91 tff(195,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')).
% 42.92/27.91 tff(196,plain,
% 42.92/27.91 (![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))))),
% 42.92/27.91 inference(modus_ponens,[status(thm)],[195, 194])).
% 42.92/27.91 tff(197,plain,(
% 42.92/27.91 ![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))))),
% 42.92/27.91 inference(skolemize,[status(sab)],[196])).
% 42.92/27.91 tff(198,plain,
% 42.92/27.91 (![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))))))),
% 42.92/27.91 inference(modus_ponens,[status(thm)],[197, 193])).
% 42.92/27.91 tff(199,plain,
% 42.92/27.91 (![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))))))),
% 42.92/27.91 inference(modus_ponens,[status(thm)],[198, 191])).
% 42.92/27.91 tff(200,plain,
% 42.92/27.91 ((~![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)))))))),
% 42.92/27.91 inference(quant_inst,[status(thm)],[])).
% 42.92/27.91 tff(201,plain,
% 42.92/27.91 (~((~(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))))))),
% 42.92/27.91 inference(unit_resolution,[status(thm)],[200, 199])).
% 42.92/27.91 tff(202,plain,
% 42.92/27.91 (((~(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))))),
% 42.92/27.91 inference(tautology,[status(thm)],[])).
% 42.92/27.91 tff(203,plain,
% 42.92/27.91 (f5(P!7, not1(false)) = phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 42.92/27.91 inference(unit_resolution,[status(thm)],[202, 201])).
% 42.92/27.91 tff(204,plain,
% 42.92/27.91 (f5(P!7, not1(false)) = err),
% 42.92/27.91 inference(transitivity,[status(thm)],[203, 173])).
% 42.92/27.91 tff(205,plain,
% 42.92/27.91 (phi(f5(P!7, not1(false))) = phi(err)),
% 42.92/27.91 inference(monotonicity,[status(thm)],[204])).
% 42.92/27.91 tff(206,plain,
% 42.92/27.91 (bool(f5(P!7, not1(false))) <=> bool(err)),
% 42.92/27.91 inference(monotonicity,[status(thm)],[204])).
% 42.92/27.91 tff(207,plain,
% 42.92/27.91 (bool(err) <=> bool(f5(P!7, not1(false)))),
% 42.92/27.91 inference(symmetry,[status(thm)],[206])).
% 42.92/27.91 tff(208,plain,
% 42.92/27.91 ((~bool(err)) <=> (~bool(f5(P!7, not1(false))))),
% 42.92/27.91 inference(monotonicity,[status(thm)],[207])).
% 42.92/27.91 tff(209,plain,
% 42.92/27.91 (^[X: $i] : refl((bool(X) <=> ((X = false) | (X = not1(false)))) <=> (bool(X) <=> ((X = false) | (X = not1(false)))))),
% 42.92/27.91 inference(bind,[status(th)],[])).
% 42.92/27.91 tff(210,plain,
% 42.92/27.91 (![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false)))) <=> ![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))),
% 42.92/27.91 inference(quant_intro,[status(thm)],[209])).
% 42.92/27.91 tff(211,plain,
% 42.92/27.91 (^[X: $i] : rewrite((bool(X) <=> ((X = false) | (X = true))) <=> (bool(X) <=> ((X = false) | (X = not1(false)))))),
% 42.92/27.91 inference(bind,[status(th)],[])).
% 42.92/27.91 tff(212,plain,
% 42.92/27.91 (![X: $i] : (bool(X) <=> ((X = false) | (X = true))) <=> ![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))),
% 42.92/27.91 inference(quant_intro,[status(thm)],[211])).
% 42.92/27.91 tff(213,plain,
% 42.92/27.91 (![X: $i] : (bool(X) <=> ((X = false) | (X = true))) <=> ![X: $i] : (bool(X) <=> ((X = false) | (X = true)))),
% 42.92/27.91 inference(rewrite,[status(thm)],[])).
% 42.92/27.91 tff(214,axiom,(![X: $i] : (bool(X) <=> ((X = false) | (X = true)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','def_bool')).
% 42.92/27.91 tff(215,plain,
% 42.92/27.91 (![X: $i] : (bool(X) <=> ((X = false) | (X = true)))),
% 42.92/27.91 inference(modus_ponens,[status(thm)],[214, 213])).
% 42.92/27.91 tff(216,plain,
% 42.92/27.91 (![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))),
% 42.92/27.91 inference(modus_ponens,[status(thm)],[215, 212])).
% 42.92/27.91 tff(217,plain,(
% 42.92/27.91 ![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))),
% 42.92/27.91 inference(skolemize,[status(sab)],[216])).
% 42.92/27.91 tff(218,plain,
% 42.92/27.91 (![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))),
% 42.92/27.91 inference(modus_ponens,[status(thm)],[217, 210])).
% 42.92/27.91 tff(219,plain,
% 42.92/27.91 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(err) <=> ((err = false) | (err = not1(false))))),
% 42.92/27.91 inference(quant_inst,[status(thm)],[])).
% 42.92/27.91 tff(220,plain,
% 42.92/27.91 (bool(err) <=> ((err = false) | (err = not1(false)))),
% 42.92/27.91 inference(unit_resolution,[status(thm)],[219, 218])).
% 42.92/27.91 tff(221,plain,
% 42.92/27.91 ((err = false) <=> (false = err)),
% 42.92/27.91 inference(commutativity,[status(thm)],[])).
% 42.92/27.91 tff(222,plain,
% 42.92/27.91 ((false = err) <=> (err = false)),
% 42.92/27.91 inference(symmetry,[status(thm)],[221])).
% 42.92/27.91 tff(223,plain,
% 42.92/27.91 ((~(false = err)) <=> (~(err = false))),
% 42.92/27.91 inference(monotonicity,[status(thm)],[222])).
% 42.92/27.91 tff(224,plain,
% 42.92/27.91 ((~(false = err)) <=> (~(false = err))),
% 42.92/27.91 inference(rewrite,[status(thm)],[])).
% 42.92/27.91 tff(225,plain,
% 42.92/27.91 (~(false = err)),
% 42.92/27.91 inference(and_elim,[status(thm)],[41])).
% 42.92/27.91 tff(226,plain,
% 42.92/27.91 (~(false = err)),
% 42.92/27.91 inference(modus_ponens,[status(thm)],[225, 224])).
% 42.92/27.91 tff(227,plain,
% 42.92/27.91 (~(err = false)),
% 42.92/27.91 inference(modus_ponens,[status(thm)],[226, 223])).
% 42.92/27.91 tff(228,plain,
% 42.92/27.91 ((err = not1(false)) <=> (not1(false) = err)),
% 42.92/27.91 inference(commutativity,[status(thm)],[])).
% 42.92/27.91 tff(229,plain,
% 42.92/27.91 ((not1(false) = err) <=> (err = not1(false))),
% 42.92/27.91 inference(symmetry,[status(thm)],[228])).
% 42.92/27.91 tff(230,plain,
% 42.92/27.91 ((~(not1(false) = err)) <=> (~(err = not1(false)))),
% 42.92/27.91 inference(monotonicity,[status(thm)],[229])).
% 42.92/27.91 tff(231,plain,
% 42.92/27.91 ((~(true = err)) <=> (~(not1(false) = err))),
% 42.92/27.91 inference(rewrite,[status(thm)],[])).
% 42.92/27.91 tff(232,plain,
% 42.92/27.91 ((~(true = err)) <=> (~(true = err))),
% 42.92/27.91 inference(rewrite,[status(thm)],[])).
% 42.92/27.91 tff(233,plain,
% 42.92/27.91 (~(true = err)),
% 42.92/27.91 inference(and_elim,[status(thm)],[42])).
% 42.92/27.91 tff(234,plain,
% 42.92/27.91 (~(true = err)),
% 42.92/27.91 inference(modus_ponens,[status(thm)],[233, 232])).
% 42.92/27.91 tff(235,plain,
% 42.92/27.91 (~(not1(false) = err)),
% 42.92/27.91 inference(modus_ponens,[status(thm)],[234, 231])).
% 42.92/27.91 tff(236,plain,
% 42.92/27.91 (~(err = not1(false))),
% 42.92/27.91 inference(modus_ponens,[status(thm)],[235, 230])).
% 42.92/27.91 tff(237,plain,
% 42.92/27.91 ((~((err = false) | (err = not1(false)))) | (err = false) | (err = not1(false))),
% 42.92/27.91 inference(tautology,[status(thm)],[])).
% 42.92/27.91 tff(238,plain,
% 42.92/27.91 ((~((err = false) | (err = not1(false)))) | (err = false)),
% 42.92/27.91 inference(unit_resolution,[status(thm)],[237, 236])).
% 42.92/27.91 tff(239,plain,
% 42.92/27.91 (~((err = false) | (err = not1(false)))),
% 42.92/27.91 inference(unit_resolution,[status(thm)],[238, 227])).
% 42.92/27.91 tff(240,plain,
% 42.92/27.91 ((~(bool(err) <=> ((err = false) | (err = not1(false))))) | (~bool(err)) | ((err = false) | (err = not1(false)))),
% 42.92/27.91 inference(tautology,[status(thm)],[])).
% 42.92/27.91 tff(241,plain,
% 42.92/27.91 (~bool(err)),
% 42.92/27.91 inference(unit_resolution,[status(thm)],[240, 239, 220])).
% 42.92/27.91 tff(242,plain,
% 42.92/27.91 (~bool(f5(P!7, not1(false)))),
% 42.92/27.91 inference(modus_ponens,[status(thm)],[241, 208])).
% 42.92/27.91 tff(243,plain,
% 42.92/27.91 (^[A: $i, B: $i] : refl((bool(A) | (impl(A, B) = phi(A))) <=> (bool(A) | (impl(A, B) = phi(A))))),
% 42.92/27.91 inference(bind,[status(th)],[])).
% 42.92/27.91 tff(244,plain,
% 42.92/27.91 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A))) <=> ![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 42.92/27.91 inference(quant_intro,[status(thm)],[243])).
% 42.92/27.91 tff(245,plain,
% 42.92/27.91 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A))) <=> ![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 42.92/27.91 inference(rewrite,[status(thm)],[])).
% 42.92/27.91 tff(246,plain,
% 42.92/27.91 (^[A: $i, B: $i] : rewrite(((~bool(A)) => (impl(A, B) = phi(A))) <=> (bool(A) | (impl(A, B) = phi(A))))),
% 42.92/27.91 inference(bind,[status(th)],[])).
% 42.92/27.91 tff(247,plain,
% 42.92/27.91 (![A: $i, B: $i] : ((~bool(A)) => (impl(A, B) = phi(A))) <=> ![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 42.92/27.91 inference(quant_intro,[status(thm)],[246])).
% 42.92/27.91 tff(248,axiom,(![A: $i, B: $i] : ((~bool(A)) => (impl(A, B) = phi(A)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','impl_axiom1')).
% 42.92/27.91 tff(249,plain,
% 42.92/27.91 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 42.92/27.91 inference(modus_ponens,[status(thm)],[248, 247])).
% 42.92/27.91 tff(250,plain,
% 42.92/27.91 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 42.92/27.91 inference(modus_ponens,[status(thm)],[249, 245])).
% 42.92/27.91 tff(251,plain,(
% 42.92/27.91 ![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 42.92/27.91 inference(skolemize,[status(sab)],[250])).
% 42.92/27.91 tff(252,plain,
% 42.92/27.91 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 42.92/27.91 inference(modus_ponens,[status(thm)],[251, 244])).
% 42.92/27.91 tff(253,plain,
% 42.92/27.91 (((~![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)))))),
% 42.92/27.91 inference(rewrite,[status(thm)],[])).
% 42.92/27.91 tff(254,plain,
% 42.92/27.91 ((~![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)))))),
% 42.92/27.91 inference(quant_inst,[status(thm)],[])).
% 42.92/27.91 tff(255,plain,
% 42.92/27.91 ((~![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))))),
% 42.92/27.91 inference(modus_ponens,[status(thm)],[254, 253])).
% 42.92/27.91 tff(256,plain,
% 42.92/27.91 (bool(f5(P!7, not1(false))) | (impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false))))),
% 42.92/27.91 inference(unit_resolution,[status(thm)],[255, 252])).
% 42.92/27.91 tff(257,plain,
% 42.92/27.91 (impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false)))),
% 42.92/27.91 inference(unit_resolution,[status(thm)],[256, 242])).
% 42.92/27.91 tff(258,plain,
% 42.92/27.91 (impl(f5(P!7, not1(false)), not1(false)) = err),
% 42.92/27.91 inference(transitivity,[status(thm)],[257, 205, 184])).
% 42.92/27.91 tff(259,plain,
% 42.92/27.91 ((~![X: $i] : ((prop(X) = not1(false)) <=> bool(X))) | ((prop(not1(false)) = not1(false)) <=> bool(not1(false)))),
% 42.92/27.91 inference(quant_inst,[status(thm)],[])).
% 42.92/27.91 tff(260,plain,
% 42.92/27.91 ((prop(not1(false)) = not1(false)) <=> bool(not1(false))),
% 42.92/27.91 inference(unit_resolution,[status(thm)],[259, 111])).
% 42.92/27.91 tff(261,plain,
% 42.92/27.91 ((~((prop(not1(false)) = not1(false)) <=> bool(not1(false)))) | (prop(not1(false)) = not1(false)) | (~bool(not1(false)))),
% 42.92/27.91 inference(tautology,[status(thm)],[])).
% 42.92/27.91 tff(262,plain,
% 42.92/27.91 ((~((prop(not1(false)) = not1(false)) <=> bool(not1(false)))) | (prop(not1(false)) = not1(false))),
% 42.92/27.91 inference(unit_resolution,[status(thm)],[261, 157])).
% 42.92/27.91 tff(263,plain,
% 42.92/27.91 (prop(not1(false)) = not1(false)),
% 42.92/27.91 inference(unit_resolution,[status(thm)],[262, 260])).
% 42.92/27.91 tff(264,plain,
% 42.92/27.91 (lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = lazy_impl(not1(false), err)),
% 42.92/27.91 inference(monotonicity,[status(thm)],[263, 258])).
% 42.92/27.91 tff(265,plain,
% 42.92/27.91 (^[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))))),
% 42.92/27.91 inference(bind,[status(th)],[])).
% 42.92/27.91 tff(266,plain,
% 42.92/27.91 (![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)))),
% 42.92/27.91 inference(quant_intro,[status(thm)],[265])).
% 42.92/27.91 tff(267,plain,
% 42.92/27.91 (![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)))),
% 42.92/27.91 inference(rewrite,[status(thm)],[])).
% 42.92/27.91 tff(268,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')).
% 42.92/27.91 tff(269,plain,
% 42.92/27.91 (![P: $i, R: $i] : (f6(P, R) = lazy_impl(prop(R), impl(f5(P, R), R)))),
% 42.92/27.91 inference(modus_ponens,[status(thm)],[268, 267])).
% 42.92/27.91 tff(270,plain,(
% 42.92/27.91 ![P: $i, R: $i] : (f6(P, R) = lazy_impl(prop(R), impl(f5(P, R), R)))),
% 42.92/27.91 inference(skolemize,[status(sab)],[269])).
% 42.92/27.91 tff(271,plain,
% 42.92/27.91 (![P: $i, R: $i] : (f6(P, R) = lazy_impl(prop(R), impl(f5(P, R), R)))),
% 42.92/27.91 inference(modus_ponens,[status(thm)],[270, 266])).
% 42.92/27.91 tff(272,plain,
% 42.92/27.91 ((~![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))))),
% 42.92/27.91 inference(quant_inst,[status(thm)],[])).
% 42.92/27.91 tff(273,plain,
% 42.92/27.91 (f6(P!7, not1(false)) = lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))),
% 42.92/27.91 inference(unit_resolution,[status(thm)],[272, 271])).
% 42.92/27.91 tff(274,assumption,(tptp_fun_R_5(P!7) = not1(false)), introduced(assumption)).
% 42.92/27.91 tff(275,plain,
% 42.92/27.91 (f6(P!7, tptp_fun_R_5(P!7)) = f6(P!7, not1(false))),
% 42.92/27.91 inference(monotonicity,[status(thm)],[274])).
% 42.92/27.91 tff(276,plain,
% 42.92/27.91 (f6(P!7, tptp_fun_R_5(P!7)) = err),
% 42.92/27.91 inference(transitivity,[status(thm)],[275, 273, 264, 186, 184])).
% 42.92/27.91 tff(277,plain,
% 42.92/27.91 (phi(f6(P!7, tptp_fun_R_5(P!7))) = phi(err)),
% 42.92/27.91 inference(monotonicity,[status(thm)],[276])).
% 42.92/27.91 tff(278,plain,
% 42.92/27.91 (^[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))))))))),
% 42.92/27.91 inference(bind,[status(th)],[])).
% 42.92/27.91 tff(279,plain,
% 42.92/27.91 (![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)))))))),
% 42.92/27.91 inference(quant_intro,[status(thm)],[278])).
% 42.92/27.91 tff(280,plain,
% 42.92/27.91 (^[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))))))))),
% 42.92/27.91 inference(bind,[status(th)],[])).
% 42.92/27.91 tff(281,plain,
% 42.92/27.91 (![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)))))))),
% 42.92/27.91 inference(quant_intro,[status(thm)],[280])).
% 42.92/27.91 tff(282,plain,
% 42.92/27.91 (![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)))))))),
% 42.92/27.91 inference(transitivity,[status(thm)],[281, 279])).
% 42.92/27.91 tff(283,plain,
% 42.92/27.91 (^[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))))))))),
% 42.92/27.91 inference(bind,[status(th)],[])).
% 42.92/27.91 tff(284,plain,
% 42.92/27.91 (![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)))))))),
% 42.92/27.91 inference(quant_intro,[status(thm)],[283])).
% 42.92/27.91 tff(285,plain,
% 42.92/27.91 (![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))))),
% 42.92/27.91 inference(rewrite,[status(thm)],[])).
% 42.92/27.91 tff(286,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')).
% 42.92/27.91 tff(287,plain,
% 42.92/27.91 (![P: $i] : ?[R: $i] : ((exists2(P) = phi(f6(P, R))) & (~?[R1: $i] : forallprefers(f6(P, R1), f6(P, R))))),
% 42.92/27.91 inference(modus_ponens,[status(thm)],[286, 285])).
% 42.92/27.91 tff(288,plain,(
% 42.92/27.91 ![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)))))),
% 42.92/27.92 inference(skolemize,[status(sab)],[287])).
% 42.92/27.92 tff(289,plain,
% 42.92/27.92 (![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)))))))),
% 42.92/27.92 inference(modus_ponens,[status(thm)],[288, 284])).
% 42.92/27.92 tff(290,plain,
% 42.92/27.92 (![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)))))))),
% 42.92/27.92 inference(modus_ponens,[status(thm)],[289, 282])).
% 42.92/27.92 tff(291,plain,
% 42.92/27.92 ((~![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)))))))),
% 42.92/27.92 inference(quant_inst,[status(thm)],[])).
% 42.92/27.92 tff(292,plain,
% 42.92/27.92 (~((~(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))))))),
% 42.92/27.92 inference(unit_resolution,[status(thm)],[291, 290])).
% 42.92/27.92 tff(293,plain,
% 42.92/27.92 (((~(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))))),
% 42.92/27.92 inference(tautology,[status(thm)],[])).
% 42.92/27.92 tff(294,plain,
% 42.92/27.92 (exists2(P!7) = phi(f6(P!7, tptp_fun_R_5(P!7)))),
% 42.92/27.92 inference(unit_resolution,[status(thm)],[293, 292])).
% 42.92/27.92 tff(295,plain,
% 42.92/27.92 (exists2(P!7) = err),
% 42.92/27.92 inference(transitivity,[status(thm)],[294, 277, 184])).
% 42.92/27.92 tff(296,plain,
% 42.92/27.92 (bool(exists2(P!7)) <=> bool(err)),
% 42.92/27.92 inference(monotonicity,[status(thm)],[295])).
% 42.92/27.92 tff(297,plain,
% 42.92/27.92 (bool(err) <=> bool(exists2(P!7))),
% 42.92/27.92 inference(symmetry,[status(thm)],[296])).
% 42.92/27.92 tff(298,plain,
% 42.92/27.92 ((~bool(err)) <=> (~bool(exists2(P!7)))),
% 42.92/27.92 inference(monotonicity,[status(thm)],[297])).
% 42.92/27.92 tff(299,plain,
% 42.92/27.92 (~bool(exists2(P!7))),
% 42.92/27.92 inference(modus_ponens,[status(thm)],[241, 298])).
% 42.92/27.92 tff(300,plain,
% 42.92/27.92 (^[P: $i] : refl((f7(P) = lazy_impl(prop(P), P)) <=> (f7(P) = lazy_impl(prop(P), P)))),
% 42.92/27.92 inference(bind,[status(th)],[])).
% 42.92/27.92 tff(301,plain,
% 42.92/27.92 (![P: $i] : (f7(P) = lazy_impl(prop(P), P)) <=> ![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 42.92/27.92 inference(quant_intro,[status(thm)],[300])).
% 42.92/27.92 tff(302,plain,
% 42.92/27.92 (![P: $i] : (f7(P) = lazy_impl(prop(P), P)) <=> ![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 42.92/27.92 inference(rewrite,[status(thm)],[])).
% 42.92/27.92 tff(303,axiom,(![P: $i] : (f7(P) = lazy_impl(prop(P), P))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','def_f7')).
% 42.92/27.92 tff(304,plain,
% 42.92/27.92 (![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 42.92/27.92 inference(modus_ponens,[status(thm)],[303, 302])).
% 42.92/27.92 tff(305,plain,(
% 42.92/27.92 ![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 42.92/27.92 inference(skolemize,[status(sab)],[304])).
% 42.92/27.92 tff(306,plain,
% 42.92/27.92 (![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 42.92/27.92 inference(modus_ponens,[status(thm)],[305, 301])).
% 42.92/27.92 tff(307,plain,
% 42.92/27.92 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(P!6) = lazy_impl(prop(P!6), P!6))),
% 42.92/27.92 inference(quant_inst,[status(thm)],[])).
% 42.92/27.92 tff(308,plain,
% 42.92/27.92 (f7(P!6) = lazy_impl(prop(P!6), P!6)),
% 42.92/27.92 inference(unit_resolution,[status(thm)],[307, 306])).
% 42.92/27.92 tff(309,plain,
% 42.92/27.92 (lazy_impl(prop(P!6), P!6) = f7(P!6)),
% 42.92/27.92 inference(symmetry,[status(thm)],[308])).
% 42.92/27.92 tff(310,plain,
% 42.92/27.92 (d(lazy_impl(prop(P!6), P!6)) <=> d(f7(P!6))),
% 42.92/27.92 inference(monotonicity,[status(thm)],[309])).
% 42.92/27.92 tff(311,plain,
% 42.92/27.92 (d(f7(P!6)) <=> d(lazy_impl(prop(P!6), P!6))),
% 42.92/27.92 inference(symmetry,[status(thm)],[310])).
% 42.92/27.92 tff(312,plain,
% 42.92/27.92 (lazy_impl(prop(false), false) = lazy_impl(not1(false), false)),
% 42.92/27.92 inference(monotonicity,[status(thm)],[116])).
% 42.92/27.92 tff(313,plain,
% 42.92/27.92 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(false) = lazy_impl(prop(false), false))),
% 42.92/27.92 inference(quant_inst,[status(thm)],[])).
% 42.92/27.92 tff(314,plain,
% 42.92/27.92 (f7(false) = lazy_impl(prop(false), false)),
% 42.92/27.92 inference(unit_resolution,[status(thm)],[313, 306])).
% 42.92/27.92 tff(315,plain,
% 42.92/27.92 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), not1(false)) = phi(not1(false)))),
% 42.92/27.92 inference(quant_inst,[status(thm)],[])).
% 42.92/27.92 tff(316,plain,
% 42.92/27.92 (lazy_impl(not1(false), not1(false)) = phi(not1(false))),
% 42.92/27.92 inference(unit_resolution,[status(thm)],[315, 33])).
% 42.92/27.92 tff(317,plain,
% 42.92/27.92 (lazy_impl(prop(not1(false)), not1(false)) = lazy_impl(not1(false), not1(false))),
% 42.92/27.92 inference(monotonicity,[status(thm)],[263])).
% 42.92/27.92 tff(318,plain,
% 42.92/27.92 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(not1(false)) = lazy_impl(prop(not1(false)), not1(false)))),
% 42.92/27.92 inference(quant_inst,[status(thm)],[])).
% 42.92/27.92 tff(319,plain,
% 42.92/27.92 (f7(not1(false)) = lazy_impl(prop(not1(false)), not1(false))),
% 42.92/27.92 inference(unit_resolution,[status(thm)],[318, 306])).
% 42.92/27.92 tff(320,assumption,(P!6 = not1(false)), introduced(assumption)).
% 42.92/27.92 tff(321,plain,
% 42.92/27.92 (f7(P!6) = f7(not1(false))),
% 42.92/27.92 inference(monotonicity,[status(thm)],[320])).
% 42.92/27.92 tff(322,plain,
% 42.92/27.92 (lazy_impl(prop(P!6), P!6) = not1(false)),
% 42.92/27.92 inference(transitivity,[status(thm)],[309, 321, 319, 317, 316, 142])).
% 42.92/27.92 tff(323,plain,
% 42.92/27.92 (^[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))))))))),
% 42.92/27.92 inference(bind,[status(th)],[])).
% 42.92/27.92 tff(324,plain,
% 42.92/27.92 (![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)))))))),
% 42.92/27.92 inference(quant_intro,[status(thm)],[323])).
% 42.92/27.92 tff(325,plain,
% 42.92/27.92 (^[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))))))))),
% 42.92/27.92 inference(bind,[status(th)],[])).
% 42.92/27.92 tff(326,plain,
% 42.92/27.92 (![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)))))))),
% 42.92/27.92 inference(quant_intro,[status(thm)],[325])).
% 42.92/27.92 tff(327,plain,
% 42.92/27.92 (^[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))))))),
% 42.92/27.92 inference(bind,[status(th)],[])).
% 42.92/27.92 tff(328,plain,
% 42.92/27.92 (![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)))))),
% 42.92/27.92 inference(quant_intro,[status(thm)],[327])).
% 42.92/27.92 tff(329,plain,
% 42.92/27.92 (![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))))),
% 42.92/27.92 inference(rewrite,[status(thm)],[])).
% 42.92/27.92 tff(330,plain,
% 42.92/27.92 (^[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)))))),
% 42.92/27.92 inference(bind,[status(th)],[])).
% 42.92/27.92 tff(331,plain,
% 42.92/27.92 (![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))))),
% 42.92/27.92 inference(quant_intro,[status(thm)],[330])).
% 42.92/27.92 tff(332,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')).
% 42.92/27.92 tff(333,plain,
% 42.92/27.92 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 42.92/27.92 inference(modus_ponens,[status(thm)],[332, 331])).
% 42.92/27.92 tff(334,plain,
% 42.92/27.92 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 42.92/27.92 inference(modus_ponens,[status(thm)],[333, 329])).
% 42.92/27.92 tff(335,plain,
% 42.92/27.92 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)) | ((X = false) & (Y = not1(false)))))),
% 42.92/27.92 inference(modus_ponens,[status(thm)],[334, 328])).
% 42.92/27.92 tff(336,plain,(
% 42.92/27.92 ![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)) | ((X = false) & (Y = not1(false)))))),
% 42.92/27.92 inference(skolemize,[status(sab)],[335])).
% 42.92/27.92 tff(337,plain,
% 42.92/27.92 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))),
% 42.92/27.92 inference(modus_ponens,[status(thm)],[336, 326])).
% 42.92/27.92 tff(338,plain,
% 42.92/27.92 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))),
% 42.92/27.92 inference(modus_ponens,[status(thm)],[337, 324])).
% 42.92/27.92 tff(339,plain,
% 42.92/27.92 (((~![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)))))),
% 42.92/27.92 inference(rewrite,[status(thm)],[])).
% 42.92/27.92 tff(340,plain,
% 42.92/27.92 ((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))))),
% 42.92/27.92 inference(rewrite,[status(thm)],[])).
% 42.92/27.92 tff(341,plain,
% 42.92/27.92 (((~![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)))))),
% 42.92/27.92 inference(monotonicity,[status(thm)],[340])).
% 42.92/27.92 tff(342,plain,
% 42.92/27.92 (((~![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)))))),
% 42.92/27.92 inference(transitivity,[status(thm)],[341, 339])).
% 42.92/27.92 tff(343,plain,
% 42.92/27.92 ((~![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)))))))),
% 42.92/27.92 inference(quant_inst,[status(thm)],[])).
% 42.92/27.92 tff(344,plain,
% 42.92/27.92 ((~![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))))),
% 42.92/27.92 inference(modus_ponens,[status(thm)],[343, 342])).
% 42.92/27.92 tff(345,plain,
% 42.92/27.92 (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)))),
% 42.92/27.92 inference(unit_resolution,[status(thm)],[344, 338])).
% 42.92/27.92 tff(346,plain,
% 42.92/27.92 (lazy_impl(prop(false), false) = f7(false)),
% 42.92/27.92 inference(symmetry,[status(thm)],[314])).
% 42.92/27.92 tff(347,plain,
% 42.92/27.92 (lazy_impl(not1(false), false) = lazy_impl(prop(false), false)),
% 42.92/27.92 inference(symmetry,[status(thm)],[312])).
% 42.92/27.92 tff(348,plain,
% 42.92/27.92 (phi(false) = lazy_impl(not1(false), false)),
% 42.92/27.92 inference(symmetry,[status(thm)],[35])).
% 42.92/27.92 tff(349,plain,
% 42.92/27.92 (false = phi(false)),
% 42.92/27.92 inference(symmetry,[status(thm)],[23])).
% 42.92/27.92 tff(350,plain,
% 42.92/27.92 (false = f7(false)),
% 42.92/27.92 inference(transitivity,[status(thm)],[349, 348, 347, 346])).
% 42.92/27.92 tff(351,plain,
% 42.92/27.92 (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> forallprefers(f7(false), f7(P!6))),
% 42.92/27.92 inference(monotonicity,[status(thm)],[350, 309])).
% 42.92/27.92 tff(352,plain,
% 42.92/27.92 (forallprefers(f7(false), f7(P!6)) <=> forallprefers(false, lazy_impl(prop(P!6), P!6))),
% 42.92/27.92 inference(symmetry,[status(thm)],[351])).
% 42.92/27.92 tff(353,plain,
% 42.92/27.92 ((~forallprefers(f7(false), f7(P!6))) <=> (~forallprefers(false, lazy_impl(prop(P!6), P!6)))),
% 42.92/27.92 inference(monotonicity,[status(thm)],[352])).
% 42.92/27.92 tff(354,plain,
% 42.92/27.92 (^[P1: $i] : refl((~forallprefers(f7(P1), f7(P!6))) <=> (~forallprefers(f7(P1), f7(P!6))))),
% 42.92/27.92 inference(bind,[status(th)],[])).
% 42.92/27.92 tff(355,plain,
% 42.92/27.92 (![P1: $i] : (~forallprefers(f7(P1), f7(P!6))) <=> ![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 42.92/27.92 inference(quant_intro,[status(thm)],[354])).
% 42.92/27.92 tff(356,plain,
% 42.92/27.92 (((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))))),
% 42.92/27.92 inference(rewrite,[status(thm)],[])).
% 42.92/27.92 tff(357,plain,
% 42.92/27.92 (?[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))))),
% 42.92/27.92 inference(rewrite,[status(thm)],[])).
% 42.92/27.92 tff(358,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')).
% 42.92/27.92 tff(359,plain,
% 42.92/27.92 (?[P: $i] : ((false2 = phi(f7(P))) & (~?[P1: $i] : forallprefers(f7(P1), f7(P))))),
% 42.92/27.92 inference(modus_ponens,[status(thm)],[358, 357])).
% 42.92/27.92 tff(360,plain,
% 42.92/27.92 ((false2 = phi(f7(P!6))) & ![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 42.92/27.92 inference(modus_ponens,[status(thm)],[359, 356])).
% 42.92/27.92 tff(361,plain,
% 42.92/27.92 (![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 42.92/27.92 inference(and_elim,[status(thm)],[360])).
% 42.92/27.92 tff(362,plain,
% 42.92/27.92 (![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 42.92/27.92 inference(modus_ponens,[status(thm)],[361, 355])).
% 42.92/27.92 tff(363,plain,
% 42.92/27.92 ((~![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))) | (~forallprefers(f7(false), f7(P!6)))),
% 42.92/27.92 inference(quant_inst,[status(thm)],[])).
% 42.92/27.92 tff(364,plain,
% 42.92/27.92 (~forallprefers(f7(false), f7(P!6))),
% 42.92/27.92 inference(unit_resolution,[status(thm)],[363, 362])).
% 42.92/27.92 tff(365,plain,
% 42.92/27.92 (~forallprefers(false, lazy_impl(prop(P!6), P!6))),
% 42.92/27.92 inference(modus_ponens,[status(thm)],[364, 353])).
% 42.92/27.92 tff(366,plain,
% 42.92/27.92 ((~(forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))) | (lazy_impl(prop(P!6), P!6) = not1(false))))) | forallprefers(false, lazy_impl(prop(P!6), P!6)) | (~((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))) | (lazy_impl(prop(P!6), P!6) = not1(false))))),
% 42.92/27.92 inference(tautology,[status(thm)],[])).
% 42.92/27.92 tff(367,plain,
% 42.92/27.92 (~((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))) | (lazy_impl(prop(P!6), P!6) = not1(false)))),
% 42.92/27.92 inference(unit_resolution,[status(thm)],[366, 365, 345])).
% 42.92/27.92 tff(368,plain,
% 42.92/27.92 (((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))) | (lazy_impl(prop(P!6), P!6) = not1(false))) | (~(lazy_impl(prop(P!6), P!6) = not1(false)))),
% 42.92/27.92 inference(tautology,[status(thm)],[])).
% 42.92/27.92 tff(369,plain,
% 42.92/27.92 (~(lazy_impl(prop(P!6), P!6) = not1(false))),
% 42.92/27.92 inference(unit_resolution,[status(thm)],[368, 367])).
% 42.92/27.92 tff(370,plain,
% 42.92/27.92 ($false),
% 42.92/27.92 inference(unit_resolution,[status(thm)],[369, 322])).
% 42.92/27.92 tff(371,plain,(~(P!6 = not1(false))), inference(lemma,lemma(discharge,[]))).
% 42.92/27.92 tff(372,plain,
% 42.92/27.92 (^[B: $i] : refl((lazy_impl(false, B) = not1(false)) <=> (lazy_impl(false, B) = not1(false)))),
% 42.92/27.92 inference(bind,[status(th)],[])).
% 42.92/27.92 tff(373,plain,
% 42.92/27.92 (![B: $i] : (lazy_impl(false, B) = not1(false)) <=> ![B: $i] : (lazy_impl(false, B) = not1(false))),
% 42.92/27.92 inference(quant_intro,[status(thm)],[372])).
% 42.92/27.92 tff(374,plain,
% 42.92/27.92 (^[B: $i] : rewrite((lazy_impl(false, B) = true) <=> (lazy_impl(false, B) = not1(false)))),
% 42.92/27.92 inference(bind,[status(th)],[])).
% 42.92/27.92 tff(375,plain,
% 42.92/27.92 (![B: $i] : (lazy_impl(false, B) = true) <=> ![B: $i] : (lazy_impl(false, B) = not1(false))),
% 42.92/27.92 inference(quant_intro,[status(thm)],[374])).
% 42.93/27.92 tff(376,plain,
% 42.93/27.92 (![B: $i] : (lazy_impl(false, B) = true) <=> ![B: $i] : (lazy_impl(false, B) = true)),
% 42.93/27.92 inference(rewrite,[status(thm)],[])).
% 42.93/27.92 tff(377,axiom,(![B: $i] : (lazy_impl(false, B) = true)), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','lazy_impl_axiom2')).
% 42.93/27.92 tff(378,plain,
% 42.93/27.92 (![B: $i] : (lazy_impl(false, B) = true)),
% 42.93/27.92 inference(modus_ponens,[status(thm)],[377, 376])).
% 42.93/27.92 tff(379,plain,
% 42.93/27.92 (![B: $i] : (lazy_impl(false, B) = not1(false))),
% 42.93/27.92 inference(modus_ponens,[status(thm)],[378, 375])).
% 42.93/27.92 tff(380,plain,(
% 42.93/27.92 ![B: $i] : (lazy_impl(false, B) = not1(false))),
% 42.93/27.92 inference(skolemize,[status(sab)],[379])).
% 42.93/27.92 tff(381,plain,
% 42.93/27.92 (![B: $i] : (lazy_impl(false, B) = not1(false))),
% 42.93/27.92 inference(modus_ponens,[status(thm)],[380, 373])).
% 42.93/27.92 tff(382,plain,
% 42.93/27.92 ((~![B: $i] : (lazy_impl(false, B) = not1(false))) | (lazy_impl(false, P!6) = not1(false))),
% 42.93/27.92 inference(quant_inst,[status(thm)],[])).
% 42.93/27.92 tff(383,plain,
% 42.93/27.92 (lazy_impl(false, P!6) = not1(false)),
% 42.93/27.92 inference(unit_resolution,[status(thm)],[382, 381])).
% 42.93/27.92 tff(384,assumption,(prop(P!6) = false), introduced(assumption)).
% 42.93/27.92 tff(385,plain,
% 42.93/27.92 (lazy_impl(prop(P!6), P!6) = lazy_impl(false, P!6)),
% 42.93/27.92 inference(monotonicity,[status(thm)],[384])).
% 42.93/27.92 tff(386,plain,
% 42.93/27.92 (lazy_impl(prop(P!6), P!6) = not1(false)),
% 42.93/27.92 inference(transitivity,[status(thm)],[385, 383])).
% 42.93/27.92 tff(387,plain,
% 42.93/27.92 ($false),
% 42.93/27.92 inference(unit_resolution,[status(thm)],[369, 386])).
% 42.93/27.92 tff(388,plain,(~(prop(P!6) = false)), inference(lemma,lemma(discharge,[]))).
% 42.93/27.92 tff(389,plain,
% 42.93/27.92 (^[X: $i] : refl(((prop(X) = false) <=> (~bool(X))) <=> ((prop(X) = false) <=> (~bool(X))))),
% 42.93/27.92 inference(bind,[status(th)],[])).
% 42.93/27.92 tff(390,plain,
% 42.93/27.92 (![X: $i] : ((prop(X) = false) <=> (~bool(X))) <=> ![X: $i] : ((prop(X) = false) <=> (~bool(X)))),
% 42.93/27.92 inference(quant_intro,[status(thm)],[389])).
% 42.93/27.92 tff(391,plain,
% 42.93/27.92 (![X: $i] : ((prop(X) = false) <=> (~bool(X))) <=> ![X: $i] : ((prop(X) = false) <=> (~bool(X)))),
% 42.93/27.92 inference(rewrite,[status(thm)],[])).
% 42.93/27.92 tff(392,axiom,(![X: $i] : ((prop(X) = false) <=> (~bool(X)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','prop_false')).
% 42.93/27.92 tff(393,plain,
% 42.93/27.92 (![X: $i] : ((prop(X) = false) <=> (~bool(X)))),
% 42.93/27.92 inference(modus_ponens,[status(thm)],[392, 391])).
% 42.93/27.92 tff(394,plain,(
% 42.93/27.92 ![X: $i] : ((prop(X) = false) <=> (~bool(X)))),
% 42.93/27.92 inference(skolemize,[status(sab)],[393])).
% 42.93/27.92 tff(395,plain,
% 42.93/27.92 (![X: $i] : ((prop(X) = false) <=> (~bool(X)))),
% 42.93/27.92 inference(modus_ponens,[status(thm)],[394, 390])).
% 42.93/27.92 tff(396,plain,
% 42.93/27.92 ((~![X: $i] : ((prop(X) = false) <=> (~bool(X)))) | ((prop(P!6) = false) <=> (~bool(P!6)))),
% 42.93/27.92 inference(quant_inst,[status(thm)],[])).
% 42.93/27.92 tff(397,plain,
% 42.93/27.92 ((prop(P!6) = false) <=> (~bool(P!6))),
% 42.93/27.92 inference(unit_resolution,[status(thm)],[396, 395])).
% 42.93/27.92 tff(398,plain,
% 42.93/27.92 ((~((prop(P!6) = false) <=> (~bool(P!6)))) | (prop(P!6) = false) | bool(P!6)),
% 42.93/27.92 inference(tautology,[status(thm)],[])).
% 42.93/27.92 tff(399,plain,
% 42.93/27.92 ((prop(P!6) = false) | bool(P!6)),
% 42.93/27.92 inference(unit_resolution,[status(thm)],[398, 397])).
% 42.93/27.92 tff(400,plain,
% 42.93/27.92 (bool(P!6)),
% 42.93/27.92 inference(unit_resolution,[status(thm)],[399, 388])).
% 42.93/27.92 tff(401,plain,
% 42.93/27.92 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(P!6) <=> ((P!6 = false) | (P!6 = not1(false))))),
% 42.93/27.92 inference(quant_inst,[status(thm)],[])).
% 42.93/27.92 tff(402,plain,
% 42.93/27.92 (bool(P!6) <=> ((P!6 = false) | (P!6 = not1(false)))),
% 42.93/27.92 inference(unit_resolution,[status(thm)],[401, 218])).
% 42.93/27.92 tff(403,plain,
% 42.93/27.92 ((~(bool(P!6) <=> ((P!6 = false) | (P!6 = not1(false))))) | (~bool(P!6)) | ((P!6 = false) | (P!6 = not1(false)))),
% 42.93/27.92 inference(tautology,[status(thm)],[])).
% 42.93/27.92 tff(404,plain,
% 42.93/27.92 ((~bool(P!6)) | ((P!6 = false) | (P!6 = not1(false)))),
% 42.93/27.92 inference(unit_resolution,[status(thm)],[403, 402])).
% 42.93/27.92 tff(405,plain,
% 42.93/27.92 ((P!6 = false) | (P!6 = not1(false))),
% 42.93/27.92 inference(unit_resolution,[status(thm)],[404, 400])).
% 42.93/27.92 tff(406,plain,
% 42.93/27.92 ((~((P!6 = false) | (P!6 = not1(false)))) | (P!6 = false) | (P!6 = not1(false))),
% 42.93/27.92 inference(tautology,[status(thm)],[])).
% 42.93/27.92 tff(407,plain,
% 42.93/27.92 ((P!6 = false) | (P!6 = not1(false))),
% 42.93/27.92 inference(unit_resolution,[status(thm)],[406, 405])).
% 42.93/27.92 tff(408,plain,
% 42.93/27.92 (P!6 = false),
% 42.93/27.92 inference(unit_resolution,[status(thm)],[407, 371])).
% 42.93/27.92 tff(409,plain,
% 42.93/27.92 (f7(P!6) = f7(false)),
% 42.93/27.92 inference(monotonicity,[status(thm)],[408])).
% 42.93/27.92 tff(410,plain,
% 42.93/27.92 (f7(P!6) = false),
% 42.93/27.92 inference(transitivity,[status(thm)],[409, 314, 312, 35, 23])).
% 42.93/27.92 tff(411,plain,
% 42.93/27.92 (d(f7(P!6)) <=> d(false)),
% 42.93/27.92 inference(monotonicity,[status(thm)],[410])).
% 42.93/27.92 tff(412,plain,
% 42.93/27.92 (d(false) <=> d(f7(P!6))),
% 42.93/27.92 inference(symmetry,[status(thm)],[411])).
% 42.93/27.92 tff(413,plain,
% 42.93/27.92 (d(false) <=> d(lazy_impl(prop(P!6), P!6))),
% 42.93/27.92 inference(transitivity,[status(thm)],[412, 311])).
% 42.93/27.92 tff(414,plain,
% 42.93/27.92 (d(lazy_impl(prop(P!6), P!6))),
% 42.93/27.92 inference(modus_ponens,[status(thm)],[5, 413])).
% 42.93/27.92 tff(415,plain,
% 42.93/27.92 (((~![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)))))))),
% 42.93/27.92 inference(rewrite,[status(thm)],[])).
% 42.93/27.92 tff(416,plain,
% 42.93/27.92 ((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))))))),
% 42.93/27.92 inference(rewrite,[status(thm)],[])).
% 42.93/27.92 tff(417,plain,
% 42.93/27.92 (((~![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)))))))),
% 42.93/27.92 inference(monotonicity,[status(thm)],[416])).
% 42.93/27.92 tff(418,plain,
% 42.93/27.92 (((~![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)))))))),
% 42.93/27.93 inference(transitivity,[status(thm)],[417, 415])).
% 42.93/27.93 tff(419,plain,
% 42.93/27.93 ((~![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)))))))),
% 42.93/27.93 inference(quant_inst,[status(thm)],[])).
% 42.93/27.93 tff(420,plain,
% 42.93/27.93 ((~![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))))))),
% 42.93/27.93 inference(modus_ponens,[status(thm)],[419, 418])).
% 42.93/27.93 tff(421,plain,
% 42.93/27.93 (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)))))),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[420, 338])).
% 42.93/27.93 tff(422,plain,
% 42.93/27.93 ((~![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)))),
% 42.93/27.93 inference(quant_inst,[status(thm)],[])).
% 42.93/27.93 tff(423,plain,
% 42.93/27.93 (f7(tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[422, 306])).
% 42.93/27.93 tff(424,plain,
% 42.93/27.93 (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = f7(tptp_fun_R_5(P!7))),
% 42.93/27.93 inference(symmetry,[status(thm)],[423])).
% 42.93/27.93 tff(425,plain,
% 42.93/27.93 (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))),
% 42.93/27.93 inference(monotonicity,[status(thm)],[424, 309])).
% 42.93/27.93 tff(426,plain,
% 42.93/27.93 (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))),
% 42.93/27.93 inference(symmetry,[status(thm)],[425])).
% 42.93/27.93 tff(427,plain,
% 42.93/27.93 ((~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)))),
% 42.93/27.93 inference(monotonicity,[status(thm)],[426])).
% 42.93/27.93 tff(428,plain,
% 42.93/27.93 ((~![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))) | (~forallprefers(f7(tptp_fun_R_5(P!7)), f7(P!6)))),
% 42.93/27.93 inference(quant_inst,[status(thm)],[])).
% 42.93/27.93 tff(429,plain,
% 42.93/27.93 (~forallprefers(f7(tptp_fun_R_5(P!7)), f7(P!6))),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[428, 362])).
% 42.93/27.93 tff(430,plain,
% 42.93/27.93 (~forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6))),
% 42.93/27.93 inference(modus_ponens,[status(thm)],[429, 427])).
% 42.93/27.93 tff(431,plain,
% 42.93/27.93 ((~(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))))))),
% 42.93/27.93 inference(tautology,[status(thm)],[])).
% 42.93/27.93 tff(432,plain,
% 42.93/27.93 (~((~(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)))))),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[431, 430, 421])).
% 42.93/27.93 tff(433,plain,
% 42.93/27.93 (((~(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))))),
% 42.93/27.93 inference(tautology,[status(thm)],[])).
% 42.93/27.93 tff(434,plain,
% 42.93/27.93 (d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6)))),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[433, 432])).
% 42.93/27.93 tff(435,plain,
% 42.93/27.93 ((~(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)))),
% 42.93/27.93 inference(tautology,[status(thm)],[])).
% 42.93/27.93 tff(436,plain,
% 42.93/27.93 (d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6)))),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[435, 434])).
% 42.93/27.93 tff(437,plain,
% 42.93/27.93 (d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[436, 414])).
% 42.93/27.93 tff(438,plain,
% 42.93/27.93 ((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))))),
% 42.93/27.93 inference(tautology,[status(thm)],[])).
% 42.93/27.93 tff(439,plain,
% 42.93/27.93 (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))),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[438, 437])).
% 42.93/27.93 tff(440,plain,
% 42.93/27.93 (((~![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)))))),
% 42.93/27.93 inference(rewrite,[status(thm)],[])).
% 42.93/27.93 tff(441,plain,
% 42.93/27.93 ((~![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)))))),
% 42.93/27.93 inference(quant_inst,[status(thm)],[])).
% 42.93/27.93 tff(442,plain,
% 42.93/27.93 ((~![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))))),
% 42.93/27.93 inference(modus_ponens,[status(thm)],[441, 440])).
% 42.93/27.93 tff(443,plain,
% 42.93/27.93 (~((~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)))))),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[442, 17, 439])).
% 42.93/27.93 tff(444,plain,
% 42.93/27.93 (((~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)))),
% 42.93/27.93 inference(tautology,[status(thm)],[])).
% 42.93/27.93 tff(445,plain,
% 42.93/27.93 (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))),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[444, 443])).
% 42.93/27.93 tff(446,assumption,(~bool(exists2(P!7))), introduced(assumption)).
% 42.93/27.93 tff(447,plain,
% 42.93/27.93 ((~![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))),
% 42.93/27.93 inference(quant_inst,[status(thm)],[])).
% 42.93/27.93 tff(448,plain,
% 42.93/27.93 (lazy_impl(false, impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = not1(false)),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[447, 381])).
% 42.93/27.93 tff(449,assumption,(prop(tptp_fun_R_5(P!7)) = false), introduced(assumption)).
% 42.93/27.93 tff(450,plain,
% 42.93/27.93 (lazy_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)))),
% 42.93/27.93 inference(monotonicity,[status(thm)],[449])).
% 42.93/27.93 tff(451,plain,
% 42.93/27.93 ((~![P: $i, R: $i] : (f6(P, R) = lazy_impl(prop(R), impl(f5(P, R), R)))) | (f6(P!7, tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 42.93/27.93 inference(quant_inst,[status(thm)],[])).
% 42.93/27.93 tff(452,plain,
% 42.93/27.93 (f6(P!7, tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[451, 271])).
% 42.93/27.93 tff(453,plain,
% 42.93/27.93 (f6(P!7, tptp_fun_R_5(P!7)) = not1(false)),
% 42.93/27.93 inference(transitivity,[status(thm)],[452, 450, 448])).
% 42.93/27.93 tff(454,plain,
% 42.93/27.93 (phi(f6(P!7, tptp_fun_R_5(P!7))) = phi(not1(false))),
% 42.93/27.93 inference(monotonicity,[status(thm)],[453])).
% 42.93/27.93 tff(455,plain,
% 42.93/27.93 (exists2(P!7) = not1(false)),
% 42.93/27.93 inference(transitivity,[status(thm)],[294, 454, 142])).
% 42.93/27.93 tff(456,plain,
% 42.93/27.93 (bool(exists2(P!7)) <=> bool(not1(false))),
% 42.93/27.93 inference(monotonicity,[status(thm)],[455])).
% 42.93/27.93 tff(457,plain,
% 42.93/27.93 (bool(not1(false)) <=> bool(exists2(P!7))),
% 42.93/27.93 inference(symmetry,[status(thm)],[456])).
% 42.93/27.93 tff(458,plain,
% 42.93/27.93 (bool(exists2(P!7))),
% 42.93/27.93 inference(modus_ponens,[status(thm)],[157, 457])).
% 42.93/27.93 tff(459,plain,
% 42.93/27.93 ($false),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[446, 458])).
% 42.93/27.93 tff(460,plain,((~(prop(tptp_fun_R_5(P!7)) = false)) | bool(exists2(P!7))), inference(lemma,lemma(discharge,[]))).
% 42.93/27.93 tff(461,plain,
% 42.93/27.93 (~(prop(tptp_fun_R_5(P!7)) = false)),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[460, 446])).
% 42.93/27.93 tff(462,plain,
% 42.93/27.93 ((~![X: $i] : ((prop(X) = false) <=> (~bool(X)))) | ((prop(tptp_fun_R_5(P!7)) = false) <=> (~bool(tptp_fun_R_5(P!7))))),
% 42.93/27.93 inference(quant_inst,[status(thm)],[])).
% 42.93/27.93 tff(463,plain,
% 42.93/27.93 ((prop(tptp_fun_R_5(P!7)) = false) <=> (~bool(tptp_fun_R_5(P!7)))),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[462, 395])).
% 42.93/27.93 tff(464,plain,
% 42.93/27.93 ((~((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))),
% 42.93/27.93 inference(tautology,[status(thm)],[])).
% 42.93/27.93 tff(465,plain,
% 42.93/27.93 ((prop(tptp_fun_R_5(P!7)) = false) | bool(tptp_fun_R_5(P!7))),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[464, 463])).
% 42.93/27.93 tff(466,plain,
% 42.93/27.93 (bool(tptp_fun_R_5(P!7))),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[465, 461])).
% 42.93/27.93 tff(467,plain,
% 42.93/27.93 (((~![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)))),
% 42.93/27.93 inference(rewrite,[status(thm)],[])).
% 42.93/27.93 tff(468,plain,
% 42.93/27.93 ((~![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)))),
% 42.93/27.93 inference(quant_inst,[status(thm)],[])).
% 42.93/27.93 tff(469,plain,
% 42.93/27.93 ((~![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))),
% 42.93/27.93 inference(modus_ponens,[status(thm)],[468, 467])).
% 42.93/27.93 tff(470,plain,
% 42.93/27.93 ((~bool(tptp_fun_R_5(P!7))) | (impl(not1(false), tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[469, 91])).
% 42.93/27.93 tff(471,plain,
% 42.93/27.93 (impl(not1(false), tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[470, 466])).
% 42.93/27.93 tff(472,plain,
% 42.93/27.93 (lazy_impl(not1(false), impl(not1(false), false)) = lazy_impl(not1(false), false)),
% 42.93/27.93 inference(monotonicity,[status(thm)],[95])).
% 42.93/27.93 tff(473,plain,
% 42.93/27.93 (lazy_impl(not1(false), impl(not1(false), false)) = false),
% 42.93/27.93 inference(transitivity,[status(thm)],[472, 35, 23])).
% 42.93/27.93 tff(474,plain,
% 42.93/27.93 (impl(lazy_impl(not1(false), impl(not1(false), false)), false) = impl(false, false)),
% 42.93/27.93 inference(monotonicity,[status(thm)],[473])).
% 42.93/27.93 tff(475,plain,
% 42.93/27.93 (impl(lazy_impl(not1(false), impl(not1(false), false)), false) = not1(false)),
% 42.93/27.93 inference(transitivity,[status(thm)],[474, 78])).
% 42.93/27.93 tff(476,plain,
% 42.93/27.93 (lazy_impl(prop(false), impl(lazy_impl(not1(false), impl(not1(false), false)), false)) = lazy_impl(not1(false), not1(false))),
% 42.93/27.93 inference(monotonicity,[status(thm)],[116, 475])).
% 42.93/27.93 tff(477,plain,
% 42.93/27.93 (^[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))))),
% 42.93/27.93 inference(bind,[status(th)],[])).
% 42.93/27.93 tff(478,plain,
% 42.93/27.93 (![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)))),
% 42.93/27.93 inference(quant_intro,[status(thm)],[477])).
% 42.93/27.93 tff(479,plain,
% 42.93/27.93 (![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)))),
% 42.93/27.93 inference(rewrite,[status(thm)],[])).
% 42.93/27.93 tff(480,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')).
% 42.93/27.93 tff(481,plain,
% 42.93/27.93 (![P: $i, Q: $i, R: $i] : (f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R)))),
% 42.93/27.93 inference(modus_ponens,[status(thm)],[480, 479])).
% 42.93/27.93 tff(482,plain,(
% 42.93/27.93 ![P: $i, Q: $i, R: $i] : (f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R)))),
% 42.93/27.93 inference(skolemize,[status(sab)],[481])).
% 42.93/27.93 tff(483,plain,
% 42.93/27.93 (![P: $i, Q: $i, R: $i] : (f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R)))),
% 42.93/27.93 inference(modus_ponens,[status(thm)],[482, 478])).
% 42.93/27.93 tff(484,plain,
% 42.93/27.93 ((~![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)))),
% 42.93/27.93 inference(quant_inst,[status(thm)],[])).
% 42.93/27.93 tff(485,plain,
% 42.93/27.93 (f2(not1(false), not1(false), false) = lazy_impl(prop(false), impl(lazy_impl(not1(false), impl(not1(false), false)), false))),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[484, 483])).
% 42.93/27.93 tff(486,plain,
% 42.93/27.93 ((~![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))))),
% 42.93/27.93 inference(quant_inst,[status(thm)],[])).
% 42.93/27.93 tff(487,plain,
% 42.93/27.93 (bool(tptp_fun_R_5(P!7)) <=> ((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = not1(false)))),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[486, 218])).
% 42.93/27.93 tff(488,plain,
% 42.93/27.93 ((~(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)))),
% 42.93/27.93 inference(tautology,[status(thm)],[])).
% 42.93/27.93 tff(489,plain,
% 42.93/27.93 ((~bool(tptp_fun_R_5(P!7))) | ((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = not1(false)))),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[488, 487])).
% 42.93/27.93 tff(490,plain,
% 42.93/27.93 ((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = not1(false))),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[489, 466])).
% 42.93/27.93 tff(491,plain,
% 42.93/27.93 ((~![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))))),
% 42.93/27.93 inference(quant_inst,[status(thm)],[])).
% 42.93/27.93 tff(492,plain,
% 42.93/27.93 (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)))),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[491, 218])).
% 42.93/27.93 tff(493,plain,
% 42.93/27.93 ((~![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))))),
% 42.93/27.93 inference(quant_inst,[status(thm)],[])).
% 42.93/27.93 tff(494,plain,
% 42.93/27.93 (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)))),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[493, 218])).
% 42.93/27.93 tff(495,plain,
% 42.93/27.93 (^[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))))))))),
% 42.93/27.93 inference(bind,[status(th)],[])).
% 42.93/27.93 tff(496,plain,
% 42.93/27.93 (![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)))))))),
% 42.93/27.93 inference(quant_intro,[status(thm)],[495])).
% 42.93/27.93 tff(497,plain,
% 42.93/27.93 (^[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))))))))),
% 42.93/27.93 inference(bind,[status(th)],[])).
% 42.93/27.93 tff(498,plain,
% 42.93/27.93 (![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)))))))),
% 42.93/27.93 inference(quant_intro,[status(thm)],[497])).
% 42.93/27.93 tff(499,plain,
% 42.93/27.93 (![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)))))))),
% 42.93/27.93 inference(transitivity,[status(thm)],[498, 496])).
% 42.93/27.93 tff(500,plain,
% 42.93/27.93 (^[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))))))))),
% 42.93/27.93 inference(bind,[status(th)],[])).
% 42.93/27.93 tff(501,plain,
% 42.93/27.93 (![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)))))))),
% 42.93/27.93 inference(quant_intro,[status(thm)],[500])).
% 42.93/27.93 tff(502,plain,
% 42.93/27.93 (![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))))),
% 42.93/27.93 inference(rewrite,[status(thm)],[])).
% 42.93/27.93 tff(503,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')).
% 42.93/27.93 tff(504,plain,
% 42.93/27.93 (![P: $i] : ?[X: $i] : ((exists1(P) = phi(apply(P, X))) & (~?[X1: $i] : existsprefers(apply(P, X1), apply(P, X))))),
% 42.93/27.93 inference(modus_ponens,[status(thm)],[503, 502])).
% 42.93/27.93 tff(505,plain,(
% 42.93/27.93 ![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)))))),
% 42.93/27.93 inference(skolemize,[status(sab)],[504])).
% 42.93/27.93 tff(506,plain,
% 42.93/27.93 (![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)))))))),
% 42.93/27.93 inference(modus_ponens,[status(thm)],[505, 501])).
% 42.93/27.93 tff(507,plain,
% 42.93/27.93 (![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)))))))),
% 42.93/27.93 inference(modus_ponens,[status(thm)],[506, 499])).
% 42.93/27.93 tff(508,plain,
% 42.93/27.93 ((~![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)))))))),
% 42.93/27.93 inference(quant_inst,[status(thm)],[])).
% 42.93/27.93 tff(509,plain,
% 42.93/27.93 (~((~(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))))))),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[508, 507])).
% 42.93/27.93 tff(510,plain,
% 42.93/27.93 (((~(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))))),
% 42.93/27.93 inference(tautology,[status(thm)],[])).
% 42.93/27.93 tff(511,plain,
% 42.93/27.93 (exists1(P!7) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[510, 509])).
% 42.93/27.93 tff(512,plain,
% 42.93/27.93 (phi(apply(P!7, tptp_fun_X_3(P!7))) = exists1(P!7)),
% 42.93/27.93 inference(symmetry,[status(thm)],[511])).
% 42.93/27.93 tff(513,plain,
% 42.93/27.93 (bool(phi(apply(P!7, tptp_fun_X_3(P!7)))) <=> bool(exists1(P!7))),
% 42.93/27.93 inference(monotonicity,[status(thm)],[512])).
% 42.93/27.93 tff(514,plain,
% 42.93/27.93 (bool(exists1(P!7)) <=> bool(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 42.93/27.93 inference(symmetry,[status(thm)],[513])).
% 42.93/27.93 tff(515,plain,
% 42.93/27.93 ((~![P: $i] : ((~(bool(exists1(P)) | bool(exists2(P)))) | (exists1(P) = exists2(P)))) <=> (~![P: $i] : ((~(bool(exists1(P)) | bool(exists2(P)))) | (exists1(P) = exists2(P))))),
% 42.93/27.93 inference(rewrite,[status(thm)],[])).
% 42.93/27.93 tff(516,plain,
% 42.93/27.93 ((~![P: $i] : ((bool(exists1(P)) | bool(exists2(P))) => (exists1(P) = exists2(P)))) <=> (~![P: $i] : ((~(bool(exists1(P)) | bool(exists2(P)))) | (exists1(P) = exists2(P))))),
% 42.93/27.93 inference(rewrite,[status(thm)],[])).
% 42.93/27.93 tff(517,axiom,(~![P: $i] : ((bool(exists1(P)) | bool(exists2(P))) => (exists1(P) = exists2(P)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','exists1_exists2')).
% 42.93/27.93 tff(518,plain,
% 42.93/27.93 (~![P: $i] : ((~(bool(exists1(P)) | bool(exists2(P)))) | (exists1(P) = exists2(P)))),
% 42.93/27.93 inference(modus_ponens,[status(thm)],[517, 516])).
% 42.93/27.93 tff(519,plain,
% 42.93/27.93 (~![P: $i] : ((~(bool(exists1(P)) | bool(exists2(P)))) | (exists1(P) = exists2(P)))),
% 42.93/27.93 inference(modus_ponens,[status(thm)],[518, 515])).
% 42.93/27.93 tff(520,plain,
% 42.93/27.93 (~![P: $i] : ((~(bool(exists1(P)) | bool(exists2(P)))) | (exists1(P) = exists2(P)))),
% 42.93/27.93 inference(modus_ponens,[status(thm)],[519, 515])).
% 42.93/27.93 tff(521,plain,
% 42.93/27.93 (~![P: $i] : ((~(bool(exists1(P)) | bool(exists2(P)))) | (exists1(P) = exists2(P)))),
% 42.93/27.93 inference(modus_ponens,[status(thm)],[520, 515])).
% 42.93/27.93 tff(522,plain,
% 42.93/27.93 (~![P: $i] : ((~(bool(exists1(P)) | bool(exists2(P)))) | (exists1(P) = exists2(P)))),
% 42.93/27.93 inference(modus_ponens,[status(thm)],[521, 515])).
% 42.93/27.93 tff(523,plain,
% 42.93/27.93 (~![P: $i] : ((~(bool(exists1(P)) | bool(exists2(P)))) | (exists1(P) = exists2(P)))),
% 42.93/27.93 inference(modus_ponens,[status(thm)],[522, 515])).
% 42.93/27.93 tff(524,plain,
% 42.93/27.93 (~![P: $i] : ((~(bool(exists1(P)) | bool(exists2(P)))) | (exists1(P) = exists2(P)))),
% 42.93/27.93 inference(modus_ponens,[status(thm)],[523, 515])).
% 42.93/27.93 tff(525,plain,
% 42.93/27.93 (~![P: $i] : ((~(bool(exists1(P)) | bool(exists2(P)))) | (exists1(P) = exists2(P)))),
% 42.93/27.93 inference(modus_ponens,[status(thm)],[524, 515])).
% 42.93/27.93 tff(526,plain,(
% 42.93/27.93 ~((~(bool(exists1(P!7)) | bool(exists2(P!7)))) | (exists1(P!7) = exists2(P!7)))),
% 42.93/27.93 inference(skolemize,[status(sab)],[525])).
% 42.93/27.93 tff(527,plain,
% 42.93/27.93 (bool(exists1(P!7)) | bool(exists2(P!7))),
% 42.93/27.93 inference(or_elim,[status(thm)],[526])).
% 42.93/27.93 tff(528,plain,
% 42.93/27.93 (bool(exists1(P!7))),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[527, 446])).
% 42.93/27.93 tff(529,plain,
% 42.93/27.93 (bool(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 42.93/27.93 inference(modus_ponens,[status(thm)],[528, 514])).
% 42.93/27.93 tff(530,plain,
% 42.93/27.93 ((~(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)))),
% 42.93/27.93 inference(tautology,[status(thm)],[])).
% 42.93/27.93 tff(531,plain,
% 42.93/27.93 ((phi(apply(P!7, tptp_fun_X_3(P!7))) = false) | (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[530, 529, 494])).
% 42.93/27.93 tff(532,assumption,((phi(apply(P!7, tptp_fun_X_3(P!7))) = false) | (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))), introduced(assumption)).
% 42.93/27.93 tff(533,assumption,(phi(apply(P!7, tptp_fun_X_3(P!7))) = err), introduced(assumption)).
% 42.93/27.93 tff(534,plain,
% 42.93/27.93 ((phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)) <=> (err = not1(false))),
% 42.93/27.93 inference(monotonicity,[status(thm)],[533])).
% 42.93/27.93 tff(535,plain,
% 42.93/27.93 ((phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)) <=> (not1(false) = err)),
% 42.93/27.93 inference(transitivity,[status(thm)],[534, 228])).
% 42.93/27.93 tff(536,plain,
% 42.93/27.93 ((not1(false) = err) <=> (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))),
% 42.93/27.93 inference(symmetry,[status(thm)],[535])).
% 42.93/27.93 tff(537,plain,
% 42.93/27.93 ((~(not1(false) = err)) <=> (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)))),
% 42.93/27.93 inference(monotonicity,[status(thm)],[536])).
% 42.93/27.93 tff(538,plain,
% 42.93/27.93 (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))),
% 42.93/27.93 inference(modus_ponens,[status(thm)],[235, 537])).
% 42.93/27.93 tff(539,plain,
% 42.93/27.93 ((phi(apply(P!7, tptp_fun_X_3(P!7))) = false) <=> (err = false)),
% 42.93/27.93 inference(monotonicity,[status(thm)],[533])).
% 42.93/27.93 tff(540,plain,
% 42.93/27.93 ((phi(apply(P!7, tptp_fun_X_3(P!7))) = false) <=> (false = err)),
% 42.93/27.93 inference(transitivity,[status(thm)],[539, 221])).
% 42.93/27.93 tff(541,plain,
% 42.93/27.93 ((false = err) <=> (phi(apply(P!7, tptp_fun_X_3(P!7))) = false)),
% 42.93/27.93 inference(symmetry,[status(thm)],[540])).
% 42.93/27.93 tff(542,plain,
% 42.93/27.93 ((~(false = err)) <=> (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = false))),
% 42.93/27.93 inference(monotonicity,[status(thm)],[541])).
% 42.93/27.93 tff(543,plain,
% 42.93/27.93 (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = false)),
% 42.93/27.93 inference(modus_ponens,[status(thm)],[226, 542])).
% 42.93/27.93 tff(544,plain,
% 42.93/27.93 ((~((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))),
% 42.93/27.93 inference(tautology,[status(thm)],[])).
% 42.93/27.93 tff(545,plain,
% 42.93/27.93 ($false),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[544, 543, 538, 532])).
% 42.93/27.93 tff(546,plain,((~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err)) | (~((phi(apply(P!7, tptp_fun_X_3(P!7))) = false) | (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))))), inference(lemma,lemma(discharge,[]))).
% 42.93/27.93 tff(547,plain,
% 42.93/27.93 (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err)),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[546, 531])).
% 42.93/27.93 tff(548,plain,
% 42.93/27.93 ((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)),
% 42.93/27.93 inference(tautology,[status(thm)],[])).
% 42.93/27.93 tff(549,plain,
% 42.93/27.93 (d(apply(P!7, tptp_fun_X_3(P!7))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err))),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[548, 547])).
% 42.93/27.93 tff(550,plain,
% 42.93/27.93 (((~![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)))))),
% 42.93/27.93 inference(rewrite,[status(thm)],[])).
% 42.93/27.93 tff(551,plain,
% 42.93/27.93 ((~![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)))))),
% 42.93/27.93 inference(quant_inst,[status(thm)],[])).
% 42.93/27.93 tff(552,plain,
% 42.93/27.93 ((~![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))))),
% 42.93/27.93 inference(modus_ponens,[status(thm)],[551, 550])).
% 42.93/27.93 tff(553,plain,
% 42.93/27.93 ((~((~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))))),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[552, 17])).
% 42.93/27.93 tff(554,plain,
% 42.93/27.93 (~((~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)))))),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[553, 549])).
% 42.93/27.93 tff(555,plain,
% 42.93/27.93 (((~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)))),
% 42.93/27.93 inference(tautology,[status(thm)],[])).
% 42.93/27.93 tff(556,plain,
% 42.93/27.93 (d(apply(P!7, tptp_fun_X_3(P!7)))),
% 42.93/27.93 inference(unit_resolution,[status(thm)],[555, 554])).
% 42.93/27.93 tff(557,plain,
% 42.93/27.93 (^[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)))))))),
% 42.93/27.94 inference(bind,[status(th)],[])).
% 42.93/27.94 tff(558,plain,
% 42.93/27.94 (![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))))))),
% 42.93/27.94 inference(quant_intro,[status(thm)],[557])).
% 42.93/27.94 tff(559,plain,
% 42.93/27.94 (^[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)))))))),
% 42.93/27.94 inference(bind,[status(th)],[])).
% 42.93/27.94 tff(560,plain,
% 42.93/27.94 (![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))))))),
% 42.93/27.94 inference(quant_intro,[status(thm)],[559])).
% 42.93/27.94 tff(561,plain,
% 42.93/27.94 (^[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)))))),
% 42.93/27.94 inference(bind,[status(th)],[])).
% 42.93/27.94 tff(562,plain,
% 42.93/27.94 (![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))))),
% 42.93/27.94 inference(quant_intro,[status(thm)],[561])).
% 42.93/27.94 tff(563,plain,
% 42.93/27.94 (![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))))),
% 42.93/27.94 inference(rewrite,[status(thm)],[])).
% 42.93/27.94 tff(564,plain,
% 42.93/27.94 (^[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)))))),
% 42.93/27.94 inference(bind,[status(th)],[])).
% 42.93/27.94 tff(565,plain,
% 42.93/27.94 (![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))))),
% 42.93/27.94 inference(quant_intro,[status(thm)],[564])).
% 42.93/27.94 tff(566,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')).
% 42.93/27.94 tff(567,plain,
% 42.93/27.94 (![X: $i, Y: $i] : (existsprefers(X, Y) <=> (((~d(X)) & d(Y)) | ((X = true) & (Y = false)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 42.93/27.94 inference(modus_ponens,[status(thm)],[566, 565])).
% 42.93/27.94 tff(568,plain,
% 42.93/27.94 (![X: $i, Y: $i] : (existsprefers(X, Y) <=> (((~d(X)) & d(Y)) | ((X = true) & (Y = false)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 42.93/27.94 inference(modus_ponens,[status(thm)],[567, 563])).
% 42.93/27.94 tff(569,plain,
% 42.93/27.94 (![X: $i, Y: $i] : (existsprefers(X, Y) <=> (((~d(X)) & d(Y)) | ((X = not1(false)) & (Y = false)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 42.93/27.94 inference(modus_ponens,[status(thm)],[568, 562])).
% 42.93/27.94 tff(570,plain,(
% 42.93/27.94 ![X: $i, Y: $i] : (existsprefers(X, Y) <=> (((~d(X)) & d(Y)) | ((X = not1(false)) & (Y = false)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 42.93/27.94 inference(skolemize,[status(sab)],[569])).
% 42.93/27.94 tff(571,plain,
% 42.93/27.94 (![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = not1(false))) | (~(Y = false))))))),
% 42.93/27.94 inference(modus_ponens,[status(thm)],[570, 560])).
% 42.93/27.94 tff(572,plain,
% 42.93/27.94 (![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = not1(false))) | (~(Y = false))))))),
% 42.93/27.94 inference(modus_ponens,[status(thm)],[571, 558])).
% 42.93/27.94 tff(573,plain,
% 42.93/27.94 (((~![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))))))))),
% 42.93/27.94 inference(rewrite,[status(thm)],[])).
% 42.93/27.94 tff(574,plain,
% 42.93/27.94 ((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)))))))),
% 42.93/27.94 inference(rewrite,[status(thm)],[])).
% 42.93/27.94 tff(575,plain,
% 42.93/27.94 (((~![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))))))))),
% 42.93/27.94 inference(monotonicity,[status(thm)],[574])).
% 42.93/27.94 tff(576,plain,
% 42.93/27.94 (((~![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))))))))),
% 42.93/27.94 inference(transitivity,[status(thm)],[575, 573])).
% 42.93/27.94 tff(577,plain,
% 42.93/27.94 ((~![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))))))),
% 42.93/27.94 inference(quant_inst,[status(thm)],[])).
% 42.93/27.94 tff(578,plain,
% 42.93/27.94 ((~![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)))))))),
% 42.93/27.94 inference(modus_ponens,[status(thm)],[577, 576])).
% 42.93/27.94 tff(579,plain,
% 42.93/27.94 (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))))))),
% 42.93/27.94 inference(unit_resolution,[status(thm)],[578, 572])).
% 42.93/27.94 tff(580,plain,
% 42.93/27.94 (((~(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))))),
% 42.93/27.94 inference(tautology,[status(thm)],[])).
% 42.93/27.94 tff(581,plain,
% 42.93/27.94 (![X1: $i] : (~existsprefers(apply(P!7, X1), apply(P!7, tptp_fun_X_3(P!7))))),
% 42.93/27.94 inference(unit_resolution,[status(thm)],[580, 509])).
% 42.93/27.94 tff(582,plain,
% 42.93/27.94 ((~![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))))),
% 42.93/27.94 inference(quant_inst,[status(thm)],[])).
% 42.93/27.94 tff(583,plain,
% 42.93/27.94 (~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)))),
% 42.93/27.94 inference(unit_resolution,[status(thm)],[582, 581])).
% 42.93/27.94 tff(584,plain,
% 42.93/27.94 ((~(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)))))))),
% 42.93/27.94 inference(tautology,[status(thm)],[])).
% 42.93/27.94 tff(585,plain,
% 42.93/27.94 ((~(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)))))))),
% 42.93/27.94 inference(unit_resolution,[status(thm)],[584, 583])).
% 42.93/27.94 tff(586,plain,
% 42.93/27.94 (~((~(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))))))),
% 42.93/27.94 inference(unit_resolution,[status(thm)],[585, 579])).
% 42.93/27.94 tff(587,plain,
% 42.93/27.94 (((~(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)))))),
% 42.93/27.94 inference(tautology,[status(thm)],[])).
% 42.93/27.94 tff(588,plain,
% 42.93/27.94 (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))))),
% 42.93/27.94 inference(unit_resolution,[status(thm)],[587, 586])).
% 42.93/27.94 tff(589,plain,
% 42.93/27.94 ((~(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))))),
% 42.93/27.94 inference(tautology,[status(thm)],[])).
% 42.93/27.94 tff(590,plain,
% 42.93/27.94 (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))))),
% 42.93/27.94 inference(unit_resolution,[status(thm)],[589, 588])).
% 42.93/27.94 tff(591,plain,
% 42.93/27.94 (d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 42.93/27.94 inference(unit_resolution,[status(thm)],[590, 556])).
% 42.93/27.94 tff(592,plain,
% 42.93/27.94 (((~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)))),
% 42.93/27.94 inference(tautology,[status(thm)],[])).
% 42.93/27.94 tff(593,plain,
% 42.93/27.94 (phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))),
% 42.93/27.94 inference(unit_resolution,[status(thm)],[592, 554])).
% 42.93/27.94 tff(594,plain,
% 42.93/27.94 (apply(P!7, tptp_fun_X_3(P!7)) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 42.93/27.94 inference(symmetry,[status(thm)],[593])).
% 42.93/27.94 tff(595,plain,
% 42.93/27.94 (apply(P!7, tptp_fun_X_3(P!7)) = exists1(P!7)),
% 42.93/27.94 inference(transitivity,[status(thm)],[594, 512])).
% 42.93/27.94 tff(596,plain,
% 42.93/27.94 (bool(apply(P!7, tptp_fun_X_3(P!7))) <=> bool(exists1(P!7))),
% 42.93/27.94 inference(monotonicity,[status(thm)],[595])).
% 42.93/27.94 tff(597,plain,
% 42.93/27.94 (bool(exists1(P!7)) <=> bool(apply(P!7, tptp_fun_X_3(P!7)))),
% 42.93/27.94 inference(symmetry,[status(thm)],[596])).
% 42.93/27.94 tff(598,plain,
% 42.93/27.94 (bool(apply(P!7, tptp_fun_X_3(P!7)))),
% 42.93/27.94 inference(modus_ponens,[status(thm)],[528, 597])).
% 42.93/27.94 tff(599,plain,
% 42.93/27.94 (((~(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)))))),
% 42.93/27.94 inference(tautology,[status(thm)],[])).
% 42.93/27.94 tff(600,plain,
% 42.93/27.94 ((~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))))),
% 42.93/27.94 inference(unit_resolution,[status(thm)],[599, 586])).
% 42.93/27.94 tff(601,plain,
% 42.93/27.94 ((~((~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))))),
% 42.93/27.94 inference(tautology,[status(thm)],[])).
% 42.93/27.94 tff(602,plain,
% 42.93/27.94 ((~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))))),
% 42.93/27.94 inference(unit_resolution,[status(thm)],[601, 600])).
% 42.93/27.94 tff(603,plain,
% 42.93/27.94 (bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 42.93/27.94 inference(unit_resolution,[status(thm)],[602, 598, 556, 591])).
% 42.93/27.94 tff(604,plain,
% 42.93/27.94 ((~(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)))),
% 42.93/27.94 inference(tautology,[status(thm)],[])).
% 42.93/27.94 tff(605,plain,
% 42.93/27.94 ((~(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)))),
% 42.93/27.94 inference(unit_resolution,[status(thm)],[604, 603])).
% 42.93/27.94 tff(606,plain,
% 42.93/27.94 ((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))),
% 42.93/27.94 inference(unit_resolution,[status(thm)],[605, 492])).
% 42.93/27.94 tff(607,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)).
% 42.93/27.94 tff(608,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)).
% 42.93/27.94 tff(609,plain,
% 42.93/27.94 (((~![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)))),
% 42.93/27.94 inference(rewrite,[status(thm)],[])).
% 42.93/27.94 tff(610,plain,
% 42.93/27.94 ((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | ((~bool(not1(false))) | (impl(not1(false), not1(false)) = not1(false)))),
% 42.93/27.94 inference(quant_inst,[status(thm)],[])).
% 42.93/27.94 tff(611,plain,
% 42.93/27.94 ((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | (~bool(not1(false))) | (impl(not1(false), not1(false)) = not1(false))),
% 42.93/27.94 inference(modus_ponens,[status(thm)],[610, 609])).
% 42.93/27.94 tff(612,plain,
% 42.93/27.94 (impl(not1(false), not1(false)) = not1(false)),
% 42.93/27.94 inference(unit_resolution,[status(thm)],[611, 91, 157])).
% 42.93/27.94 tff(613,assumption,(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false)), introduced(assumption)).
% 42.93/27.94 tff(614,plain,
% 42.93/27.94 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = impl(not1(false), not1(false))),
% 42.93/27.94 inference(monotonicity,[status(thm)],[613, 274])).
% 42.93/27.94 tff(615,plain,
% 42.93/27.94 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)),
% 42.93/27.94 inference(transitivity,[status(thm)],[614, 612])).
% 42.93/27.94 tff(616,plain,
% 42.93/27.94 ($false),
% 42.93/27.94 inference(unit_resolution,[status(thm)],[607, 615])).
% 42.93/27.94 tff(617,plain,((~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), 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)) | (~(tptp_fun_R_5(P!7) = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 42.93/27.94 tff(618,plain,
% 42.93/27.94 (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false))),
% 42.93/27.94 inference(unit_resolution,[status(thm)],[617, 274, 607])).
% 42.93/27.94 tff(619,plain,
% 42.93/27.94 ((~((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))),
% 42.93/27.94 inference(tautology,[status(thm)],[])).
% 42.93/27.94 tff(620,plain,
% 42.93/27.94 (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false),
% 42.93/27.94 inference(unit_resolution,[status(thm)],[619, 618, 608])).
% 42.93/27.94 tff(621,plain,
% 42.93/27.94 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = impl(false, not1(false))),
% 42.93/27.94 inference(monotonicity,[status(thm)],[620, 274])).
% 42.93/27.94 tff(622,plain,
% 42.93/27.94 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)),
% 42.93/27.94 inference(transitivity,[status(thm)],[621, 161])).
% 42.93/27.94 tff(623,plain,
% 42.93/27.94 ($false),
% 42.93/27.94 inference(unit_resolution,[status(thm)],[607, 622])).
% 42.93/27.94 tff(624,plain,((~(tptp_fun_R_5(P!7) = not1(false))) | (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)) | (~((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false))))), inference(lemma,lemma(discharge,[]))).
% 42.93/27.94 tff(625,plain,
% 42.93/27.94 (~(tptp_fun_R_5(P!7) = not1(false))),
% 42.93/27.94 inference(unit_resolution,[status(thm)],[624, 607, 606])).
% 42.93/27.94 tff(626,plain,
% 42.93/27.94 ((~((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = not1(false)))) | (tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = not1(false))),
% 42.93/27.94 inference(tautology,[status(thm)],[])).
% 42.93/27.94 tff(627,plain,
% 42.93/27.94 (tptp_fun_R_5(P!7) = false),
% 42.93/27.94 inference(unit_resolution,[status(thm)],[626, 625, 490])).
% 42.93/27.94 tff(628,assumption,(tptp_fun_R_5(P!7) = false), introduced(assumption)).
% 42.93/27.95 tff(629,assumption,(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false), introduced(assumption)).
% 42.93/27.95 tff(630,plain,
% 42.93/27.95 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = impl(false, false)),
% 42.93/27.95 inference(monotonicity,[status(thm)],[629, 628])).
% 42.93/27.95 tff(631,plain,
% 42.93/27.95 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)),
% 42.93/27.95 inference(transitivity,[status(thm)],[630, 78])).
% 42.93/27.95 tff(632,plain,
% 42.93/27.95 ($false),
% 42.93/27.95 inference(unit_resolution,[status(thm)],[607, 631])).
% 42.93/27.95 tff(633,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)) | (~(tptp_fun_R_5(P!7) = false))), inference(lemma,lemma(discharge,[]))).
% 42.93/27.95 tff(634,plain,
% 42.93/27.95 (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false)),
% 42.93/27.95 inference(unit_resolution,[status(thm)],[633, 627, 607])).
% 42.93/27.95 tff(635,plain,
% 42.93/27.95 (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = not1(false)),
% 42.93/27.95 inference(unit_resolution,[status(thm)],[619, 634, 606])).
% 42.93/27.95 tff(636,plain,
% 42.93/27.95 (f2(not1(false), apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = f2(not1(false), not1(false), false)),
% 42.93/27.95 inference(monotonicity,[status(thm)],[635, 627])).
% 42.93/27.95 tff(637,plain,
% 42.93/27.95 ((~![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(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(lazy_impl(not1(false), impl(apply(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))))),
% 42.93/27.95 inference(quant_inst,[status(thm)],[])).
% 42.93/27.95 tff(638,plain,
% 42.93/27.95 (f2(not1(false), apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(lazy_impl(not1(false), impl(apply(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)))),
% 42.93/27.95 inference(unit_resolution,[status(thm)],[637, 483])).
% 42.93/27.95 tff(639,plain,
% 42.93/27.95 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(lazy_impl(not1(false), impl(apply(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), apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))),
% 42.93/27.95 inference(symmetry,[status(thm)],[638])).
% 42.93/27.95 tff(640,plain,
% 42.93/27.95 ((~![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)))))))),
% 42.93/27.95 inference(quant_inst,[status(thm)],[])).
% 42.93/27.95 tff(641,plain,
% 42.93/27.95 (~((~(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))))))),
% 42.93/27.95 inference(unit_resolution,[status(thm)],[640, 199])).
% 42.93/27.95 tff(642,plain,
% 42.93/27.95 (((~(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))))),
% 42.93/27.95 inference(tautology,[status(thm)],[])).
% 42.93/27.95 tff(643,plain,
% 42.93/27.95 (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)))),
% 42.93/27.95 inference(unit_resolution,[status(thm)],[642, 641])).
% 42.93/27.95 tff(644,plain,
% 42.93/27.95 (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))),
% 42.93/27.95 inference(symmetry,[status(thm)],[643])).
% 42.93/27.95 tff(645,plain,
% 42.93/27.95 ((~![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))))),
% 42.93/27.95 inference(quant_inst,[status(thm)],[])).
% 42.93/27.95 tff(646,plain,
% 42.93/27.95 (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)))),
% 42.93/27.95 inference(unit_resolution,[status(thm)],[645, 33])).
% 42.93/27.95 tff(647,plain,
% 42.93/27.95 ((~![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)))),
% 42.93/27.95 inference(quant_inst,[status(thm)],[])).
% 42.93/27.95 tff(648,plain,
% 42.93/27.95 (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))),
% 42.93/27.95 inference(unit_resolution,[status(thm)],[647, 170])).
% 42.93/27.95 tff(649,plain,
% 42.93/27.95 (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))),
% 42.93/27.95 inference(symmetry,[status(thm)],[648])).
% 42.93/27.95 tff(650,plain,
% 42.93/27.95 (lazy_impl(not1(false), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), 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)))),
% 42.93/27.95 inference(monotonicity,[status(thm)],[649])).
% 42.93/27.95 tff(651,plain,
% 42.93/27.95 (lazy_impl(not1(false), impl(apply(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))),
% 42.93/27.95 inference(transitivity,[status(thm)],[650, 646, 644])).
% 42.93/27.95 tff(652,plain,
% 42.93/27.95 (impl(lazy_impl(not1(false), impl(apply(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))),
% 42.93/27.95 inference(monotonicity,[status(thm)],[651])).
% 42.93/27.95 tff(653,plain,
% 42.93/27.95 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = impl(lazy_impl(not1(false), impl(apply(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))),
% 42.93/27.95 inference(symmetry,[status(thm)],[652])).
% 42.93/27.95 tff(654,plain,
% 42.93/27.95 (lazy_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(lazy_impl(not1(false), impl(apply(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)))),
% 42.93/27.95 inference(monotonicity,[status(thm)],[653])).
% 42.93/27.95 tff(655,plain,
% 42.93/27.95 (f6(P!7, tptp_fun_R_5(P!7)) = not1(false)),
% 42.93/27.95 inference(transitivity,[status(thm)],[452, 654, 639, 636, 485, 476, 316, 142])).
% 42.93/27.95 tff(656,plain,
% 42.93/27.95 (phi(f6(P!7, tptp_fun_R_5(P!7))) = phi(not1(false))),
% 42.93/27.95 inference(monotonicity,[status(thm)],[655])).
% 42.93/27.95 tff(657,plain,
% 42.93/27.95 (exists2(P!7) = not1(false)),
% 42.93/27.95 inference(transitivity,[status(thm)],[294, 656, 142])).
% 42.93/27.95 tff(658,plain,
% 42.93/27.95 (bool(exists2(P!7)) <=> bool(not1(false))),
% 42.93/27.95 inference(monotonicity,[status(thm)],[657])).
% 42.93/27.95 tff(659,plain,
% 42.93/27.95 (bool(not1(false)) <=> bool(exists2(P!7))),
% 42.93/27.95 inference(symmetry,[status(thm)],[658])).
% 42.93/27.95 tff(660,plain,
% 42.93/27.95 (bool(exists2(P!7))),
% 42.93/27.95 inference(modus_ponens,[status(thm)],[157, 659])).
% 42.93/27.95 tff(661,plain,
% 42.93/27.95 ($false),
% 42.93/27.95 inference(unit_resolution,[status(thm)],[446, 660])).
% 42.93/27.95 tff(662,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(exists2(P!7))), inference(lemma,lemma(discharge,[]))).
% 42.93/27.95 tff(663,plain,
% 42.93/27.95 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = not1(false)),
% 42.93/27.95 inference(unit_resolution,[status(thm)],[662, 446])).
% 42.93/27.95 tff(664,plain,
% 42.93/27.95 (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = not1(false)),
% 42.93/27.95 inference(transitivity,[status(thm)],[648, 663])).
% 42.93/27.95 tff(665,plain,
% 42.93/27.95 (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))),
% 42.93/27.95 inference(monotonicity,[status(thm)],[664])).
% 42.93/27.95 tff(666,plain,
% 42.93/27.95 (f5(P!7, tptp_fun_R_5(P!7)) = not1(false)),
% 42.93/27.95 inference(transitivity,[status(thm)],[643, 665, 142])).
% 42.93/27.95 tff(667,plain,
% 42.93/27.95 (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))),
% 42.93/27.95 inference(monotonicity,[status(thm)],[666])).
% 42.93/27.95 tff(668,plain,
% 42.93/27.95 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)),
% 42.93/27.95 inference(transitivity,[status(thm)],[667, 471])).
% 42.93/27.95 tff(669,plain,
% 42.93/27.95 (lazy_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))),
% 42.93/27.95 inference(monotonicity,[status(thm)],[668])).
% 42.93/27.95 tff(670,plain,
% 42.93/27.95 (f6(P!7, tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 42.93/27.95 inference(transitivity,[status(thm)],[452, 669])).
% 42.93/27.95 tff(671,plain,
% 42.93/27.95 (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)))),
% 42.93/27.95 inference(monotonicity,[status(thm)],[670])).
% 42.93/27.95 tff(672,plain,
% 42.93/27.95 (exists2(P!7) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 42.93/27.95 inference(transitivity,[status(thm)],[294, 671, 445])).
% 42.93/27.95 tff(673,plain,
% 42.93/27.95 (bool(exists2(P!7)) <=> bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 42.93/27.95 inference(monotonicity,[status(thm)],[672])).
% 42.93/27.95 tff(674,plain,
% 42.93/27.95 (bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) <=> bool(exists2(P!7))),
% 42.93/27.95 inference(symmetry,[status(thm)],[673])).
% 42.93/27.95 tff(675,plain,
% 42.93/27.95 (bool(lazy_impl(prop(P!6), P!6)) <=> bool(f7(P!6))),
% 42.93/27.95 inference(monotonicity,[status(thm)],[309])).
% 42.93/27.95 tff(676,plain,
% 42.93/27.95 (bool(f7(P!6)) <=> bool(lazy_impl(prop(P!6), P!6))),
% 42.93/27.95 inference(symmetry,[status(thm)],[675])).
% 42.93/27.95 tff(677,plain,
% 42.93/27.95 (bool(f7(P!6)) <=> bool(false)),
% 42.93/27.95 inference(monotonicity,[status(thm)],[410])).
% 42.93/27.95 tff(678,plain,
% 42.93/27.95 (bool(false) <=> bool(f7(P!6))),
% 42.93/27.95 inference(symmetry,[status(thm)],[677])).
% 42.93/27.95 tff(679,plain,
% 42.93/27.95 (bool(false) <=> bool(lazy_impl(prop(P!6), P!6))),
% 42.93/27.95 inference(transitivity,[status(thm)],[678, 676])).
% 42.93/27.95 tff(680,plain,
% 42.93/27.95 (bool(lazy_impl(prop(P!6), P!6))),
% 42.93/27.95 inference(modus_ponens,[status(thm)],[61, 679])).
% 42.93/27.95 tff(681,plain,
% 42.93/27.95 (((~(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)))))),
% 42.93/27.95 inference(tautology,[status(thm)],[])).
% 42.93/27.95 tff(682,plain,
% 42.93/27.95 ((~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))))),
% 42.93/27.95 inference(unit_resolution,[status(thm)],[681, 432])).
% 42.93/27.95 tff(683,plain,
% 42.93/27.95 ((~((~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))))),
% 42.93/27.95 inference(tautology,[status(thm)],[])).
% 42.93/27.95 tff(684,plain,
% 42.93/27.95 ((~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))))),
% 42.93/27.95 inference(unit_resolution,[status(thm)],[683, 682])).
% 42.93/27.95 tff(685,plain,
% 42.93/27.95 (bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 42.93/27.95 inference(unit_resolution,[status(thm)],[684, 437, 680, 414])).
% 42.93/27.95 tff(686,plain,
% 42.93/27.95 (bool(exists2(P!7))),
% 42.93/27.95 inference(modus_ponens,[status(thm)],[685, 674])).
% 42.93/27.95 tff(687,plain,
% 42.93/27.95 ($false),
% 42.93/27.95 inference(unit_resolution,[status(thm)],[446, 686])).
% 42.93/27.95 tff(688,plain,(bool(exists2(P!7))), inference(lemma,lemma(discharge,[]))).
% 42.93/27.95 tff(689,plain,
% 42.93/27.95 ($false),
% 42.93/27.95 inference(unit_resolution,[status(thm)],[688, 299])).
% 42.93/27.95 tff(690,plain,((~(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,[]))).
% 42.93/27.95 tff(691,plain,
% 42.93/27.95 (~(tptp_fun_R_5(P!7) = not1(false))),
% 42.93/27.95 inference(unit_resolution,[status(thm)],[690, 173])).
% 42.93/27.95 tff(692,plain,
% 42.93/27.95 (lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = err),
% 42.93/27.95 inference(transitivity,[status(thm)],[264, 186, 184])).
% 42.93/27.95 tff(693,plain,
% 42.93/27.95 (bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) <=> bool(err)),
% 42.93/27.95 inference(monotonicity,[status(thm)],[692])).
% 42.93/27.95 tff(694,plain,
% 42.93/27.95 (bool(err) <=> bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))),
% 42.93/27.95 inference(symmetry,[status(thm)],[693])).
% 42.93/27.95 tff(695,plain,
% 42.93/27.95 ((~bool(err)) <=> (~bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))))),
% 42.93/27.95 inference(monotonicity,[status(thm)],[694])).
% 42.93/27.95 tff(696,plain,
% 42.93/27.95 (~bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))),
% 42.93/27.95 inference(modus_ponens,[status(thm)],[241, 695])).
% 42.93/27.95 tff(697,plain,
% 42.93/27.95 (d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))) <=> d(err)),
% 42.93/27.95 inference(monotonicity,[status(thm)],[692])).
% 42.93/27.95 tff(698,plain,
% 42.93/27.95 (d(err) <=> d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))),
% 42.93/27.95 inference(symmetry,[status(thm)],[697])).
% 42.93/27.95 tff(699,plain,
% 42.93/27.95 (d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))),
% 42.93/27.95 inference(modus_ponens,[status(thm)],[176, 698])).
% 42.93/27.95 tff(700,assumption,(~bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))), introduced(assumption)).
% 42.93/27.95 tff(701,assumption,(d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))), introduced(assumption)).
% 42.93/27.95 tff(702,plain,
% 42.93/27.95 (lazy_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))),
% 42.93/27.95 inference(symmetry,[status(thm)],[452])).
% 42.93/27.95 tff(703,plain,
% 42.93/27.95 (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)))),
% 42.93/27.95 inference(monotonicity,[status(thm)],[702])).
% 42.93/27.95 tff(704,plain,
% 42.93/27.95 (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))))),
% 42.93/27.95 inference(symmetry,[status(thm)],[703])).
% 42.93/27.95 tff(705,plain,
% 42.93/27.95 (bool(f6(P!7, tptp_fun_R_5(P!7))) <=> bool(not1(false))),
% 42.93/27.95 inference(monotonicity,[status(thm)],[453])).
% 42.93/27.95 tff(706,plain,
% 42.93/27.95 (bool(not1(false)) <=> bool(f6(P!7, tptp_fun_R_5(P!7)))),
% 42.93/27.95 inference(symmetry,[status(thm)],[705])).
% 42.93/27.95 tff(707,plain,
% 42.93/27.95 (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))))),
% 42.93/27.95 inference(transitivity,[status(thm)],[706, 704])).
% 42.93/27.95 tff(708,plain,
% 42.93/27.95 (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))))),
% 42.93/27.95 inference(modus_ponens,[status(thm)],[157, 707])).
% 42.93/27.95 tff(709,plain,
% 42.93/27.95 (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)))),
% 42.93/27.95 inference(monotonicity,[status(thm)],[702])).
% 42.93/27.95 tff(710,plain,
% 42.93/27.95 (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))))),
% 42.93/27.95 inference(symmetry,[status(thm)],[709])).
% 42.93/27.95 tff(711,plain,
% 42.93/27.95 (d(f6(P!7, tptp_fun_R_5(P!7))) <=> d(not1(false))),
% 42.93/27.95 inference(monotonicity,[status(thm)],[453])).
% 42.93/27.95 tff(712,plain,
% 42.93/27.95 (d(not1(false)) <=> d(f6(P!7, tptp_fun_R_5(P!7)))),
% 42.93/27.95 inference(symmetry,[status(thm)],[711])).
% 42.93/27.95 tff(713,plain,
% 42.93/27.95 (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))))),
% 42.93/27.95 inference(transitivity,[status(thm)],[712, 710])).
% 42.93/27.95 tff(714,plain,
% 42.93/27.95 (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))))),
% 42.93/27.95 inference(modus_ponens,[status(thm)],[134, 713])).
% 42.93/27.95 tff(715,plain,
% 42.93/27.95 (((~![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))))) | (~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)))))) | (~((~(lazy_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))))))) <=> ((~![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))))) | (~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)))))) | (~((~(lazy_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)))))))),
% 42.93/27.95 inference(rewrite,[status(thm)],[])).
% 42.93/27.95 tff(716,plain,
% 42.93/27.95 ((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)))) <=> ((~(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))))) | (~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)))))) | (~((~(lazy_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))))))),
% 42.93/27.95 inference(rewrite,[status(thm)],[])).
% 42.93/27.95 tff(717,plain,
% 42.93/27.95 (((~![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)))) <=> ((~(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))))) | (~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)))))) | (~((~(lazy_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)))))))),
% 42.93/27.95 inference(monotonicity,[status(thm)],[716])).
% 42.93/27.95 tff(718,plain,
% 42.93/27.95 (((~![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)))) <=> ((~(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))))) | (~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)))))) | (~((~(lazy_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)))))))),
% 42.93/27.95 inference(transitivity,[status(thm)],[717, 715])).
% 42.93/27.95 tff(719,plain,
% 42.93/27.95 ((~![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)))))))),
% 42.93/27.95 inference(quant_inst,[status(thm)],[])).
% 42.93/27.95 tff(720,plain,
% 42.93/27.95 ((~![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))))) | (~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)))))) | (~((~(lazy_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))))))),
% 42.93/27.95 inference(modus_ponens,[status(thm)],[719, 718])).
% 42.93/27.95 tff(721,plain,
% 42.93/27.95 (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))))) | (~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)))))) | (~((~(lazy_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)))))),
% 42.93/27.95 inference(unit_resolution,[status(thm)],[720, 338])).
% 42.93/27.95 tff(722,plain,
% 42.93/27.95 (lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = f6(P!7, not1(false))),
% 42.93/27.95 inference(symmetry,[status(thm)],[273])).
% 42.93/27.95 tff(723,plain,
% 42.93/27.95 (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)))),
% 42.93/27.95 inference(monotonicity,[status(thm)],[722, 702])).
% 42.93/27.95 tff(724,plain,
% 42.93/27.95 (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))))),
% 42.93/27.96 inference(symmetry,[status(thm)],[723])).
% 42.93/27.96 tff(725,plain,
% 42.93/27.96 ((~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)))))),
% 42.93/27.96 inference(monotonicity,[status(thm)],[724])).
% 42.93/27.96 tff(726,plain,
% 42.93/27.96 (((~(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))))),
% 42.93/27.96 inference(tautology,[status(thm)],[])).
% 42.93/27.96 tff(727,plain,
% 42.93/27.96 (![R1: $i] : (~forallprefers(f6(P!7, R1), f6(P!7, tptp_fun_R_5(P!7))))),
% 42.93/27.96 inference(unit_resolution,[status(thm)],[726, 292])).
% 42.93/27.96 tff(728,plain,
% 42.93/27.96 ((~![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))))),
% 42.93/27.96 inference(quant_inst,[status(thm)],[])).
% 42.93/27.96 tff(729,plain,
% 42.93/27.96 (~forallprefers(f6(P!7, not1(false)), f6(P!7, tptp_fun_R_5(P!7)))),
% 42.93/27.96 inference(unit_resolution,[status(thm)],[728, 727])).
% 42.93/27.96 tff(730,plain,
% 42.93/27.96 (~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))))),
% 42.93/27.96 inference(modus_ponens,[status(thm)],[729, 725])).
% 42.93/27.96 tff(731,plain,
% 42.93/27.96 ((~(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))))) | (~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)))))) | (~((~(lazy_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))))))) | 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))))) | (~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)))))) | (~((~(lazy_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))))))),
% 42.93/27.96 inference(tautology,[status(thm)],[])).
% 42.93/27.96 tff(732,plain,
% 42.93/27.96 (~((~(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))))) | (~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)))))) | (~((~(lazy_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)))))),
% 42.93/27.96 inference(unit_resolution,[status(thm)],[731, 730, 721])).
% 42.93/27.96 tff(733,plain,
% 42.93/27.96 (((~(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))))) | (~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)))))) | (~((~(lazy_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(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(not1(false)), impl(f5(P!7, not1(false)), not1(false))))) | bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false)))))),
% 42.93/27.96 inference(tautology,[status(thm)],[])).
% 42.93/27.96 tff(734,plain,
% 42.93/27.96 ((~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(not1(false)), impl(f5(P!7, not1(false)), not1(false))))) | bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))),
% 42.93/27.96 inference(unit_resolution,[status(thm)],[733, 732])).
% 42.93/27.96 tff(735,plain,
% 42.93/27.96 ((~((~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(not1(false)), impl(f5(P!7, not1(false)), not1(false))))) | bool(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))))) | (~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))))),
% 42.93/27.96 inference(tautology,[status(thm)],[])).
% 42.93/27.96 tff(736,plain,
% 42.93/27.96 ((~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(not1(false)), impl(f5(P!7, not1(false)), not1(false))))) | bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))),
% 42.93/27.96 inference(unit_resolution,[status(thm)],[735, 734])).
% 42.93/27.96 tff(737,plain,
% 42.93/27.96 ($false),
% 42.93/27.96 inference(unit_resolution,[status(thm)],[736, 714, 708, 701, 700])).
% 42.93/27.96 tff(738,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,[]))).
% 42.93/27.96 tff(739,plain,
% 42.93/27.96 (~(prop(tptp_fun_R_5(P!7)) = false)),
% 42.93/27.96 inference(unit_resolution,[status(thm)],[738, 699, 696])).
% 42.93/27.96 tff(740,plain,
% 42.93/27.96 (bool(tptp_fun_R_5(P!7))),
% 42.93/27.96 inference(unit_resolution,[status(thm)],[465, 739])).
% 42.93/27.96 tff(741,plain,
% 42.93/27.96 ((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = not1(false))),
% 42.93/27.96 inference(unit_resolution,[status(thm)],[489, 740])).
% 42.93/27.96 tff(742,plain,
% 42.93/27.96 ((~![X: $i] : ((prop(X) = not1(false)) <=> bool(X))) | ((prop(tptp_fun_R_5(P!7)) = not1(false)) <=> bool(tptp_fun_R_5(P!7)))),
% 42.93/27.96 inference(quant_inst,[status(thm)],[])).
% 42.93/27.96 tff(743,plain,
% 42.93/27.96 ((prop(tptp_fun_R_5(P!7)) = not1(false)) <=> bool(tptp_fun_R_5(P!7))),
% 42.93/27.96 inference(unit_resolution,[status(thm)],[742, 111])).
% 42.93/27.96 tff(744,plain,
% 42.93/27.96 ((~((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)))),
% 42.93/27.96 inference(tautology,[status(thm)],[])).
% 42.93/27.96 tff(745,plain,
% 42.93/27.96 ((prop(tptp_fun_R_5(P!7)) = not1(false)) | (~bool(tptp_fun_R_5(P!7)))),
% 42.93/27.96 inference(unit_resolution,[status(thm)],[744, 743])).
% 42.93/27.96 tff(746,plain,
% 42.93/27.96 (prop(tptp_fun_R_5(P!7)) = not1(false)),
% 42.93/27.96 inference(unit_resolution,[status(thm)],[745, 740])).
% 42.93/27.96 tff(747,assumption,(prop(tptp_fun_R_5(P!7)) = not1(false)), introduced(assumption)).
% 42.93/27.96 tff(748,plain,
% 42.93/27.96 (not1(false) = prop(not1(false))),
% 42.93/27.96 inference(symmetry,[status(thm)],[263])).
% 42.93/27.96 tff(749,plain,
% 42.93/27.96 (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)))),
% 42.93/27.96 inference(monotonicity,[status(thm)],[748])).
% 42.93/27.96 tff(750,plain,
% 42.93/27.96 ((~![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))))),
% 42.93/27.96 inference(quant_inst,[status(thm)],[])).
% 42.93/27.96 tff(751,plain,
% 42.93/27.96 (lazy_impl(not1(false), impl(f5(P!7, not1(false)), not1(false))) = phi(impl(f5(P!7, not1(false)), not1(false)))),
% 42.93/27.96 inference(unit_resolution,[status(thm)],[750, 33])).
% 42.93/27.96 tff(752,plain,
% 42.93/27.96 (phi(impl(f5(P!7, not1(false)), not1(false))) = lazy_impl(not1(false), impl(f5(P!7, not1(false)), not1(false)))),
% 42.93/27.96 inference(symmetry,[status(thm)],[751])).
% 42.93/27.96 tff(753,plain,
% 42.93/27.96 (bool(impl(f5(P!7, not1(false)), not1(false))) <=> bool(err)),
% 42.93/27.96 inference(monotonicity,[status(thm)],[258])).
% 42.93/27.96 tff(754,plain,
% 42.93/27.96 (bool(err) <=> bool(impl(f5(P!7, not1(false)), not1(false)))),
% 42.93/27.96 inference(symmetry,[status(thm)],[753])).
% 42.93/27.96 tff(755,plain,
% 42.93/27.96 ((~bool(err)) <=> (~bool(impl(f5(P!7, not1(false)), not1(false))))),
% 42.93/27.96 inference(monotonicity,[status(thm)],[754])).
% 42.93/27.96 tff(756,plain,
% 42.93/27.96 (~bool(impl(f5(P!7, not1(false)), not1(false)))),
% 42.93/27.96 inference(modus_ponens,[status(thm)],[241, 755])).
% 42.93/27.96 tff(757,plain,
% 42.93/27.96 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(f5(P!7, not1(false)), not1(false))) | (impl(impl(f5(P!7, not1(false)), not1(false)), false) = phi(impl(f5(P!7, not1(false)), not1(false)))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(f5(P!7, not1(false)), not1(false))) | (impl(impl(f5(P!7, not1(false)), not1(false)), false) = phi(impl(f5(P!7, not1(false)), not1(false)))))),
% 42.93/27.96 inference(rewrite,[status(thm)],[])).
% 42.93/27.96 tff(758,plain,
% 42.93/27.96 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(f5(P!7, not1(false)), not1(false))) | (impl(impl(f5(P!7, not1(false)), not1(false)), false) = phi(impl(f5(P!7, not1(false)), not1(false)))))),
% 42.93/27.96 inference(quant_inst,[status(thm)],[])).
% 42.93/27.96 tff(759,plain,
% 42.93/27.96 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(f5(P!7, not1(false)), not1(false))) | (impl(impl(f5(P!7, not1(false)), not1(false)), false) = phi(impl(f5(P!7, not1(false)), not1(false))))),
% 42.93/27.96 inference(modus_ponens,[status(thm)],[758, 757])).
% 42.93/27.96 tff(760,plain,
% 42.93/27.96 (bool(impl(f5(P!7, not1(false)), not1(false))) | (impl(impl(f5(P!7, not1(false)), not1(false)), false) = phi(impl(f5(P!7, not1(false)), not1(false))))),
% 42.93/27.96 inference(unit_resolution,[status(thm)],[759, 252])).
% 42.93/27.96 tff(761,plain,
% 42.93/27.96 (impl(impl(f5(P!7, not1(false)), not1(false)), false) = phi(impl(f5(P!7, not1(false)), not1(false)))),
% 42.93/27.96 inference(unit_resolution,[status(thm)],[760, 756])).
% 42.93/27.96 tff(762,plain,
% 42.93/27.96 (impl(f5(P!7, not1(false)), impl(false, false)) = impl(f5(P!7, not1(false)), not1(false))),
% 42.93/27.96 inference(monotonicity,[status(thm)],[78])).
% 42.93/27.96 tff(763,plain,
% 42.93/27.96 (impl(impl(f5(P!7, not1(false)), impl(false, false)), false) = impl(impl(f5(P!7, not1(false)), not1(false)), false)),
% 42.93/27.96 inference(monotonicity,[status(thm)],[762])).
% 42.93/27.96 tff(764,plain,
% 42.93/27.96 (impl(f5(P!7, not1(false)), not1(false)) = impl(f5(P!7, not1(false)), impl(false, false))),
% 42.93/27.96 inference(symmetry,[status(thm)],[762])).
% 42.93/27.96 tff(765,plain,
% 42.93/27.96 (phi(f5(P!7, not1(false))) = impl(f5(P!7, not1(false)), not1(false))),
% 42.93/27.96 inference(symmetry,[status(thm)],[257])).
% 42.93/27.96 tff(766,plain,
% 42.93/27.96 (phi(err) = phi(f5(P!7, not1(false)))),
% 42.93/27.96 inference(symmetry,[status(thm)],[205])).
% 42.93/27.96 tff(767,plain,
% 42.93/27.96 (err = phi(err)),
% 42.93/27.96 inference(symmetry,[status(thm)],[184])).
% 42.93/27.96 tff(768,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)).
% 42.93/27.96 tff(769,plain,
% 42.93/27.96 (false = tptp_fun_R_5(P!7)),
% 42.93/27.96 inference(symmetry,[status(thm)],[628])).
% 42.93/27.96 tff(770,plain,
% 42.93/27.96 (f5(P!7, false) = f5(P!7, tptp_fun_R_5(P!7))),
% 42.93/27.96 inference(monotonicity,[status(thm)],[769])).
% 42.93/27.96 tff(771,plain,
% 42.93/27.96 (f5(P!7, false) = impl(f5(P!7, not1(false)), impl(false, false))),
% 42.93/27.96 inference(transitivity,[status(thm)],[770, 643, 768, 767, 766, 765, 764])).
% 42.93/27.96 tff(772,plain,
% 42.93/27.96 (impl(f5(P!7, false), false) = impl(impl(f5(P!7, not1(false)), impl(false, false)), false)),
% 42.93/27.96 inference(monotonicity,[status(thm)],[771])).
% 42.93/27.96 tff(773,plain,
% 42.93/27.96 (f5(P!7, tptp_fun_R_5(P!7)) = f5(P!7, false)),
% 42.93/27.96 inference(symmetry,[status(thm)],[770])).
% 42.93/27.96 tff(774,plain,
% 42.93/27.96 (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, false)),
% 42.93/27.96 inference(transitivity,[status(thm)],[644, 773])).
% 42.93/27.96 tff(775,plain,
% 42.93/27.96 (impl(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))), false) = impl(f5(P!7, false), false)),
% 42.93/27.96 inference(monotonicity,[status(thm)],[774])).
% 42.93/27.96 tff(776,plain,
% 42.93/27.96 (impl(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))), false) = err),
% 42.93/27.96 inference(transitivity,[status(thm)],[775, 772, 763, 761, 752, 749, 264, 186, 184])).
% 42.93/27.96 tff(777,plain,
% 42.93/27.96 (phi(impl(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))), false)) = phi(err)),
% 42.93/27.96 inference(monotonicity,[status(thm)],[776])).
% 42.93/27.96 tff(778,plain,
% 42.93/27.96 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = impl(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))), false)),
% 42.93/27.96 inference(monotonicity,[status(thm)],[643, 628])).
% 42.93/27.96 tff(779,plain,
% 42.93/27.96 (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = phi(impl(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))), false))),
% 42.93/27.96 inference(monotonicity,[status(thm)],[778])).
% 42.93/27.96 tff(780,plain,
% 42.93/27.96 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 42.93/27.96 inference(quant_inst,[status(thm)],[])).
% 42.93/27.96 tff(781,plain,
% 42.93/27.96 (lazy_impl(not1(false), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 42.93/27.96 inference(unit_resolution,[status(thm)],[780, 33])).
% 42.93/27.96 tff(782,plain,
% 42.93/27.96 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(not1(false), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 42.93/27.96 inference(monotonicity,[status(thm)],[747])).
% 42.93/27.96 tff(783,plain,
% 42.93/27.96 (f6(P!7, tptp_fun_R_5(P!7)) = err),
% 42.93/27.96 inference(transitivity,[status(thm)],[452, 782, 781, 779, 777, 184])).
% 42.93/27.96 tff(784,plain,
% 42.93/27.96 (phi(f6(P!7, tptp_fun_R_5(P!7))) = phi(err)),
% 42.93/27.96 inference(monotonicity,[status(thm)],[783])).
% 42.93/27.96 tff(785,plain,
% 42.93/27.96 (exists2(P!7) = err),
% 42.93/27.96 inference(transitivity,[status(thm)],[294, 784, 184])).
% 42.93/27.96 tff(786,plain,
% 42.93/27.96 (bool(exists2(P!7)) <=> bool(err)),
% 42.93/27.96 inference(monotonicity,[status(thm)],[785])).
% 42.93/27.96 tff(787,plain,
% 42.93/27.96 (bool(err) <=> bool(exists2(P!7))),
% 42.93/27.96 inference(symmetry,[status(thm)],[786])).
% 42.93/27.96 tff(788,plain,
% 42.93/27.96 ((~bool(err)) <=> (~bool(exists2(P!7)))),
% 42.93/27.96 inference(monotonicity,[status(thm)],[787])).
% 42.93/27.96 tff(789,plain,
% 42.93/27.96 (~bool(exists2(P!7))),
% 42.93/27.96 inference(modus_ponens,[status(thm)],[241, 788])).
% 42.93/27.96 tff(790,plain,
% 42.93/27.96 ($false),
% 42.93/27.96 inference(unit_resolution,[status(thm)],[688, 789])).
% 42.93/27.96 tff(791,plain,((~(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(not1(false), P!7), not1(false))) = err)) | (~(tptp_fun_R_5(P!7) = false)) | (~(prop(tptp_fun_R_5(P!7)) = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 42.93/27.96 tff(792,plain,
% 42.93/27.96 (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = err)),
% 42.93/27.96 inference(unit_resolution,[status(thm)],[791, 628, 173, 747])).
% 42.93/27.96 tff(793,plain,
% 42.93/27.96 ((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)),
% 42.93/27.96 inference(tautology,[status(thm)],[])).
% 42.93/27.96 tff(794,plain,
% 42.93/27.96 (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))),
% 42.93/27.96 inference(unit_resolution,[status(thm)],[793, 792])).
% 42.93/27.96 tff(795,plain,
% 42.93/27.96 (((~![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)))))),
% 42.93/27.96 inference(rewrite,[status(thm)],[])).
% 42.93/27.96 tff(796,plain,
% 42.93/27.96 ((~![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)))))),
% 42.93/27.96 inference(quant_inst,[status(thm)],[])).
% 42.93/27.96 tff(797,plain,
% 42.93/27.96 ((~![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))))),
% 42.93/27.96 inference(modus_ponens,[status(thm)],[796, 795])).
% 42.93/27.96 tff(798,plain,
% 42.93/27.96 ((~((~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))))),
% 42.93/27.96 inference(unit_resolution,[status(thm)],[797, 17])).
% 42.93/27.96 tff(799,plain,
% 42.93/27.96 (~((~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)))))),
% 42.93/27.96 inference(unit_resolution,[status(thm)],[798, 794])).
% 42.93/27.96 tff(800,plain,
% 42.93/27.96 (((~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)))),
% 42.93/27.96 inference(tautology,[status(thm)],[])).
% 42.93/27.96 tff(801,plain,
% 42.93/27.96 (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))),
% 42.93/27.96 inference(unit_resolution,[status(thm)],[800, 799])).
% 42.93/27.96 tff(802,assumption,(phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) = err), introduced(assumption)).
% 42.93/27.96 tff(803,plain,
% 42.93/27.96 (phi(f7(P!6)) = phi(false)),
% 42.93/27.96 inference(monotonicity,[status(thm)],[410])).
% 42.93/27.96 tff(804,plain,
% 42.93/27.96 (false2 = phi(f7(P!6))),
% 42.93/27.96 inference(and_elim,[status(thm)],[360])).
% 42.93/27.96 tff(805,plain,
% 42.93/27.96 (false2 = false),
% 42.93/27.96 inference(transitivity,[status(thm)],[804, 803, 23])).
% 42.93/27.96 tff(806,plain,
% 42.93/27.96 (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)),
% 42.93/27.96 inference(monotonicity,[status(thm)],[95])).
% 42.93/27.96 tff(807,plain,
% 42.93/27.96 (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))),
% 42.93/27.96 inference(symmetry,[status(thm)],[806])).
% 42.93/27.96 tff(808,plain,
% 42.93/27.96 (impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2) = impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false)),
% 42.93/27.96 inference(monotonicity,[status(thm)],[807, 805])).
% 42.93/27.96 tff(809,plain,
% 42.93/27.96 (impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false) = impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)),
% 42.93/27.96 inference(symmetry,[status(thm)],[808])).
% 42.93/27.96 tff(810,plain,
% 42.93/27.96 (phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false)) = phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2))),
% 42.93/27.96 inference(monotonicity,[status(thm)],[809])).
% 42.93/27.96 tff(811,plain,
% 42.93/27.96 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false)) = phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false)))),
% 42.93/27.96 inference(quant_inst,[status(thm)],[])).
% 42.93/27.96 tff(812,plain,
% 42.93/27.96 (lazy_impl(not1(false), impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false)) = phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false))),
% 42.93/27.96 inference(unit_resolution,[status(thm)],[811, 33])).
% 42.93/27.96 tff(813,plain,
% 42.93/27.96 (lazy_impl(prop(false), impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false)) = lazy_impl(not1(false), impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false))),
% 42.93/27.96 inference(monotonicity,[status(thm)],[116])).
% 42.93/27.96 tff(814,plain,
% 42.93/27.96 (f5(P!7, tptp_fun_R_5(P!7)) = f5(P!7, false)),
% 42.93/27.96 inference(monotonicity,[status(thm)],[628])).
% 42.93/27.96 tff(815,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)).
% 42.93/27.96 tff(816,plain,
% 42.93/27.96 (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)))),
% 42.93/27.96 inference(symmetry,[status(thm)],[815])).
% 42.93/27.96 tff(817,plain,
% 42.93/27.96 (tptp_fun_X_4(false, P!7) = tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)),
% 42.93/27.96 inference(monotonicity,[status(thm)],[769])).
% 42.93/27.96 tff(818,plain,
% 42.93/27.96 (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))),
% 42.93/27.96 inference(monotonicity,[status(thm)],[817, 769])).
% 42.93/27.96 tff(819,plain,
% 42.93/27.96 ((~![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))),
% 42.93/27.96 inference(quant_inst,[status(thm)],[])).
% 42.93/27.96 tff(820,plain,
% 42.93/27.96 (f4(P!7, tptp_fun_X_4(false, P!7), false) = impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)),
% 42.93/27.96 inference(unit_resolution,[status(thm)],[819, 170])).
% 42.93/27.96 tff(821,plain,
% 42.93/27.96 (impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = f4(P!7, tptp_fun_X_4(false, P!7), false)),
% 42.93/27.96 inference(symmetry,[status(thm)],[820])).
% 42.93/27.96 tff(822,plain,
% 42.93/27.96 (impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)) = f5(P!7, false)),
% 42.93/27.96 inference(transitivity,[status(thm)],[806, 821, 818, 816, 644, 814])).
% 42.93/27.96 tff(823,plain,
% 42.93/27.96 (impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false) = impl(f5(P!7, false), false)),
% 42.93/27.96 inference(monotonicity,[status(thm)],[822])).
% 42.93/27.96 tff(824,plain,
% 42.93/27.96 (impl(f5(P!7, false), false) = impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false)),
% 42.93/27.96 inference(symmetry,[status(thm)],[823])).
% 42.93/27.96 tff(825,plain,
% 42.93/27.96 (f5(P!7, false) = f5(P!7, tptp_fun_R_5(P!7))),
% 42.93/27.96 inference(symmetry,[status(thm)],[814])).
% 42.93/27.96 tff(826,plain,
% 42.93/27.96 (f5(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)))),
% 42.93/27.97 inference(transitivity,[status(thm)],[825, 643])).
% 42.93/27.97 tff(827,plain,
% 42.93/27.97 (impl(f5(P!7, false), false) = impl(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))), false)),
% 42.93/27.97 inference(monotonicity,[status(thm)],[826])).
% 42.93/27.97 tff(828,plain,
% 42.93/27.97 (impl(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))), false) = impl(f5(P!7, false), false)),
% 42.93/27.97 inference(symmetry,[status(thm)],[827])).
% 42.93/27.97 tff(829,plain,
% 42.93/27.97 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false)),
% 42.93/27.97 inference(transitivity,[status(thm)],[778, 828, 824])).
% 42.93/27.97 tff(830,plain,
% 42.93/27.97 (prop(tptp_fun_R_5(P!7)) = prop(false)),
% 42.93/27.97 inference(transitivity,[status(thm)],[747, 117])).
% 42.93/27.97 tff(831,plain,
% 42.93/27.97 (lazy_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(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false))),
% 42.93/27.97 inference(monotonicity,[status(thm)],[830, 829])).
% 42.93/27.97 tff(832,plain,
% 42.93/27.97 (f6(P!7, tptp_fun_R_5(P!7)) = err),
% 42.93/27.97 inference(transitivity,[status(thm)],[452, 831, 813, 812, 810, 802])).
% 42.93/27.97 tff(833,plain,
% 42.93/27.97 (phi(f6(P!7, tptp_fun_R_5(P!7))) = phi(err)),
% 42.93/27.97 inference(monotonicity,[status(thm)],[832])).
% 42.93/27.97 tff(834,plain,
% 42.93/27.97 (exists2(P!7) = err),
% 42.93/27.97 inference(transitivity,[status(thm)],[294, 833, 184])).
% 42.93/27.97 tff(835,plain,
% 42.93/27.97 (bool(exists2(P!7)) <=> bool(err)),
% 42.93/27.97 inference(monotonicity,[status(thm)],[834])).
% 42.93/27.97 tff(836,plain,
% 42.93/27.97 (bool(err) <=> bool(exists2(P!7))),
% 42.93/27.97 inference(symmetry,[status(thm)],[835])).
% 42.93/27.97 tff(837,plain,
% 42.93/27.97 ((~bool(err)) <=> (~bool(exists2(P!7)))),
% 42.93/27.97 inference(monotonicity,[status(thm)],[836])).
% 42.93/27.97 tff(838,plain,
% 42.93/27.97 (~bool(exists2(P!7))),
% 42.93/27.97 inference(modus_ponens,[status(thm)],[241, 837])).
% 42.93/27.97 tff(839,plain,
% 42.93/27.97 ($false),
% 42.93/27.97 inference(unit_resolution,[status(thm)],[688, 838])).
% 42.93/27.97 tff(840,plain,((~(phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) = 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)))) | (~(tptp_fun_R_5(P!7) = false)) | (~(prop(tptp_fun_R_5(P!7)) = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 42.93/27.97 tff(841,plain,
% 42.93/27.97 (~(phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) = err)),
% 42.93/27.97 inference(unit_resolution,[status(thm)],[840, 801, 628, 747])).
% 42.93/27.97 tff(842,plain,
% 42.93/27.97 ((d(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) = err))) | (phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) = err)),
% 42.93/27.97 inference(tautology,[status(thm)],[])).
% 42.93/27.97 tff(843,plain,
% 42.93/27.97 (d(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) = err))),
% 42.93/27.97 inference(unit_resolution,[status(thm)],[842, 841])).
% 42.93/27.97 tff(844,plain,
% 42.93/27.97 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~(d(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) = err)))) | (~((~d(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2))) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) = impl(impl(apply(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(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) = err)))) | (~((~d(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2))) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) = impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2))))))),
% 42.93/27.97 inference(rewrite,[status(thm)],[])).
% 42.93/27.97 tff(845,plain,
% 42.93/27.97 (((~((~d(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2))) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) = impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2))))) | (~(d(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) = err))))) <=> ((~(d(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) = err)))) | (~((~d(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2))) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) = impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2))))))),
% 42.93/27.97 inference(rewrite,[status(thm)],[])).
% 42.93/27.97 tff(846,plain,
% 42.93/27.97 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2))) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) = impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2))))) | (~(d(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) | (~(phi(impl(impl(apply(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(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) = err)))) | (~((~d(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2))) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) = impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)))))))),
% 42.93/27.97 inference(monotonicity,[status(thm)],[845])).
% 42.93/27.97 tff(847,plain,
% 42.93/27.97 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2))) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) = impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2))))) | (~(d(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) | (~(phi(impl(impl(apply(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(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) = err)))) | (~((~d(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2))) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) = impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2))))))),
% 42.93/27.97 inference(transitivity,[status(thm)],[846, 844])).
% 42.93/27.97 tff(848,plain,
% 42.93/27.97 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2))) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) = impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2))))) | (~(d(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) = err)))))),
% 42.93/27.97 inference(quant_inst,[status(thm)],[])).
% 42.93/27.97 tff(849,plain,
% 42.93/27.97 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~(d(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) = err)))) | (~((~d(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2))) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) = impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)))))),
% 42.93/27.97 inference(modus_ponens,[status(thm)],[848, 847])).
% 42.93/27.97 tff(850,plain,
% 42.93/27.97 ((~(d(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) = err)))) | (~((~d(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2))) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) = impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)))))),
% 42.93/27.97 inference(unit_resolution,[status(thm)],[849, 17])).
% 42.93/27.97 tff(851,plain,
% 42.93/27.97 (~((~d(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2))) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) = impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2))))),
% 42.93/27.97 inference(unit_resolution,[status(thm)],[850, 843])).
% 42.93/27.97 tff(852,plain,
% 42.93/27.97 (((~d(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2))) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) = impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)))) | d(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2))),
% 42.93/27.97 inference(tautology,[status(thm)],[])).
% 42.93/27.97 tff(853,plain,
% 42.93/27.97 (d(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2))),
% 42.93/27.97 inference(unit_resolution,[status(thm)],[852, 851])).
% 42.93/27.97 tff(854,plain,
% 42.93/27.97 (((~d(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2))) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) = impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)))) | (phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) = impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2))),
% 42.93/27.97 inference(tautology,[status(thm)],[])).
% 42.93/27.97 tff(855,plain,
% 42.93/27.97 (phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) = impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)),
% 42.93/27.97 inference(unit_resolution,[status(thm)],[854, 851])).
% 42.93/27.97 tff(856,plain,
% 42.93/27.97 ((~![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)))),
% 42.93/27.97 inference(quant_inst,[status(thm)],[])).
% 42.93/27.97 tff(857,plain,
% 42.93/27.97 (f6(P!7, false) = lazy_impl(prop(false), impl(f5(P!7, false), false))),
% 42.93/27.97 inference(unit_resolution,[status(thm)],[856, 271])).
% 42.93/27.97 tff(858,plain,
% 42.93/27.97 (f6(P!7, false) = f6(P!7, tptp_fun_R_5(P!7))),
% 42.93/27.97 inference(monotonicity,[status(thm)],[769])).
% 42.93/27.97 tff(859,plain,
% 42.93/27.97 (f6(P!7, tptp_fun_R_5(P!7)) = f6(P!7, false)),
% 42.93/27.97 inference(symmetry,[status(thm)],[858])).
% 42.93/27.97 tff(860,plain,
% 42.93/27.97 (f6(P!7, tptp_fun_R_5(P!7)) = lazy_impl(prop(false), impl(f5(P!7, false), false))),
% 42.93/27.97 inference(transitivity,[status(thm)],[859, 857])).
% 42.93/27.97 tff(861,plain,
% 42.93/27.97 (d(f6(P!7, tptp_fun_R_5(P!7))) <=> d(lazy_impl(prop(false), impl(f5(P!7, false), false)))),
% 42.93/27.97 inference(monotonicity,[status(thm)],[860])).
% 42.93/27.97 tff(862,plain,
% 42.93/27.97 (d(lazy_impl(prop(false), impl(f5(P!7, false), false))) <=> d(f6(P!7, tptp_fun_R_5(P!7)))),
% 42.93/27.97 inference(symmetry,[status(thm)],[861])).
% 42.93/27.97 tff(863,assumption,(phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) = impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)), introduced(assumption)).
% 42.93/27.97 tff(864,plain,
% 42.93/27.97 (phi(f7(P!6)) = false2),
% 42.93/27.97 inference(symmetry,[status(thm)],[804])).
% 42.93/27.97 tff(865,plain,
% 42.93/27.97 (phi(false) = phi(f7(P!6))),
% 42.93/27.97 inference(symmetry,[status(thm)],[803])).
% 42.93/27.97 tff(866,plain,
% 42.93/27.97 (false = false2),
% 42.93/27.97 inference(transitivity,[status(thm)],[349, 865, 864])).
% 42.93/27.97 tff(867,plain,
% 42.93/27.97 (impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false) = impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)),
% 42.93/27.97 inference(monotonicity,[status(thm)],[806, 866])).
% 42.93/27.97 tff(868,plain,
% 42.93/27.97 (impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2) = impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false)),
% 42.93/27.97 inference(symmetry,[status(thm)],[867])).
% 42.93/27.97 tff(869,plain,
% 42.93/27.97 (phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) = phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false))),
% 42.93/27.97 inference(monotonicity,[status(thm)],[868])).
% 42.93/27.97 tff(870,plain,
% 42.93/27.97 (phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false)) = phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2))),
% 42.93/27.97 inference(symmetry,[status(thm)],[869])).
% 42.93/27.97 tff(871,plain,
% 42.93/27.97 (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)),
% 42.93/27.97 inference(symmetry,[status(thm)],[818])).
% 42.93/27.97 tff(872,plain,
% 42.93/27.97 (f5(P!7, false) = impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false))),
% 42.93/27.97 inference(transitivity,[status(thm)],[825, 643, 815, 871, 820, 807])).
% 42.93/27.97 tff(873,plain,
% 42.93/27.97 (impl(f5(P!7, false), false) = impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false)),
% 42.93/27.97 inference(monotonicity,[status(thm)],[872])).
% 42.93/27.97 tff(874,plain,
% 42.93/27.97 (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, false)),
% 42.93/27.97 inference(transitivity,[status(thm)],[644, 814])).
% 42.93/27.97 tff(875,plain,
% 42.93/27.97 (impl(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))), false) = impl(f5(P!7, false), false)),
% 42.93/27.97 inference(monotonicity,[status(thm)],[874])).
% 42.93/27.97 tff(876,plain,
% 42.93/27.97 (impl(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))), false) = impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false)),
% 42.93/27.97 inference(transitivity,[status(thm)],[875, 873])).
% 42.93/27.97 tff(877,plain,
% 42.93/27.97 (phi(impl(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))), false)) = phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false))),
% 42.93/27.97 inference(monotonicity,[status(thm)],[876])).
% 42.93/27.97 tff(878,plain,
% 42.93/27.97 (lazy_impl(prop(false), impl(f5(P!7, false), false)) = f6(P!7, false)),
% 42.93/27.97 inference(symmetry,[status(thm)],[857])).
% 42.93/27.97 tff(879,plain,
% 42.93/27.97 (lazy_impl(prop(false), impl(f5(P!7, false), false)) = impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)),
% 42.93/27.97 inference(transitivity,[status(thm)],[878, 858, 452, 782, 781, 779, 877, 870, 863])).
% 42.93/27.97 tff(880,plain,
% 42.93/27.97 (d(lazy_impl(prop(false), impl(f5(P!7, false), false))) <=> d(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2))),
% 42.93/27.97 inference(monotonicity,[status(thm)],[879])).
% 42.93/27.97 tff(881,plain,
% 42.93/27.97 (d(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) <=> d(lazy_impl(prop(false), impl(f5(P!7, false), false)))),
% 42.93/27.97 inference(symmetry,[status(thm)],[880])).
% 42.93/27.97 tff(882,plain,
% 42.93/27.97 (d(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) <=> 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))))),
% 42.93/27.97 inference(transitivity,[status(thm)],[881, 862, 710])).
% 42.93/27.97 tff(883,assumption,(d(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2))), introduced(assumption)).
% 42.93/27.97 tff(884,plain,
% 42.93/27.97 (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))))),
% 42.93/27.97 inference(modus_ponens,[status(thm)],[883, 882])).
% 42.93/27.97 tff(885,plain,
% 42.93/27.97 (bool(f6(P!7, tptp_fun_R_5(P!7))) <=> bool(lazy_impl(prop(false), impl(f5(P!7, false), false)))),
% 42.93/27.97 inference(monotonicity,[status(thm)],[860])).
% 42.93/27.97 tff(886,plain,
% 42.93/27.97 (bool(lazy_impl(prop(false), impl(f5(P!7, false), false))) <=> bool(f6(P!7, tptp_fun_R_5(P!7)))),
% 42.93/27.97 inference(symmetry,[status(thm)],[885])).
% 42.93/27.97 tff(887,plain,
% 42.93/27.97 (lazy_impl(not1(false), impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false)) = lazy_impl(prop(false), impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false))),
% 42.93/27.97 inference(monotonicity,[status(thm)],[117])).
% 42.93/27.97 tff(888,plain,
% 42.93/27.97 (phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false)) = lazy_impl(not1(false), impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false))),
% 42.93/27.97 inference(symmetry,[status(thm)],[812])).
% 42.93/27.97 tff(889,plain,
% 42.93/27.97 (lazy_impl(prop(false), impl(f5(P!7, false), false)) = lazy_impl(prop(false), impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false))),
% 42.93/27.97 inference(transitivity,[status(thm)],[878, 858, 452, 782, 781, 779, 877, 888, 887])).
% 42.93/27.97 tff(890,plain,
% 42.93/27.97 (bool(lazy_impl(prop(false), impl(f5(P!7, false), false))) <=> bool(lazy_impl(prop(false), impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false)))),
% 42.93/27.97 inference(monotonicity,[status(thm)],[889])).
% 42.93/27.97 tff(891,plain,
% 42.93/27.97 (bool(lazy_impl(prop(false), impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false))) <=> bool(lazy_impl(prop(false), impl(f5(P!7, false), false)))),
% 42.93/27.97 inference(symmetry,[status(thm)],[890])).
% 42.93/27.97 tff(892,plain,
% 42.93/27.97 (f6(P!7, tptp_fun_R_5(P!7)) = impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false)),
% 42.93/27.97 inference(transitivity,[status(thm)],[452, 782, 781, 779, 877, 870, 863, 868])).
% 42.93/27.97 tff(893,plain,
% 42.93/27.97 (phi(f6(P!7, tptp_fun_R_5(P!7))) = phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false))),
% 42.93/27.97 inference(monotonicity,[status(thm)],[892])).
% 42.93/27.97 tff(894,plain,
% 42.93/27.97 (exists2(P!7) = lazy_impl(prop(false), impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false))),
% 42.93/27.97 inference(transitivity,[status(thm)],[294, 893, 888, 887])).
% 42.93/27.97 tff(895,plain,
% 42.93/27.97 (bool(exists2(P!7)) <=> bool(lazy_impl(prop(false), impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false)))),
% 42.93/27.97 inference(monotonicity,[status(thm)],[894])).
% 42.93/27.97 tff(896,plain,
% 42.93/27.97 (bool(exists2(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))))),
% 42.93/27.97 inference(transitivity,[status(thm)],[895, 891, 886, 704])).
% 42.93/27.97 tff(897,plain,
% 42.93/27.97 (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))))),
% 42.93/27.97 inference(modus_ponens,[status(thm)],[688, 896])).
% 42.93/27.97 tff(898,plain,
% 42.93/27.97 ($false),
% 42.93/27.97 inference(unit_resolution,[status(thm)],[736, 897, 884, 701, 700])).
% 42.93/27.97 tff(899,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)))) | (~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)))) | (~(prop(tptp_fun_R_5(P!7)) = not1(false))) | (~(tptp_fun_R_5(P!7) = false)) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)) = impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2))) | (~d(impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false2)))), inference(lemma,lemma(discharge,[]))).
% 42.93/27.97 tff(900,plain,
% 42.93/27.97 ($false),
% 42.93/27.97 inference(unit_resolution,[status(thm)],[899, 855, 853, 696, 747, 628, 699, 801])).
% 42.93/27.97 tff(901,plain,((~(tptp_fun_R_5(P!7) = false)) | (~(prop(tptp_fun_R_5(P!7)) = not1(false))) | (~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err))), inference(lemma,lemma(discharge,[]))).
% 42.93/27.97 tff(902,plain,
% 42.93/27.97 (~(tptp_fun_R_5(P!7) = false)),
% 42.93/27.97 inference(unit_resolution,[status(thm)],[901, 746, 173])).
% 42.93/27.97 tff(903,plain,
% 42.93/27.97 ($false),
% 42.93/27.97 inference(unit_resolution,[status(thm)],[626, 902, 741, 691])).
% 42.93/27.97 tff(904,plain,(~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err)), inference(lemma,lemma(discharge,[]))).
% 42.93/27.97 tff(905,plain,
% 42.93/27.97 ((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)),
% 42.93/27.97 inference(tautology,[status(thm)],[])).
% 42.93/27.97 tff(906,plain,
% 42.93/27.97 (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))),
% 42.93/27.97 inference(unit_resolution,[status(thm)],[905, 904])).
% 42.93/27.97 tff(907,plain,
% 42.93/27.97 (((~![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))) = 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)))))))) <=> ((~![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))) = 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)))))))),
% 42.93/27.97 inference(rewrite,[status(thm)],[])).
% 42.93/27.97 tff(908,plain,
% 42.93/27.97 (((~((~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))))) <=> ((~(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)))) | (~(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)))))))),
% 42.93/27.97 inference(rewrite,[status(thm)],[])).
% 42.93/27.97 tff(909,plain,
% 42.93/27.97 (((~![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))) = 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))))))))),
% 42.93/27.97 inference(monotonicity,[status(thm)],[908])).
% 42.93/27.97 tff(910,plain,
% 42.93/27.97 (((~![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))) = 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)))))))),
% 42.93/27.97 inference(transitivity,[status(thm)],[909, 907])).
% 42.93/27.97 tff(911,plain,
% 42.93/27.97 ((~![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)))))),
% 42.93/27.97 inference(quant_inst,[status(thm)],[])).
% 42.93/27.97 tff(912,plain,
% 42.93/27.97 ((~![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))) = 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))))))),
% 42.93/27.97 inference(modus_ponens,[status(thm)],[911, 910])).
% 42.93/27.97 tff(913,plain,
% 42.93/27.97 ((~(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)))) | (~(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))))))),
% 42.93/27.97 inference(unit_resolution,[status(thm)],[912, 17])).
% 42.93/27.97 tff(914,plain,
% 42.93/27.97 (~((~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)))))),
% 42.93/27.97 inference(unit_resolution,[status(thm)],[913, 906])).
% 42.93/27.97 tff(915,plain,
% 42.93/27.97 (((~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)))),
% 42.93/27.98 inference(tautology,[status(thm)],[])).
% 42.93/27.98 tff(916,plain,
% 42.93/27.98 (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))),
% 42.93/27.98 inference(unit_resolution,[status(thm)],[915, 914])).
% 42.93/27.98 tff(917,plain,
% 42.93/27.98 (f5(P!7, not1(false)) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false)))),
% 42.93/27.98 inference(transitivity,[status(thm)],[203, 916, 172, 163])).
% 42.93/27.98 tff(918,plain,
% 42.93/27.98 (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))),
% 42.93/27.98 inference(monotonicity,[status(thm)],[917])).
% 42.93/27.98 tff(919,plain,
% 42.93/27.98 (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)))),
% 42.93/27.98 inference(monotonicity,[status(thm)],[918])).
% 42.93/27.98 tff(920,plain,
% 42.93/27.98 (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)))),
% 42.93/27.98 inference(symmetry,[status(thm)],[919])).
% 42.93/27.98 tff(921,plain,
% 42.93/27.98 ((lazy_impl(prop(not1(false)), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))) = false) <=> (lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = false)),
% 42.93/27.98 inference(monotonicity,[status(thm)],[920])).
% 42.93/27.98 tff(922,plain,
% 42.93/27.98 ((lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = 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))) = false)),
% 42.93/27.98 inference(symmetry,[status(thm)],[921])).
% 42.93/27.98 tff(923,plain,
% 42.93/27.98 (phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = f5(P!7, not1(false))),
% 42.93/27.98 inference(symmetry,[status(thm)],[203])).
% 42.93/27.98 tff(924,plain,
% 42.93/27.98 (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)))),
% 42.93/27.98 inference(symmetry,[status(thm)],[916])).
% 42.93/27.98 tff(925,plain,
% 42.93/27.98 (f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)) = f5(P!7, not1(false))),
% 42.93/27.98 inference(transitivity,[status(thm)],[924, 923])).
% 42.93/27.98 tff(926,plain,
% 42.93/27.98 (phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = phi(f5(P!7, not1(false)))),
% 42.93/27.98 inference(monotonicity,[status(thm)],[925])).
% 42.93/27.98 tff(927,plain,
% 42.93/27.98 (phi(f5(P!7, not1(false))) = phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 42.93/27.98 inference(symmetry,[status(thm)],[926])).
% 42.93/27.98 tff(928,plain,
% 42.93/27.98 (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))),
% 42.93/27.98 inference(symmetry,[status(thm)],[172])).
% 42.93/27.98 tff(929,plain,
% 42.93/27.98 (bool(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))) <=> bool(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 42.93/27.98 inference(monotonicity,[status(thm)],[928])).
% 42.93/27.98 tff(930,plain,
% 42.93/27.98 (bool(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) <=> bool(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)))),
% 42.93/27.98 inference(symmetry,[status(thm)],[929])).
% 42.93/27.98 tff(931,plain,
% 42.93/27.98 (f5(P!7, not1(false)) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))),
% 42.93/27.98 inference(transitivity,[status(thm)],[203, 916])).
% 42.93/27.98 tff(932,plain,
% 42.93/27.98 (bool(f5(P!7, not1(false))) <=> bool(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 42.93/27.98 inference(monotonicity,[status(thm)],[931])).
% 42.93/27.98 tff(933,plain,
% 42.93/27.98 (bool(f5(P!7, not1(false))) <=> bool(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)))),
% 42.93/27.98 inference(transitivity,[status(thm)],[932, 930])).
% 42.93/27.98 tff(934,assumption,(~(impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false))))), introduced(assumption)).
% 42.93/27.98 tff(935,plain,
% 42.93/27.98 (bool(f5(P!7, not1(false)))),
% 42.93/27.98 inference(unit_resolution,[status(thm)],[256, 934])).
% 42.93/27.98 tff(936,plain,
% 42.93/27.98 (bool(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)))),
% 42.93/27.98 inference(modus_ponens,[status(thm)],[935, 933])).
% 42.93/27.98 tff(937,assumption,(~(bool(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)), not1(false)) = false) | (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = not1(false))))), introduced(assumption)).
% 42.93/27.98 tff(938,plain,
% 42.93/27.98 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))) <=> ((impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = false) | (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = not1(false))))),
% 42.93/27.98 inference(quant_inst,[status(thm)],[])).
% 42.93/27.98 tff(939,plain,
% 42.93/27.98 ($false),
% 42.93/27.98 inference(unit_resolution,[status(thm)],[938, 218, 937])).
% 42.93/27.98 tff(940,plain,(bool(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)), not1(false)) = false) | (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 42.93/27.98 tff(941,plain,
% 42.93/27.98 ((~(bool(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)), not1(false)) = false) | (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = not1(false))))) | (~bool(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)), not1(false)) = false) | (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = not1(false)))),
% 42.93/27.98 inference(tautology,[status(thm)],[])).
% 42.93/27.98 tff(942,plain,
% 42.93/27.98 ((~bool(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)), not1(false)) = false) | (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = not1(false)))),
% 42.93/27.98 inference(unit_resolution,[status(thm)],[941, 940])).
% 42.93/27.98 tff(943,plain,
% 42.93/27.98 ((impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = false) | (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = not1(false))),
% 42.93/27.98 inference(unit_resolution,[status(thm)],[942, 936])).
% 42.93/27.98 tff(944,assumption,(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = false), introduced(assumption)).
% 42.93/27.98 tff(945,plain,
% 42.93/27.98 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7)))) <=> ((lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = false) | (lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = not1(false))))),
% 42.93/27.98 inference(quant_inst,[status(thm)],[])).
% 42.93/27.98 tff(946,plain,
% 42.93/27.98 (bool(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7)))) <=> ((lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = false) | (lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = not1(false)))),
% 42.93/27.98 inference(unit_resolution,[status(thm)],[945, 218])).
% 42.93/27.98 tff(947,plain,
% 42.93/27.98 (((~![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(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(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(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))))))) | (~((~d(false)) | d(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7)))))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), 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(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(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(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))))))) | (~((~d(false)) | d(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7)))))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = false)))))))),
% 42.93/27.98 inference(rewrite,[status(thm)],[])).
% 42.93/27.98 tff(948,plain,
% 42.93/27.98 ((forallprefers(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))), false) <=> ((~(d(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7)))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(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(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))))))) | (~((~(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = false)) | (~(false = not1(false))))))) <=> (forallprefers(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(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(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))))))) | (~((~d(false)) | d(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7)))))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = false))))))),
% 42.93/27.98 inference(rewrite,[status(thm)],[])).
% 42.93/27.98 tff(949,plain,
% 42.93/27.98 (((~![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(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))), false) <=> ((~(d(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7)))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(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(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))))))) | (~((~(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), 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(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(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(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))))))) | (~((~d(false)) | d(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7)))))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = false)))))))),
% 42.93/27.98 inference(monotonicity,[status(thm)],[948])).
% 42.93/27.98 tff(950,plain,
% 42.93/27.98 (((~![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(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))), false) <=> ((~(d(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7)))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(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(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))))))) | (~((~(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), 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(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(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(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))))))) | (~((~d(false)) | d(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7)))))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = false)))))))),
% 42.93/27.98 inference(transitivity,[status(thm)],[949, 947])).
% 42.93/27.98 tff(951,plain,
% 42.93/27.98 ((~![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(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))), false) <=> ((~(d(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7)))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(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(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))))))) | (~((~(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = false)) | (~(false = not1(false)))))))),
% 42.93/27.98 inference(quant_inst,[status(thm)],[])).
% 42.93/27.98 tff(952,plain,
% 42.93/27.98 ((~![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(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(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(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))))))) | (~((~d(false)) | d(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7)))))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = false))))))),
% 42.93/27.98 inference(modus_ponens,[status(thm)],[951, 950])).
% 42.93/27.98 tff(953,plain,
% 42.93/27.98 (forallprefers(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(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(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))))))) | (~((~d(false)) | d(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7)))))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = false)))))),
% 42.93/27.98 inference(unit_resolution,[status(thm)],[952, 338])).
% 42.93/27.98 tff(954,plain,
% 42.93/27.98 (f7(false) = f7(P!6)),
% 42.93/27.98 inference(symmetry,[status(thm)],[409])).
% 42.93/27.98 tff(955,plain,
% 42.93/27.98 (false = f7(P!6)),
% 42.93/27.98 inference(transitivity,[status(thm)],[349, 348, 347, 346, 954])).
% 42.93/27.98 tff(956,plain,
% 42.93/27.98 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))))),
% 42.93/27.98 inference(quant_inst,[status(thm)],[])).
% 42.93/27.98 tff(957,plain,
% 42.93/27.98 (f7(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 42.93/27.98 inference(unit_resolution,[status(thm)],[956, 306])).
% 42.93/27.98 tff(958,plain,
% 42.93/27.98 (lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = f7(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 42.93/27.98 inference(symmetry,[status(thm)],[957])).
% 42.93/27.98 tff(959,plain,
% 42.93/27.98 (forallprefers(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))), false) <=> forallprefers(f7(apply(P!7, tptp_fun_X_4(not1(false), P!7))), f7(P!6))),
% 42.93/27.98 inference(monotonicity,[status(thm)],[958, 955])).
% 42.93/27.98 tff(960,plain,
% 42.93/27.98 (forallprefers(f7(apply(P!7, tptp_fun_X_4(not1(false), P!7))), f7(P!6)) <=> forallprefers(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))), false)),
% 42.93/27.98 inference(symmetry,[status(thm)],[959])).
% 42.93/27.98 tff(961,plain,
% 42.93/27.98 ((~forallprefers(f7(apply(P!7, tptp_fun_X_4(not1(false), P!7))), f7(P!6))) <=> (~forallprefers(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))), false))),
% 42.93/27.98 inference(monotonicity,[status(thm)],[960])).
% 42.93/27.98 tff(962,plain,
% 42.93/27.98 ((~![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))) | (~forallprefers(f7(apply(P!7, tptp_fun_X_4(not1(false), P!7))), f7(P!6)))),
% 42.93/27.98 inference(quant_inst,[status(thm)],[])).
% 42.93/27.98 tff(963,plain,
% 42.93/27.98 (~forallprefers(f7(apply(P!7, tptp_fun_X_4(not1(false), P!7))), f7(P!6))),
% 42.93/27.98 inference(unit_resolution,[status(thm)],[962, 362])).
% 42.93/27.98 tff(964,plain,
% 42.93/27.98 (~forallprefers(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))), false)),
% 42.93/27.98 inference(modus_ponens,[status(thm)],[963, 961])).
% 42.93/27.98 tff(965,plain,
% 42.93/27.98 ((~(forallprefers(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(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(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))))))) | (~((~d(false)) | d(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7)))))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = false))))))) | forallprefers(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))), false) | (~((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(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(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))))))) | (~((~d(false)) | d(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7)))))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = false))))))),
% 42.93/27.98 inference(tautology,[status(thm)],[])).
% 42.93/27.98 tff(966,plain,
% 42.93/27.98 (~((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(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(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))))))) | (~((~d(false)) | d(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7)))))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = false)))))),
% 42.93/27.98 inference(unit_resolution,[status(thm)],[965, 964, 953])).
% 42.93/27.98 tff(967,plain,
% 42.93/27.98 (((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(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(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))))))) | (~((~d(false)) | d(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7)))))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = false))))) | ((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(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(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))))))),
% 42.93/27.98 inference(tautology,[status(thm)],[])).
% 42.93/27.98 tff(968,plain,
% 42.93/27.98 ((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(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(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7)))))),
% 42.93/27.98 inference(unit_resolution,[status(thm)],[967, 966])).
% 42.93/27.98 tff(969,plain,
% 42.93/27.98 (((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(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(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))))))) | (~((~d(false)) | d(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7)))))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = false))))) | ((~d(false)) | d(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7)))))),
% 42.93/27.98 inference(tautology,[status(thm)],[])).
% 42.93/27.98 tff(970,plain,
% 42.93/27.98 ((~d(false)) | d(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))))),
% 42.93/27.98 inference(unit_resolution,[status(thm)],[969, 966])).
% 42.93/27.98 tff(971,plain,
% 42.93/27.98 ((~((~d(false)) | d(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7)))))) | (~d(false)) | d(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))))),
% 42.93/27.98 inference(tautology,[status(thm)],[])).
% 42.93/27.98 tff(972,plain,
% 42.93/27.98 ((~((~d(false)) | d(lazy_impl(prop(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(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))))),
% 42.93/27.98 inference(unit_resolution,[status(thm)],[971, 5])).
% 42.93/27.98 tff(973,plain,
% 42.93/27.98 (d(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))))),
% 42.93/27.98 inference(unit_resolution,[status(thm)],[972, 970])).
% 42.93/27.98 tff(974,plain,
% 42.93/27.98 ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(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(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))))))) | (~d(false)) | (~bool(false)) | bool(lazy_impl(prop(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(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7)))))),
% 42.93/27.98 inference(tautology,[status(thm)],[])).
% 42.93/27.98 tff(975,plain,
% 42.93/27.98 ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(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(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))))))) | bool(lazy_impl(prop(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(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7)))))),
% 42.93/27.99 inference(unit_resolution,[status(thm)],[974, 5, 61])).
% 42.93/27.99 tff(976,plain,
% 42.93/27.99 (bool(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))))),
% 42.93/27.99 inference(unit_resolution,[status(thm)],[975, 973, 968])).
% 42.93/27.99 tff(977,plain,
% 42.93/27.99 ((~(bool(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7)))) <=> ((lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = false) | (lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = not1(false))))) | (~bool(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))))) | ((lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = false) | (lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = not1(false)))),
% 42.93/27.99 inference(tautology,[status(thm)],[])).
% 42.93/27.99 tff(978,plain,
% 42.93/27.99 ((~(bool(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7)))) <=> ((lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = false) | (lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = not1(false))))) | ((lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = false) | (lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = not1(false)))),
% 42.93/27.99 inference(unit_resolution,[status(thm)],[977, 976])).
% 42.93/27.99 tff(979,plain,
% 42.93/27.99 ((lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = false) | (lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = not1(false))),
% 42.93/27.99 inference(unit_resolution,[status(thm)],[978, 946])).
% 42.93/27.99 tff(980,plain,
% 42.93/27.99 ((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))) <=> (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))))),
% 42.93/27.99 inference(commutativity,[status(thm)],[])).
% 42.93/27.99 tff(981,plain,
% 42.93/27.99 (false = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))),
% 42.93/27.99 inference(symmetry,[status(thm)],[944])).
% 42.93/27.99 tff(982,plain,
% 42.93/27.99 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))))),
% 42.93/27.99 inference(quant_inst,[status(thm)],[])).
% 42.93/27.99 tff(983,plain,
% 42.93/27.99 (lazy_impl(not1(false), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = phi(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 42.93/27.99 inference(unit_resolution,[status(thm)],[982, 33])).
% 42.93/27.99 tff(984,plain,
% 42.93/27.99 ((~![X: $i] : ((prop(X) = not1(false)) <=> bool(X))) | ((prop(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))))),
% 42.93/27.99 inference(quant_inst,[status(thm)],[])).
% 42.93/27.99 tff(985,plain,
% 42.93/27.99 ((prop(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)))),
% 42.93/27.99 inference(unit_resolution,[status(thm)],[984, 111])).
% 42.93/27.99 tff(986,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)).
% 42.93/27.99 tff(987,plain,
% 42.93/27.99 (((~![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)))))),
% 42.93/27.99 inference(rewrite,[status(thm)],[])).
% 42.93/27.99 tff(988,plain,
% 42.93/27.99 ((~![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)))))),
% 42.93/27.99 inference(quant_inst,[status(thm)],[])).
% 42.93/27.99 tff(989,plain,
% 42.93/27.99 ((~![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))))),
% 42.93/27.99 inference(modus_ponens,[status(thm)],[988, 987])).
% 42.93/27.99 tff(990,plain,
% 42.93/27.99 (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))))),
% 42.93/27.99 inference(unit_resolution,[status(thm)],[989, 252])).
% 42.93/27.99 tff(991,plain,
% 42.93/27.99 (bool(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 42.93/27.99 inference(unit_resolution,[status(thm)],[990, 986])).
% 42.93/27.99 tff(992,plain,
% 42.93/27.99 ((~((prop(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))))) | (prop(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))))),
% 42.93/27.99 inference(tautology,[status(thm)],[])).
% 42.93/27.99 tff(993,plain,
% 42.93/27.99 ((~((prop(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))))) | (prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = not1(false))),
% 42.93/27.99 inference(unit_resolution,[status(thm)],[992, 991])).
% 42.93/27.99 tff(994,plain,
% 42.93/27.99 (prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = not1(false)),
% 42.93/27.99 inference(unit_resolution,[status(thm)],[993, 985])).
% 42.93/27.99 tff(995,plain,
% 42.93/27.99 (not1(false) = prop(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 42.93/27.99 inference(symmetry,[status(thm)],[994])).
% 42.93/27.99 tff(996,plain,
% 42.93/27.99 (lazy_impl(not1(false), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 42.93/27.99 inference(monotonicity,[status(thm)],[995])).
% 42.93/27.99 tff(997,plain,
% 42.93/27.99 (lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = lazy_impl(not1(false), apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 42.93/27.99 inference(symmetry,[status(thm)],[996])).
% 42.93/27.99 tff(998,plain,
% 42.93/27.99 (lazy_impl(prop(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)))),
% 42.93/27.99 inference(transitivity,[status(thm)],[997, 983])).
% 42.93/27.99 tff(999,plain,
% 42.93/27.99 ((lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = 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)))),
% 42.93/27.99 inference(monotonicity,[status(thm)],[998, 981])).
% 42.93/27.99 tff(1000,plain,
% 42.93/27.99 ((lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), 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))))),
% 42.93/27.99 inference(transitivity,[status(thm)],[999, 980])).
% 42.93/27.99 tff(1001,plain,
% 42.93/27.99 ((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)))) <=> (lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = false)),
% 42.93/27.99 inference(symmetry,[status(thm)],[1000])).
% 42.93/27.99 tff(1002,plain,
% 42.93/27.99 ((~(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))))) <=> (~(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = false))),
% 42.93/27.99 inference(monotonicity,[status(thm)],[1001])).
% 42.93/27.99 tff(1003,plain,
% 42.93/27.99 (~(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = false)),
% 42.93/27.99 inference(modus_ponens,[status(thm)],[986, 1002])).
% 42.93/27.99 tff(1004,plain,
% 42.93/27.99 ((~((lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = false) | (lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = not1(false)))) | (lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = false) | (lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = not1(false))),
% 42.93/27.99 inference(tautology,[status(thm)],[])).
% 42.93/27.99 tff(1005,plain,
% 42.93/27.99 ((~((lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = false) | (lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = not1(false)))) | (lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = not1(false))),
% 42.93/27.99 inference(unit_resolution,[status(thm)],[1004, 1003])).
% 42.93/27.99 tff(1006,plain,
% 42.93/27.99 (lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7))) = not1(false)),
% 42.93/27.99 inference(unit_resolution,[status(thm)],[1005, 979])).
% 42.93/27.99 tff(1007,plain,
% 42.93/27.99 (phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = lazy_impl(not1(false), apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 42.93/27.99 inference(symmetry,[status(thm)],[983])).
% 42.93/27.99 tff(1008,plain,
% 42.93/27.99 (bool(lazy_impl(prop(apply(P!7, tptp_fun_X_4(not1(false), P!7))), apply(P!7, tptp_fun_X_4(not1(false), P!7)))) <=> bool(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))))),
% 42.93/27.99 inference(monotonicity,[status(thm)],[998])).
% 42.93/27.99 tff(1009,plain,
% 42.93/27.99 (bool(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))))),
% 42.93/27.99 inference(modus_ponens,[status(thm)],[976, 1008])).
% 42.93/27.99 tff(1010,assumption,(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err), introduced(assumption)).
% 42.93/27.99 tff(1011,plain,
% 42.93/27.99 (bool(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7)))) <=> bool(err)),
% 42.93/27.99 inference(monotonicity,[status(thm)],[1010])).
% 42.93/27.99 tff(1012,plain,
% 42.93/27.99 (bool(err) <=> bool(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))))),
% 42.93/27.99 inference(symmetry,[status(thm)],[1011])).
% 42.93/27.99 tff(1013,plain,
% 42.93/27.99 ((~bool(err)) <=> (~bool(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7)))))),
% 42.93/27.99 inference(monotonicity,[status(thm)],[1012])).
% 42.93/27.99 tff(1014,plain,
% 42.93/27.99 (~bool(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))))),
% 42.93/27.99 inference(modus_ponens,[status(thm)],[241, 1013])).
% 42.93/27.99 tff(1015,assumption,(bool(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))))), introduced(assumption)).
% 42.93/27.99 tff(1016,plain,
% 42.93/27.99 ($false),
% 42.93/27.99 inference(unit_resolution,[status(thm)],[1015, 1014])).
% 42.93/27.99 tff(1017,plain,((~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err)) | (~bool(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7)))))), inference(lemma,lemma(discharge,[]))).
% 42.93/27.99 tff(1018,plain,
% 42.93/27.99 (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err)),
% 42.93/27.99 inference(unit_resolution,[status(thm)],[1017, 1009])).
% 42.93/27.99 tff(1019,plain,
% 42.93/27.99 ((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)),
% 42.93/27.99 inference(tautology,[status(thm)],[])).
% 42.93/27.99 tff(1020,plain,
% 42.93/27.99 (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))),
% 42.93/27.99 inference(unit_resolution,[status(thm)],[1019, 1018])).
% 42.93/27.99 tff(1021,plain,
% 42.93/27.99 (((~![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)))))),
% 42.93/27.99 inference(rewrite,[status(thm)],[])).
% 42.93/27.99 tff(1022,plain,
% 42.93/27.99 ((~![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)))))),
% 42.93/27.99 inference(quant_inst,[status(thm)],[])).
% 42.93/27.99 tff(1023,plain,
% 42.93/27.99 ((~![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))))),
% 42.93/27.99 inference(modus_ponens,[status(thm)],[1022, 1021])).
% 42.93/27.99 tff(1024,plain,
% 42.93/27.99 ((~((~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))))),
% 42.93/27.99 inference(unit_resolution,[status(thm)],[1023, 17])).
% 42.93/27.99 tff(1025,plain,
% 42.93/27.99 (~((~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)))))),
% 42.93/27.99 inference(unit_resolution,[status(thm)],[1024, 1020])).
% 42.93/27.99 tff(1026,plain,
% 42.93/27.99 (((~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)))),
% 42.93/27.99 inference(tautology,[status(thm)],[])).
% 42.93/27.99 tff(1027,plain,
% 42.93/27.99 (phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = apply(P!7, tptp_fun_X_4(not1(false), P!7))),
% 42.93/27.99 inference(unit_resolution,[status(thm)],[1026, 1025])).
% 42.93/27.99 tff(1028,plain,
% 42.93/27.99 (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = phi(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 42.93/27.99 inference(symmetry,[status(thm)],[1027])).
% 42.93/27.99 tff(1029,plain,
% 42.93/27.99 (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = not1(false)),
% 42.93/27.99 inference(transitivity,[status(thm)],[1028, 1007, 996, 1006])).
% 42.93/27.99 tff(1030,plain,
% 42.93/27.99 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = impl(not1(false), not1(false))),
% 42.93/27.99 inference(monotonicity,[status(thm)],[1029])).
% 42.93/27.99 tff(1031,plain,
% 42.93/27.99 (impl(not1(false), not1(false)) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))),
% 42.93/27.99 inference(symmetry,[status(thm)],[1030])).
% 42.93/27.99 tff(1032,plain,
% 42.93/27.99 (not1(false) = impl(not1(false), not1(false))),
% 42.93/27.99 inference(symmetry,[status(thm)],[612])).
% 42.93/27.99 tff(1033,plain,
% 42.93/27.99 (not1(false) = false),
% 42.93/27.99 inference(transitivity,[status(thm)],[1032, 1031, 944])).
% 42.93/27.99 tff(1034,plain,
% 42.93/27.99 ($false),
% 42.93/27.99 inference(unit_resolution,[status(thm)],[45, 1033])).
% 42.93/27.99 tff(1035,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)))) | (~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = false))), inference(lemma,lemma(discharge,[]))).
% 42.93/27.99 tff(1036,plain,
% 42.93/27.99 (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)))),
% 42.93/27.99 inference(unit_resolution,[status(thm)],[1035, 944])).
% 42.93/27.99 tff(1037,plain,
% 42.93/27.99 (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))),
% 42.93/27.99 inference(symmetry,[status(thm)],[1036])).
% 42.93/27.99 tff(1038,plain,
% 42.93/27.99 (phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = false),
% 42.93/27.99 inference(transitivity,[status(thm)],[1037, 944])).
% 42.93/27.99 tff(1039,plain,
% 42.93/27.99 ((phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err) <=> (false = err)),
% 42.93/27.99 inference(monotonicity,[status(thm)],[1038])).
% 42.93/27.99 tff(1040,plain,
% 42.93/27.99 ((false = err) <=> (phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err)),
% 42.93/27.99 inference(symmetry,[status(thm)],[1039])).
% 42.93/27.99 tff(1041,plain,
% 42.93/27.99 ((~(false = err)) <=> (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err))),
% 42.93/27.99 inference(monotonicity,[status(thm)],[1040])).
% 42.93/27.99 tff(1042,plain,
% 42.93/27.99 (~(phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = err)),
% 42.93/27.99 inference(modus_ponens,[status(thm)],[226, 1041])).
% 42.93/27.99 tff(1043,plain,
% 42.93/27.99 (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))),
% 42.93/27.99 inference(unit_resolution,[status(thm)],[1019, 1042])).
% 42.93/27.99 tff(1044,plain,
% 42.93/27.99 (~((~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)))))),
% 42.93/27.99 inference(unit_resolution,[status(thm)],[1023, 17, 1043])).
% 42.93/27.99 tff(1045,plain,
% 42.93/27.99 (phi(apply(P!7, tptp_fun_X_4(not1(false), P!7))) = apply(P!7, tptp_fun_X_4(not1(false), P!7))),
% 42.93/27.99 inference(unit_resolution,[status(thm)],[1026, 1044])).
% 42.93/27.99 tff(1046,plain,
% 42.93/27.99 (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = phi(apply(P!7, tptp_fun_X_4(not1(false), P!7)))),
% 42.93/27.99 inference(symmetry,[status(thm)],[1045])).
% 42.93/27.99 tff(1047,plain,
% 42.93/27.99 (apply(P!7, tptp_fun_X_4(not1(false), P!7)) = false),
% 42.93/27.99 inference(transitivity,[status(thm)],[1046, 1037, 944])).
% 42.93/27.99 tff(1048,plain,
% 42.93/27.99 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = impl(false, not1(false))),
% 42.93/27.99 inference(monotonicity,[status(thm)],[1047])).
% 42.93/27.99 tff(1049,plain,
% 42.93/27.99 (impl(false, not1(false)) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))),
% 42.93/27.99 inference(symmetry,[status(thm)],[1048])).
% 42.93/27.99 tff(1050,plain,
% 42.93/27.99 (not1(false) = impl(false, not1(false))),
% 42.93/27.99 inference(symmetry,[status(thm)],[161])).
% 42.93/27.99 tff(1051,plain,
% 42.93/27.99 (not1(false) = false),
% 42.93/27.99 inference(transitivity,[status(thm)],[1050, 1049, 944])).
% 42.93/27.99 tff(1052,plain,
% 42.93/27.99 ($false),
% 42.93/27.99 inference(unit_resolution,[status(thm)],[45, 1051])).
% 42.93/27.99 tff(1053,plain,(~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = false)), inference(lemma,lemma(discharge,[]))).
% 42.93/27.99 tff(1054,plain,
% 42.93/27.99 ((~((impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = false) | (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)) = false) | (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = not1(false))),
% 42.93/27.99 inference(tautology,[status(thm)],[])).
% 42.93/27.99 tff(1055,plain,
% 42.93/27.99 ((~((impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = false) | (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)) = not1(false))),
% 42.93/27.99 inference(unit_resolution,[status(thm)],[1054, 1053])).
% 42.93/27.99 tff(1056,plain,
% 42.93/27.99 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = not1(false)),
% 42.93/27.99 inference(unit_resolution,[status(thm)],[1055, 943])).
% 42.93/27.99 tff(1057,plain,
% 42.93/27.99 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))) = not1(false)),
% 42.93/27.99 inference(transitivity,[status(thm)],[162, 1056])).
% 42.93/27.99 tff(1058,plain,
% 42.93/27.99 (impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)) = impl(not1(false), not1(false))),
% 42.93/27.99 inference(monotonicity,[status(thm)],[1057])).
% 42.93/27.99 tff(1059,plain,
% 42.93/27.99 (impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)) = not1(false)),
% 42.93/27.99 inference(transitivity,[status(thm)],[1058, 612])).
% 42.93/27.99 tff(1060,plain,
% 42.93/27.99 (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), not1(false))),
% 42.93/27.99 inference(monotonicity,[status(thm)],[263, 1059])).
% 42.93/27.99 tff(1061,plain,
% 42.93/27.99 (lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = not1(false)),
% 42.93/27.99 inference(transitivity,[status(thm)],[919, 1060, 316, 142])).
% 42.93/27.99 tff(1062,plain,
% 42.93/27.99 ((not1(false) = 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)), not1(false)) = not1(false))),
% 42.93/27.99 inference(commutativity,[status(thm)],[])).
% 42.93/27.99 tff(1063,assumption,(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = not1(false)), introduced(assumption)).
% 42.93/27.99 tff(1064,plain,
% 42.93/27.99 (phi(f5(P!7, not1(false))) = err),
% 42.93/27.99 inference(transitivity,[status(thm)],[205, 184])).
% 42.93/27.99 tff(1065,plain,
% 42.93/27.99 (phi(impl(f5(P!7, not1(false)), not1(false))) = not1(false)),
% 42.93/27.99 inference(transitivity,[status(thm)],[752, 749, 1063])).
% 42.93/27.99 tff(1066,plain,
% 42.93/27.99 ((phi(impl(f5(P!7, not1(false)), not1(false))) = err) <=> (not1(false) = err)),
% 42.93/27.99 inference(monotonicity,[status(thm)],[1065])).
% 42.93/27.99 tff(1067,plain,
% 42.93/27.99 ((not1(false) = err) <=> (phi(impl(f5(P!7, not1(false)), not1(false))) = err)),
% 42.93/27.99 inference(symmetry,[status(thm)],[1066])).
% 42.93/27.99 tff(1068,plain,
% 42.93/27.99 ((~(not1(false) = err)) <=> (~(phi(impl(f5(P!7, not1(false)), not1(false))) = err))),
% 42.93/27.99 inference(monotonicity,[status(thm)],[1067])).
% 42.93/27.99 tff(1069,plain,
% 42.93/27.99 (~(phi(impl(f5(P!7, not1(false)), not1(false))) = err)),
% 42.93/27.99 inference(modus_ponens,[status(thm)],[235, 1068])).
% 42.93/27.99 tff(1070,plain,
% 42.93/27.99 ((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)),
% 42.93/27.99 inference(tautology,[status(thm)],[])).
% 42.93/27.99 tff(1071,plain,
% 42.93/27.99 (d(impl(f5(P!7, not1(false)), not1(false))) | (~(phi(impl(f5(P!7, not1(false)), not1(false))) = err))),
% 42.93/27.99 inference(unit_resolution,[status(thm)],[1070, 1069])).
% 42.93/27.99 tff(1072,plain,
% 42.93/27.99 (((~![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)))))),
% 42.93/27.99 inference(rewrite,[status(thm)],[])).
% 42.93/27.99 tff(1073,plain,
% 42.93/27.99 ((~![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)))))),
% 42.93/27.99 inference(quant_inst,[status(thm)],[])).
% 42.93/27.99 tff(1074,plain,
% 42.93/27.99 ((~![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))))),
% 42.93/27.99 inference(modus_ponens,[status(thm)],[1073, 1072])).
% 42.93/27.99 tff(1075,plain,
% 42.93/27.99 ((~((~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))))),
% 42.93/27.99 inference(unit_resolution,[status(thm)],[1074, 17])).
% 42.93/27.99 tff(1076,plain,
% 42.93/27.99 (~((~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)))))),
% 42.93/27.99 inference(unit_resolution,[status(thm)],[1075, 1071])).
% 42.93/27.99 tff(1077,plain,
% 42.93/27.99 (((~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)))),
% 42.93/27.99 inference(tautology,[status(thm)],[])).
% 42.93/27.99 tff(1078,plain,
% 42.93/27.99 (phi(impl(f5(P!7, not1(false)), not1(false))) = impl(f5(P!7, not1(false)), not1(false))),
% 42.93/27.99 inference(unit_resolution,[status(thm)],[1077, 1076])).
% 42.93/27.99 tff(1079,plain,
% 42.93/27.99 (impl(f5(P!7, not1(false)), not1(false)) = phi(impl(f5(P!7, not1(false)), not1(false)))),
% 42.93/27.99 inference(symmetry,[status(thm)],[1078])).
% 42.93/27.99 tff(1080,plain,
% 42.93/27.99 (impl(f5(P!7, not1(false)), not1(false)) = not1(false)),
% 42.93/27.99 inference(transitivity,[status(thm)],[1079, 752, 749, 1063])).
% 42.93/28.00 tff(1081,plain,
% 42.93/28.00 ((impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false)))) <=> (not1(false) = err)),
% 42.93/28.00 inference(monotonicity,[status(thm)],[1080, 1064])).
% 42.93/28.00 tff(1082,plain,
% 42.93/28.00 ((not1(false) = err) <=> (impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false))))),
% 42.93/28.00 inference(symmetry,[status(thm)],[1081])).
% 42.93/28.00 tff(1083,plain,
% 42.93/28.00 ((~(not1(false) = err)) <=> (~(impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false)))))),
% 42.93/28.00 inference(monotonicity,[status(thm)],[1082])).
% 42.93/28.00 tff(1084,plain,
% 42.93/28.00 (~(impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false))))),
% 42.93/28.00 inference(modus_ponens,[status(thm)],[235, 1083])).
% 42.93/28.00 tff(1085,plain,
% 42.93/28.00 ($false),
% 42.93/28.00 inference(unit_resolution,[status(thm)],[256, 1084, 242])).
% 42.93/28.00 tff(1086,plain,((~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err)) | (~(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 42.93/28.00 tff(1087,plain,
% 42.93/28.00 (~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err)),
% 42.93/28.00 inference(unit_resolution,[status(thm)],[1086, 1063])).
% 42.93/28.00 tff(1088,plain,
% 42.93/28.00 (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))),
% 42.93/28.00 inference(unit_resolution,[status(thm)],[905, 1087])).
% 42.93/28.00 tff(1089,plain,
% 42.93/28.00 (~((~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)))))),
% 42.93/28.00 inference(unit_resolution,[status(thm)],[913, 1088])).
% 42.93/28.00 tff(1090,plain,
% 42.93/28.00 (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))),
% 42.93/28.00 inference(unit_resolution,[status(thm)],[915, 1089])).
% 42.93/28.00 tff(1091,plain,
% 42.93/28.00 (f5(P!7, not1(false)) = f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))),
% 42.93/28.00 inference(transitivity,[status(thm)],[203, 1090])).
% 42.93/28.00 tff(1092,plain,
% 42.93/28.00 (phi(f5(P!7, not1(false))) = phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 42.93/28.00 inference(monotonicity,[status(thm)],[1091])).
% 42.93/28.00 tff(1093,plain,
% 42.93/28.00 (phi(f5(P!7, not1(false))) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))),
% 42.93/28.00 inference(transitivity,[status(thm)],[1092, 1090, 172])).
% 42.93/28.00 tff(1094,plain,
% 42.93/28.00 ((impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false)))) <=> (not1(false) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)))),
% 42.93/28.00 inference(monotonicity,[status(thm)],[1080, 1093])).
% 42.93/28.00 tff(1095,plain,
% 42.93/28.00 ((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)) = not1(false))),
% 42.93/28.00 inference(transitivity,[status(thm)],[1094, 1062])).
% 42.93/28.00 tff(1096,plain,
% 42.93/28.00 ((impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = not1(false)) <=> (impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false))))),
% 42.93/28.00 inference(symmetry,[status(thm)],[1095])).
% 42.93/28.00 tff(1097,assumption,(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = not1(false)), introduced(assumption)).
% 42.93/28.00 tff(1098,plain,
% 42.93/28.00 (impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false)))),
% 42.93/28.00 inference(modus_ponens,[status(thm)],[1097, 1096])).
% 42.93/28.00 tff(1099,plain,
% 42.93/28.00 ($false),
% 42.93/28.00 inference(unit_resolution,[status(thm)],[934, 1098])).
% 42.93/28.00 tff(1100,plain,((~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = not1(false))) | (impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false)))) | (~(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 42.93/28.00 tff(1101,plain,
% 42.93/28.00 (~(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = not1(false))),
% 42.93/28.00 inference(unit_resolution,[status(thm)],[1100, 1056, 934])).
% 42.93/28.00 tff(1102,plain,
% 42.93/28.00 ($false),
% 42.93/28.00 inference(unit_resolution,[status(thm)],[1101, 1061])).
% 42.93/28.00 tff(1103,plain,(impl(f5(P!7, not1(false)), not1(false)) = phi(f5(P!7, not1(false)))), inference(lemma,lemma(discharge,[]))).
% 42.93/28.00 tff(1104,plain,
% 42.93/28.00 (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))),
% 42.93/28.00 inference(symmetry,[status(thm)],[918])).
% 42.93/28.00 tff(1105,plain,
% 42.93/28.00 (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))),
% 42.93/28.00 inference(transitivity,[status(thm)],[1104, 1103, 927, 916])).
% 42.93/28.00 tff(1106,plain,
% 42.93/28.00 (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)))),
% 42.93/28.00 inference(monotonicity,[status(thm)],[1105])).
% 42.93/28.00 tff(1107,plain,
% 42.93/28.00 ((~![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))))),
% 42.93/28.00 inference(quant_inst,[status(thm)],[])).
% 42.93/28.00 tff(1108,plain,
% 42.93/28.00 (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)))),
% 42.93/28.00 inference(unit_resolution,[status(thm)],[1107, 33])).
% 42.93/28.00 tff(1109,plain,
% 42.93/28.00 (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)))),
% 42.93/28.00 inference(monotonicity,[status(thm)],[263])).
% 42.93/28.00 tff(1110,plain,
% 42.93/28.00 (lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false))),
% 42.93/28.00 inference(transitivity,[status(thm)],[919, 1109, 1108, 1106, 916, 172])).
% 42.93/28.00 tff(1111,plain,
% 42.93/28.00 ((lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = false) <=> (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = false)),
% 42.93/28.00 inference(monotonicity,[status(thm)],[1110])).
% 42.93/28.00 tff(1112,plain,
% 42.93/28.00 ((impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = false) <=> (lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))) = false)),
% 42.93/28.00 inference(symmetry,[status(thm)],[1111])).
% 42.93/28.00 tff(1113,plain,
% 42.93/28.00 ((impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = 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))) = false)),
% 42.93/28.00 inference(transitivity,[status(thm)],[1112, 922])).
% 42.93/28.00 tff(1114,plain,
% 42.93/28.00 ((~(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = 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))) = false))),
% 42.93/28.00 inference(monotonicity,[status(thm)],[1113])).
% 42.93/28.00 tff(1115,plain,
% 42.93/28.00 (~(lazy_impl(prop(not1(false)), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))) = false)),
% 42.93/28.00 inference(modus_ponens,[status(thm)],[1053, 1114])).
% 42.93/28.00 tff(1116,plain,
% 42.93/28.00 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = 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)))) <=> ((lazy_impl(prop(not1(false)), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))) = 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))) = not1(false))))),
% 42.93/28.00 inference(quant_inst,[status(thm)],[])).
% 42.93/28.00 tff(1117,plain,
% 42.93/28.00 (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)))) <=> ((lazy_impl(prop(not1(false)), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))) = 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))) = not1(false)))),
% 42.93/28.00 inference(unit_resolution,[status(thm)],[1116, 218])).
% 42.93/28.00 tff(1118,plain,
% 42.93/28.00 (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(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))),
% 42.93/28.00 inference(monotonicity,[status(thm)],[920])).
% 42.93/28.00 tff(1119,plain,
% 42.93/28.00 (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))))),
% 42.93/28.00 inference(symmetry,[status(thm)],[1118])).
% 42.93/28.00 tff(1120,assumption,(phi(f6(P!7, tptp_fun_R_5(P!7))) = err), introduced(assumption)).
% 42.93/28.00 tff(1121,plain,
% 42.93/28.00 (exists2(P!7) = err),
% 42.93/28.00 inference(transitivity,[status(thm)],[294, 1120])).
% 42.93/28.00 tff(1122,plain,
% 42.93/28.00 (bool(exists2(P!7)) <=> bool(err)),
% 42.93/28.00 inference(monotonicity,[status(thm)],[1121])).
% 42.93/28.00 tff(1123,plain,
% 42.93/28.00 (bool(err) <=> bool(exists2(P!7))),
% 42.93/28.00 inference(symmetry,[status(thm)],[1122])).
% 42.93/28.00 tff(1124,plain,
% 42.93/28.00 ((~bool(err)) <=> (~bool(exists2(P!7)))),
% 42.93/28.00 inference(monotonicity,[status(thm)],[1123])).
% 42.93/28.00 tff(1125,plain,
% 42.93/28.00 (~bool(exists2(P!7))),
% 42.93/28.00 inference(modus_ponens,[status(thm)],[241, 1124])).
% 42.93/28.00 tff(1126,plain,
% 42.93/28.00 ($false),
% 42.93/28.00 inference(unit_resolution,[status(thm)],[688, 1125])).
% 42.93/28.00 tff(1127,plain,(~(phi(f6(P!7, tptp_fun_R_5(P!7))) = err)), inference(lemma,lemma(discharge,[]))).
% 42.93/28.00 tff(1128,plain,
% 42.93/28.00 ((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)),
% 42.93/28.00 inference(tautology,[status(thm)],[])).
% 42.93/28.00 tff(1129,plain,
% 42.93/28.00 (d(f6(P!7, tptp_fun_R_5(P!7))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = err))),
% 42.93/28.00 inference(unit_resolution,[status(thm)],[1128, 1127])).
% 42.93/28.00 tff(1130,plain,
% 42.93/28.00 (((~![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)))))),
% 42.93/28.00 inference(rewrite,[status(thm)],[])).
% 42.93/28.00 tff(1131,plain,
% 42.93/28.00 ((~![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)))))),
% 42.93/28.00 inference(quant_inst,[status(thm)],[])).
% 42.93/28.00 tff(1132,plain,
% 42.93/28.00 ((~![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))))),
% 42.93/28.00 inference(modus_ponens,[status(thm)],[1131, 1130])).
% 42.93/28.00 tff(1133,plain,
% 42.93/28.00 ((~((~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))))),
% 42.93/28.00 inference(unit_resolution,[status(thm)],[1132, 17])).
% 42.93/28.00 tff(1134,plain,
% 42.93/28.00 (~((~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)))))),
% 42.93/28.00 inference(unit_resolution,[status(thm)],[1133, 1129])).
% 42.93/28.00 tff(1135,plain,
% 42.93/28.00 (((~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)))),
% 42.93/28.00 inference(tautology,[status(thm)],[])).
% 42.93/28.00 tff(1136,plain,
% 42.93/28.00 (d(f6(P!7, tptp_fun_R_5(P!7)))),
% 42.93/28.00 inference(unit_resolution,[status(thm)],[1135, 1134])).
% 42.93/28.00 tff(1137,plain,
% 42.93/28.00 (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))))),
% 42.93/28.00 inference(modus_ponens,[status(thm)],[1136, 710])).
% 42.93/28.00 tff(1138,plain,
% 42.93/28.00 (((~(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))))) | (~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)))))) | (~((~(lazy_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))))))),
% 42.93/28.00 inference(tautology,[status(thm)],[])).
% 42.93/28.00 tff(1139,plain,
% 42.93/28.00 (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)))))),
% 42.93/28.00 inference(unit_resolution,[status(thm)],[1138, 732])).
% 42.93/28.00 tff(1140,plain,
% 42.93/28.00 ((~(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(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)))))),
% 42.93/28.00 inference(tautology,[status(thm)],[])).
% 42.93/28.00 tff(1141,plain,
% 42.93/28.00 (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)))))),
% 42.93/28.00 inference(unit_resolution,[status(thm)],[1140, 1139])).
% 42.93/28.00 tff(1142,plain,
% 42.93/28.00 (d(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))),
% 42.93/28.00 inference(unit_resolution,[status(thm)],[1141, 1137])).
% 42.93/28.00 tff(1143,plain,
% 42.93/28.00 (phi(f6(P!7, tptp_fun_R_5(P!7))) = exists2(P!7)),
% 42.93/28.00 inference(symmetry,[status(thm)],[294])).
% 42.93/28.00 tff(1144,plain,
% 42.93/28.00 (((~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)))),
% 42.93/28.00 inference(tautology,[status(thm)],[])).
% 42.93/28.00 tff(1145,plain,
% 42.93/28.00 (phi(f6(P!7, tptp_fun_R_5(P!7))) = f6(P!7, tptp_fun_R_5(P!7))),
% 42.93/28.00 inference(unit_resolution,[status(thm)],[1144, 1134])).
% 42.93/28.00 tff(1146,plain,
% 42.93/28.00 (f6(P!7, tptp_fun_R_5(P!7)) = phi(f6(P!7, tptp_fun_R_5(P!7)))),
% 42.93/28.00 inference(symmetry,[status(thm)],[1145])).
% 42.93/28.00 tff(1147,plain,
% 42.93/28.00 (f6(P!7, tptp_fun_R_5(P!7)) = exists2(P!7)),
% 42.93/28.00 inference(transitivity,[status(thm)],[1146, 1143])).
% 42.93/28.00 tff(1148,plain,
% 42.93/28.00 (bool(f6(P!7, tptp_fun_R_5(P!7))) <=> bool(exists2(P!7))),
% 42.93/28.00 inference(monotonicity,[status(thm)],[1147])).
% 42.93/28.00 tff(1149,plain,
% 42.93/28.00 (bool(exists2(P!7)) <=> bool(f6(P!7, tptp_fun_R_5(P!7)))),
% 42.93/28.00 inference(symmetry,[status(thm)],[1148])).
% 42.93/28.00 tff(1150,plain,
% 42.93/28.00 (bool(exists2(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))))),
% 42.93/28.00 inference(transitivity,[status(thm)],[1149, 704])).
% 42.93/28.00 tff(1151,plain,
% 42.93/28.00 (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))))),
% 42.93/28.00 inference(modus_ponens,[status(thm)],[688, 1150])).
% 42.93/28.00 tff(1152,plain,
% 42.93/28.00 (bool(lazy_impl(prop(not1(false)), impl(f5(P!7, not1(false)), not1(false))))),
% 42.93/28.00 inference(unit_resolution,[status(thm)],[736, 1151, 1142, 1137])).
% 42.93/28.00 tff(1153,plain,
% 42.93/28.00 (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))))),
% 42.93/28.00 inference(modus_ponens,[status(thm)],[1152, 1119])).
% 42.93/28.00 tff(1154,plain,
% 42.93/28.00 ((~(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)))) <=> ((lazy_impl(prop(not1(false)), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))) = 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))) = 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))))) | ((lazy_impl(prop(not1(false)), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))) = 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))) = not1(false)))),
% 42.93/28.00 inference(tautology,[status(thm)],[])).
% 42.93/28.00 tff(1155,plain,
% 42.93/28.00 ((lazy_impl(prop(not1(false)), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))) = 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))) = not1(false))),
% 42.93/28.00 inference(unit_resolution,[status(thm)],[1154, 1153, 1117])).
% 42.93/28.00 tff(1156,plain,
% 42.93/28.00 ((~((lazy_impl(prop(not1(false)), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))) = 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))) = 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))) = 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))) = not1(false))),
% 42.93/28.00 inference(tautology,[status(thm)],[])).
% 42.93/28.00 tff(1157,plain,
% 42.93/28.00 ((lazy_impl(prop(not1(false)), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))) = 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))) = not1(false))),
% 42.93/28.00 inference(unit_resolution,[status(thm)],[1156, 1155])).
% 42.93/28.00 tff(1158,plain,
% 42.93/28.00 (lazy_impl(prop(not1(false)), impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))) = not1(false)),
% 42.93/28.00 inference(unit_resolution,[status(thm)],[1157, 1115])).
% 42.93/28.00 tff(1159,plain,
% 42.93/28.00 (((~![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)))),
% 42.93/28.00 inference(rewrite,[status(thm)],[])).
% 42.93/28.00 tff(1160,plain,
% 42.93/28.00 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(err) | (impl(err, false) = phi(err)))),
% 42.93/28.00 inference(quant_inst,[status(thm)],[])).
% 42.93/28.00 tff(1161,plain,
% 42.93/28.00 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(err) | (impl(err, false) = phi(err))),
% 42.93/28.00 inference(modus_ponens,[status(thm)],[1160, 1159])).
% 42.93/28.00 tff(1162,plain,
% 42.93/28.00 (impl(err, false) = phi(err)),
% 42.93/28.00 inference(unit_resolution,[status(thm)],[1161, 252, 241])).
% 42.93/28.00 tff(1163,plain,
% 42.93/28.00 ((~![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))))))),
% 42.93/28.00 inference(quant_inst,[status(thm)],[])).
% 42.93/28.00 tff(1164,plain,
% 42.93/28.00 (~((~(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)))))),
% 42.93/28.00 inference(unit_resolution,[status(thm)],[1163, 199])).
% 42.93/28.00 tff(1165,plain,
% 42.93/28.00 (((~(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)))),
% 42.93/28.00 inference(tautology,[status(thm)],[])).
% 42.93/28.00 tff(1166,plain,
% 42.93/28.00 (f5(P!7, false) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 42.93/28.00 inference(unit_resolution,[status(thm)],[1165, 1164])).
% 42.93/28.00 tff(1167,plain,
% 42.93/28.00 (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f5(P!7, false)),
% 42.93/28.00 inference(symmetry,[status(thm)],[1166])).
% 42.93/28.00 tff(1168,assumption,(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err), introduced(assumption)).
% 42.93/28.00 tff(1169,plain,
% 42.93/28.00 (err = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 42.93/28.00 inference(symmetry,[status(thm)],[1168])).
% 42.93/28.00 tff(1170,plain,
% 42.93/28.00 (err = f5(P!7, false)),
% 42.93/28.00 inference(transitivity,[status(thm)],[1169, 1167])).
% 42.93/28.00 tff(1171,plain,
% 42.93/28.00 (impl(err, false) = impl(f5(P!7, false), false)),
% 42.93/28.00 inference(monotonicity,[status(thm)],[1170])).
% 42.93/28.00 tff(1172,plain,
% 42.93/28.00 (impl(f5(P!7, false), false) = impl(err, false)),
% 42.93/28.00 inference(symmetry,[status(thm)],[1171])).
% 42.93/28.00 tff(1173,plain,
% 42.93/28.00 (impl(f5(P!7, false), false) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)),
% 42.93/28.00 inference(monotonicity,[status(thm)],[1166, 866])).
% 42.93/28.00 tff(1174,plain,
% 42.93/28.00 (impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2) = impl(f5(P!7, false), false)),
% 42.93/28.00 inference(symmetry,[status(thm)],[1173])).
% 42.93/28.00 tff(1175,plain,
% 42.93/28.00 (lazy_impl(not1(false), impl(f5(P!7, false), false)) = lazy_impl(prop(false), impl(f5(P!7, false), false))),
% 42.93/28.00 inference(monotonicity,[status(thm)],[117])).
% 42.93/28.00 tff(1176,plain,
% 42.93/28.00 ((~![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)))),
% 42.93/28.00 inference(quant_inst,[status(thm)],[])).
% 42.93/28.00 tff(1177,plain,
% 42.93/28.00 (lazy_impl(not1(false), impl(f5(P!7, false), false)) = phi(impl(f5(P!7, false), false))),
% 42.93/28.00 inference(unit_resolution,[status(thm)],[1176, 33])).
% 42.93/28.00 tff(1178,plain,
% 42.93/28.00 (phi(impl(f5(P!7, false), false)) = lazy_impl(not1(false), impl(f5(P!7, false), false))),
% 42.93/28.00 inference(symmetry,[status(thm)],[1177])).
% 42.93/28.00 tff(1179,plain,
% 42.93/28.00 (phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = phi(impl(f5(P!7, false), false))),
% 42.93/28.00 inference(monotonicity,[status(thm)],[1174])).
% 42.93/28.00 tff(1180,assumption,(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err), introduced(assumption)).
% 42.93/28.00 tff(1181,plain,
% 42.93/28.00 (err = phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))),
% 42.93/28.00 inference(symmetry,[status(thm)],[1180])).
% 42.93/28.00 tff(1182,plain,
% 42.93/28.00 (err = lazy_impl(prop(false), impl(f5(P!7, false), false))),
% 42.93/28.00 inference(transitivity,[status(thm)],[1181, 1179, 1178, 1175])).
% 42.93/28.00 tff(1183,plain,
% 42.93/28.00 (bool(err) <=> bool(lazy_impl(prop(false), impl(f5(P!7, false), false)))),
% 42.93/28.00 inference(monotonicity,[status(thm)],[1182])).
% 42.93/28.00 tff(1184,plain,
% 42.93/28.00 (bool(lazy_impl(prop(false), impl(f5(P!7, false), false))) <=> bool(err)),
% 42.93/28.00 inference(symmetry,[status(thm)],[1183])).
% 42.93/28.00 tff(1185,plain,
% 42.93/28.00 (((~![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))))))) | (~((~(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)))))))) <=> ((~![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))))))) | (~((~(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))))))))),
% 42.93/28.01 inference(rewrite,[status(thm)],[])).
% 42.93/28.01 tff(1186,plain,
% 42.93/28.01 ((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)))) <=> ((~(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))))) | (~((~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)))))))),
% 42.93/28.01 inference(rewrite,[status(thm)],[])).
% 42.93/28.01 tff(1187,plain,
% 42.93/28.01 (((~![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)))) <=> ((~(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))))) | (~((~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))))))))),
% 42.93/28.01 inference(monotonicity,[status(thm)],[1186])).
% 42.93/28.01 tff(1188,plain,
% 42.93/28.01 (((~![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)))) <=> ((~(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))))) | (~((~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))))))))),
% 42.93/28.01 inference(transitivity,[status(thm)],[1187, 1185])).
% 42.93/28.01 tff(1189,plain,
% 42.93/28.01 ((~![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)))))))),
% 42.93/28.01 inference(quant_inst,[status(thm)],[])).
% 42.93/28.01 tff(1190,plain,
% 42.93/28.01 ((~![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))))))) | (~((~(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)))))))),
% 43.02/28.01 inference(modus_ponens,[status(thm)],[1189, 1188])).
% 43.02/28.01 tff(1191,plain,
% 43.02/28.01 (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))))))) | (~((~(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))))))),
% 43.02/28.01 inference(unit_resolution,[status(thm)],[1190, 338])).
% 43.02/28.01 tff(1192,plain,
% 43.02/28.01 (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)))),
% 43.02/28.01 inference(monotonicity,[status(thm)],[878, 702])).
% 43.02/28.01 tff(1193,plain,
% 43.02/28.01 (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))))),
% 43.02/28.01 inference(symmetry,[status(thm)],[1192])).
% 43.02/28.01 tff(1194,plain,
% 43.02/28.01 ((~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)))))),
% 43.02/28.01 inference(monotonicity,[status(thm)],[1193])).
% 43.02/28.01 tff(1195,plain,
% 43.02/28.01 ((~![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))))),
% 43.02/28.01 inference(quant_inst,[status(thm)],[])).
% 43.02/28.01 tff(1196,plain,
% 43.02/28.01 (~forallprefers(f6(P!7, false), f6(P!7, tptp_fun_R_5(P!7)))),
% 43.02/28.01 inference(unit_resolution,[status(thm)],[1195, 727])).
% 43.02/28.01 tff(1197,plain,
% 43.02/28.01 (~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))))),
% 43.02/28.01 inference(modus_ponens,[status(thm)],[1196, 1194])).
% 43.02/28.01 tff(1198,plain,
% 43.02/28.01 ((~(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))))))) | (~((~(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)))))))) | 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))))))) | (~((~(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)))))))),
% 43.02/28.01 inference(tautology,[status(thm)],[])).
% 43.02/28.01 tff(1199,plain,
% 43.02/28.01 (~((~(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))))) | (~((~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))))))),
% 43.02/28.01 inference(unit_resolution,[status(thm)],[1198, 1197, 1191])).
% 43.02/28.01 tff(1200,plain,
% 43.02/28.01 (((~(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))))) | (~((~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))))))),
% 43.02/28.01 inference(tautology,[status(thm)],[])).
% 43.02/28.01 tff(1201,plain,
% 43.02/28.01 (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)))))),
% 43.02/28.01 inference(unit_resolution,[status(thm)],[1200, 1199])).
% 43.02/28.01 tff(1202,plain,
% 43.02/28.01 ((~(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)))))),
% 43.02/28.01 inference(tautology,[status(thm)],[])).
% 43.02/28.01 tff(1203,plain,
% 43.02/28.01 (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)))))),
% 43.02/28.01 inference(unit_resolution,[status(thm)],[1202, 1201])).
% 43.02/28.01 tff(1204,plain,
% 43.02/28.01 (d(lazy_impl(prop(false), impl(f5(P!7, false), false)))),
% 43.02/28.01 inference(unit_resolution,[status(thm)],[1203, 1137])).
% 43.02/28.01 tff(1205,plain,
% 43.02/28.01 (((~(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))))) | (~((~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))))),
% 43.02/28.01 inference(tautology,[status(thm)],[])).
% 43.02/28.01 tff(1206,plain,
% 43.02/28.01 ((~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)))),
% 43.02/28.01 inference(unit_resolution,[status(thm)],[1205, 1199])).
% 43.02/28.01 tff(1207,plain,
% 43.02/28.01 ((~((~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)))),
% 43.02/28.01 inference(tautology,[status(thm)],[])).
% 43.02/28.01 tff(1208,plain,
% 43.02/28.01 ((~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)))),
% 43.02/28.01 inference(unit_resolution,[status(thm)],[1207, 1206])).
% 43.02/28.01 tff(1209,plain,
% 43.02/28.01 (bool(lazy_impl(prop(false), impl(f5(P!7, false), false)))),
% 43.02/28.01 inference(unit_resolution,[status(thm)],[1208, 1204, 1151, 1137])).
% 43.02/28.01 tff(1210,plain,
% 43.02/28.01 (bool(err)),
% 43.02/28.01 inference(modus_ponens,[status(thm)],[1209, 1184])).
% 43.02/28.01 tff(1211,plain,
% 43.02/28.01 ($false),
% 43.02/28.01 inference(unit_resolution,[status(thm)],[241, 1210])).
% 43.02/28.01 tff(1212,plain,(~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err)), inference(lemma,lemma(discharge,[]))).
% 43.02/28.01 tff(1213,plain,
% 43.02/28.01 ((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)),
% 43.02/28.01 inference(tautology,[status(thm)],[])).
% 43.02/28.01 tff(1214,plain,
% 43.02/28.01 (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))),
% 43.02/28.01 inference(unit_resolution,[status(thm)],[1213, 1212])).
% 43.02/28.01 tff(1215,plain,
% 43.02/28.01 (((~![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)) = 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)))))),
% 43.02/28.01 inference(rewrite,[status(thm)],[])).
% 43.02/28.01 tff(1216,plain,
% 43.02/28.01 ((~![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)))))),
% 43.02/28.01 inference(quant_inst,[status(thm)],[])).
% 43.02/28.01 tff(1217,plain,
% 43.02/28.01 ((~![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))))),
% 43.02/28.01 inference(modus_ponens,[status(thm)],[1216, 1215])).
% 43.02/28.01 tff(1218,plain,
% 43.02/28.01 ((~((~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))))),
% 43.02/28.01 inference(unit_resolution,[status(thm)],[1217, 17])).
% 43.02/28.01 tff(1219,plain,
% 43.02/28.01 (~((~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))))),
% 43.02/28.01 inference(unit_resolution,[status(thm)],[1218, 1214])).
% 43.02/28.01 tff(1220,plain,
% 43.02/28.01 (((~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))),
% 43.02/28.01 inference(tautology,[status(thm)],[])).
% 43.02/28.01 tff(1221,plain,
% 43.02/28.01 (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)),
% 43.02/28.01 inference(unit_resolution,[status(thm)],[1220, 1219])).
% 43.02/28.01 tff(1222,plain,
% 43.02/28.01 (phi(impl(f5(P!7, false), false)) = phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))),
% 43.02/28.01 inference(symmetry,[status(thm)],[1179])).
% 43.02/28.01 tff(1223,plain,
% 43.02/28.01 (lazy_impl(prop(false), impl(f5(P!7, false), false)) = lazy_impl(not1(false), impl(f5(P!7, false), false))),
% 43.02/28.01 inference(symmetry,[status(thm)],[1175])).
% 43.02/28.01 tff(1224,plain,
% 43.02/28.01 (bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) <=> bool(err)),
% 43.02/28.01 inference(monotonicity,[status(thm)],[1168])).
% 43.02/28.01 tff(1225,plain,
% 43.02/28.01 (bool(err) <=> bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 43.02/28.01 inference(symmetry,[status(thm)],[1224])).
% 43.02/28.01 tff(1226,plain,
% 43.02/28.01 ((~bool(err)) <=> (~bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 43.02/28.01 inference(monotonicity,[status(thm)],[1225])).
% 43.02/28.01 tff(1227,plain,
% 43.02/28.01 (~bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 43.02/28.01 inference(modus_ponens,[status(thm)],[241, 1226])).
% 43.02/28.01 tff(1228,plain,
% 43.02/28.01 (phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = phi(err)),
% 43.02/28.01 inference(monotonicity,[status(thm)],[1168])).
% 43.02/28.01 tff(1229,plain,
% 43.02/28.01 (phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = err),
% 43.02/28.01 inference(transitivity,[status(thm)],[1228, 184])).
% 43.02/28.01 tff(1230,plain,
% 43.02/28.01 (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)))),
% 43.02/28.01 inference(symmetry,[status(thm)],[1158])).
% 43.02/28.01 tff(1231,assumption,(lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false)), introduced(assumption)).
% 43.02/28.01 tff(1232,plain,
% 43.02/28.01 (phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 43.02/28.01 inference(transitivity,[status(thm)],[1179, 1178, 1175, 1231, 1230, 1109, 1108, 1106])).
% 43.02/28.01 tff(1233,plain,
% 43.02/28.01 ((phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err) <=> (phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err)),
% 43.02/28.01 inference(monotonicity,[status(thm)],[1232])).
% 43.02/28.01 tff(1234,plain,
% 43.02/28.01 ((phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err) <=> (phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err)),
% 43.02/28.01 inference(symmetry,[status(thm)],[1233])).
% 43.02/28.01 tff(1235,plain,
% 43.02/28.01 ((~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err)) <=> (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err))),
% 43.02/28.01 inference(monotonicity,[status(thm)],[1234])).
% 43.02/28.01 tff(1236,plain,
% 43.02/28.01 (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err)),
% 43.02/28.01 inference(modus_ponens,[status(thm)],[904, 1235])).
% 43.02/28.01 tff(1237,plain,
% 43.02/28.01 (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))),
% 43.02/28.01 inference(unit_resolution,[status(thm)],[1213, 1236])).
% 43.02/28.01 tff(1238,plain,
% 43.02/28.01 (~((~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))))),
% 43.02/28.02 inference(unit_resolution,[status(thm)],[1218, 1237])).
% 43.02/28.02 tff(1239,plain,
% 43.02/28.02 (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)),
% 43.02/28.02 inference(unit_resolution,[status(thm)],[1220, 1238])).
% 43.02/28.02 tff(1240,plain,
% 43.02/28.02 (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))),
% 43.02/28.02 inference(symmetry,[status(thm)],[1239])).
% 43.02/28.02 tff(1241,plain,
% 43.02/28.02 (impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false) = impl(f5(P!7, false), false)),
% 43.02/28.02 inference(monotonicity,[status(thm)],[1167])).
% 43.02/28.02 tff(1242,plain,
% 43.02/28.02 (impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false) = phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false)))),
% 43.02/28.02 inference(transitivity,[status(thm)],[1241, 1173, 1240, 1179, 1178, 1175, 1231, 1230, 1109, 1108, 1106])).
% 43.02/28.02 tff(1243,plain,
% 43.02/28.02 ((impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false) = phi(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))) = err)),
% 43.02/28.02 inference(monotonicity,[status(thm)],[1242, 1229])).
% 43.02/28.02 tff(1244,plain,
% 43.02/28.02 ((phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err) <=> (impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 43.02/28.02 inference(symmetry,[status(thm)],[1243])).
% 43.02/28.02 tff(1245,plain,
% 43.02/28.02 ((~(phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = err)) <=> (~(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))))),
% 43.02/28.02 inference(monotonicity,[status(thm)],[1244])).
% 43.02/28.02 tff(1246,plain,
% 43.02/28.02 (~(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 43.02/28.02 inference(modus_ponens,[status(thm)],[904, 1245])).
% 43.02/28.02 tff(1247,plain,
% 43.02/28.02 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))))),
% 43.02/28.02 inference(rewrite,[status(thm)],[])).
% 43.02/28.02 tff(1248,plain,
% 43.02/28.02 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))))),
% 43.02/28.02 inference(quant_inst,[status(thm)],[])).
% 43.02/28.02 tff(1249,plain,
% 43.02/28.02 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 43.02/28.02 inference(modus_ponens,[status(thm)],[1248, 1247])).
% 43.02/28.02 tff(1250,plain,
% 43.02/28.02 (bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 43.02/28.02 inference(unit_resolution,[status(thm)],[1249, 252])).
% 43.02/28.02 tff(1251,plain,
% 43.02/28.02 ($false),
% 43.02/28.02 inference(unit_resolution,[status(thm)],[1250, 1246, 1227])).
% 43.02/28.02 tff(1252,plain,((~(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)))), inference(lemma,lemma(discharge,[]))).
% 43.02/28.02 tff(1253,plain,
% 43.02/28.02 (~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false))),
% 43.02/28.02 inference(unit_resolution,[status(thm)],[1252, 1168])).
% 43.02/28.02 tff(1254,plain,
% 43.02/28.02 ((~![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))))),
% 43.02/28.02 inference(quant_inst,[status(thm)],[])).
% 43.02/28.02 tff(1255,plain,
% 43.02/28.02 (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)))),
% 43.02/28.02 inference(unit_resolution,[status(thm)],[1254, 218])).
% 43.02/28.02 tff(1256,plain,
% 43.02/28.02 ((~(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)))),
% 43.02/28.02 inference(tautology,[status(thm)],[])).
% 43.02/28.02 tff(1257,plain,
% 43.02/28.02 ((~(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)))),
% 43.02/28.02 inference(unit_resolution,[status(thm)],[1256, 1209])).
% 43.02/28.02 tff(1258,plain,
% 43.02/28.02 ((lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false))),
% 43.02/28.02 inference(unit_resolution,[status(thm)],[1257, 1255])).
% 43.02/28.02 tff(1259,plain,
% 43.02/28.02 ((~((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))),
% 43.02/28.02 inference(tautology,[status(thm)],[])).
% 43.02/28.02 tff(1260,plain,
% 43.02/28.02 ((lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false))),
% 43.02/28.02 inference(unit_resolution,[status(thm)],[1259, 1258])).
% 43.02/28.02 tff(1261,plain,
% 43.02/28.02 (lazy_impl(prop(false), impl(f5(P!7, false), false)) = false),
% 43.02/28.02 inference(unit_resolution,[status(thm)],[1260, 1253])).
% 43.02/28.02 tff(1262,plain,
% 43.02/28.02 (false = lazy_impl(prop(false), impl(f5(P!7, false), false))),
% 43.02/28.02 inference(symmetry,[status(thm)],[1261])).
% 43.02/28.02 tff(1263,plain,
% 43.02/28.02 (false = err),
% 43.02/28.02 inference(transitivity,[status(thm)],[1262, 1223, 1177, 1222, 1221, 1174, 1172, 1162, 184])).
% 43.02/28.02 tff(1264,plain,
% 43.02/28.02 ($false),
% 43.02/28.02 inference(unit_resolution,[status(thm)],[226, 1263])).
% 43.02/28.02 tff(1265,plain,(~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err)), inference(lemma,lemma(discharge,[]))).
% 43.02/28.02 tff(1266,plain,
% 43.02/28.02 ((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)),
% 43.02/28.02 inference(tautology,[status(thm)],[])).
% 43.02/28.02 tff(1267,plain,
% 43.02/28.02 (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))),
% 43.02/28.02 inference(unit_resolution,[status(thm)],[1266, 1265])).
% 43.02/28.02 tff(1268,plain,
% 43.02/28.02 (((~![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)))))),
% 43.02/28.02 inference(rewrite,[status(thm)],[])).
% 43.02/28.02 tff(1269,plain,
% 43.02/28.02 ((~![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)))))),
% 43.02/28.02 inference(quant_inst,[status(thm)],[])).
% 43.02/28.02 tff(1270,plain,
% 43.02/28.02 ((~![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))))),
% 43.02/28.02 inference(modus_ponens,[status(thm)],[1269, 1268])).
% 43.02/28.02 tff(1271,plain,
% 43.02/28.02 ((~((~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))))),
% 43.02/28.02 inference(unit_resolution,[status(thm)],[1270, 17])).
% 43.02/28.02 tff(1272,plain,
% 43.02/28.02 (~((~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))))),
% 43.02/28.02 inference(unit_resolution,[status(thm)],[1271, 1267])).
% 43.02/28.02 tff(1273,plain,
% 43.02/28.02 (not1(false) = phi(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)))),
% 43.02/28.02 inference(transitivity,[status(thm)],[1230, 1109, 1108])).
% 43.02/28.02 tff(1274,plain,
% 43.02/28.02 (((~![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(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), false) <=> ((~((~(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))) = false)) | (~(false = not1(false))))) | (~((~d(false)) | d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(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(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), false) <=> ((~((~(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))) = false)) | (~(false = not1(false))))) | (~((~d(false)) | d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))))))))),
% 43.02/28.02 inference(rewrite,[status(thm)],[])).
% 43.02/28.02 tff(1275,plain,
% 43.02/28.02 ((forallprefers(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), false) <=> ((~(d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))))) | (~((~(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))) = false)) | (~(false = not1(false))))))) <=> (forallprefers(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), false) <=> ((~((~(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))) = false)) | (~(false = not1(false))))) | (~((~d(false)) | d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))))))),
% 43.02/28.02 inference(rewrite,[status(thm)],[])).
% 43.02/28.02 tff(1276,plain,
% 43.02/28.02 (((~![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(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), false) <=> ((~(d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))))) | (~((~(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(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(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), false) <=> ((~((~(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))) = false)) | (~(false = not1(false))))) | (~((~d(false)) | d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))))))))),
% 43.02/28.02 inference(monotonicity,[status(thm)],[1275])).
% 43.02/28.02 tff(1277,plain,
% 43.02/28.02 (((~![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(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), false) <=> ((~(d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))))) | (~((~(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(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(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), false) <=> ((~((~(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))) = false)) | (~(false = not1(false))))) | (~((~d(false)) | d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))))))))),
% 43.02/28.02 inference(transitivity,[status(thm)],[1276, 1274])).
% 43.02/28.02 tff(1278,plain,
% 43.02/28.02 ((~![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(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), false) <=> ((~(d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))))) | (~((~(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))) = false)) | (~(false = not1(false)))))))),
% 43.02/28.02 inference(quant_inst,[status(thm)],[])).
% 43.02/28.02 tff(1279,plain,
% 43.02/28.02 ((~![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(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), false) <=> ((~((~(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))) = false)) | (~(false = not1(false))))) | (~((~d(false)) | d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))))))),
% 43.02/28.02 inference(modus_ponens,[status(thm)],[1278, 1277])).
% 43.02/28.02 tff(1280,plain,
% 43.02/28.02 (forallprefers(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), false) <=> ((~((~(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))) = false)) | (~(false = not1(false))))) | (~((~d(false)) | d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))))))),
% 43.02/28.02 inference(unit_resolution,[status(thm)],[1279, 338])).
% 43.02/28.02 tff(1281,plain,
% 43.02/28.02 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(phi(f6(P!7, tptp_fun_R_5(P!7)))) = lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 43.02/28.02 inference(quant_inst,[status(thm)],[])).
% 43.02/28.02 tff(1282,plain,
% 43.02/28.02 (f7(phi(f6(P!7, tptp_fun_R_5(P!7)))) = lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))),
% 43.02/28.02 inference(unit_resolution,[status(thm)],[1281, 306])).
% 43.02/28.02 tff(1283,plain,
% 43.02/28.02 (lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))) = f7(phi(f6(P!7, tptp_fun_R_5(P!7))))),
% 43.02/28.02 inference(symmetry,[status(thm)],[1282])).
% 43.02/28.02 tff(1284,plain,
% 43.02/28.02 (forallprefers(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), false) <=> forallprefers(f7(phi(f6(P!7, tptp_fun_R_5(P!7)))), f7(P!6))),
% 43.02/28.02 inference(monotonicity,[status(thm)],[1283, 955])).
% 43.02/28.02 tff(1285,plain,
% 43.02/28.02 (forallprefers(f7(phi(f6(P!7, tptp_fun_R_5(P!7)))), f7(P!6)) <=> forallprefers(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), false)),
% 43.02/28.02 inference(symmetry,[status(thm)],[1284])).
% 43.02/28.02 tff(1286,plain,
% 43.02/28.02 ((~forallprefers(f7(phi(f6(P!7, tptp_fun_R_5(P!7)))), f7(P!6))) <=> (~forallprefers(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), false))),
% 43.02/28.02 inference(monotonicity,[status(thm)],[1285])).
% 43.02/28.02 tff(1287,plain,
% 43.02/28.02 ((~![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))) | (~forallprefers(f7(phi(f6(P!7, tptp_fun_R_5(P!7)))), f7(P!6)))),
% 43.02/28.02 inference(quant_inst,[status(thm)],[])).
% 43.02/28.02 tff(1288,plain,
% 43.02/28.02 (~forallprefers(f7(phi(f6(P!7, tptp_fun_R_5(P!7)))), f7(P!6))),
% 43.02/28.02 inference(unit_resolution,[status(thm)],[1287, 362])).
% 43.02/28.02 tff(1289,plain,
% 43.02/28.02 (~forallprefers(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), false)),
% 43.02/28.02 inference(modus_ponens,[status(thm)],[1288, 1286])).
% 43.02/28.02 tff(1290,plain,
% 43.02/28.02 ((~(forallprefers(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), false) <=> ((~((~(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))) = false)) | (~(false = not1(false))))) | (~((~d(false)) | d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))))))) | forallprefers(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), false) | (~((~((~(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))) = false)) | (~(false = not1(false))))) | (~((~d(false)) | d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))))))),
% 43.02/28.02 inference(tautology,[status(thm)],[])).
% 43.02/28.02 tff(1291,plain,
% 43.02/28.02 (~((~((~(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))) = false)) | (~(false = not1(false))))) | (~((~d(false)) | d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))))))),
% 43.02/28.02 inference(unit_resolution,[status(thm)],[1290, 1289, 1280])).
% 43.02/28.02 tff(1292,plain,
% 43.02/28.02 (((~((~(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))) = false)) | (~(false = not1(false))))) | (~((~d(false)) | d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))))) | ((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))))),
% 43.02/28.02 inference(tautology,[status(thm)],[])).
% 43.02/28.02 tff(1293,plain,
% 43.02/28.02 ((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 43.02/28.02 inference(unit_resolution,[status(thm)],[1292, 1291])).
% 43.02/28.02 tff(1294,plain,
% 43.02/28.02 (((~((~(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))) = false)) | (~(false = not1(false))))) | (~((~d(false)) | d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))))) | ((~d(false)) | d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 43.02/28.02 inference(tautology,[status(thm)],[])).
% 43.02/28.02 tff(1295,plain,
% 43.02/28.02 ((~d(false)) | d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 43.02/28.02 inference(unit_resolution,[status(thm)],[1294, 1291])).
% 43.02/28.02 tff(1296,plain,
% 43.02/28.02 ((~((~d(false)) | d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~d(false)) | d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 43.02/28.02 inference(tautology,[status(thm)],[])).
% 43.02/28.02 tff(1297,plain,
% 43.02/28.02 ((~((~d(false)) | d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 43.02/28.02 inference(unit_resolution,[status(thm)],[1296, 5])).
% 43.02/28.02 tff(1298,plain,
% 43.02/28.02 (d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 43.02/28.02 inference(unit_resolution,[status(thm)],[1297, 1295])).
% 43.02/28.02 tff(1299,plain,
% 43.02/28.02 ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))))) | (~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 43.02/28.02 inference(tautology,[status(thm)],[])).
% 43.02/28.02 tff(1300,plain,
% 43.02/28.02 ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))))) | bool(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 43.02/28.02 inference(unit_resolution,[status(thm)],[1299, 5, 61])).
% 43.02/28.03 tff(1301,plain,
% 43.02/28.03 (bool(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 43.02/28.03 inference(unit_resolution,[status(thm)],[1300, 1298, 1293])).
% 43.02/28.03 tff(1302,plain,
% 43.02/28.03 (((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | ((~bool(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) | (impl(false, lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = not1(false)))) <=> ((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | (~bool(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) | (impl(false, lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = not1(false)))),
% 43.02/28.03 inference(rewrite,[status(thm)],[])).
% 43.02/28.03 tff(1303,plain,
% 43.02/28.03 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | ((~bool(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) | (impl(false, lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = not1(false)))),
% 43.02/28.03 inference(quant_inst,[status(thm)],[])).
% 43.02/28.03 tff(1304,plain,
% 43.02/28.03 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | (~bool(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) | (impl(false, lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = not1(false))),
% 43.02/28.03 inference(modus_ponens,[status(thm)],[1303, 1302])).
% 43.02/28.03 tff(1305,plain,
% 43.02/28.03 (impl(false, lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = not1(false)),
% 43.02/28.03 inference(unit_resolution,[status(thm)],[1304, 74, 1301])).
% 43.02/28.03 tff(1306,plain,
% 43.02/28.03 (impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(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))),
% 43.02/28.03 inference(monotonicity,[status(thm)],[163, 1305])).
% 43.02/28.03 tff(1307,plain,
% 43.02/28.03 (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(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 43.02/28.03 inference(symmetry,[status(thm)],[1306])).
% 43.02/28.03 tff(1308,plain,
% 43.02/28.03 (impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(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(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 43.02/28.03 inference(monotonicity,[status(thm)],[1307])).
% 43.02/28.03 tff(1309,plain,
% 43.02/28.03 (impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 43.02/28.03 inference(symmetry,[status(thm)],[1308])).
% 43.02/28.03 tff(1310,plain,
% 43.02/28.03 (lazy_impl(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(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)))),
% 43.02/28.03 inference(symmetry,[status(thm)],[1109])).
% 43.02/28.03 tff(1311,plain,
% 43.02/28.03 (phi(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)))),
% 43.02/28.03 inference(symmetry,[status(thm)],[1108])).
% 43.02/28.03 tff(1312,plain,
% 43.02/28.03 (phi(f4(P!7, tptp_fun_X_4(not1(false), P!7), not1(false))) = phi(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)))),
% 43.02/28.03 inference(symmetry,[status(thm)],[1106])).
% 43.02/28.03 tff(1313,plain,
% 43.02/28.03 (impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) = not1(false)),
% 43.02/28.03 inference(transitivity,[status(thm)],[1306, 1104, 1103, 927, 1312, 1311, 1310, 1158])).
% 43.02/28.03 tff(1314,plain,
% 43.02/28.03 (impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = impl(not1(false), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 43.02/28.03 inference(monotonicity,[status(thm)],[1313])).
% 43.02/28.03 tff(1315,plain,
% 43.02/28.03 (impl(not1(false), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(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(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 43.02/28.03 inference(symmetry,[status(thm)],[1314])).
% 43.02/28.03 tff(1316,plain,
% 43.02/28.03 (((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | ((~bool(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) | (impl(not1(false), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) <=> ((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | (~bool(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) | (impl(not1(false), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 43.02/28.03 inference(rewrite,[status(thm)],[])).
% 43.02/28.03 tff(1317,plain,
% 43.02/28.03 ((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | ((~bool(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) | (impl(not1(false), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 43.02/28.03 inference(quant_inst,[status(thm)],[])).
% 43.02/28.03 tff(1318,plain,
% 43.02/28.03 ((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | (~bool(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) | (impl(not1(false), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 43.02/28.03 inference(modus_ponens,[status(thm)],[1317, 1316])).
% 43.02/28.03 tff(1319,plain,
% 43.02/28.03 (impl(not1(false), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))),
% 43.02/28.03 inference(unit_resolution,[status(thm)],[1318, 91, 1301])).
% 43.02/28.03 tff(1320,plain,
% 43.02/28.03 (lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))) = impl(not1(false), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 43.02/28.03 inference(symmetry,[status(thm)],[1319])).
% 43.02/28.03 tff(1321,plain,
% 43.02/28.03 ((~![X: $i] : ((prop(X) = not1(false)) <=> bool(X))) | ((prop(phi(f6(P!7, tptp_fun_R_5(P!7)))) = not1(false)) <=> bool(phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 43.02/28.03 inference(quant_inst,[status(thm)],[])).
% 43.02/28.03 tff(1322,plain,
% 43.02/28.03 ((prop(phi(f6(P!7, tptp_fun_R_5(P!7)))) = not1(false)) <=> bool(phi(f6(P!7, tptp_fun_R_5(P!7))))),
% 43.02/28.03 inference(unit_resolution,[status(thm)],[1321, 111])).
% 43.02/28.03 tff(1323,plain,
% 43.02/28.03 (bool(phi(f6(P!7, tptp_fun_R_5(P!7)))) <=> bool(exists2(P!7))),
% 43.02/28.03 inference(monotonicity,[status(thm)],[1143])).
% 43.02/28.03 tff(1324,plain,
% 43.02/28.03 (bool(exists2(P!7)) <=> bool(phi(f6(P!7, tptp_fun_R_5(P!7))))),
% 43.02/28.03 inference(symmetry,[status(thm)],[1323])).
% 43.02/28.03 tff(1325,plain,
% 43.02/28.03 (bool(phi(f6(P!7, tptp_fun_R_5(P!7))))),
% 43.02/28.03 inference(modus_ponens,[status(thm)],[688, 1324])).
% 43.02/28.03 tff(1326,plain,
% 43.02/28.03 ((~((prop(phi(f6(P!7, tptp_fun_R_5(P!7)))) = not1(false)) <=> bool(phi(f6(P!7, tptp_fun_R_5(P!7)))))) | (prop(phi(f6(P!7, tptp_fun_R_5(P!7)))) = not1(false)) | (~bool(phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 43.02/28.03 inference(tautology,[status(thm)],[])).
% 43.02/28.03 tff(1327,plain,
% 43.02/28.03 (prop(phi(f6(P!7, tptp_fun_R_5(P!7)))) = not1(false)),
% 43.02/28.03 inference(unit_resolution,[status(thm)],[1326, 1325, 1322])).
% 43.02/28.03 tff(1328,plain,
% 43.02/28.03 (lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))) = lazy_impl(not1(false), phi(f6(P!7, tptp_fun_R_5(P!7))))),
% 43.02/28.03 inference(monotonicity,[status(thm)],[1327])).
% 43.02/28.03 tff(1329,plain,
% 43.02/28.03 (lazy_impl(not1(false), phi(f6(P!7, tptp_fun_R_5(P!7)))) = lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))),
% 43.02/28.03 inference(symmetry,[status(thm)],[1328])).
% 43.02/28.03 tff(1330,plain,
% 43.02/28.03 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), phi(f6(P!7, tptp_fun_R_5(P!7)))) = phi(phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 43.02/28.03 inference(quant_inst,[status(thm)],[])).
% 43.02/28.03 tff(1331,plain,
% 43.02/28.03 (lazy_impl(not1(false), phi(f6(P!7, tptp_fun_R_5(P!7)))) = phi(phi(f6(P!7, tptp_fun_R_5(P!7))))),
% 43.02/28.03 inference(unit_resolution,[status(thm)],[1330, 33])).
% 43.02/28.03 tff(1332,plain,
% 43.02/28.03 (phi(phi(f6(P!7, tptp_fun_R_5(P!7)))) = lazy_impl(not1(false), phi(f6(P!7, tptp_fun_R_5(P!7))))),
% 43.02/28.03 inference(symmetry,[status(thm)],[1331])).
% 43.02/28.03 tff(1333,plain,
% 43.02/28.03 (phi(phi(f6(P!7, tptp_fun_R_5(P!7)))) = phi(f6(P!7, tptp_fun_R_5(P!7)))),
% 43.02/28.03 inference(monotonicity,[status(thm)],[1145])).
% 43.02/28.03 tff(1334,plain,
% 43.02/28.03 (phi(f6(P!7, tptp_fun_R_5(P!7))) = phi(phi(f6(P!7, tptp_fun_R_5(P!7))))),
% 43.02/28.03 inference(symmetry,[status(thm)],[1333])).
% 43.02/28.03 tff(1335,assumption,(~(tptp_fun_R_5(P!7) = not1(false))), introduced(assumption)).
% 43.02/28.03 tff(1336,plain,
% 43.02/28.03 (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))),
% 43.02/28.03 inference(monotonicity,[status(thm)],[821])).
% 43.02/28.03 tff(1337,plain,
% 43.02/28.03 (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))),
% 43.02/28.03 inference(symmetry,[status(thm)],[1336])).
% 43.02/28.03 tff(1338,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)).
% 43.02/28.03 tff(1339,plain,
% 43.02/28.03 (((~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))),
% 43.02/28.03 inference(tautology,[status(thm)],[])).
% 43.02/28.03 tff(1340,plain,
% 43.02/28.03 (d(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 43.02/28.03 inference(unit_resolution,[status(thm)],[1339, 1338])).
% 43.02/28.03 tff(1341,plain,
% 43.02/28.03 (d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))),
% 43.02/28.03 inference(modus_ponens,[status(thm)],[1340, 1337])).
% 43.02/28.03 tff(1342,plain,
% 43.02/28.03 (((~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))),
% 43.02/28.03 inference(tautology,[status(thm)],[])).
% 43.02/28.03 tff(1343,plain,
% 43.02/28.03 (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false)),
% 43.02/28.03 inference(unit_resolution,[status(thm)],[1342, 1338])).
% 43.02/28.03 tff(1344,plain,
% 43.02/28.03 ((~![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))))),
% 43.02/28.03 inference(quant_inst,[status(thm)],[])).
% 43.02/28.03 tff(1345,plain,
% 43.02/28.03 (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)))),
% 43.02/28.03 inference(unit_resolution,[status(thm)],[1344, 218])).
% 43.02/28.03 tff(1346,assumption,(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)).
% 43.02/28.03 tff(1347,plain,
% 43.02/28.03 (f4(P!7, tptp_fun_X_4(false, P!7), false) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 43.02/28.03 inference(symmetry,[status(thm)],[1346])).
% 43.02/28.03 tff(1348,plain,
% 43.02/28.03 (bool(f4(P!7, tptp_fun_X_4(false, P!7), false)) <=> bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 43.02/28.03 inference(monotonicity,[status(thm)],[1347])).
% 43.02/28.03 tff(1349,plain,
% 43.02/28.03 (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))),
% 43.02/28.03 inference(monotonicity,[status(thm)],[821])).
% 43.02/28.03 tff(1350,plain,
% 43.02/28.03 (bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) <=> bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 43.02/28.03 inference(transitivity,[status(thm)],[1349, 1348])).
% 43.02/28.03 tff(1351,plain,
% 43.02/28.03 (lazy_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(f6(P!7, tptp_fun_R_5(P!7)))),
% 43.02/28.03 inference(transitivity,[status(thm)],[702, 1146])).
% 43.02/28.03 tff(1352,plain,
% 43.02/28.03 ((lazy_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)) <=> (phi(f6(P!7, tptp_fun_R_5(P!7))) = not1(false))),
% 43.02/28.03 inference(monotonicity,[status(thm)],[1351])).
% 43.02/28.03 tff(1353,plain,
% 43.02/28.03 ((phi(f6(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))),
% 43.02/28.03 inference(symmetry,[status(thm)],[1352])).
% 43.02/28.03 tff(1354,plain,
% 43.02/28.03 (phi(f6(P!7, tptp_fun_R_5(P!7))) = lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))),
% 43.02/28.03 inference(transitivity,[status(thm)],[1334, 1332, 1329])).
% 43.02/28.03 tff(1355,plain,
% 43.02/28.03 ((phi(f6(P!7, tptp_fun_R_5(P!7))) = not1(false)) <=> (lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))) = not1(false))),
% 43.02/28.03 inference(monotonicity,[status(thm)],[1354])).
% 43.02/28.03 tff(1356,plain,
% 43.02/28.03 ((lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))) = not1(false)) <=> (phi(f6(P!7, tptp_fun_R_5(P!7))) = not1(false))),
% 43.02/28.03 inference(symmetry,[status(thm)],[1355])).
% 43.02/28.03 tff(1357,plain,
% 43.02/28.03 (lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))) = impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 43.02/28.03 inference(transitivity,[status(thm)],[1320, 1315, 1309])).
% 43.02/28.03 tff(1358,plain,
% 43.02/28.03 ((lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))) = not1(false)) <=> (impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = phi(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))))),
% 43.02/28.03 inference(monotonicity,[status(thm)],[1357, 1273])).
% 43.02/28.03 tff(1359,plain,
% 43.02/28.03 ((impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = phi(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)))) <=> (lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))) = not1(false))),
% 43.02/28.03 inference(symmetry,[status(thm)],[1358])).
% 43.02/28.03 tff(1360,plain,
% 43.02/28.03 ((impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = phi(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, 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))) = not1(false))),
% 43.02/28.03 inference(transitivity,[status(thm)],[1359, 1356, 1353])).
% 43.02/28.03 tff(1361,plain,
% 43.02/28.03 (impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = phi(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)))),
% 43.02/28.03 inference(transitivity,[status(thm)],[1308, 1314, 1319, 1328, 1331, 1333, 1145, 452, 450, 448, 1230, 1109, 1108])).
% 43.02/28.03 tff(1362,plain,
% 43.02/28.03 (lazy_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)),
% 43.02/28.03 inference(modus_ponens,[status(thm)],[1361, 1360])).
% 43.02/28.03 tff(1363,plain,
% 43.02/28.03 (((~(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))))) | (~((~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)))))) | ((~(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))))),
% 43.02/28.03 inference(tautology,[status(thm)],[])).
% 43.02/28.03 tff(1364,plain,
% 43.02/28.03 ((~(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)))),
% 43.02/28.03 inference(unit_resolution,[status(thm)],[1363, 1199])).
% 43.02/28.03 tff(1365,plain,
% 43.02/28.03 ((~((~(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)))),
% 43.02/28.03 inference(tautology,[status(thm)],[])).
% 43.02/28.03 tff(1366,plain,
% 43.02/28.03 ((~(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)))),
% 43.02/28.03 inference(unit_resolution,[status(thm)],[1365, 1364])).
% 43.02/28.03 tff(1367,plain,
% 43.02/28.03 (~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)),
% 43.02/28.03 inference(unit_resolution,[status(thm)],[1366, 1362])).
% 43.02/28.03 tff(1368,plain,
% 43.02/28.03 (lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false)),
% 43.02/28.03 inference(unit_resolution,[status(thm)],[1260, 1367])).
% 43.02/28.03 tff(1369,plain,
% 43.02/28.03 (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))),
% 43.02/28.03 inference(monotonicity,[status(thm)],[163, 78])).
% 43.02/28.03 tff(1370,plain,
% 43.02/28.03 (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))),
% 43.02/28.03 inference(symmetry,[status(thm)],[1369])).
% 43.02/28.03 tff(1371,plain,
% 43.02/28.03 (phi(f5(P!7, not1(false))) = impl(f5(P!7, not1(false)), not1(false))),
% 43.02/28.03 inference(symmetry,[status(thm)],[1103])).
% 43.02/28.03 tff(1372,plain,
% 43.02/28.03 (not1(false) = impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, false))),
% 43.02/28.03 inference(transitivity,[status(thm)],[1230, 1109, 1108, 1106, 926, 1371, 918, 1370])).
% 43.02/28.03 tff(1373,plain,
% 43.02/28.03 (impl(not1(false), false) = impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, false)), false)),
% 43.02/28.03 inference(monotonicity,[status(thm)],[1372])).
% 43.02/28.03 tff(1374,plain,
% 43.02/28.03 (impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, false)), false) = impl(not1(false), false)),
% 43.02/28.03 inference(symmetry,[status(thm)],[1373])).
% 43.02/28.03 tff(1375,plain,
% 43.02/28.03 (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = phi(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))),
% 43.02/28.03 inference(monotonicity,[status(thm)],[820])).
% 43.02/28.03 tff(1376,plain,
% 43.02/28.03 (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))),
% 43.02/28.03 inference(symmetry,[status(thm)],[1375])).
% 43.02/28.03 tff(1377,assumption,(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))), introduced(assumption)).
% 43.02/28.03 tff(1378,plain,
% 43.02/28.03 (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)),
% 43.02/28.03 inference(monotonicity,[status(thm)],[807])).
% 43.02/28.03 tff(1379,plain,
% 43.02/28.03 (impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false) = impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false)),
% 43.02/28.03 inference(symmetry,[status(thm)],[1378])).
% 43.02/28.03 tff(1380,plain,
% 43.02/28.03 (impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)) = f5(P!7, false)),
% 43.02/28.03 inference(transitivity,[status(thm)],[806, 821, 1347, 1167])).
% 43.02/28.03 tff(1381,plain,
% 43.02/28.03 (impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false) = impl(f5(P!7, false), false)),
% 43.02/28.03 inference(monotonicity,[status(thm)],[1380])).
% 43.02/28.03 tff(1382,plain,
% 43.02/28.03 (impl(f5(P!7, false), false) = impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false)),
% 43.02/28.03 inference(symmetry,[status(thm)],[1381])).
% 43.02/28.03 tff(1383,plain,
% 43.02/28.03 (not1(false) = lazy_impl(prop(false), impl(f5(P!7, false), false))),
% 43.02/28.03 inference(symmetry,[status(thm)],[1231])).
% 43.02/28.03 tff(1384,plain,
% 43.02/28.03 (impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, false)) = f5(P!7, false)),
% 43.02/28.03 inference(transitivity,[status(thm)],[1369, 1104, 1103, 927, 1312, 1311, 1310, 1158, 1383, 1223, 1177, 1222, 1221, 1174, 1382, 1379, 1377, 1376, 1167])).
% 43.02/28.03 tff(1385,plain,
% 43.02/28.03 (impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, false)), false) = impl(f5(P!7, false), false)),
% 43.02/28.03 inference(monotonicity,[status(thm)],[1384])).
% 43.02/28.03 tff(1386,plain,
% 43.02/28.03 (impl(f5(P!7, false), false) = impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, false)), false)),
% 43.02/28.03 inference(symmetry,[status(thm)],[1385])).
% 43.02/28.03 tff(1387,plain,
% 43.02/28.03 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = false),
% 43.02/28.03 inference(transitivity,[status(thm)],[928, 924, 1312, 1311, 1310, 1158, 1383, 1223, 1177, 1222, 1221, 1174, 1386, 1374, 95])).
% 43.02/28.03 tff(1388,plain,
% 43.02/28.03 ($false),
% 43.02/28.03 inference(unit_resolution,[status(thm)],[1053, 1387])).
% 43.02/28.03 tff(1389,plain,((~(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)))) | (~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false))) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false)))), inference(lemma,lemma(discharge,[]))).
% 43.02/28.03 tff(1390,plain,
% 43.02/28.03 (~(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)))),
% 43.02/28.03 inference(unit_resolution,[status(thm)],[1389, 1368, 1346])).
% 43.02/28.03 tff(1391,plain,
% 43.02/28.03 (((~![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))))),
% 43.02/28.03 inference(rewrite,[status(thm)],[])).
% 43.02/28.03 tff(1392,plain,
% 43.02/28.03 ((~![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))))),
% 43.02/28.03 inference(quant_inst,[status(thm)],[])).
% 43.02/28.03 tff(1393,plain,
% 43.02/28.03 ((~![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)))),
% 43.02/28.03 inference(modus_ponens,[status(thm)],[1392, 1391])).
% 43.02/28.03 tff(1394,plain,
% 43.02/28.03 (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)))),
% 43.02/28.04 inference(unit_resolution,[status(thm)],[1393, 252])).
% 43.02/28.04 tff(1395,plain,
% 43.02/28.04 (bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))),
% 43.02/28.04 inference(unit_resolution,[status(thm)],[1394, 1390])).
% 43.02/28.04 tff(1396,plain,
% 43.02/28.04 (bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 43.02/28.04 inference(modus_ponens,[status(thm)],[1395, 1350])).
% 43.02/28.04 tff(1397,plain,
% 43.02/28.04 ((~(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)))),
% 43.02/28.04 inference(tautology,[status(thm)],[])).
% 43.02/28.04 tff(1398,plain,
% 43.02/28.04 ((~(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))))) | ((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)))),
% 43.02/28.04 inference(unit_resolution,[status(thm)],[1397, 1396])).
% 43.02/28.04 tff(1399,plain,
% 43.02/28.04 ((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))),
% 43.02/28.04 inference(unit_resolution,[status(thm)],[1398, 1345])).
% 43.02/28.04 tff(1400,plain,
% 43.02/28.04 (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)),
% 43.02/28.04 inference(transitivity,[status(thm)],[1346, 820])).
% 43.02/28.04 tff(1401,plain,
% 43.02/28.04 ((phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false)) <=> (impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))),
% 43.02/28.04 inference(monotonicity,[status(thm)],[1400])).
% 43.02/28.04 tff(1402,plain,
% 43.02/28.04 ((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))),
% 43.02/28.04 inference(symmetry,[status(thm)],[1401])).
% 43.02/28.04 tff(1403,plain,
% 43.02/28.04 ((~(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)))),
% 43.02/28.04 inference(monotonicity,[status(thm)],[1402])).
% 43.02/28.04 tff(1404,plain,
% 43.02/28.04 ((not1(false) = 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))),
% 43.02/28.04 inference(commutativity,[status(thm)],[])).
% 43.02/28.04 tff(1405,plain,
% 43.02/28.04 (phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 43.02/28.04 inference(monotonicity,[status(thm)],[1346])).
% 43.02/28.04 tff(1406,plain,
% 43.02/28.04 (phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)),
% 43.02/28.04 inference(transitivity,[status(thm)],[1405, 1346, 820])).
% 43.02/28.04 tff(1407,plain,
% 43.02/28.04 (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))),
% 43.02/28.04 inference(symmetry,[status(thm)],[1221])).
% 43.02/28.04 tff(1408,plain,
% 43.02/28.04 (impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false) = not1(false)),
% 43.02/28.04 inference(transitivity,[status(thm)],[1241, 1173, 1407, 1179, 1178, 1175, 1368])).
% 43.02/28.04 tff(1409,plain,
% 43.02/28.04 ((impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) <=> (not1(false) = impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))),
% 43.02/28.04 inference(monotonicity,[status(thm)],[1408, 1406])).
% 43.02/28.04 tff(1410,plain,
% 43.02/28.04 ((impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) <=> (impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))),
% 43.02/28.04 inference(transitivity,[status(thm)],[1409, 1404])).
% 43.02/28.04 tff(1411,plain,
% 43.02/28.04 (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 43.02/28.04 inference(symmetry,[status(thm)],[1405])).
% 43.02/28.04 tff(1412,plain,
% 43.02/28.04 (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))),
% 43.02/28.04 inference(monotonicity,[status(thm)],[821])).
% 43.02/28.04 tff(1413,plain,
% 43.02/28.04 (phi(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 43.02/28.04 inference(transitivity,[status(thm)],[1412, 1411])).
% 43.02/28.04 tff(1414,plain,
% 43.02/28.04 (impl(f5(P!7, false), false) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false)),
% 43.02/28.04 inference(symmetry,[status(thm)],[1241])).
% 43.02/28.04 tff(1415,plain,
% 43.02/28.04 (impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false), false) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false)),
% 43.02/28.04 inference(transitivity,[status(thm)],[1378, 1381, 1414])).
% 43.02/28.04 tff(1416,plain,
% 43.02/28.04 ((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))) <=> (impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 43.02/28.04 inference(monotonicity,[status(thm)],[1415, 1413])).
% 43.02/28.04 tff(1417,plain,
% 43.02/28.04 ((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))) <=> (impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))),
% 43.02/28.04 inference(transitivity,[status(thm)],[1416, 1410])).
% 43.02/28.04 tff(1418,plain,
% 43.02/28.04 ((~(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)))) <=> (~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false)))),
% 43.02/28.04 inference(monotonicity,[status(thm)],[1417])).
% 43.02/28.04 tff(1419,plain,
% 43.02/28.04 (~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))),
% 43.02/28.04 inference(modus_ponens,[status(thm)],[1390, 1418])).
% 43.02/28.04 tff(1420,plain,
% 43.02/28.04 (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false))),
% 43.02/28.04 inference(modus_ponens,[status(thm)],[1419, 1403])).
% 43.02/28.04 tff(1421,plain,
% 43.02/28.04 ((~((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))),
% 43.02/28.04 inference(tautology,[status(thm)],[])).
% 43.02/28.04 tff(1422,plain,
% 43.02/28.04 (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = false),
% 43.02/28.04 inference(unit_resolution,[status(thm)],[1421, 1420, 1399])).
% 43.02/28.04 tff(1423,plain,
% 43.02/28.04 ((~![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))))),
% 43.02/28.04 inference(quant_inst,[status(thm)],[])).
% 43.02/28.04 tff(1424,plain,
% 43.02/28.04 (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)))),
% 43.02/28.04 inference(unit_resolution,[status(thm)],[1423, 218])).
% 43.02/28.04 tff(1425,plain,
% 43.02/28.04 (exists2(P!7) = not1(false)),
% 43.02/28.04 inference(transitivity,[status(thm)],[294, 1145, 452, 450, 448])).
% 43.02/28.04 tff(1426,plain,
% 43.02/28.04 ((exists1(P!7) = exists2(P!7)) <=> (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))),
% 43.02/28.04 inference(monotonicity,[status(thm)],[511, 1425])).
% 43.02/28.04 tff(1427,plain,
% 43.02/28.04 ((~(exists1(P!7) = exists2(P!7))) <=> (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)))),
% 43.02/28.04 inference(monotonicity,[status(thm)],[1426])).
% 43.02/28.04 tff(1428,plain,
% 43.02/28.04 (~(exists1(P!7) = exists2(P!7))),
% 43.02/28.04 inference(or_elim,[status(thm)],[526])).
% 43.02/28.04 tff(1429,plain,
% 43.02/28.04 (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))),
% 43.02/28.04 inference(modus_ponens,[status(thm)],[1428, 1427])).
% 43.02/28.04 tff(1430,assumption,(apply(P!7, tptp_fun_X_3(P!7)) = not1(false)), introduced(assumption)).
% 43.02/28.04 tff(1431,plain,
% 43.02/28.04 (apply(P!7, tptp_fun_X_3(P!7)) = impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))),
% 43.02/28.04 inference(transitivity,[status(thm)],[1430, 1230, 1109, 1108, 1106, 926, 1371, 918])).
% 43.02/28.04 tff(1432,plain,
% 43.02/28.04 (phi(apply(P!7, tptp_fun_X_3(P!7))) = phi(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)))),
% 43.02/28.04 inference(monotonicity,[status(thm)],[1431])).
% 43.02/28.04 tff(1433,plain,
% 43.02/28.04 (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)),
% 43.02/28.04 inference(transitivity,[status(thm)],[1432, 1311, 1310, 1158])).
% 43.02/28.04 tff(1434,assumption,(~(phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))), introduced(assumption)).
% 43.02/28.04 tff(1435,plain,
% 43.02/28.04 ($false),
% 43.02/28.04 inference(unit_resolution,[status(thm)],[1434, 1433])).
% 43.02/28.04 tff(1436,plain,((~(apply(P!7, tptp_fun_X_3(P!7)) = not1(false))) | (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))), inference(lemma,lemma(discharge,[]))).
% 43.02/28.04 tff(1437,plain,
% 43.02/28.04 (~(apply(P!7, tptp_fun_X_3(P!7)) = not1(false))),
% 43.02/28.04 inference(unit_resolution,[status(thm)],[1436, 1429])).
% 43.02/28.04 tff(1438,assumption,(d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))), introduced(assumption)).
% 43.02/28.04 tff(1439,plain,
% 43.02/28.04 (((~![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)) <=> ((~((~(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))))) | (~(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))))) | (~((~bool(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_3(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)) <=> ((~((~(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))))) | (~(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))))) | (~((~bool(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_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false))))))))),
% 43.02/28.04 inference(rewrite,[status(thm)],[])).
% 43.02/28.04 tff(1440,plain,
% 43.02/28.04 ((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)) <=> ((~((~(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))))) | (~(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))))) | (~((~bool(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_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)))))))),
% 43.02/28.04 inference(rewrite,[status(thm)],[])).
% 43.02/28.04 tff(1441,plain,
% 43.02/28.04 (((~![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)) <=> ((~((~(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))))) | (~(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))))) | (~((~bool(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_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false))))))))),
% 43.02/28.04 inference(monotonicity,[status(thm)],[1440])).
% 43.02/28.04 tff(1442,plain,
% 43.02/28.04 (((~![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)) <=> ((~((~(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))))) | (~(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))))) | (~((~bool(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_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false))))))))),
% 43.02/28.04 inference(transitivity,[status(thm)],[1441, 1439])).
% 43.02/28.04 tff(1443,plain,
% 43.02/28.04 ((~![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)))))))),
% 43.02/28.04 inference(quant_inst,[status(thm)],[])).
% 43.02/28.04 tff(1444,plain,
% 43.02/28.04 ((~![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)) <=> ((~((~(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))))) | (~(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))))) | (~((~bool(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_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)))))))),
% 43.02/28.04 inference(modus_ponens,[status(thm)],[1443, 1442])).
% 43.02/28.04 tff(1445,plain,
% 43.02/28.04 (forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), false), 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))))) | (~(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))))) | (~((~bool(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_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false))))))),
% 43.02/28.04 inference(unit_resolution,[status(thm)],[1444, 338])).
% 43.02/28.04 tff(1446,plain,
% 43.02/28.04 ((~![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))),
% 43.02/28.04 inference(quant_inst,[status(thm)],[])).
% 43.02/28.04 tff(1447,plain,
% 43.02/28.04 (f4(P!7, tptp_fun_X_3(P!7), false) = impl(apply(P!7, tptp_fun_X_3(P!7)), false)),
% 43.02/28.04 inference(unit_resolution,[status(thm)],[1446, 170])).
% 43.02/28.04 tff(1448,plain,
% 43.02/28.04 (impl(apply(P!7, tptp_fun_X_3(P!7)), false) = f4(P!7, tptp_fun_X_3(P!7), false)),
% 43.02/28.04 inference(symmetry,[status(thm)],[1447])).
% 43.02/28.04 tff(1449,plain,
% 43.02/28.04 (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))),
% 43.02/28.04 inference(monotonicity,[status(thm)],[1448, 821])).
% 43.02/28.04 tff(1450,plain,
% 43.02/28.04 (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))),
% 43.02/28.04 inference(symmetry,[status(thm)],[1449])).
% 43.02/28.04 tff(1451,plain,
% 43.02/28.04 ((~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)))),
% 43.02/28.04 inference(monotonicity,[status(thm)],[1450])).
% 43.02/28.04 tff(1452,plain,
% 43.02/28.04 (((~(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)))),
% 43.02/28.04 inference(tautology,[status(thm)],[])).
% 43.02/28.04 tff(1453,plain,
% 43.02/28.04 (![X1: $i] : (~forallprefers(f4(P!7, X1, false), f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 43.02/28.04 inference(unit_resolution,[status(thm)],[1452, 1164])).
% 43.02/28.04 tff(1454,plain,
% 43.02/28.04 ((~![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)))),
% 43.02/28.04 inference(quant_inst,[status(thm)],[])).
% 43.02/28.04 tff(1455,plain,
% 43.02/28.04 (~forallprefers(f4(P!7, tptp_fun_X_3(P!7), false), f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 43.02/28.04 inference(unit_resolution,[status(thm)],[1454, 1453])).
% 43.02/28.04 tff(1456,plain,
% 43.02/28.04 (~forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), false), impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))),
% 43.02/28.04 inference(modus_ponens,[status(thm)],[1455, 1451])).
% 43.02/28.04 tff(1457,plain,
% 43.02/28.04 ((~(forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), false), 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))))) | (~(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))))) | (~((~bool(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_3(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)) | (~((~((~(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))))) | (~(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))))) | (~((~bool(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_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)))))))),
% 43.02/28.05 inference(tautology,[status(thm)],[])).
% 43.02/28.05 tff(1458,plain,
% 43.02/28.05 (~((~((~(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))))) | (~(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))))) | (~((~bool(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_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false))))))),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1457, 1456, 1445])).
% 43.02/28.05 tff(1459,plain,
% 43.02/28.05 (((~((~(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))))) | (~(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))))) | (~((~bool(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_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_3(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))))),
% 43.02/28.05 inference(tautology,[status(thm)],[])).
% 43.02/28.05 tff(1460,plain,
% 43.02/28.05 (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)))),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1459, 1458])).
% 43.02/28.05 tff(1461,plain,
% 43.02/28.05 ((~(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_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)))),
% 43.02/28.05 inference(tautology,[status(thm)],[])).
% 43.02/28.05 tff(1462,plain,
% 43.02/28.05 (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)))),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1461, 1460])).
% 43.02/28.05 tff(1463,plain,
% 43.02/28.05 (d(impl(apply(P!7, tptp_fun_X_3(P!7)), false))),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1462, 1438])).
% 43.02/28.05 tff(1464,plain,
% 43.02/28.05 (((~((~(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))))) | (~(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))))) | (~((~bool(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_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)))))) | ((~bool(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_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false))))),
% 43.02/28.05 inference(tautology,[status(thm)],[])).
% 43.02/28.05 tff(1465,plain,
% 43.02/28.05 ((~bool(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_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)))),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1464, 1458])).
% 43.02/28.05 tff(1466,plain,
% 43.02/28.05 ((~((~bool(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_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false))))) | (~bool(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_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)))),
% 43.02/28.05 inference(tautology,[status(thm)],[])).
% 43.02/28.05 tff(1467,plain,
% 43.02/28.05 ((~bool(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_3(P!7)), false)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), false)))),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1466, 1465])).
% 43.02/28.05 tff(1468,plain,
% 43.02/28.05 (bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false))),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1467, 1395, 1438, 1463])).
% 43.02/28.05 tff(1469,assumption,(~(apply(P!7, tptp_fun_X_3(P!7)) = not1(false))), introduced(assumption)).
% 43.02/28.05 tff(1470,assumption,(~bool(exists1(P!7))), introduced(assumption)).
% 43.02/28.05 tff(1471,assumption,(apply(P!7, tptp_fun_X_3(P!7)) = false), introduced(assumption)).
% 43.02/28.05 tff(1472,plain,
% 43.02/28.05 (phi(apply(P!7, tptp_fun_X_3(P!7))) = phi(false)),
% 43.02/28.05 inference(monotonicity,[status(thm)],[1471])).
% 43.02/28.05 tff(1473,plain,
% 43.02/28.05 (exists1(P!7) = false),
% 43.02/28.05 inference(transitivity,[status(thm)],[511, 1472, 23])).
% 43.02/28.05 tff(1474,plain,
% 43.02/28.05 (bool(exists1(P!7)) <=> bool(false)),
% 43.02/28.05 inference(monotonicity,[status(thm)],[1473])).
% 43.02/28.05 tff(1475,plain,
% 43.02/28.05 (bool(false) <=> bool(exists1(P!7))),
% 43.02/28.05 inference(symmetry,[status(thm)],[1474])).
% 43.02/28.05 tff(1476,plain,
% 43.02/28.05 (bool(exists1(P!7))),
% 43.02/28.05 inference(modus_ponens,[status(thm)],[61, 1475])).
% 43.02/28.05 tff(1477,plain,
% 43.02/28.05 ($false),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1470, 1476])).
% 43.02/28.05 tff(1478,plain,((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | bool(exists1(P!7))), inference(lemma,lemma(discharge,[]))).
% 43.02/28.05 tff(1479,plain,
% 43.02/28.05 (~(apply(P!7, tptp_fun_X_3(P!7)) = false)),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1478, 1470])).
% 43.02/28.05 tff(1480,plain,
% 43.02/28.05 ((~((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))),
% 43.02/28.05 inference(tautology,[status(thm)],[])).
% 43.02/28.05 tff(1481,plain,
% 43.02/28.05 (~((apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = not1(false)))),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1480, 1479, 1469])).
% 43.02/28.05 tff(1482,assumption,(~(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))))), introduced(assumption)).
% 43.02/28.05 tff(1483,plain,
% 43.02/28.05 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(apply(P!7, tptp_fun_X_3(P!7))) <=> ((apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = not1(false))))),
% 43.02/28.05 inference(quant_inst,[status(thm)],[])).
% 43.02/28.05 tff(1484,plain,
% 43.02/28.05 ($false),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1483, 218, 1482])).
% 43.02/28.05 tff(1485,plain,(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)))), inference(lemma,lemma(discharge,[]))).
% 43.02/28.05 tff(1486,plain,
% 43.02/28.05 ((~(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)))),
% 43.02/28.05 inference(tautology,[status(thm)],[])).
% 43.02/28.05 tff(1487,plain,
% 43.02/28.05 ((~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)))),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1486, 1485])).
% 43.02/28.05 tff(1488,plain,
% 43.02/28.05 (~bool(apply(P!7, tptp_fun_X_3(P!7)))),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1487, 1481])).
% 43.02/28.05 tff(1489,plain,
% 43.02/28.05 (((~![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)))))),
% 43.02/28.05 inference(rewrite,[status(thm)],[])).
% 43.02/28.05 tff(1490,plain,
% 43.02/28.05 ((~![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)))))),
% 43.02/28.05 inference(quant_inst,[status(thm)],[])).
% 43.02/28.05 tff(1491,plain,
% 43.02/28.05 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), false) = phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 43.02/28.05 inference(modus_ponens,[status(thm)],[1490, 1489])).
% 43.02/28.05 tff(1492,plain,
% 43.02/28.05 (bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), false) = phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1491, 252])).
% 43.02/28.05 tff(1493,plain,
% 43.02/28.05 (impl(apply(P!7, tptp_fun_X_3(P!7)), false) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1492, 1488])).
% 43.02/28.05 tff(1494,plain,
% 43.02/28.05 (impl(apply(P!7, tptp_fun_X_3(P!7)), false) = exists1(P!7)),
% 43.02/28.05 inference(transitivity,[status(thm)],[1493, 512])).
% 43.02/28.05 tff(1495,plain,
% 43.02/28.05 (bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)) <=> bool(exists1(P!7))),
% 43.02/28.05 inference(monotonicity,[status(thm)],[1494])).
% 43.02/28.05 tff(1496,plain,
% 43.02/28.05 (bool(exists1(P!7)) <=> bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false))),
% 43.02/28.05 inference(symmetry,[status(thm)],[1495])).
% 43.02/28.05 tff(1497,plain,
% 43.02/28.05 ((~bool(exists1(P!7))) <=> (~bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)))),
% 43.02/28.05 inference(monotonicity,[status(thm)],[1496])).
% 43.02/28.05 tff(1498,plain,
% 43.02/28.05 (~bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false))),
% 43.02/28.05 inference(modus_ponens,[status(thm)],[1470, 1497])).
% 43.02/28.05 tff(1499,assumption,(bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false))), introduced(assumption)).
% 43.02/28.05 tff(1500,plain,
% 43.02/28.05 ($false),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1499, 1498])).
% 43.02/28.05 tff(1501,plain,(bool(exists1(P!7)) | (~bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false))) | (apply(P!7, tptp_fun_X_3(P!7)) = not1(false))), inference(lemma,lemma(discharge,[]))).
% 43.02/28.05 tff(1502,plain,
% 43.02/28.05 (bool(exists1(P!7))),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1501, 1468, 1437])).
% 43.02/28.05 tff(1503,plain,
% 43.02/28.05 (bool(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 43.02/28.05 inference(modus_ponens,[status(thm)],[1502, 514])).
% 43.02/28.05 tff(1504,plain,
% 43.02/28.05 ((~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)))),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[530, 494])).
% 43.02/28.05 tff(1505,plain,
% 43.02/28.05 ((phi(apply(P!7, tptp_fun_X_3(P!7))) = false) | (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1504, 1503])).
% 43.02/28.05 tff(1506,plain,
% 43.02/28.05 (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err)),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[546, 1505])).
% 43.02/28.05 tff(1507,plain,
% 43.02/28.05 (d(apply(P!7, tptp_fun_X_3(P!7))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err))),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[548, 1506])).
% 43.02/28.05 tff(1508,plain,
% 43.02/28.05 (~((~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)))))),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[553, 1507])).
% 43.02/28.05 tff(1509,plain,
% 43.02/28.05 (d(apply(P!7, tptp_fun_X_3(P!7)))),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[555, 1508])).
% 43.02/28.05 tff(1510,plain,
% 43.02/28.05 (((~![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)))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))) | bool(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)))))))) <=> ((~![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)))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))) | bool(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))))))))),
% 43.02/28.05 inference(rewrite,[status(thm)],[])).
% 43.02/28.05 tff(1511,plain,
% 43.02/28.05 ((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))) <=> ((~(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)))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))) | bool(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)))))))),
% 43.02/28.05 inference(rewrite,[status(thm)],[])).
% 43.02/28.05 tff(1512,plain,
% 43.02/28.05 (((~![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))) <=> ((~(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)))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))) | bool(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))))))))),
% 43.02/28.05 inference(monotonicity,[status(thm)],[1511])).
% 43.02/28.05 tff(1513,plain,
% 43.02/28.05 (((~![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))) <=> ((~(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)))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))) | bool(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))))))))),
% 43.02/28.05 inference(transitivity,[status(thm)],[1512, 1510])).
% 43.02/28.05 tff(1514,plain,
% 43.02/28.05 ((~![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))))))),
% 43.02/28.05 inference(quant_inst,[status(thm)],[])).
% 43.02/28.05 tff(1515,plain,
% 43.02/28.05 ((~![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)))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))) | bool(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)))))))),
% 43.02/28.05 inference(modus_ponens,[status(thm)],[1514, 1513])).
% 43.02/28.05 tff(1516,plain,
% 43.02/28.05 (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)))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))) | bool(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))))))),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1515, 572])).
% 43.02/28.05 tff(1517,plain,
% 43.02/28.05 ((~![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))))),
% 43.02/28.05 inference(quant_inst,[status(thm)],[])).
% 43.02/28.05 tff(1518,plain,
% 43.02/28.05 (~existsprefers(apply(P!7, tptp_fun_X_4(false, P!7)), apply(P!7, tptp_fun_X_3(P!7)))),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1517, 581])).
% 43.02/28.05 tff(1519,plain,
% 43.02/28.05 ((~(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)))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))) | bool(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)))))))) | 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)))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))) | bool(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)))))))),
% 43.02/28.05 inference(tautology,[status(thm)],[])).
% 43.02/28.05 tff(1520,plain,
% 43.02/28.05 ((~(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)))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))) | bool(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)))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))) | bool(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)))))))),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1519, 1518])).
% 43.02/28.05 tff(1521,plain,
% 43.02/28.05 (~((~(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)))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))) | bool(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))))))),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1520, 1516])).
% 43.02/28.05 tff(1522,plain,
% 43.02/28.05 (((~(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)))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))) | bool(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)))))),
% 43.02/28.05 inference(tautology,[status(thm)],[])).
% 43.02/28.05 tff(1523,plain,
% 43.02/28.05 (d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7))))),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1522, 1521])).
% 43.02/28.05 tff(1524,plain,
% 43.02/28.05 ((~(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))))),
% 43.02/28.05 inference(tautology,[status(thm)],[])).
% 43.02/28.05 tff(1525,plain,
% 43.02/28.05 (d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7))))),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1524, 1523])).
% 43.02/28.05 tff(1526,plain,
% 43.02/28.05 (d(apply(P!7, tptp_fun_X_4(false, P!7)))),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1525, 1509])).
% 43.02/28.05 tff(1527,plain,
% 43.02/28.05 (phi(apply(P!7, tptp_fun_X_3(P!7))) = false),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[544, 1505, 1429])).
% 43.02/28.05 tff(1528,plain,
% 43.02/28.05 (phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[592, 1508])).
% 43.02/28.05 tff(1529,plain,
% 43.02/28.05 (apply(P!7, tptp_fun_X_3(P!7)) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 43.02/28.05 inference(symmetry,[status(thm)],[1528])).
% 43.02/28.05 tff(1530,plain,
% 43.02/28.05 (apply(P!7, tptp_fun_X_3(P!7)) = false),
% 43.02/28.05 inference(transitivity,[status(thm)],[1529, 1527])).
% 43.02/28.05 tff(1531,plain,
% 43.02/28.05 (bool(apply(P!7, tptp_fun_X_3(P!7))) <=> bool(false)),
% 43.02/28.05 inference(monotonicity,[status(thm)],[1530])).
% 43.02/28.05 tff(1532,plain,
% 43.02/28.05 (bool(false) <=> bool(apply(P!7, tptp_fun_X_3(P!7)))),
% 43.02/28.05 inference(symmetry,[status(thm)],[1531])).
% 43.02/28.05 tff(1533,plain,
% 43.02/28.05 (bool(apply(P!7, tptp_fun_X_3(P!7)))),
% 43.02/28.05 inference(modus_ponens,[status(thm)],[61, 1532])).
% 43.02/28.05 tff(1534,plain,
% 43.02/28.05 (((~(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)))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))) | bool(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_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))))),
% 43.02/28.05 inference(tautology,[status(thm)],[])).
% 43.02/28.05 tff(1535,plain,
% 43.02/28.05 ((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7)))),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1534, 1521])).
% 43.02/28.05 tff(1536,plain,
% 43.02/28.05 ((~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))) | bool(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)))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7)))),
% 43.02/28.05 inference(tautology,[status(thm)],[])).
% 43.02/28.05 tff(1537,plain,
% 43.02/28.05 ((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7)))),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1536, 1535])).
% 43.02/28.05 tff(1538,plain,
% 43.02/28.05 (bool(apply(P!7, tptp_fun_X_4(false, P!7)))),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1537, 1533, 1509, 1526])).
% 43.02/28.05 tff(1539,plain,
% 43.02/28.05 ((~(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)))),
% 43.02/28.05 inference(tautology,[status(thm)],[])).
% 43.02/28.05 tff(1540,plain,
% 43.02/28.05 ((~(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)))),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1539, 1538])).
% 43.02/28.05 tff(1541,plain,
% 43.02/28.05 ((apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1540, 1424])).
% 43.02/28.05 tff(1542,plain,
% 43.02/28.05 (((~(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)))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))) | bool(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)))))) | ((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))))),
% 43.02/28.05 inference(tautology,[status(thm)],[])).
% 43.02/28.05 tff(1543,plain,
% 43.02/28.05 ((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false)))),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1542, 1521])).
% 43.02/28.05 tff(1544,plain,
% 43.02/28.05 ((~((~(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)))),
% 43.02/28.05 inference(tautology,[status(thm)],[])).
% 43.02/28.05 tff(1545,plain,
% 43.02/28.05 ((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false)))),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1544, 1543])).
% 43.02/28.05 tff(1546,plain,
% 43.02/28.05 (~(apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1545, 1530])).
% 43.02/28.05 tff(1547,plain,
% 43.02/28.05 ((~((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))),
% 43.02/28.05 inference(tautology,[status(thm)],[])).
% 43.02/28.05 tff(1548,plain,
% 43.02/28.05 ((~((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)),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1547, 1546])).
% 43.02/28.05 tff(1549,plain,
% 43.02/28.05 (apply(P!7, tptp_fun_X_4(false, P!7)) = false),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1548, 1541])).
% 43.02/28.05 tff(1550,plain,
% 43.02/28.05 (impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = impl(false, false)),
% 43.02/28.05 inference(monotonicity,[status(thm)],[1549])).
% 43.02/28.05 tff(1551,plain,
% 43.02/28.05 (impl(false, false) = impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)),
% 43.02/28.05 inference(symmetry,[status(thm)],[1550])).
% 43.02/28.05 tff(1552,plain,
% 43.02/28.05 (not1(false) = impl(false, false)),
% 43.02/28.05 inference(symmetry,[status(thm)],[78])).
% 43.02/28.05 tff(1553,plain,
% 43.02/28.05 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = false),
% 43.02/28.05 inference(transitivity,[status(thm)],[928, 924, 1312, 1311, 1310, 1158, 1552, 1551, 821, 1347, 1422])).
% 43.02/28.05 tff(1554,plain,
% 43.02/28.05 ($false),
% 43.02/28.05 inference(unit_resolution,[status(thm)],[1053, 1553])).
% 43.02/28.06 tff(1555,plain,((~(prop(tptp_fun_R_5(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(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)))), inference(lemma,lemma(discharge,[]))).
% 43.02/28.06 tff(1556,plain,
% 43.02/28.06 (~(prop(tptp_fun_R_5(P!7)) = false)),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1555, 1343, 1341])).
% 43.02/28.06 tff(1557,plain,
% 43.02/28.06 (bool(tptp_fun_R_5(P!7))),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[465, 1556])).
% 43.02/28.06 tff(1558,plain,
% 43.02/28.06 ((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = not1(false))),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[489, 1557])).
% 43.02/28.06 tff(1559,plain,
% 43.02/28.06 (tptp_fun_R_5(P!7) = false),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[626, 1558, 1335])).
% 43.02/28.06 tff(1560,plain,
% 43.02/28.06 (f6(P!7, tptp_fun_R_5(P!7)) = f6(P!7, false)),
% 43.02/28.06 inference(monotonicity,[status(thm)],[1559])).
% 43.02/28.06 tff(1561,plain,
% 43.02/28.06 (f6(P!7, false) = f6(P!7, tptp_fun_R_5(P!7))),
% 43.02/28.06 inference(symmetry,[status(thm)],[1560])).
% 43.02/28.06 tff(1562,plain,
% 43.02/28.06 (lazy_impl(prop(false), impl(f5(P!7, false), false)) = impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 43.02/28.06 inference(transitivity,[status(thm)],[878, 1561, 1146, 1334, 1332, 1329, 1320, 1315, 1309])).
% 43.02/28.06 tff(1563,plain,
% 43.02/28.06 ((lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false)) <=> (impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = phi(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))))),
% 43.02/28.06 inference(monotonicity,[status(thm)],[1562, 1273])).
% 43.02/28.06 tff(1564,plain,
% 43.02/28.06 ((impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = phi(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)))) <=> (lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false))),
% 43.02/28.06 inference(symmetry,[status(thm)],[1563])).
% 43.02/28.06 tff(1565,plain,
% 43.02/28.06 ((phi(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), 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)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) <=> (impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = phi(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))))),
% 43.02/28.06 inference(commutativity,[status(thm)],[])).
% 43.02/28.06 tff(1566,plain,
% 43.02/28.06 (exists2(P!7) = impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 43.02/28.06 inference(transitivity,[status(thm)],[294, 1334, 1332, 1329, 1320, 1315, 1309])).
% 43.02/28.06 tff(1567,plain,
% 43.02/28.06 (d(impl(apply(P!7, tptp_fun_X_3(P!7)), false))),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1462, 1341])).
% 43.02/28.06 tff(1568,plain,
% 43.02/28.06 (f6(P!7, tptp_fun_R_5(P!7)) = f6(P!7, false)),
% 43.02/28.06 inference(monotonicity,[status(thm)],[628])).
% 43.02/28.06 tff(1569,plain,
% 43.02/28.06 (f6(P!7, false) = f6(P!7, tptp_fun_R_5(P!7))),
% 43.02/28.06 inference(symmetry,[status(thm)],[1568])).
% 43.02/28.06 tff(1570,assumption,(~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))), introduced(assumption)).
% 43.02/28.06 tff(1571,plain,
% 43.02/28.06 (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))),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1394, 1570])).
% 43.02/28.06 tff(1572,plain,
% 43.02/28.06 (phi(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)),
% 43.02/28.06 inference(symmetry,[status(thm)],[1571])).
% 43.02/28.06 tff(1573,plain,
% 43.02/28.06 (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 43.02/28.06 inference(transitivity,[status(thm)],[1375, 1572, 1378, 1381, 1173, 1407, 1179, 1178, 1175, 878, 1569, 1146, 1334, 1332, 1329, 1320, 1315])).
% 43.02/28.06 tff(1574,plain,
% 43.02/28.06 (bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) <=> bool(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 43.02/28.06 inference(monotonicity,[status(thm)],[1573])).
% 43.02/28.06 tff(1575,plain,
% 43.02/28.06 (bool(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) <=> bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 43.02/28.06 inference(symmetry,[status(thm)],[1574])).
% 43.02/28.06 tff(1576,plain,
% 43.02/28.06 (lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(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(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 43.02/28.06 inference(transitivity,[status(thm)],[1320, 1315])).
% 43.02/28.06 tff(1577,plain,
% 43.02/28.06 (bool(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) <=> bool(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 43.02/28.06 inference(monotonicity,[status(thm)],[1576])).
% 43.02/28.06 tff(1578,plain,
% 43.02/28.06 (bool(impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 43.02/28.06 inference(modus_ponens,[status(thm)],[1301, 1577])).
% 43.02/28.06 tff(1579,plain,
% 43.02/28.06 (bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 43.02/28.06 inference(modus_ponens,[status(thm)],[1578, 1575])).
% 43.02/28.06 tff(1580,plain,
% 43.02/28.06 ((~bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))) <=> (~bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 43.02/28.06 inference(monotonicity,[status(thm)],[1350])).
% 43.02/28.06 tff(1581,plain,
% 43.02/28.06 (~bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 43.02/28.06 inference(modus_ponens,[status(thm)],[1570, 1580])).
% 43.02/28.06 tff(1582,plain,
% 43.02/28.06 ($false),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1581, 1579])).
% 43.02/28.06 tff(1583,plain,(bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~(tptp_fun_R_5(P!7) = false))), inference(lemma,lemma(discharge,[]))).
% 43.02/28.06 tff(1584,plain,
% 43.02/28.06 (bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1583, 1343, 1559])).
% 43.02/28.06 tff(1585,plain,
% 43.02/28.06 (bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false))),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1467, 1584, 1341, 1567])).
% 43.02/28.06 tff(1586,assumption,(bool(phi(apply(P!7, tptp_fun_X_3(P!7))))), introduced(assumption)).
% 43.02/28.06 tff(1587,plain,
% 43.02/28.06 (bool(exists1(P!7))),
% 43.02/28.06 inference(modus_ponens,[status(thm)],[1586, 513])).
% 43.02/28.06 tff(1588,plain,
% 43.02/28.06 ($false),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1470, 1587])).
% 43.02/28.06 tff(1589,plain,((~bool(phi(apply(P!7, tptp_fun_X_3(P!7))))) | bool(exists1(P!7))), inference(lemma,lemma(discharge,[]))).
% 43.02/28.06 tff(1590,plain,
% 43.02/28.06 (~bool(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1589, 1470])).
% 43.02/28.06 tff(1591,plain,
% 43.02/28.06 ((~(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))))),
% 43.02/28.06 inference(tautology,[status(thm)],[])).
% 43.02/28.06 tff(1592,plain,
% 43.02/28.06 (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))))),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1591, 494])).
% 43.02/28.06 tff(1593,plain,
% 43.02/28.06 (~((phi(apply(P!7, tptp_fun_X_3(P!7))) = false) | (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)))),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1592, 1590])).
% 43.02/28.06 tff(1594,plain,
% 43.02/28.06 (apply(P!7, tptp_fun_X_3(P!7)) = not1(false)),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1501, 1470, 1499])).
% 43.02/28.06 tff(1595,plain,
% 43.02/28.06 (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1436, 1594])).
% 43.02/28.06 tff(1596,plain,
% 43.02/28.06 (((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)))),
% 43.02/28.06 inference(tautology,[status(thm)],[])).
% 43.02/28.06 tff(1597,plain,
% 43.02/28.06 ($false),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1596, 1595, 1593])).
% 43.02/28.06 tff(1598,plain,(bool(exists1(P!7)) | (~bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false)))), inference(lemma,lemma(discharge,[]))).
% 43.02/28.06 tff(1599,plain,
% 43.02/28.06 (bool(exists1(P!7))),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1598, 1585])).
% 43.02/28.06 tff(1600,plain,
% 43.02/28.06 (bool(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 43.02/28.06 inference(modus_ponens,[status(thm)],[1599, 514])).
% 43.02/28.06 tff(1601,plain,
% 43.02/28.06 ((phi(apply(P!7, tptp_fun_X_3(P!7))) = false) | (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1504, 1600])).
% 43.02/28.06 tff(1602,plain,
% 43.02/28.06 (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err)),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[546, 1601])).
% 43.02/28.06 tff(1603,plain,
% 43.02/28.06 (d(apply(P!7, tptp_fun_X_3(P!7))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err))),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[548, 1602])).
% 43.02/28.06 tff(1604,plain,
% 43.02/28.06 (~((~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)))))),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[553, 1603])).
% 43.02/28.06 tff(1605,plain,
% 43.02/28.06 (phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[592, 1604])).
% 43.02/28.06 tff(1606,plain,
% 43.02/28.06 (apply(P!7, tptp_fun_X_3(P!7)) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 43.02/28.06 inference(symmetry,[status(thm)],[1605])).
% 43.02/28.06 tff(1607,plain,
% 43.02/28.06 (apply(P!7, tptp_fun_X_3(P!7)) = exists1(P!7)),
% 43.02/28.06 inference(transitivity,[status(thm)],[1606, 512])).
% 43.02/28.06 tff(1608,plain,
% 43.02/28.06 (bool(apply(P!7, tptp_fun_X_3(P!7))) <=> bool(exists1(P!7))),
% 43.02/28.06 inference(monotonicity,[status(thm)],[1607])).
% 43.02/28.06 tff(1609,plain,
% 43.02/28.06 (bool(exists1(P!7)) <=> bool(apply(P!7, tptp_fun_X_3(P!7)))),
% 43.02/28.06 inference(symmetry,[status(thm)],[1608])).
% 43.02/28.06 tff(1610,plain,
% 43.02/28.06 (bool(apply(P!7, tptp_fun_X_3(P!7)))),
% 43.02/28.06 inference(modus_ponens,[status(thm)],[1599, 1609])).
% 43.02/28.06 tff(1611,plain,
% 43.02/28.06 ((apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = not1(false))),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1487, 1610])).
% 43.02/28.06 tff(1612,plain,
% 43.02/28.06 (d(apply(P!7, tptp_fun_X_3(P!7)))),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[555, 1604])).
% 43.02/28.06 tff(1613,plain,
% 43.02/28.06 (d(apply(P!7, tptp_fun_X_4(false, P!7)))),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1525, 1612])).
% 43.02/28.06 tff(1614,plain,
% 43.02/28.06 (bool(apply(P!7, tptp_fun_X_4(false, P!7)))),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1537, 1610, 1612, 1613])).
% 43.02/28.06 tff(1615,plain,
% 43.02/28.06 ((~(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)))),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1539, 1614])).
% 43.02/28.06 tff(1616,plain,
% 43.02/28.06 ((apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1615, 1424])).
% 43.02/28.06 tff(1617,plain,
% 43.02/28.06 ((~![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)))))),
% 43.02/28.06 inference(quant_inst,[status(thm)],[])).
% 43.02/28.06 tff(1618,plain,
% 43.02/28.06 ((prop(phi(apply(P!7, tptp_fun_X_3(P!7)))) = not1(false)) <=> bool(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1617, 111])).
% 43.02/28.06 tff(1619,plain,
% 43.02/28.06 ((~((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)))))),
% 43.02/28.06 inference(tautology,[status(thm)],[])).
% 43.02/28.06 tff(1620,plain,
% 43.02/28.06 ((prop(phi(apply(P!7, tptp_fun_X_3(P!7)))) = not1(false)) | (~bool(phi(apply(P!7, tptp_fun_X_3(P!7)))))),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1619, 1618])).
% 43.02/28.06 tff(1621,plain,
% 43.02/28.06 (prop(phi(apply(P!7, tptp_fun_X_3(P!7)))) = not1(false)),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1620, 1600])).
% 43.02/28.06 tff(1622,assumption,(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))), introduced(assumption)).
% 43.02/28.06 tff(1623,plain,
% 43.02/28.06 (apply(P!7, tptp_fun_X_3(P!7)) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 43.02/28.06 inference(symmetry,[status(thm)],[1622])).
% 43.02/28.06 tff(1624,plain,
% 43.02/28.06 ((apply(P!7, tptp_fun_X_3(P!7)) = false) <=> (phi(apply(P!7, tptp_fun_X_3(P!7))) = false)),
% 43.02/28.06 inference(monotonicity,[status(thm)],[1623])).
% 43.02/28.06 tff(1625,plain,
% 43.02/28.06 ((phi(apply(P!7, tptp_fun_X_3(P!7))) = false) <=> (apply(P!7, tptp_fun_X_3(P!7)) = false)),
% 43.02/28.06 inference(symmetry,[status(thm)],[1624])).
% 43.02/28.06 tff(1626,plain,
% 43.02/28.06 ((~![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))))),
% 43.02/28.06 inference(quant_inst,[status(thm)],[])).
% 43.02/28.06 tff(1627,plain,
% 43.02/28.06 (lazy_impl(not1(false), apply(P!7, tptp_fun_X_3(P!7))) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1626, 33])).
% 43.02/28.06 tff(1628,assumption,(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))) = not1(false)), introduced(assumption)).
% 43.02/28.06 tff(1629,plain,
% 43.02/28.06 (not1(false) = prop(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 43.02/28.06 inference(symmetry,[status(thm)],[1628])).
% 43.02/28.06 tff(1630,plain,
% 43.02/28.06 (lazy_impl(not1(false), 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))))),
% 43.02/28.06 inference(monotonicity,[status(thm)],[1629, 1623])).
% 43.02/28.06 tff(1631,plain,
% 43.02/28.06 (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), apply(P!7, tptp_fun_X_3(P!7)))),
% 43.02/28.06 inference(symmetry,[status(thm)],[1630])).
% 43.02/28.06 tff(1632,plain,
% 43.02/28.06 (lazy_impl(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))), phi(apply(P!7, tptp_fun_X_3(P!7)))) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 43.02/28.06 inference(transitivity,[status(thm)],[1631, 1627])).
% 43.02/28.06 tff(1633,plain,
% 43.02/28.06 ((lazy_impl(prop(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))) = false)),
% 43.02/28.06 inference(monotonicity,[status(thm)],[1632])).
% 43.02/28.06 tff(1634,plain,
% 43.02/28.06 (impl(impl(false, impl(not1(false), false)), false) = false),
% 43.02/28.06 inference(transitivity,[status(thm)],[98, 95])).
% 43.02/28.06 tff(1635,plain,
% 43.02/28.06 (lazy_impl(prop(false), impl(impl(false, impl(not1(false), false)), false)) = lazy_impl(not1(false), false)),
% 43.02/28.06 inference(monotonicity,[status(thm)],[116, 1634])).
% 43.02/28.06 tff(1636,assumption,((apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))), introduced(assumption)).
% 43.02/28.06 tff(1637,plain,
% 43.02/28.06 (~(apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1545, 1471])).
% 43.02/28.06 tff(1638,plain,
% 43.02/28.06 (apply(P!7, tptp_fun_X_4(false, P!7)) = false),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1547, 1637, 1636])).
% 43.02/28.06 tff(1639,plain,
% 43.02/28.06 (f1(apply(P!7, tptp_fun_X_4(false, P!7)), not1(false), false) = f1(false, not1(false), false)),
% 43.02/28.06 inference(monotonicity,[status(thm)],[1638])).
% 43.02/28.06 tff(1640,plain,
% 43.02/28.06 ((~![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(false, P!7)), not1(false), false) = lazy_impl(prop(false), impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false)))),
% 43.02/28.06 inference(quant_inst,[status(thm)],[])).
% 43.02/28.06 tff(1641,plain,
% 43.02/28.06 (f1(apply(P!7, tptp_fun_X_4(false, P!7)), not1(false), false) = lazy_impl(prop(false), impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false))),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1640, 126])).
% 43.02/28.06 tff(1642,plain,
% 43.02/28.06 (lazy_impl(prop(false), impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false)) = f1(apply(P!7, tptp_fun_X_4(false, P!7)), not1(false), false)),
% 43.02/28.06 inference(symmetry,[status(thm)],[1641])).
% 43.02/28.06 tff(1643,plain,
% 43.02/28.06 (lazy_impl(prop(false), impl(f5(P!7, false), false)) = impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false)),
% 43.02/28.06 inference(transitivity,[status(thm)],[1223, 1177, 1222, 1221, 1174, 1382])).
% 43.02/28.06 tff(1644,plain,
% 43.02/28.06 (lazy_impl(not1(false), lazy_impl(prop(false), impl(f5(P!7, false), false))) = lazy_impl(prop(false), impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false))),
% 43.02/28.06 inference(monotonicity,[status(thm)],[117, 1643])).
% 43.02/28.06 tff(1645,plain,
% 43.02/28.06 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), lazy_impl(prop(false), impl(f5(P!7, false), false))) = phi(lazy_impl(prop(false), impl(f5(P!7, false), false))))),
% 43.02/28.06 inference(quant_inst,[status(thm)],[])).
% 43.02/28.06 tff(1646,plain,
% 43.02/28.06 (lazy_impl(not1(false), lazy_impl(prop(false), impl(f5(P!7, false), false))) = phi(lazy_impl(prop(false), impl(f5(P!7, false), false)))),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1645, 33])).
% 43.02/28.06 tff(1647,plain,
% 43.02/28.06 (phi(lazy_impl(prop(false), impl(f5(P!7, false), false))) = lazy_impl(not1(false), lazy_impl(prop(false), impl(f5(P!7, false), false)))),
% 43.02/28.06 inference(symmetry,[status(thm)],[1646])).
% 43.02/28.06 tff(1648,plain,
% 43.02/28.06 ((d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~(phi(lazy_impl(prop(false), impl(f5(P!7, false), false))) = err))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false))))),
% 43.02/28.06 inference(tautology,[status(thm)],[])).
% 43.02/28.06 tff(1649,plain,
% 43.02/28.06 (d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~(phi(lazy_impl(prop(false), impl(f5(P!7, false), false))) = err))),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1648, 1204])).
% 43.02/28.06 tff(1650,plain,
% 43.02/28.06 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | (~(phi(lazy_impl(prop(false), impl(f5(P!7, false), false))) = lazy_impl(prop(false), impl(f5(P!7, false), false)))))) | (~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~(phi(lazy_impl(prop(false), impl(f5(P!7, false), false))) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | (~(phi(lazy_impl(prop(false), impl(f5(P!7, false), false))) = lazy_impl(prop(false), impl(f5(P!7, false), false)))))) | (~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~(phi(lazy_impl(prop(false), impl(f5(P!7, false), false))) = err)))))),
% 43.02/28.06 inference(rewrite,[status(thm)],[])).
% 43.02/28.06 tff(1651,plain,
% 43.02/28.06 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | (~(phi(lazy_impl(prop(false), impl(f5(P!7, false), false))) = lazy_impl(prop(false), impl(f5(P!7, false), false)))))) | (~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~(phi(lazy_impl(prop(false), impl(f5(P!7, false), false))) = err)))))),
% 43.02/28.06 inference(quant_inst,[status(thm)],[])).
% 43.02/28.06 tff(1652,plain,
% 43.02/28.06 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | (~(phi(lazy_impl(prop(false), impl(f5(P!7, false), false))) = lazy_impl(prop(false), impl(f5(P!7, false), false)))))) | (~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~(phi(lazy_impl(prop(false), impl(f5(P!7, false), false))) = err))))),
% 43.02/28.06 inference(modus_ponens,[status(thm)],[1651, 1650])).
% 43.02/28.06 tff(1653,plain,
% 43.02/28.06 (~((~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | (~(phi(lazy_impl(prop(false), impl(f5(P!7, false), false))) = lazy_impl(prop(false), impl(f5(P!7, false), false)))))),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1652, 17, 1649])).
% 43.02/28.06 tff(1654,plain,
% 43.02/28.06 (((~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | (~(phi(lazy_impl(prop(false), impl(f5(P!7, false), false))) = lazy_impl(prop(false), impl(f5(P!7, false), false))))) | (phi(lazy_impl(prop(false), impl(f5(P!7, false), false))) = lazy_impl(prop(false), impl(f5(P!7, false), false)))),
% 43.02/28.06 inference(tautology,[status(thm)],[])).
% 43.02/28.06 tff(1655,plain,
% 43.02/28.06 (phi(lazy_impl(prop(false), impl(f5(P!7, false), false))) = lazy_impl(prop(false), impl(f5(P!7, false), false))),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1654, 1653])).
% 43.02/28.06 tff(1656,plain,
% 43.02/28.06 (lazy_impl(prop(false), impl(f5(P!7, false), false)) = phi(lazy_impl(prop(false), impl(f5(P!7, false), false)))),
% 43.02/28.06 inference(symmetry,[status(thm)],[1655])).
% 43.02/28.06 tff(1657,plain,
% 43.02/28.06 (exists2(P!7) = false),
% 43.02/28.06 inference(transitivity,[status(thm)],[294, 1145, 1568, 857, 1656, 1647, 1644, 1642, 1639, 128, 1635, 35, 23])).
% 43.02/28.06 tff(1658,plain,
% 43.02/28.06 (phi(apply(P!7, tptp_fun_X_3(P!7))) = lazy_impl(not1(false), apply(P!7, tptp_fun_X_3(P!7)))),
% 43.02/28.06 inference(symmetry,[status(thm)],[1627])).
% 43.02/28.06 tff(1659,plain,
% 43.02/28.06 (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))))),
% 43.02/28.06 inference(transitivity,[status(thm)],[511, 1658, 1630])).
% 43.02/28.06 tff(1660,plain,
% 43.02/28.06 ((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)),
% 43.02/28.06 inference(monotonicity,[status(thm)],[1659, 1657])).
% 43.02/28.06 tff(1661,plain,
% 43.02/28.06 ((exists1(P!7) = exists2(P!7)) <=> (apply(P!7, tptp_fun_X_3(P!7)) = false)),
% 43.02/28.06 inference(transitivity,[status(thm)],[1660, 1633, 1625])).
% 43.02/28.06 tff(1662,plain,
% 43.02/28.06 ((~(exists1(P!7) = exists2(P!7))) <=> (~(apply(P!7, tptp_fun_X_3(P!7)) = false))),
% 43.02/28.06 inference(monotonicity,[status(thm)],[1661])).
% 43.02/28.06 tff(1663,plain,
% 43.02/28.06 (~(apply(P!7, tptp_fun_X_3(P!7)) = false)),
% 43.02/28.06 inference(modus_ponens,[status(thm)],[1428, 1662])).
% 43.02/28.06 tff(1664,plain,
% 43.02/28.06 ($false),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1471, 1663])).
% 43.02/28.06 tff(1665,plain,((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))) | (~(prop(phi(apply(P!7, tptp_fun_X_3(P!7)))) = not1(false))) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~(tptp_fun_R_5(P!7) = false)) | (~((apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))))), inference(lemma,lemma(discharge,[]))).
% 43.02/28.06 tff(1666,plain,
% 43.02/28.06 (~(apply(P!7, tptp_fun_X_3(P!7)) = false)),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1665, 1605, 1621, 1343, 1559, 1616])).
% 43.02/28.06 tff(1667,plain,
% 43.02/28.06 (apply(P!7, tptp_fun_X_3(P!7)) = not1(false)),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1480, 1666, 1611])).
% 43.02/28.06 tff(1668,plain,
% 43.02/28.06 (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1436, 1667])).
% 43.02/28.06 tff(1669,plain,
% 43.02/28.06 (exists1(P!7) = phi(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)))),
% 43.02/28.06 inference(transitivity,[status(thm)],[511, 1668, 1230, 1109, 1108])).
% 43.02/28.06 tff(1670,plain,
% 43.02/28.06 ((exists1(P!7) = exists2(P!7)) <=> (phi(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), 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)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 43.02/28.06 inference(monotonicity,[status(thm)],[1669, 1566])).
% 43.02/28.06 tff(1671,plain,
% 43.02/28.06 ((exists1(P!7) = exists2(P!7)) <=> (impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = phi(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false))))),
% 43.02/28.06 inference(transitivity,[status(thm)],[1670, 1565])).
% 43.02/28.06 tff(1672,plain,
% 43.02/28.06 ((exists1(P!7) = exists2(P!7)) <=> (lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false))),
% 43.02/28.06 inference(transitivity,[status(thm)],[1671, 1564])).
% 43.02/28.06 tff(1673,plain,
% 43.02/28.06 ((~(exists1(P!7) = exists2(P!7))) <=> (~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false)))),
% 43.02/28.06 inference(monotonicity,[status(thm)],[1672])).
% 43.02/28.06 tff(1674,plain,
% 43.02/28.06 (~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false))),
% 43.02/28.06 inference(modus_ponens,[status(thm)],[1428, 1673])).
% 43.02/28.06 tff(1675,plain,
% 43.02/28.06 (lazy_impl(prop(false), impl(f5(P!7, false), false)) = false),
% 43.02/28.06 inference(unit_resolution,[status(thm)],[1260, 1674])).
% 43.02/28.06 tff(1676,plain,
% 43.02/28.06 (lazy_impl(prop(false), impl(f5(P!7, false), false)) = lazy_impl(not1(false), impl(f5(P!7, false), false))),
% 43.02/28.06 inference(monotonicity,[status(thm)],[116])).
% 43.02/28.06 tff(1677,plain,
% 43.02/28.06 (lazy_impl(not1(false), impl(f5(P!7, false), false)) = lazy_impl(prop(false), impl(f5(P!7, false), false))),
% 43.02/28.07 inference(symmetry,[status(thm)],[1676])).
% 43.02/28.07 tff(1678,plain,
% 43.02/28.07 (impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2) = impl(f5(P!7, false), false)),
% 43.02/28.07 inference(monotonicity,[status(thm)],[1167, 805])).
% 43.02/28.07 tff(1679,plain,
% 43.02/28.07 (impl(f5(P!7, false), false) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)),
% 43.02/28.07 inference(symmetry,[status(thm)],[1678])).
% 43.02/28.07 tff(1680,plain,
% 43.02/28.07 (phi(impl(f5(P!7, false), false)) = phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))),
% 43.02/28.07 inference(monotonicity,[status(thm)],[1679])).
% 43.02/28.07 tff(1681,plain,
% 43.02/28.07 (phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = phi(impl(f5(P!7, false), false))),
% 43.02/28.07 inference(symmetry,[status(thm)],[1680])).
% 43.02/28.07 tff(1682,plain,
% 43.02/28.07 (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))),
% 43.02/28.07 inference(monotonicity,[status(thm)],[1343])).
% 43.02/28.07 tff(1683,plain,
% 43.02/28.07 (bool(f4(P!7, tptp_fun_X_4(false, P!7), false)) <=> bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 43.02/28.07 inference(symmetry,[status(thm)],[1682])).
% 43.02/28.07 tff(1684,plain,
% 43.02/28.07 (bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) <=> bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 43.02/28.07 inference(transitivity,[status(thm)],[1349, 1683])).
% 43.02/28.07 tff(1685,plain,
% 43.02/28.07 (bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 43.02/28.07 inference(modus_ponens,[status(thm)],[1584, 1684])).
% 43.02/28.07 tff(1686,plain,
% 43.02/28.07 ((~(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))))) | ((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)))),
% 43.02/28.07 inference(unit_resolution,[status(thm)],[1397, 1685])).
% 43.02/28.07 tff(1687,plain,
% 43.02/28.07 ((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))),
% 43.02/28.07 inference(unit_resolution,[status(thm)],[1686, 1345])).
% 43.02/28.07 tff(1688,plain,
% 43.02/28.07 (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)),
% 43.02/28.07 inference(transitivity,[status(thm)],[1343, 820])).
% 43.02/28.07 tff(1689,plain,
% 43.02/28.07 ((phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false)) <=> (impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))),
% 43.02/28.07 inference(monotonicity,[status(thm)],[1688])).
% 43.02/28.07 tff(1690,plain,
% 43.02/28.07 ((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))),
% 43.02/28.07 inference(symmetry,[status(thm)],[1689])).
% 43.02/28.07 tff(1691,plain,
% 43.02/28.07 ((~(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)))),
% 43.02/28.07 inference(monotonicity,[status(thm)],[1690])).
% 43.02/28.07 tff(1692,plain,
% 43.02/28.07 (impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, false)) = not1(false)),
% 43.02/28.07 inference(transitivity,[status(thm)],[1369, 1104, 1103, 927, 1312, 1311, 1310, 1158])).
% 43.02/28.07 tff(1693,plain,
% 43.02/28.07 (impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, false)), false) = impl(not1(false), false)),
% 43.02/28.07 inference(monotonicity,[status(thm)],[1692])).
% 43.02/28.07 tff(1694,plain,
% 43.02/28.07 (apply(P!7, tptp_fun_X_3(P!7)) = impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, false))),
% 43.02/28.07 inference(transitivity,[status(thm)],[1606, 1668, 1230, 1109, 1108, 1106, 926, 1371, 918, 1370])).
% 43.02/28.07 tff(1695,plain,
% 43.02/28.07 (impl(apply(P!7, tptp_fun_X_3(P!7)), false) = impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)), impl(false, false)), false)),
% 43.02/28.07 inference(monotonicity,[status(thm)],[1694])).
% 43.02/28.07 tff(1696,plain,
% 43.02/28.07 (impl(apply(P!7, tptp_fun_X_3(P!7)), false) = false),
% 43.02/28.07 inference(transitivity,[status(thm)],[1695, 1693, 95])).
% 43.02/28.07 tff(1697,plain,
% 43.02/28.07 (((~((~(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))))) | (~(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))))) | (~((~bool(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_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))))),
% 43.02/28.07 inference(tautology,[status(thm)],[])).
% 43.02/28.07 tff(1698,plain,
% 43.02/28.07 ((~(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)))),
% 43.02/28.07 inference(unit_resolution,[status(thm)],[1697, 1458])).
% 43.02/28.07 tff(1699,plain,
% 43.02/28.07 ((~((~(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)))),
% 43.02/28.07 inference(tautology,[status(thm)],[])).
% 43.02/28.07 tff(1700,plain,
% 43.02/28.07 ((~(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)))),
% 43.02/28.07 inference(unit_resolution,[status(thm)],[1699, 1698])).
% 43.02/28.07 tff(1701,plain,
% 43.02/28.07 (~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = not1(false))),
% 43.02/28.07 inference(unit_resolution,[status(thm)],[1700, 1696])).
% 43.02/28.07 tff(1702,plain,
% 43.02/28.07 (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = not1(false))),
% 43.02/28.07 inference(modus_ponens,[status(thm)],[1701, 1691])).
% 43.02/28.07 tff(1703,plain,
% 43.02/28.07 (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = false),
% 43.02/28.07 inference(unit_resolution,[status(thm)],[1421, 1702, 1687])).
% 43.02/28.07 tff(1704,plain,
% 43.02/28.07 (f5(P!7, false) = false),
% 43.02/28.07 inference(transitivity,[status(thm)],[1166, 1703])).
% 43.02/28.07 tff(1705,plain,
% 43.02/28.07 (impl(f5(P!7, false), false) = impl(false, false)),
% 43.02/28.07 inference(monotonicity,[status(thm)],[1704])).
% 43.02/28.07 tff(1706,plain,
% 43.02/28.07 (impl(false, false) = impl(f5(P!7, false), false)),
% 43.02/28.07 inference(symmetry,[status(thm)],[1705])).
% 43.02/28.07 tff(1707,plain,
% 43.02/28.07 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = false),
% 43.02/28.07 inference(transitivity,[status(thm)],[928, 924, 1312, 1311, 1310, 1158, 1552, 1706, 1679, 1407, 1681, 1178, 1677, 1675])).
% 43.02/28.07 tff(1708,plain,
% 43.02/28.07 ($false),
% 43.02/28.07 inference(unit_resolution,[status(thm)],[1053, 1707])).
% 43.02/28.07 tff(1709,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)))) | (tptp_fun_R_5(P!7) = not1(false))), inference(lemma,lemma(discharge,[]))).
% 43.02/28.07 tff(1710,plain,
% 43.02/28.07 (tptp_fun_R_5(P!7) = not1(false)),
% 43.02/28.07 inference(unit_resolution,[status(thm)],[1709, 1272])).
% 43.02/28.07 tff(1711,plain,
% 43.02/28.07 (f6(P!7, tptp_fun_R_5(P!7)) = f6(P!7, not1(false))),
% 43.02/28.07 inference(monotonicity,[status(thm)],[1710])).
% 43.02/28.07 tff(1712,plain,
% 43.02/28.07 (exists2(P!7) = not1(false)),
% 43.02/28.07 inference(transitivity,[status(thm)],[294, 1145, 1711, 273, 919, 1158])).
% 43.02/28.07 tff(1713,plain,
% 43.02/28.07 ((exists1(P!7) = exists2(P!7)) <=> (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))),
% 43.02/28.07 inference(monotonicity,[status(thm)],[511, 1712])).
% 43.02/28.07 tff(1714,plain,
% 43.02/28.07 ((~(exists1(P!7) = exists2(P!7))) <=> (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false)))),
% 43.02/28.07 inference(monotonicity,[status(thm)],[1713])).
% 43.02/28.07 tff(1715,plain,
% 43.02/28.07 (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))),
% 43.02/28.07 inference(modus_ponens,[status(thm)],[1428, 1714])).
% 43.02/28.07 tff(1716,plain,
% 43.02/28.07 (d(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 43.02/28.07 inference(unit_resolution,[status(thm)],[1339, 1272])).
% 43.02/28.07 tff(1717,plain,
% 43.02/28.07 (d(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))),
% 43.02/28.07 inference(modus_ponens,[status(thm)],[1716, 1337])).
% 43.02/28.07 tff(1718,plain,
% 43.02/28.07 (d(impl(apply(P!7, tptp_fun_X_3(P!7)), false))),
% 43.02/28.07 inference(unit_resolution,[status(thm)],[1462, 1717])).
% 43.02/28.07 tff(1719,plain,
% 43.02/28.07 (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false)),
% 43.02/28.07 inference(unit_resolution,[status(thm)],[1342, 1272])).
% 43.02/28.07 tff(1720,plain,
% 43.02/28.07 (impl(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = phi(impl(impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), impl(false, not1(false))), not1(false)))),
% 43.02/28.07 inference(transitivity,[status(thm)],[1308, 1314, 1319, 1328, 1331, 1333, 1145, 1711, 273, 919, 1109, 1108])).
% 43.02/28.07 tff(1721,plain,
% 43.02/28.07 (lazy_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)),
% 43.02/28.07 inference(modus_ponens,[status(thm)],[1720, 1360])).
% 43.02/28.07 tff(1722,plain,
% 43.02/28.07 (~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)),
% 43.02/28.07 inference(unit_resolution,[status(thm)],[1366, 1721])).
% 43.02/28.07 tff(1723,plain,
% 43.02/28.07 (lazy_impl(prop(false), impl(f5(P!7, false), false)) = not1(false)),
% 43.02/28.07 inference(unit_resolution,[status(thm)],[1260, 1722])).
% 43.02/28.07 tff(1724,plain,
% 43.02/28.07 (~(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)))),
% 43.02/28.07 inference(unit_resolution,[status(thm)],[1389, 1723, 1719])).
% 43.02/28.07 tff(1725,plain,
% 43.02/28.07 (bool(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))),
% 43.02/28.07 inference(unit_resolution,[status(thm)],[1394, 1724])).
% 43.02/28.07 tff(1726,plain,
% 43.02/28.07 (bool(impl(apply(P!7, tptp_fun_X_3(P!7)), false))),
% 43.02/28.07 inference(unit_resolution,[status(thm)],[1467, 1725, 1717, 1718])).
% 43.02/28.07 tff(1727,plain,
% 43.02/28.07 (bool(exists1(P!7))),
% 43.02/28.07 inference(unit_resolution,[status(thm)],[1598, 1726])).
% 43.02/28.07 tff(1728,plain,
% 43.02/28.07 (bool(phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 43.02/28.07 inference(modus_ponens,[status(thm)],[1727, 514])).
% 43.02/28.07 tff(1729,plain,
% 43.02/28.07 ((phi(apply(P!7, tptp_fun_X_3(P!7))) = false) | (phi(apply(P!7, tptp_fun_X_3(P!7))) = not1(false))),
% 43.02/28.07 inference(unit_resolution,[status(thm)],[1504, 1728])).
% 43.02/28.07 tff(1730,plain,
% 43.02/28.07 (phi(apply(P!7, tptp_fun_X_3(P!7))) = false),
% 43.02/28.07 inference(unit_resolution,[status(thm)],[544, 1729, 1715])).
% 43.02/28.07 tff(1731,plain,
% 43.02/28.07 (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err)),
% 43.02/28.07 inference(unit_resolution,[status(thm)],[546, 1729])).
% 43.02/28.07 tff(1732,plain,
% 43.02/28.07 (d(apply(P!7, tptp_fun_X_3(P!7))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err))),
% 43.02/28.07 inference(unit_resolution,[status(thm)],[548, 1731])).
% 43.02/28.07 tff(1733,plain,
% 43.02/28.07 (~((~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)))))),
% 43.02/28.07 inference(unit_resolution,[status(thm)],[553, 1732])).
% 43.02/28.07 tff(1734,plain,
% 43.02/28.07 (phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))),
% 43.02/28.07 inference(unit_resolution,[status(thm)],[592, 1733])).
% 43.02/28.07 tff(1735,plain,
% 43.02/28.07 (apply(P!7, tptp_fun_X_3(P!7)) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 43.02/28.07 inference(symmetry,[status(thm)],[1734])).
% 43.02/28.07 tff(1736,plain,
% 43.02/28.07 (apply(P!7, tptp_fun_X_3(P!7)) = false),
% 43.02/28.07 inference(transitivity,[status(thm)],[1735, 1730])).
% 43.02/28.07 tff(1737,plain,
% 43.02/28.07 (~(apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))),
% 43.02/28.07 inference(unit_resolution,[status(thm)],[1545, 1736])).
% 43.02/28.07 tff(1738,plain,
% 43.02/28.07 (d(apply(P!7, tptp_fun_X_3(P!7)))),
% 43.02/28.07 inference(unit_resolution,[status(thm)],[555, 1733])).
% 43.02/28.07 tff(1739,plain,
% 43.02/28.07 (d(apply(P!7, tptp_fun_X_4(false, P!7)))),
% 43.02/28.07 inference(unit_resolution,[status(thm)],[1525, 1738])).
% 43.02/28.07 tff(1740,plain,
% 43.02/28.07 (bool(apply(P!7, tptp_fun_X_3(P!7))) <=> bool(false)),
% 43.02/28.07 inference(monotonicity,[status(thm)],[1736])).
% 43.02/28.07 tff(1741,plain,
% 43.02/28.07 (bool(false) <=> bool(apply(P!7, tptp_fun_X_3(P!7)))),
% 43.02/28.07 inference(symmetry,[status(thm)],[1740])).
% 43.02/28.07 tff(1742,plain,
% 43.02/28.07 (bool(apply(P!7, tptp_fun_X_3(P!7)))),
% 43.02/28.07 inference(modus_ponens,[status(thm)],[61, 1741])).
% 43.02/28.07 tff(1743,plain,
% 43.02/28.07 (bool(apply(P!7, tptp_fun_X_4(false, P!7)))),
% 43.02/28.07 inference(unit_resolution,[status(thm)],[1537, 1742, 1738, 1739])).
% 43.02/28.07 tff(1744,plain,
% 43.02/28.07 ((~(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)))),
% 43.02/28.07 inference(unit_resolution,[status(thm)],[1539, 1743])).
% 43.02/28.07 tff(1745,plain,
% 43.02/28.07 ((apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = not1(false))),
% 43.02/28.07 inference(unit_resolution,[status(thm)],[1744, 1424])).
% 43.02/28.07 tff(1746,plain,
% 43.02/28.07 (apply(P!7, tptp_fun_X_4(false, P!7)) = false),
% 43.02/28.07 inference(unit_resolution,[status(thm)],[1547, 1745, 1737])).
% 43.02/28.07 tff(1747,plain,
% 43.02/28.07 (false = apply(P!7, tptp_fun_X_4(false, P!7))),
% 43.02/28.07 inference(symmetry,[status(thm)],[1746])).
% 43.02/28.07 tff(1748,plain,
% 43.02/28.07 (f1(false, not1(false), false) = f1(apply(P!7, tptp_fun_X_4(false, P!7)), not1(false), false)),
% 43.02/28.07 inference(monotonicity,[status(thm)],[1747])).
% 43.02/28.07 tff(1749,plain,
% 43.02/28.07 (f1(apply(P!7, tptp_fun_X_4(false, P!7)), not1(false), false) = f1(false, not1(false), false)),
% 43.02/28.07 inference(symmetry,[status(thm)],[1748])).
% 43.02/28.07 tff(1750,plain,
% 43.02/28.07 (f4(P!7, tptp_fun_X_4(false, P!7), false) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 43.02/28.07 inference(symmetry,[status(thm)],[1719])).
% 43.02/28.07 tff(1751,plain,
% 43.02/28.07 (impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)) = f5(P!7, false)),
% 43.02/28.07 inference(transitivity,[status(thm)],[806, 821, 1750, 1167])).
% 43.02/28.07 tff(1752,plain,
% 43.02/28.07 (impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false) = impl(f5(P!7, false), false)),
% 43.02/28.07 inference(monotonicity,[status(thm)],[1751])).
% 43.02/28.07 tff(1753,plain,
% 43.02/28.07 (impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false) = lazy_impl(prop(false), impl(f5(P!7, false), false))),
% 43.02/28.07 inference(transitivity,[status(thm)],[1752, 1173, 1407, 1179, 1178, 1175])).
% 43.02/28.07 tff(1754,plain,
% 43.02/28.07 (lazy_impl(prop(false), impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false)) = lazy_impl(not1(false), lazy_impl(prop(false), impl(f5(P!7, false), false)))),
% 43.02/28.07 inference(monotonicity,[status(thm)],[116, 1753])).
% 43.02/28.07 tff(1755,plain,
% 43.02/28.07 (lazy_impl(not1(false), lazy_impl(prop(false), impl(f5(P!7, false), false))) = lazy_impl(prop(false), impl(impl(apply(P!7, tptp_fun_X_4(false, P!7)), impl(not1(false), false)), false))),
% 43.02/28.07 inference(symmetry,[status(thm)],[1754])).
% 43.02/28.07 tff(1756,plain,
% 43.02/28.07 (not1(false) = lazy_impl(prop(false), impl(f5(P!7, false), false))),
% 43.02/28.07 inference(symmetry,[status(thm)],[1723])).
% 43.02/28.07 tff(1757,plain,
% 43.02/28.07 (impl(apply(P!7, tptp_fun_X_4(not1(false), P!7)), not1(false)) = false),
% 43.02/28.07 inference(transitivity,[status(thm)],[928, 924, 1312, 1311, 1310, 1158, 1756, 1656, 1647, 1755, 1642, 1749, 128, 119, 35, 23])).
% 43.02/28.07 tff(1758,plain,
% 43.02/28.07 ($false),
% 43.02/28.07 inference(unit_resolution,[status(thm)],[1053, 1757])).
% 43.02/28.07 % SZS output end Proof
%------------------------------------------------------------------------------