TSTP Solution File: SWW096+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW096+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 20:57:45 EDT 2022
% Result : Theorem 262.02s 166.38s
% Output : Proof 262.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW096+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n004.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Sep 4 11:59:34 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 262.02/166.38 % SZS status Theorem
% 262.02/166.38 % SZS output start Proof
% 262.02/166.38 tff(false_type, type, (
% 262.02/166.38 false: $i)).
% 262.02/166.38 tff(not1_type, type, (
% 262.02/166.38 not1: $i > $i)).
% 262.02/166.38 tff(phi_type, type, (
% 262.02/166.38 phi: $i > $i)).
% 262.02/166.38 tff(d_type, type, (
% 262.02/166.38 d: $i > $o)).
% 262.02/166.38 tff(err_type, type, (
% 262.02/166.38 err: $i)).
% 262.02/166.38 tff(true_type, type, (
% 262.02/166.38 true: $i)).
% 262.02/166.38 tff(lazy_impl_type, type, (
% 262.02/166.38 lazy_impl: ( $i * $i ) > $i)).
% 262.02/166.38 tff(impl_type, type, (
% 262.02/166.38 impl: ( $i * $i ) > $i)).
% 262.02/166.38 tff(prop_type, type, (
% 262.02/166.38 prop: $i > $i)).
% 262.02/166.38 tff(bool_type, type, (
% 262.02/166.38 bool: $i > $o)).
% 262.02/166.38 tff(f1_type, type, (
% 262.02/166.38 f1: ( $i * $i * $i ) > $i)).
% 262.02/166.38 tff(tptp_fun_P_8_type, type, (
% 262.02/166.38 tptp_fun_P_8: $i)).
% 262.02/166.38 tff(forallprefers_type, type, (
% 262.02/166.38 forallprefers: ( $i * $i ) > $o)).
% 262.02/166.38 tff(tptp_fun_R_0_type, type, (
% 262.02/166.38 tptp_fun_R_0: ( $i * $i ) > $i)).
% 262.02/166.38 tff(tptp_fun_Q_7_type, type, (
% 262.02/166.38 tptp_fun_Q_7: $i)).
% 262.02/166.38 tff(and1_type, type, (
% 262.02/166.38 and1: ( $i * $i ) > $i)).
% 262.02/166.38 tff(and2_type, type, (
% 262.02/166.38 and2: ( $i * $i ) > $i)).
% 262.02/166.38 tff(false2_type, type, (
% 262.02/166.38 false2: $i)).
% 262.02/166.38 tff(f7_type, type, (
% 262.02/166.38 f7: $i > $i)).
% 262.02/166.38 tff(tptp_fun_P_6_type, type, (
% 262.02/166.38 tptp_fun_P_6: $i)).
% 262.02/166.38 tff(1,plain,
% 262.02/166.38 (d(false) <=> d(false)),
% 262.02/166.38 inference(rewrite,[status(thm)],[])).
% 262.02/166.38 tff(2,axiom,((d(true) & d(false)) & d(err)), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','false_true_err_in_d')).
% 262.02/166.38 tff(3,plain,
% 262.02/166.38 (d(true) & d(false)),
% 262.02/166.38 inference(and_elim,[status(thm)],[2])).
% 262.02/166.38 tff(4,plain,
% 262.02/166.38 (d(false)),
% 262.02/166.38 inference(and_elim,[status(thm)],[3])).
% 262.02/166.38 tff(5,plain,
% 262.02/166.38 (d(false)),
% 262.02/166.38 inference(modus_ponens,[status(thm)],[4, 1])).
% 262.02/166.38 tff(6,plain,
% 262.02/166.38 ((d(false) | (~(phi(false) = err))) | (~d(false))),
% 262.02/166.38 inference(tautology,[status(thm)],[])).
% 262.02/166.38 tff(7,plain,
% 262.02/166.38 (d(false) | (~(phi(false) = err))),
% 262.02/166.38 inference(unit_resolution,[status(thm)],[6, 5])).
% 262.02/166.38 tff(8,plain,
% 262.02/166.38 (^[X: $i] : refl(((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err))))) <=> ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err))))))),
% 262.02/166.38 inference(bind,[status(th)],[])).
% 262.02/166.38 tff(9,plain,
% 262.02/166.38 (![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err))))) <=> ![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 262.02/166.38 inference(quant_intro,[status(thm)],[8])).
% 262.02/166.38 tff(10,plain,
% 262.02/166.38 (^[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)))))))),
% 262.02/166.38 inference(bind,[status(th)],[])).
% 262.02/166.38 tff(11,plain,
% 262.02/166.38 (![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err))) <=> ![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 262.02/166.38 inference(quant_intro,[status(thm)],[10])).
% 262.02/166.38 tff(12,plain,
% 262.02/166.38 (![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err))) <=> ![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err)))),
% 262.02/166.38 inference(rewrite,[status(thm)],[])).
% 262.02/166.38 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')).
% 262.02/166.38 tff(14,plain,
% 262.02/166.38 (![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err)))),
% 262.02/166.38 inference(modus_ponens,[status(thm)],[13, 12])).
% 262.02/166.38 tff(15,plain,(
% 262.02/166.38 ![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err)))),
% 262.02/166.38 inference(skolemize,[status(sab)],[14])).
% 262.02/166.38 tff(16,plain,
% 262.02/166.38 (![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 262.02/166.38 inference(modus_ponens,[status(thm)],[15, 11])).
% 262.02/166.38 tff(17,plain,
% 262.02/166.38 (![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 262.02/166.38 inference(modus_ponens,[status(thm)],[16, 9])).
% 262.02/166.38 tff(18,plain,
% 262.02/166.38 (((~![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)))))),
% 262.02/166.39 inference(rewrite,[status(thm)],[])).
% 262.02/166.39 tff(19,plain,
% 262.02/166.39 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(false)) | (~(phi(false) = false)))) | (~(d(false) | (~(phi(false) = err)))))),
% 262.02/166.39 inference(quant_inst,[status(thm)],[])).
% 262.02/166.39 tff(20,plain,
% 262.02/166.39 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(false)) | (~(phi(false) = false)))) | (~(d(false) | (~(phi(false) = err))))),
% 262.02/166.39 inference(modus_ponens,[status(thm)],[19, 18])).
% 262.02/166.39 tff(21,plain,
% 262.02/166.39 (~((~d(false)) | (~(phi(false) = false)))),
% 262.02/166.39 inference(unit_resolution,[status(thm)],[20, 17, 7])).
% 262.02/166.39 tff(22,plain,
% 262.02/166.39 (((~d(false)) | (~(phi(false) = false))) | (phi(false) = false)),
% 262.02/166.39 inference(tautology,[status(thm)],[])).
% 262.02/166.39 tff(23,plain,
% 262.02/166.39 (phi(false) = false),
% 262.02/166.39 inference(unit_resolution,[status(thm)],[22, 21])).
% 262.02/166.39 tff(24,plain,
% 262.02/166.39 (^[B: $i] : refl((lazy_impl(not1(false), B) = phi(B)) <=> (lazy_impl(not1(false), B) = phi(B)))),
% 262.02/166.39 inference(bind,[status(th)],[])).
% 262.02/166.39 tff(25,plain,
% 262.02/166.39 (![B: $i] : (lazy_impl(not1(false), B) = phi(B)) <=> ![B: $i] : (lazy_impl(not1(false), B) = phi(B))),
% 262.02/166.39 inference(quant_intro,[status(thm)],[24])).
% 262.02/166.39 tff(26,plain,
% 262.02/166.39 (^[B: $i] : rewrite((lazy_impl(true, B) = phi(B)) <=> (lazy_impl(not1(false), B) = phi(B)))),
% 262.02/166.39 inference(bind,[status(th)],[])).
% 262.02/166.39 tff(27,plain,
% 262.02/166.39 (![B: $i] : (lazy_impl(true, B) = phi(B)) <=> ![B: $i] : (lazy_impl(not1(false), B) = phi(B))),
% 262.02/166.39 inference(quant_intro,[status(thm)],[26])).
% 262.02/166.39 tff(28,plain,
% 262.02/166.39 (![B: $i] : (lazy_impl(true, B) = phi(B)) <=> ![B: $i] : (lazy_impl(true, B) = phi(B))),
% 262.02/166.39 inference(rewrite,[status(thm)],[])).
% 262.02/166.39 tff(29,axiom,(![B: $i] : (lazy_impl(true, B) = phi(B))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','lazy_impl_axiom3')).
% 262.02/166.39 tff(30,plain,
% 262.02/166.39 (![B: $i] : (lazy_impl(true, B) = phi(B))),
% 262.02/166.39 inference(modus_ponens,[status(thm)],[29, 28])).
% 262.02/166.39 tff(31,plain,
% 262.02/166.39 (![B: $i] : (lazy_impl(not1(false), B) = phi(B))),
% 262.02/166.39 inference(modus_ponens,[status(thm)],[30, 27])).
% 262.02/166.39 tff(32,plain,(
% 262.02/166.39 ![B: $i] : (lazy_impl(not1(false), B) = phi(B))),
% 262.02/166.39 inference(skolemize,[status(sab)],[31])).
% 262.02/166.39 tff(33,plain,
% 262.02/166.39 (![B: $i] : (lazy_impl(not1(false), B) = phi(B))),
% 262.02/166.39 inference(modus_ponens,[status(thm)],[32, 25])).
% 262.02/166.39 tff(34,plain,
% 262.02/166.39 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), false) = phi(false))),
% 262.02/166.39 inference(quant_inst,[status(thm)],[])).
% 262.02/166.39 tff(35,plain,
% 262.02/166.39 (lazy_impl(not1(false), false) = phi(false)),
% 262.02/166.39 inference(unit_resolution,[status(thm)],[34, 33])).
% 262.02/166.39 tff(36,plain,
% 262.02/166.39 ((false = not1(false)) <=> (not1(false) = false)),
% 262.02/166.39 inference(commutativity,[status(thm)],[])).
% 262.02/166.39 tff(37,plain,
% 262.02/166.39 (d(true) <=> d(not1(false))),
% 262.02/166.39 inference(rewrite,[status(thm)],[])).
% 262.02/166.39 tff(38,plain,
% 262.02/166.39 (d(true) <=> d(true)),
% 262.02/166.39 inference(rewrite,[status(thm)],[])).
% 262.02/166.39 tff(39,plain,
% 262.02/166.39 (d(true)),
% 262.02/166.39 inference(and_elim,[status(thm)],[3])).
% 262.02/166.39 tff(40,plain,
% 262.02/166.39 (d(true)),
% 262.02/166.39 inference(modus_ponens,[status(thm)],[39, 38])).
% 262.02/166.39 tff(41,plain,
% 262.02/166.39 (d(not1(false))),
% 262.02/166.39 inference(modus_ponens,[status(thm)],[40, 37])).
% 262.02/166.39 tff(42,plain,
% 262.02/166.39 ((d(not1(false)) | (~(phi(not1(false)) = err))) | (~d(not1(false)))),
% 262.02/166.39 inference(tautology,[status(thm)],[])).
% 262.02/166.39 tff(43,plain,
% 262.02/166.39 (d(not1(false)) | (~(phi(not1(false)) = err))),
% 262.02/166.39 inference(unit_resolution,[status(thm)],[42, 41])).
% 262.02/166.39 tff(44,plain,
% 262.02/166.39 (((~![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)))))),
% 262.02/166.39 inference(rewrite,[status(thm)],[])).
% 262.02/166.39 tff(45,plain,
% 262.02/166.39 ((~![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)))))),
% 262.02/166.39 inference(quant_inst,[status(thm)],[])).
% 262.02/166.39 tff(46,plain,
% 262.02/166.39 ((~![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))))),
% 262.02/166.39 inference(modus_ponens,[status(thm)],[45, 44])).
% 262.02/166.39 tff(47,plain,
% 262.02/166.39 (~((~d(not1(false))) | (~(phi(not1(false)) = not1(false))))),
% 262.02/166.39 inference(unit_resolution,[status(thm)],[46, 17, 43])).
% 262.02/166.39 tff(48,plain,
% 262.02/166.39 (((~d(not1(false))) | (~(phi(not1(false)) = not1(false)))) | (phi(not1(false)) = not1(false))),
% 262.02/166.39 inference(tautology,[status(thm)],[])).
% 262.02/166.39 tff(49,plain,
% 262.02/166.39 (phi(not1(false)) = not1(false)),
% 262.02/166.39 inference(unit_resolution,[status(thm)],[48, 47])).
% 262.02/166.39 tff(50,plain,
% 262.02/166.39 ((not1(true) = false) <=> (not1(not1(false)) = false)),
% 262.02/166.39 inference(rewrite,[status(thm)],[])).
% 262.02/166.39 tff(51,plain,
% 262.02/166.39 ((not1(true) = false) <=> (not1(true) = false)),
% 262.02/166.39 inference(rewrite,[status(thm)],[])).
% 262.02/166.39 tff(52,axiom,(not1(true) = false), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','not1_axiom3')).
% 262.02/166.39 tff(53,plain,
% 262.02/166.39 (not1(true) = false),
% 262.02/166.39 inference(modus_ponens,[status(thm)],[52, 51])).
% 262.02/166.39 tff(54,plain,
% 262.02/166.39 (not1(not1(false)) = false),
% 262.02/166.39 inference(modus_ponens,[status(thm)],[53, 50])).
% 262.02/166.39 tff(55,plain,
% 262.02/166.39 ((not1(not1(false)) = phi(not1(false))) <=> (false = not1(false))),
% 262.02/166.39 inference(monotonicity,[status(thm)],[54, 49])).
% 262.02/166.39 tff(56,plain,
% 262.02/166.39 ((not1(not1(false)) = phi(not1(false))) <=> (not1(false) = false)),
% 262.02/166.39 inference(transitivity,[status(thm)],[55, 36])).
% 262.02/166.39 tff(57,plain,
% 262.02/166.39 ((not1(false) = false) <=> (not1(not1(false)) = phi(not1(false)))),
% 262.02/166.39 inference(symmetry,[status(thm)],[56])).
% 262.02/166.39 tff(58,plain,
% 262.02/166.39 ((~(not1(false) = false)) <=> (~(not1(not1(false)) = phi(not1(false))))),
% 262.02/166.39 inference(monotonicity,[status(thm)],[57])).
% 262.02/166.39 tff(59,plain,
% 262.02/166.39 ((~(true = false)) <=> (~(not1(false) = false))),
% 262.02/166.39 inference(rewrite,[status(thm)],[])).
% 262.02/166.39 tff(60,plain,
% 262.02/166.39 ((~(true = false)) <=> (~(true = false))),
% 262.02/166.39 inference(rewrite,[status(thm)],[])).
% 262.02/166.39 tff(61,axiom,(((~(true = false)) & (~(true = err))) & (~(false = err))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','distinct_false_true_err')).
% 262.02/166.39 tff(62,plain,
% 262.02/166.39 ((~(true = false)) & (~(true = err))),
% 262.02/166.39 inference(and_elim,[status(thm)],[61])).
% 262.02/166.39 tff(63,plain,
% 262.02/166.39 (~(true = false)),
% 262.02/166.39 inference(and_elim,[status(thm)],[62])).
% 262.02/166.39 tff(64,plain,
% 262.02/166.39 (~(true = false)),
% 262.02/166.39 inference(modus_ponens,[status(thm)],[63, 60])).
% 262.02/166.39 tff(65,plain,
% 262.02/166.39 (~(not1(false) = false)),
% 262.02/166.39 inference(modus_ponens,[status(thm)],[64, 59])).
% 262.02/166.39 tff(66,plain,
% 262.02/166.39 (~(not1(not1(false)) = phi(not1(false)))),
% 262.02/166.39 inference(modus_ponens,[status(thm)],[65, 58])).
% 262.02/166.39 tff(67,plain,
% 262.02/166.39 (^[A: $i] : refl((bool(A) | (not1(A) = phi(A))) <=> (bool(A) | (not1(A) = phi(A))))),
% 262.02/166.39 inference(bind,[status(th)],[])).
% 262.02/166.39 tff(68,plain,
% 262.02/166.39 (![A: $i] : (bool(A) | (not1(A) = phi(A))) <=> ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 262.02/166.39 inference(quant_intro,[status(thm)],[67])).
% 262.02/166.39 tff(69,plain,
% 262.02/166.39 (![A: $i] : (bool(A) | (not1(A) = phi(A))) <=> ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 262.02/166.39 inference(rewrite,[status(thm)],[])).
% 262.02/166.39 tff(70,plain,
% 262.02/166.39 (^[A: $i] : rewrite(((~bool(A)) => (not1(A) = phi(A))) <=> (bool(A) | (not1(A) = phi(A))))),
% 262.02/166.39 inference(bind,[status(th)],[])).
% 262.02/166.39 tff(71,plain,
% 262.02/166.39 (![A: $i] : ((~bool(A)) => (not1(A) = phi(A))) <=> ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 262.02/166.39 inference(quant_intro,[status(thm)],[70])).
% 262.02/166.39 tff(72,axiom,(![A: $i] : ((~bool(A)) => (not1(A) = phi(A)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','not1_axiom1')).
% 262.02/166.39 tff(73,plain,
% 262.02/166.39 (![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 262.02/166.39 inference(modus_ponens,[status(thm)],[72, 71])).
% 262.02/166.39 tff(74,plain,
% 262.02/166.39 (![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 262.02/166.39 inference(modus_ponens,[status(thm)],[73, 69])).
% 262.02/166.39 tff(75,plain,(
% 262.02/166.39 ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 262.02/166.39 inference(skolemize,[status(sab)],[74])).
% 262.02/166.39 tff(76,plain,
% 262.02/166.39 (![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 262.02/166.39 inference(modus_ponens,[status(thm)],[75, 68])).
% 262.02/166.39 tff(77,plain,
% 262.02/166.39 (((~![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))))),
% 262.02/166.39 inference(rewrite,[status(thm)],[])).
% 262.02/166.39 tff(78,plain,
% 262.02/166.39 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | (bool(not1(false)) | (not1(not1(false)) = phi(not1(false))))),
% 262.02/166.39 inference(quant_inst,[status(thm)],[])).
% 262.02/166.39 tff(79,plain,
% 262.02/166.39 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | bool(not1(false)) | (not1(not1(false)) = phi(not1(false)))),
% 262.02/166.39 inference(modus_ponens,[status(thm)],[78, 77])).
% 262.02/166.39 tff(80,plain,
% 262.02/166.39 (bool(not1(false)) | (not1(not1(false)) = phi(not1(false)))),
% 262.02/166.39 inference(unit_resolution,[status(thm)],[79, 76])).
% 262.02/166.39 tff(81,plain,
% 262.02/166.39 (bool(not1(false))),
% 262.02/166.39 inference(unit_resolution,[status(thm)],[80, 66])).
% 262.02/166.39 tff(82,plain,
% 262.02/166.39 (^[B: $i] : refl(((~bool(B)) | (impl(not1(false), B) = B)) <=> ((~bool(B)) | (impl(not1(false), B) = B)))),
% 262.02/166.39 inference(bind,[status(th)],[])).
% 262.02/166.39 tff(83,plain,
% 262.02/166.39 (![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B)) <=> ![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))),
% 262.02/166.39 inference(quant_intro,[status(thm)],[82])).
% 262.02/166.39 tff(84,plain,
% 262.02/166.39 (^[B: $i] : rewrite(((~bool(B)) | (impl(true, B) = B)) <=> ((~bool(B)) | (impl(not1(false), B) = B)))),
% 262.02/166.39 inference(bind,[status(th)],[])).
% 262.02/166.39 tff(85,plain,
% 262.02/166.39 (![B: $i] : ((~bool(B)) | (impl(true, B) = B)) <=> ![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))),
% 262.02/166.39 inference(quant_intro,[status(thm)],[84])).
% 262.02/166.39 tff(86,plain,
% 262.02/166.39 (![B: $i] : ((~bool(B)) | (impl(true, B) = B)) <=> ![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 262.02/166.39 inference(rewrite,[status(thm)],[])).
% 262.02/166.39 tff(87,plain,
% 262.02/166.39 (^[B: $i] : rewrite((bool(B) => (impl(true, B) = B)) <=> ((~bool(B)) | (impl(true, B) = B)))),
% 262.02/166.39 inference(bind,[status(th)],[])).
% 262.02/166.39 tff(88,plain,
% 262.02/166.39 (![B: $i] : (bool(B) => (impl(true, B) = B)) <=> ![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 262.02/166.39 inference(quant_intro,[status(thm)],[87])).
% 262.02/166.39 tff(89,axiom,(![B: $i] : (bool(B) => (impl(true, B) = B))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','impl_axiom4')).
% 262.02/166.39 tff(90,plain,
% 262.02/166.39 (![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 262.02/166.39 inference(modus_ponens,[status(thm)],[89, 88])).
% 262.02/166.39 tff(91,plain,
% 262.02/166.39 (![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 262.02/166.39 inference(modus_ponens,[status(thm)],[90, 86])).
% 262.02/166.39 tff(92,plain,
% 262.02/166.39 (![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))),
% 262.02/166.39 inference(modus_ponens,[status(thm)],[91, 85])).
% 262.02/166.39 tff(93,plain,(
% 262.02/166.39 ![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))),
% 262.02/166.39 inference(skolemize,[status(sab)],[92])).
% 262.02/166.39 tff(94,plain,
% 262.02/166.39 (![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))),
% 262.02/166.39 inference(modus_ponens,[status(thm)],[93, 83])).
% 262.02/166.39 tff(95,plain,
% 262.02/166.39 (((~![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)))),
% 262.02/166.39 inference(rewrite,[status(thm)],[])).
% 262.02/166.39 tff(96,plain,
% 262.02/166.39 ((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | ((~bool(not1(false))) | (impl(not1(false), not1(false)) = not1(false)))),
% 262.02/166.39 inference(quant_inst,[status(thm)],[])).
% 262.02/166.39 tff(97,plain,
% 262.02/166.39 ((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | (~bool(not1(false))) | (impl(not1(false), not1(false)) = not1(false))),
% 262.02/166.39 inference(modus_ponens,[status(thm)],[96, 95])).
% 262.02/166.39 tff(98,plain,
% 262.02/166.39 (impl(not1(false), not1(false)) = not1(false)),
% 262.02/166.39 inference(unit_resolution,[status(thm)],[97, 94, 81])).
% 262.02/166.39 tff(99,plain,
% 262.02/166.39 ((not1(false) = phi(false)) <=> (not1(false) = false)),
% 262.02/166.39 inference(monotonicity,[status(thm)],[23])).
% 262.02/166.39 tff(100,plain,
% 262.02/166.39 ((not1(false) = false) <=> (not1(false) = phi(false))),
% 262.02/166.39 inference(symmetry,[status(thm)],[99])).
% 262.02/166.39 tff(101,plain,
% 262.02/166.39 ((~(not1(false) = false)) <=> (~(not1(false) = phi(false)))),
% 262.02/166.39 inference(monotonicity,[status(thm)],[100])).
% 262.02/166.39 tff(102,plain,
% 262.02/166.39 (~(not1(false) = phi(false))),
% 262.02/166.39 inference(modus_ponens,[status(thm)],[65, 101])).
% 262.02/166.39 tff(103,plain,
% 262.02/166.39 (((~![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)))),
% 262.02/166.39 inference(rewrite,[status(thm)],[])).
% 262.02/166.39 tff(104,plain,
% 262.02/166.39 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | (bool(false) | (not1(false) = phi(false)))),
% 262.02/166.39 inference(quant_inst,[status(thm)],[])).
% 262.02/166.39 tff(105,plain,
% 262.02/166.39 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | bool(false) | (not1(false) = phi(false))),
% 262.02/166.39 inference(modus_ponens,[status(thm)],[104, 103])).
% 262.02/166.39 tff(106,plain,
% 262.02/166.39 (bool(false) | (not1(false) = phi(false))),
% 262.02/166.39 inference(unit_resolution,[status(thm)],[105, 76])).
% 262.02/166.39 tff(107,plain,
% 262.02/166.39 (bool(false)),
% 262.02/166.39 inference(unit_resolution,[status(thm)],[106, 102])).
% 262.02/166.39 tff(108,plain,
% 262.02/166.39 (^[B: $i] : refl(((~bool(B)) | (impl(false, B) = not1(false))) <=> ((~bool(B)) | (impl(false, B) = not1(false))))),
% 262.02/166.39 inference(bind,[status(th)],[])).
% 262.02/166.39 tff(109,plain,
% 262.02/166.39 (![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false))) <=> ![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))),
% 262.02/166.39 inference(quant_intro,[status(thm)],[108])).
% 262.02/166.39 tff(110,plain,
% 262.02/166.39 (^[B: $i] : rewrite(((~bool(B)) | (impl(false, B) = true)) <=> ((~bool(B)) | (impl(false, B) = not1(false))))),
% 262.02/166.39 inference(bind,[status(th)],[])).
% 262.02/166.39 tff(111,plain,
% 262.02/166.39 (![B: $i] : ((~bool(B)) | (impl(false, B) = true)) <=> ![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))),
% 262.02/166.39 inference(quant_intro,[status(thm)],[110])).
% 262.02/166.39 tff(112,plain,
% 262.02/166.39 (![B: $i] : ((~bool(B)) | (impl(false, B) = true)) <=> ![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 262.02/166.39 inference(rewrite,[status(thm)],[])).
% 262.02/166.39 tff(113,plain,
% 262.02/166.39 (^[B: $i] : rewrite((bool(B) => (impl(false, B) = true)) <=> ((~bool(B)) | (impl(false, B) = true)))),
% 262.02/166.39 inference(bind,[status(th)],[])).
% 262.02/166.39 tff(114,plain,
% 262.02/166.39 (![B: $i] : (bool(B) => (impl(false, B) = true)) <=> ![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 262.02/166.39 inference(quant_intro,[status(thm)],[113])).
% 262.02/166.39 tff(115,axiom,(![B: $i] : (bool(B) => (impl(false, B) = true))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','impl_axiom3')).
% 262.02/166.39 tff(116,plain,
% 262.02/166.39 (![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 262.02/166.39 inference(modus_ponens,[status(thm)],[115, 114])).
% 262.02/166.39 tff(117,plain,
% 262.02/166.39 (![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 262.02/166.39 inference(modus_ponens,[status(thm)],[116, 112])).
% 262.02/166.39 tff(118,plain,
% 262.02/166.39 (![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))),
% 262.02/166.39 inference(modus_ponens,[status(thm)],[117, 111])).
% 262.02/166.39 tff(119,plain,(
% 262.02/166.39 ![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))),
% 262.02/166.39 inference(skolemize,[status(sab)],[118])).
% 262.02/166.39 tff(120,plain,
% 262.02/166.39 (![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))),
% 262.02/166.39 inference(modus_ponens,[status(thm)],[119, 109])).
% 262.02/166.39 tff(121,plain,
% 262.02/166.39 (((~![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)))),
% 262.02/166.39 inference(rewrite,[status(thm)],[])).
% 262.02/166.39 tff(122,plain,
% 262.02/166.39 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | ((~bool(false)) | (impl(false, false) = not1(false)))),
% 262.02/166.39 inference(quant_inst,[status(thm)],[])).
% 262.02/166.39 tff(123,plain,
% 262.02/166.39 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | (~bool(false)) | (impl(false, false) = not1(false))),
% 262.02/166.39 inference(modus_ponens,[status(thm)],[122, 121])).
% 262.02/166.39 tff(124,plain,
% 262.02/166.39 (impl(false, false) = not1(false)),
% 262.02/166.39 inference(unit_resolution,[status(thm)],[123, 120, 107])).
% 262.02/166.39 tff(125,plain,
% 262.02/166.39 (impl(not1(false), impl(false, false)) = impl(not1(false), not1(false))),
% 262.02/166.39 inference(monotonicity,[status(thm)],[124])).
% 262.02/166.39 tff(126,plain,
% 262.02/166.39 (impl(not1(false), impl(false, false)) = not1(false)),
% 262.02/166.39 inference(transitivity,[status(thm)],[125, 98])).
% 262.02/166.39 tff(127,plain,
% 262.02/166.39 (impl(impl(not1(false), impl(false, false)), false) = impl(not1(false), false)),
% 262.02/166.39 inference(monotonicity,[status(thm)],[126])).
% 262.02/166.39 tff(128,plain,
% 262.02/166.39 (impl(not1(false), false) = impl(impl(not1(false), impl(false, false)), false)),
% 262.02/166.39 inference(symmetry,[status(thm)],[127])).
% 262.02/166.40 tff(129,plain,
% 262.02/166.40 (((~![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))),
% 262.02/166.40 inference(rewrite,[status(thm)],[])).
% 262.02/166.40 tff(130,plain,
% 262.02/166.40 ((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | ((~bool(false)) | (impl(not1(false), false) = false))),
% 262.02/166.40 inference(quant_inst,[status(thm)],[])).
% 262.02/166.40 tff(131,plain,
% 262.02/166.40 ((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | (~bool(false)) | (impl(not1(false), false) = false)),
% 262.02/166.40 inference(modus_ponens,[status(thm)],[130, 129])).
% 262.02/166.40 tff(132,plain,
% 262.02/166.40 (impl(not1(false), false) = false),
% 262.02/166.40 inference(unit_resolution,[status(thm)],[131, 94, 107])).
% 262.02/166.40 tff(133,plain,
% 262.02/166.40 (false = impl(not1(false), false)),
% 262.02/166.40 inference(symmetry,[status(thm)],[132])).
% 262.02/166.40 tff(134,plain,
% 262.02/166.40 (false = impl(impl(not1(false), impl(false, false)), false)),
% 262.02/166.40 inference(transitivity,[status(thm)],[133, 128])).
% 262.02/166.40 tff(135,plain,
% 262.02/166.40 (^[X: $i] : refl(((prop(X) = not1(false)) <=> bool(X)) <=> ((prop(X) = not1(false)) <=> bool(X)))),
% 262.02/166.40 inference(bind,[status(th)],[])).
% 262.02/166.40 tff(136,plain,
% 262.02/166.40 (![X: $i] : ((prop(X) = not1(false)) <=> bool(X)) <=> ![X: $i] : ((prop(X) = not1(false)) <=> bool(X))),
% 262.02/166.40 inference(quant_intro,[status(thm)],[135])).
% 262.02/166.40 tff(137,plain,
% 262.02/166.40 (^[X: $i] : rewrite(((prop(X) = true) <=> bool(X)) <=> ((prop(X) = not1(false)) <=> bool(X)))),
% 262.02/166.40 inference(bind,[status(th)],[])).
% 262.02/166.40 tff(138,plain,
% 262.02/166.40 (![X: $i] : ((prop(X) = true) <=> bool(X)) <=> ![X: $i] : ((prop(X) = not1(false)) <=> bool(X))),
% 262.02/166.40 inference(quant_intro,[status(thm)],[137])).
% 262.02/166.40 tff(139,plain,
% 262.02/166.40 (![X: $i] : ((prop(X) = true) <=> bool(X)) <=> ![X: $i] : ((prop(X) = true) <=> bool(X))),
% 262.02/166.40 inference(rewrite,[status(thm)],[])).
% 262.02/166.40 tff(140,axiom,(![X: $i] : ((prop(X) = true) <=> bool(X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','prop_true')).
% 262.02/166.40 tff(141,plain,
% 262.02/166.40 (![X: $i] : ((prop(X) = true) <=> bool(X))),
% 262.02/166.40 inference(modus_ponens,[status(thm)],[140, 139])).
% 262.02/166.40 tff(142,plain,
% 262.02/166.40 (![X: $i] : ((prop(X) = not1(false)) <=> bool(X))),
% 262.02/166.40 inference(modus_ponens,[status(thm)],[141, 138])).
% 262.02/166.40 tff(143,plain,(
% 262.02/166.40 ![X: $i] : ((prop(X) = not1(false)) <=> bool(X))),
% 262.02/166.40 inference(skolemize,[status(sab)],[142])).
% 262.02/166.40 tff(144,plain,
% 262.02/166.40 (![X: $i] : ((prop(X) = not1(false)) <=> bool(X))),
% 262.02/166.40 inference(modus_ponens,[status(thm)],[143, 136])).
% 262.02/166.40 tff(145,plain,
% 262.02/166.40 ((~![X: $i] : ((prop(X) = not1(false)) <=> bool(X))) | ((prop(false) = not1(false)) <=> bool(false))),
% 262.02/166.40 inference(quant_inst,[status(thm)],[])).
% 262.02/166.40 tff(146,plain,
% 262.02/166.40 ((prop(false) = not1(false)) <=> bool(false)),
% 262.02/166.40 inference(unit_resolution,[status(thm)],[145, 144])).
% 262.02/166.40 tff(147,plain,
% 262.02/166.40 ((~((prop(false) = not1(false)) <=> bool(false))) | (prop(false) = not1(false)) | (~bool(false))),
% 262.02/166.40 inference(tautology,[status(thm)],[])).
% 262.02/166.40 tff(148,plain,
% 262.02/166.40 ((~((prop(false) = not1(false)) <=> bool(false))) | (prop(false) = not1(false))),
% 262.02/166.40 inference(unit_resolution,[status(thm)],[147, 107])).
% 262.02/166.40 tff(149,plain,
% 262.02/166.40 (prop(false) = not1(false)),
% 262.02/166.40 inference(unit_resolution,[status(thm)],[148, 146])).
% 262.02/166.40 tff(150,plain,
% 262.02/166.40 (not1(false) = prop(false)),
% 262.02/166.40 inference(symmetry,[status(thm)],[149])).
% 262.02/166.40 tff(151,plain,
% 262.02/166.40 (lazy_impl(not1(false), false) = lazy_impl(prop(false), impl(impl(not1(false), impl(false, false)), false))),
% 262.02/166.40 inference(monotonicity,[status(thm)],[150, 134])).
% 262.02/166.40 tff(152,plain,
% 262.02/166.40 (lazy_impl(prop(false), impl(impl(not1(false), impl(false, false)), false)) = lazy_impl(not1(false), false)),
% 262.02/166.40 inference(symmetry,[status(thm)],[151])).
% 262.02/166.40 tff(153,plain,
% 262.02/166.40 (^[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))))),
% 262.02/166.40 inference(bind,[status(th)],[])).
% 262.02/166.40 tff(154,plain,
% 262.02/166.40 (![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)))),
% 262.02/166.40 inference(quant_intro,[status(thm)],[153])).
% 262.02/166.40 tff(155,plain,
% 262.02/166.40 (![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)))),
% 262.02/166.40 inference(rewrite,[status(thm)],[])).
% 262.02/166.40 tff(156,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')).
% 262.02/166.40 tff(157,plain,
% 262.02/166.40 (![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))),
% 262.02/166.40 inference(modus_ponens,[status(thm)],[156, 155])).
% 262.02/166.40 tff(158,plain,(
% 262.02/166.40 ![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))),
% 262.02/166.40 inference(skolemize,[status(sab)],[157])).
% 262.02/166.40 tff(159,plain,
% 262.02/166.40 (![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))),
% 262.02/166.40 inference(modus_ponens,[status(thm)],[158, 154])).
% 262.02/166.40 tff(160,plain,
% 262.02/166.40 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(not1(false), false, false) = lazy_impl(prop(false), impl(impl(not1(false), impl(false, false)), false)))),
% 262.02/166.40 inference(quant_inst,[status(thm)],[])).
% 262.02/166.40 tff(161,plain,
% 262.02/166.40 (f1(not1(false), false, false) = lazy_impl(prop(false), impl(impl(not1(false), impl(false, false)), false))),
% 262.02/166.40 inference(unit_resolution,[status(thm)],[160, 159])).
% 262.02/166.40 tff(162,plain,
% 262.02/166.40 (((~![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)))),
% 262.02/166.40 inference(rewrite,[status(thm)],[])).
% 262.02/166.40 tff(163,plain,
% 262.02/166.40 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | ((~bool(not1(false))) | (impl(false, not1(false)) = not1(false)))),
% 262.02/166.40 inference(quant_inst,[status(thm)],[])).
% 262.02/166.40 tff(164,plain,
% 262.02/166.40 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | (~bool(not1(false))) | (impl(false, not1(false)) = not1(false))),
% 262.02/166.40 inference(modus_ponens,[status(thm)],[163, 162])).
% 262.02/166.40 tff(165,plain,
% 262.02/166.40 (impl(false, not1(false)) = not1(false)),
% 262.02/166.40 inference(unit_resolution,[status(thm)],[164, 120, 81])).
% 262.02/166.40 tff(166,plain,
% 262.02/166.40 (impl(false, impl(false, false)) = impl(false, not1(false))),
% 262.02/166.40 inference(monotonicity,[status(thm)],[124])).
% 262.02/166.40 tff(167,plain,
% 262.02/166.40 (impl(false, impl(false, false)) = not1(false)),
% 262.02/166.40 inference(transitivity,[status(thm)],[166, 165])).
% 262.02/166.40 tff(168,plain,
% 262.02/166.40 (impl(impl(false, impl(false, false)), false) = impl(not1(false), false)),
% 262.02/166.40 inference(monotonicity,[status(thm)],[167])).
% 262.02/166.40 tff(169,plain,
% 262.02/166.40 (impl(not1(false), false) = impl(impl(false, impl(false, false)), false)),
% 262.02/166.40 inference(symmetry,[status(thm)],[168])).
% 262.02/166.40 tff(170,plain,
% 262.02/166.40 (false = impl(impl(false, impl(false, false)), false)),
% 262.02/166.40 inference(transitivity,[status(thm)],[133, 169])).
% 262.02/166.40 tff(171,plain,
% 262.02/166.40 (lazy_impl(not1(false), false) = lazy_impl(prop(false), impl(impl(false, impl(false, false)), false))),
% 262.02/166.40 inference(monotonicity,[status(thm)],[150, 170])).
% 262.02/166.40 tff(172,plain,
% 262.02/166.40 (lazy_impl(prop(false), impl(impl(false, impl(false, false)), false)) = lazy_impl(not1(false), false)),
% 262.02/166.40 inference(symmetry,[status(thm)],[171])).
% 262.02/166.40 tff(173,plain,
% 262.02/166.40 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(false, false, false) = lazy_impl(prop(false), impl(impl(false, impl(false, false)), false)))),
% 262.02/166.40 inference(quant_inst,[status(thm)],[])).
% 262.02/166.40 tff(174,plain,
% 262.02/166.40 (f1(false, false, false) = lazy_impl(prop(false), impl(impl(false, impl(false, false)), false))),
% 262.02/166.40 inference(unit_resolution,[status(thm)],[173, 159])).
% 262.02/166.40 tff(175,plain,
% 262.02/166.40 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))),
% 262.02/166.40 inference(quant_inst,[status(thm)],[])).
% 262.02/166.40 tff(176,plain,
% 262.02/166.40 (f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))),
% 262.02/166.40 inference(unit_resolution,[status(thm)],[175, 159])).
% 262.02/166.40 tff(177,plain,
% 262.02/166.40 (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))),
% 262.02/166.40 inference(symmetry,[status(thm)],[176])).
% 262.02/166.40 tff(178,assumption,(~bool(P!8)), introduced(assumption)).
% 262.02/166.40 tff(179,plain,
% 262.02/166.40 (^[A: $i, B: $i] : refl((bool(A) | (impl(A, B) = phi(A))) <=> (bool(A) | (impl(A, B) = phi(A))))),
% 262.02/166.40 inference(bind,[status(th)],[])).
% 262.02/166.40 tff(180,plain,
% 262.02/166.40 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A))) <=> ![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 262.02/166.40 inference(quant_intro,[status(thm)],[179])).
% 262.02/166.40 tff(181,plain,
% 262.02/166.40 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A))) <=> ![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 262.02/166.40 inference(rewrite,[status(thm)],[])).
% 262.02/166.40 tff(182,plain,
% 262.02/166.40 (^[A: $i, B: $i] : rewrite(((~bool(A)) => (impl(A, B) = phi(A))) <=> (bool(A) | (impl(A, B) = phi(A))))),
% 262.02/166.40 inference(bind,[status(th)],[])).
% 262.02/166.40 tff(183,plain,
% 262.02/166.40 (![A: $i, B: $i] : ((~bool(A)) => (impl(A, B) = phi(A))) <=> ![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 262.02/166.40 inference(quant_intro,[status(thm)],[182])).
% 262.02/166.40 tff(184,axiom,(![A: $i, B: $i] : ((~bool(A)) => (impl(A, B) = phi(A)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','impl_axiom1')).
% 262.02/166.40 tff(185,plain,
% 262.02/166.40 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 262.02/166.40 inference(modus_ponens,[status(thm)],[184, 183])).
% 262.02/166.40 tff(186,plain,
% 262.02/166.40 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 262.02/166.40 inference(modus_ponens,[status(thm)],[185, 181])).
% 262.02/166.40 tff(187,plain,(
% 262.02/166.40 ![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 262.02/166.40 inference(skolemize,[status(sab)],[186])).
% 262.02/166.40 tff(188,plain,
% 262.02/166.40 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 262.02/166.40 inference(modus_ponens,[status(thm)],[187, 180])).
% 262.02/166.40 tff(189,plain,
% 262.02/166.40 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(P!8) | (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(P!8)))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(P!8) | (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(P!8)))),
% 262.02/166.40 inference(rewrite,[status(thm)],[])).
% 262.02/166.40 tff(190,plain,
% 262.02/166.40 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(P!8) | (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(P!8)))),
% 262.02/166.40 inference(quant_inst,[status(thm)],[])).
% 262.02/166.40 tff(191,plain,
% 262.02/166.40 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(P!8) | (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(P!8))),
% 262.02/166.40 inference(modus_ponens,[status(thm)],[190, 189])).
% 262.02/166.40 tff(192,plain,
% 262.02/166.40 (bool(P!8) | (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(P!8))),
% 262.02/166.40 inference(unit_resolution,[status(thm)],[191, 188])).
% 262.02/166.40 tff(193,plain,
% 262.02/166.40 (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(P!8)),
% 262.02/166.40 inference(unit_resolution,[status(thm)],[192, 178])).
% 262.02/166.40 tff(194,plain,
% 262.02/166.40 (phi(P!8) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.02/166.40 inference(symmetry,[status(thm)],[193])).
% 262.02/166.40 tff(195,assumption,(bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))), introduced(assumption)).
% 262.02/166.40 tff(196,assumption,(phi(P!8) = P!8), introduced(assumption)).
% 262.02/166.40 tff(197,plain,
% 262.02/166.40 (P!8 = phi(P!8)),
% 262.02/166.40 inference(symmetry,[status(thm)],[196])).
% 262.02/166.40 tff(198,plain,
% 262.02/166.40 (P!8 = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.02/166.40 inference(transitivity,[status(thm)],[197, 194])).
% 262.02/166.40 tff(199,plain,
% 262.02/166.40 (bool(P!8) <=> bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.02/166.40 inference(monotonicity,[status(thm)],[198])).
% 262.02/166.40 tff(200,plain,
% 262.02/166.40 (bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) <=> bool(P!8)),
% 262.02/166.40 inference(symmetry,[status(thm)],[199])).
% 262.02/166.40 tff(201,plain,
% 262.02/166.40 (bool(P!8)),
% 262.02/166.40 inference(modus_ponens,[status(thm)],[195, 200])).
% 262.02/166.40 tff(202,plain,
% 262.02/166.40 ($false),
% 262.02/166.40 inference(unit_resolution,[status(thm)],[178, 201])).
% 262.02/166.40 tff(203,plain,((~(phi(P!8) = P!8)) | bool(P!8) | (~bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))), inference(lemma,lemma(discharge,[]))).
% 262.02/166.40 tff(204,plain,
% 262.02/166.40 (~(phi(P!8) = P!8)),
% 262.02/166.40 inference(unit_resolution,[status(thm)],[203, 195, 178])).
% 262.02/166.40 tff(205,plain,
% 262.02/166.40 (((~d(P!8)) | (~(phi(P!8) = P!8))) | (phi(P!8) = P!8)),
% 262.02/166.40 inference(tautology,[status(thm)],[])).
% 262.02/166.40 tff(206,plain,
% 262.02/166.40 ((~d(P!8)) | (~(phi(P!8) = P!8))),
% 262.02/166.40 inference(unit_resolution,[status(thm)],[205, 204])).
% 262.02/166.40 tff(207,plain,
% 262.02/166.40 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(P!8)) | (~(phi(P!8) = P!8)))) | (~(d(P!8) | (~(phi(P!8) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(P!8)) | (~(phi(P!8) = P!8)))) | (~(d(P!8) | (~(phi(P!8) = err)))))),
% 262.02/166.40 inference(rewrite,[status(thm)],[])).
% 262.02/166.40 tff(208,plain,
% 262.02/166.40 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(P!8)) | (~(phi(P!8) = P!8)))) | (~(d(P!8) | (~(phi(P!8) = err)))))),
% 262.02/166.40 inference(quant_inst,[status(thm)],[])).
% 262.02/166.40 tff(209,plain,
% 262.02/166.40 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(P!8)) | (~(phi(P!8) = P!8)))) | (~(d(P!8) | (~(phi(P!8) = err))))),
% 262.02/166.40 inference(modus_ponens,[status(thm)],[208, 207])).
% 262.02/166.40 tff(210,plain,
% 262.02/166.40 ((~((~d(P!8)) | (~(phi(P!8) = P!8)))) | (~(d(P!8) | (~(phi(P!8) = err))))),
% 262.02/166.40 inference(unit_resolution,[status(thm)],[209, 17])).
% 262.02/166.40 tff(211,plain,
% 262.02/166.40 (~(d(P!8) | (~(phi(P!8) = err)))),
% 262.02/166.40 inference(unit_resolution,[status(thm)],[210, 206])).
% 262.02/166.40 tff(212,plain,
% 262.02/166.40 ((d(P!8) | (~(phi(P!8) = err))) | (phi(P!8) = err)),
% 262.02/166.40 inference(tautology,[status(thm)],[])).
% 262.02/166.40 tff(213,plain,
% 262.02/166.40 (phi(P!8) = err),
% 262.02/166.40 inference(unit_resolution,[status(thm)],[212, 211])).
% 262.02/166.40 tff(214,plain,
% 262.02/166.40 (err = phi(P!8)),
% 262.02/166.40 inference(symmetry,[status(thm)],[213])).
% 262.02/166.40 tff(215,plain,
% 262.02/166.40 (err = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.02/166.40 inference(transitivity,[status(thm)],[214, 194])).
% 262.02/166.40 tff(216,plain,
% 262.02/166.40 (bool(err) <=> bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.02/166.40 inference(monotonicity,[status(thm)],[215])).
% 262.02/166.40 tff(217,plain,
% 262.02/166.40 (bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) <=> bool(err)),
% 262.02/166.40 inference(symmetry,[status(thm)],[216])).
% 262.02/166.40 tff(218,plain,
% 262.02/166.40 (bool(err)),
% 262.02/166.40 inference(modus_ponens,[status(thm)],[195, 217])).
% 262.02/166.40 tff(219,assumption,(~(bool(err) <=> ((err = false) | (err = not1(false))))), introduced(assumption)).
% 262.02/166.40 tff(220,plain,
% 262.02/166.40 (^[X: $i] : refl((bool(X) <=> ((X = false) | (X = not1(false)))) <=> (bool(X) <=> ((X = false) | (X = not1(false)))))),
% 262.02/166.40 inference(bind,[status(th)],[])).
% 262.02/166.40 tff(221,plain,
% 262.02/166.40 (![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false)))) <=> ![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))),
% 262.02/166.40 inference(quant_intro,[status(thm)],[220])).
% 262.02/166.40 tff(222,plain,
% 262.02/166.40 (^[X: $i] : rewrite((bool(X) <=> ((X = false) | (X = true))) <=> (bool(X) <=> ((X = false) | (X = not1(false)))))),
% 262.02/166.40 inference(bind,[status(th)],[])).
% 262.02/166.40 tff(223,plain,
% 262.02/166.40 (![X: $i] : (bool(X) <=> ((X = false) | (X = true))) <=> ![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))),
% 262.02/166.40 inference(quant_intro,[status(thm)],[222])).
% 262.02/166.40 tff(224,plain,
% 262.02/166.40 (![X: $i] : (bool(X) <=> ((X = false) | (X = true))) <=> ![X: $i] : (bool(X) <=> ((X = false) | (X = true)))),
% 262.02/166.40 inference(rewrite,[status(thm)],[])).
% 262.02/166.40 tff(225,axiom,(![X: $i] : (bool(X) <=> ((X = false) | (X = true)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','def_bool')).
% 262.02/166.40 tff(226,plain,
% 262.02/166.40 (![X: $i] : (bool(X) <=> ((X = false) | (X = true)))),
% 262.02/166.40 inference(modus_ponens,[status(thm)],[225, 224])).
% 262.02/166.40 tff(227,plain,
% 262.02/166.40 (![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))),
% 262.02/166.40 inference(modus_ponens,[status(thm)],[226, 223])).
% 262.02/166.40 tff(228,plain,(
% 262.02/166.40 ![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))),
% 262.02/166.40 inference(skolemize,[status(sab)],[227])).
% 262.02/166.40 tff(229,plain,
% 262.02/166.40 (![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))),
% 262.02/166.40 inference(modus_ponens,[status(thm)],[228, 221])).
% 262.02/166.40 tff(230,plain,
% 262.02/166.40 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(err) <=> ((err = false) | (err = not1(false))))),
% 262.02/166.40 inference(quant_inst,[status(thm)],[])).
% 262.02/166.40 tff(231,plain,
% 262.02/166.40 ($false),
% 262.02/166.40 inference(unit_resolution,[status(thm)],[230, 229, 219])).
% 262.02/166.41 tff(232,plain,(bool(err) <=> ((err = false) | (err = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 262.02/166.41 tff(233,assumption,((err = false) | (err = not1(false))), introduced(assumption)).
% 262.02/166.41 tff(234,plain,
% 262.02/166.41 ((err = false) <=> (false = err)),
% 262.02/166.41 inference(commutativity,[status(thm)],[])).
% 262.02/166.41 tff(235,plain,
% 262.02/166.41 ((false = err) <=> (err = false)),
% 262.02/166.41 inference(symmetry,[status(thm)],[234])).
% 262.02/166.41 tff(236,plain,
% 262.02/166.41 ((~(false = err)) <=> (~(err = false))),
% 262.02/166.41 inference(monotonicity,[status(thm)],[235])).
% 262.02/166.41 tff(237,plain,
% 262.02/166.41 ((~(false = err)) <=> (~(false = err))),
% 262.02/166.41 inference(rewrite,[status(thm)],[])).
% 262.02/166.41 tff(238,plain,
% 262.02/166.41 (~(false = err)),
% 262.02/166.41 inference(and_elim,[status(thm)],[61])).
% 262.02/166.41 tff(239,plain,
% 262.02/166.41 (~(false = err)),
% 262.02/166.41 inference(modus_ponens,[status(thm)],[238, 237])).
% 262.02/166.41 tff(240,plain,
% 262.02/166.41 (~(err = false)),
% 262.02/166.41 inference(modus_ponens,[status(thm)],[239, 236])).
% 262.02/166.41 tff(241,plain,
% 262.02/166.41 ((err = not1(false)) <=> (not1(false) = err)),
% 262.02/166.41 inference(commutativity,[status(thm)],[])).
% 262.02/166.41 tff(242,plain,
% 262.02/166.41 ((not1(false) = err) <=> (err = not1(false))),
% 262.02/166.41 inference(symmetry,[status(thm)],[241])).
% 262.02/166.41 tff(243,plain,
% 262.02/166.41 ((~(not1(false) = err)) <=> (~(err = not1(false)))),
% 262.02/166.41 inference(monotonicity,[status(thm)],[242])).
% 262.02/166.41 tff(244,plain,
% 262.02/166.41 ((~(true = err)) <=> (~(not1(false) = err))),
% 262.02/166.41 inference(rewrite,[status(thm)],[])).
% 262.02/166.41 tff(245,plain,
% 262.02/166.41 ((~(true = err)) <=> (~(true = err))),
% 262.02/166.41 inference(rewrite,[status(thm)],[])).
% 262.02/166.41 tff(246,plain,
% 262.02/166.41 (~(true = err)),
% 262.02/166.41 inference(and_elim,[status(thm)],[62])).
% 262.02/166.41 tff(247,plain,
% 262.02/166.41 (~(true = err)),
% 262.02/166.41 inference(modus_ponens,[status(thm)],[246, 245])).
% 262.02/166.41 tff(248,plain,
% 262.02/166.41 (~(not1(false) = err)),
% 262.02/166.41 inference(modus_ponens,[status(thm)],[247, 244])).
% 262.02/166.41 tff(249,plain,
% 262.02/166.41 (~(err = not1(false))),
% 262.02/166.41 inference(modus_ponens,[status(thm)],[248, 243])).
% 262.02/166.41 tff(250,plain,
% 262.02/166.41 ((~((err = false) | (err = not1(false)))) | (err = false) | (err = not1(false))),
% 262.02/166.41 inference(tautology,[status(thm)],[])).
% 262.02/166.41 tff(251,plain,
% 262.02/166.41 ($false),
% 262.02/166.41 inference(unit_resolution,[status(thm)],[250, 249, 240, 233])).
% 262.02/166.41 tff(252,plain,(~((err = false) | (err = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 262.02/166.41 tff(253,plain,
% 262.02/166.41 ((~(bool(err) <=> ((err = false) | (err = not1(false))))) | (~bool(err)) | ((err = false) | (err = not1(false)))),
% 262.02/166.41 inference(tautology,[status(thm)],[])).
% 262.02/166.41 tff(254,plain,
% 262.02/166.41 ((~(bool(err) <=> ((err = false) | (err = not1(false))))) | (~bool(err))),
% 262.02/166.41 inference(unit_resolution,[status(thm)],[253, 252])).
% 262.02/166.41 tff(255,plain,
% 262.02/166.41 (~bool(err)),
% 262.02/166.41 inference(unit_resolution,[status(thm)],[254, 232])).
% 262.02/166.41 tff(256,plain,
% 262.02/166.41 ($false),
% 262.02/166.41 inference(unit_resolution,[status(thm)],[255, 218])).
% 262.02/166.41 tff(257,plain,((~bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | bool(P!8)), inference(lemma,lemma(discharge,[]))).
% 262.02/166.41 tff(258,plain,
% 262.02/166.41 (~bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.02/166.41 inference(unit_resolution,[status(thm)],[257, 178])).
% 262.02/166.41 tff(259,plain,
% 262.02/166.41 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) | (impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) | (impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))),
% 262.02/166.41 inference(rewrite,[status(thm)],[])).
% 262.02/166.41 tff(260,plain,
% 262.02/166.41 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) | (impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))),
% 262.02/166.41 inference(quant_inst,[status(thm)],[])).
% 262.02/166.41 tff(261,plain,
% 262.02/166.41 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) | (impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))),
% 262.02/166.41 inference(modus_ponens,[status(thm)],[260, 259])).
% 262.02/166.41 tff(262,plain,
% 262.02/166.41 (bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) | (impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))),
% 262.02/166.41 inference(unit_resolution,[status(thm)],[261, 188])).
% 262.02/166.41 tff(263,plain,
% 262.02/166.41 (impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.02/166.41 inference(unit_resolution,[status(thm)],[262, 258])).
% 262.02/166.41 tff(264,plain,
% 262.02/166.41 (^[A: $i, B: $i] : refl((bool(A) | (and1(A, B) = phi(A))) <=> (bool(A) | (and1(A, B) = phi(A))))),
% 262.02/166.41 inference(bind,[status(th)],[])).
% 262.02/166.41 tff(265,plain,
% 262.02/166.41 (![A: $i, B: $i] : (bool(A) | (and1(A, B) = phi(A))) <=> ![A: $i, B: $i] : (bool(A) | (and1(A, B) = phi(A)))),
% 262.02/166.41 inference(quant_intro,[status(thm)],[264])).
% 262.02/166.41 tff(266,plain,
% 262.02/166.41 (![A: $i, B: $i] : (bool(A) | (and1(A, B) = phi(A))) <=> ![A: $i, B: $i] : (bool(A) | (and1(A, B) = phi(A)))),
% 262.02/166.41 inference(rewrite,[status(thm)],[])).
% 262.02/166.41 tff(267,plain,
% 262.02/166.41 (^[A: $i, B: $i] : rewrite(((~bool(A)) => (and1(A, B) = phi(A))) <=> (bool(A) | (and1(A, B) = phi(A))))),
% 262.02/166.41 inference(bind,[status(th)],[])).
% 262.02/166.41 tff(268,plain,
% 262.02/166.41 (![A: $i, B: $i] : ((~bool(A)) => (and1(A, B) = phi(A))) <=> ![A: $i, B: $i] : (bool(A) | (and1(A, B) = phi(A)))),
% 262.02/166.41 inference(quant_intro,[status(thm)],[267])).
% 262.02/166.41 tff(269,axiom,(![A: $i, B: $i] : ((~bool(A)) => (and1(A, B) = phi(A)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','and1_axiom1')).
% 262.02/166.41 tff(270,plain,
% 262.02/166.41 (![A: $i, B: $i] : (bool(A) | (and1(A, B) = phi(A)))),
% 262.02/166.41 inference(modus_ponens,[status(thm)],[269, 268])).
% 262.02/166.41 tff(271,plain,
% 262.02/166.41 (![A: $i, B: $i] : (bool(A) | (and1(A, B) = phi(A)))),
% 262.02/166.41 inference(modus_ponens,[status(thm)],[270, 266])).
% 262.02/166.41 tff(272,plain,(
% 262.02/166.41 ![A: $i, B: $i] : (bool(A) | (and1(A, B) = phi(A)))),
% 262.02/166.41 inference(skolemize,[status(sab)],[271])).
% 262.02/166.41 tff(273,plain,
% 262.02/166.41 (![A: $i, B: $i] : (bool(A) | (and1(A, B) = phi(A)))),
% 262.02/166.41 inference(modus_ponens,[status(thm)],[272, 265])).
% 262.02/166.41 tff(274,plain,
% 262.02/166.41 (((~![A: $i, B: $i] : (bool(A) | (and1(A, B) = phi(A)))) | (bool(P!8) | (and1(P!8, Q!7) = phi(P!8)))) <=> ((~![A: $i, B: $i] : (bool(A) | (and1(A, B) = phi(A)))) | bool(P!8) | (and1(P!8, Q!7) = phi(P!8)))),
% 262.02/166.41 inference(rewrite,[status(thm)],[])).
% 262.02/166.41 tff(275,plain,
% 262.02/166.41 ((~![A: $i, B: $i] : (bool(A) | (and1(A, B) = phi(A)))) | (bool(P!8) | (and1(P!8, Q!7) = phi(P!8)))),
% 262.02/166.41 inference(quant_inst,[status(thm)],[])).
% 262.02/166.41 tff(276,plain,
% 262.02/166.41 ((~![A: $i, B: $i] : (bool(A) | (and1(A, B) = phi(A)))) | bool(P!8) | (and1(P!8, Q!7) = phi(P!8))),
% 262.02/166.41 inference(modus_ponens,[status(thm)],[275, 274])).
% 262.02/166.41 tff(277,plain,
% 262.02/166.41 (bool(P!8) | (and1(P!8, Q!7) = phi(P!8))),
% 262.02/166.41 inference(unit_resolution,[status(thm)],[276, 273])).
% 262.02/166.41 tff(278,plain,
% 262.02/166.41 (and1(P!8, Q!7) = phi(P!8)),
% 262.02/166.41 inference(unit_resolution,[status(thm)],[277, 178])).
% 262.02/166.41 tff(279,plain,
% 262.02/166.41 (^[P: $i, Q: $i] : refl((~((~(and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P))))) | (~![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P))))))) <=> (~((~(and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P))))) | (~![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P))))))))),
% 262.02/166.41 inference(bind,[status(th)],[])).
% 262.02/166.41 tff(280,plain,
% 262.02/166.41 (![P: $i, Q: $i] : (~((~(and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P))))) | (~![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P))))))) <=> ![P: $i, Q: $i] : (~((~(and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P))))) | (~![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P)))))))),
% 262.02/166.41 inference(quant_intro,[status(thm)],[279])).
% 262.02/166.41 tff(281,plain,
% 262.02/166.41 (^[P: $i, Q: $i] : rewrite((~((~(and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P))))) | (~![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P))))))) <=> (~((~(and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P))))) | (~![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P))))))))),
% 262.02/166.41 inference(bind,[status(th)],[])).
% 262.02/166.41 tff(282,plain,
% 262.02/166.41 (![P: $i, Q: $i] : (~((~(and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P))))) | (~![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P))))))) <=> ![P: $i, Q: $i] : (~((~(and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P))))) | (~![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P)))))))),
% 262.07/166.41 inference(quant_intro,[status(thm)],[281])).
% 262.07/166.41 tff(283,plain,
% 262.07/166.41 (![P: $i, Q: $i] : (~((~(and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P))))) | (~![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P))))))) <=> ![P: $i, Q: $i] : (~((~(and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P))))) | (~![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P)))))))),
% 262.07/166.41 inference(transitivity,[status(thm)],[282, 280])).
% 262.07/166.41 tff(284,plain,
% 262.07/166.41 (^[P: $i, Q: $i] : rewrite(((and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P)))) & ![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P))))) <=> (~((~(and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P))))) | (~![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P))))))))),
% 262.07/166.41 inference(bind,[status(th)],[])).
% 262.07/166.41 tff(285,plain,
% 262.07/166.41 (![P: $i, Q: $i] : ((and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P)))) & ![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P))))) <=> ![P: $i, Q: $i] : (~((~(and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P))))) | (~![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P)))))))),
% 262.07/166.41 inference(quant_intro,[status(thm)],[284])).
% 262.07/166.41 tff(286,plain,
% 262.07/166.41 (![P: $i, Q: $i] : ?[R: $i] : ((and2(P, Q) = phi(f1(P, Q, R))) & (~?[R1: $i] : forallprefers(f1(P, Q, R1), f1(P, Q, R)))) <=> ![P: $i, Q: $i] : ?[R: $i] : ((and2(P, Q) = phi(f1(P, Q, R))) & (~?[R1: $i] : forallprefers(f1(P, Q, R1), f1(P, Q, R))))),
% 262.07/166.41 inference(rewrite,[status(thm)],[])).
% 262.07/166.41 tff(287,axiom,(![P: $i, Q: $i] : ?[R: $i] : ((and2(P, Q) = phi(f1(P, Q, R))) & (~?[R1: $i] : forallprefers(f1(P, Q, R1), f1(P, Q, R))))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','def_and2')).
% 262.07/166.41 tff(288,plain,
% 262.07/166.41 (![P: $i, Q: $i] : ?[R: $i] : ((and2(P, Q) = phi(f1(P, Q, R))) & (~?[R1: $i] : forallprefers(f1(P, Q, R1), f1(P, Q, R))))),
% 262.07/166.41 inference(modus_ponens,[status(thm)],[287, 286])).
% 262.07/166.41 tff(289,plain,(
% 262.07/166.41 ![P: $i, Q: $i] : ((and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P)))) & ![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P)))))),
% 262.07/166.41 inference(skolemize,[status(sab)],[288])).
% 262.07/166.41 tff(290,plain,
% 262.07/166.41 (![P: $i, Q: $i] : (~((~(and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P))))) | (~![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P)))))))),
% 262.07/166.41 inference(modus_ponens,[status(thm)],[289, 285])).
% 262.07/166.41 tff(291,plain,
% 262.07/166.41 (![P: $i, Q: $i] : (~((~(and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P))))) | (~![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P)))))))),
% 262.07/166.41 inference(modus_ponens,[status(thm)],[290, 283])).
% 262.07/166.41 tff(292,plain,
% 262.07/166.41 ((~![P: $i, Q: $i] : (~((~(and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P))))) | (~![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P)))))))) | (~((~(and2(P!8, Q!7) = phi(f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~![R1: $i] : (~forallprefers(f1(P!8, Q!7, R1), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))))))),
% 262.07/166.41 inference(quant_inst,[status(thm)],[])).
% 262.07/166.41 tff(293,plain,
% 262.07/166.41 (~((~(and2(P!8, Q!7) = phi(f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~![R1: $i] : (~forallprefers(f1(P!8, Q!7, R1), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))))))),
% 262.07/166.41 inference(unit_resolution,[status(thm)],[292, 291])).
% 262.07/166.41 tff(294,plain,
% 262.07/166.41 (((~(and2(P!8, Q!7) = phi(f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~![R1: $i] : (~forallprefers(f1(P!8, Q!7, R1), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))))) | (and2(P!8, Q!7) = phi(f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.07/166.41 inference(tautology,[status(thm)],[])).
% 262.07/166.41 tff(295,plain,
% 262.07/166.41 (and2(P!8, Q!7) = phi(f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.07/166.41 inference(unit_resolution,[status(thm)],[294, 293])).
% 262.07/166.41 tff(296,plain,
% 262.07/166.41 (phi(f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))) = and2(P!8, Q!7)),
% 262.07/166.41 inference(symmetry,[status(thm)],[295])).
% 262.07/166.41 tff(297,assumption,(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(P!8)), introduced(assumption)).
% 262.07/166.41 tff(298,plain,
% 262.07/166.41 (phi(P!8) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.07/166.41 inference(symmetry,[status(thm)],[297])).
% 262.07/166.41 tff(299,plain,
% 262.07/166.42 (d(phi(P!8)) <=> d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.07/166.42 inference(monotonicity,[status(thm)],[298])).
% 262.07/166.42 tff(300,plain,
% 262.07/166.42 (d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) <=> d(phi(P!8))),
% 262.07/166.42 inference(symmetry,[status(thm)],[299])).
% 262.07/166.42 tff(301,assumption,(~d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))), introduced(assumption)).
% 262.07/166.42 tff(302,assumption,(~((~d(P!8)) | (~(phi(P!8) = P!8)))), introduced(assumption)).
% 262.07/166.42 tff(303,plain,
% 262.07/166.42 (phi(P!8) = P!8),
% 262.07/166.42 inference(unit_resolution,[status(thm)],[205, 302])).
% 262.07/166.42 tff(304,plain,
% 262.07/166.42 (P!8 = phi(P!8)),
% 262.07/166.42 inference(symmetry,[status(thm)],[303])).
% 262.07/166.42 tff(305,plain,
% 262.07/166.42 (P!8 = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.07/166.42 inference(transitivity,[status(thm)],[304, 298])).
% 262.07/166.42 tff(306,plain,
% 262.07/166.42 (d(P!8) <=> d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.07/166.42 inference(monotonicity,[status(thm)],[305])).
% 262.07/166.42 tff(307,plain,
% 262.07/166.42 (d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) <=> d(P!8)),
% 262.07/166.42 inference(symmetry,[status(thm)],[306])).
% 262.07/166.42 tff(308,plain,
% 262.07/166.42 ((~d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) <=> (~d(P!8))),
% 262.07/166.42 inference(monotonicity,[status(thm)],[307])).
% 262.07/166.42 tff(309,plain,
% 262.07/166.42 (~d(P!8)),
% 262.07/166.42 inference(modus_ponens,[status(thm)],[301, 308])).
% 262.07/166.42 tff(310,plain,
% 262.07/166.42 (((~d(P!8)) | (~(phi(P!8) = P!8))) | d(P!8)),
% 262.07/166.42 inference(tautology,[status(thm)],[])).
% 262.07/166.42 tff(311,plain,
% 262.07/166.42 (d(P!8)),
% 262.07/166.42 inference(unit_resolution,[status(thm)],[310, 302])).
% 262.07/166.42 tff(312,plain,
% 262.07/166.42 ($false),
% 262.07/166.42 inference(unit_resolution,[status(thm)],[311, 309])).
% 262.07/166.42 tff(313,plain,(((~d(P!8)) | (~(phi(P!8) = P!8))) | d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) | (~(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(P!8)))), inference(lemma,lemma(discharge,[]))).
% 262.07/166.42 tff(314,plain,
% 262.07/166.42 ((~d(P!8)) | (~(phi(P!8) = P!8))),
% 262.07/166.42 inference(unit_resolution,[status(thm)],[313, 301, 297])).
% 262.07/166.42 tff(315,plain,
% 262.07/166.42 (~(d(P!8) | (~(phi(P!8) = err)))),
% 262.07/166.42 inference(unit_resolution,[status(thm)],[210, 314])).
% 262.07/166.42 tff(316,plain,
% 262.07/166.42 (phi(P!8) = err),
% 262.07/166.42 inference(unit_resolution,[status(thm)],[212, 315])).
% 262.07/166.42 tff(317,plain,
% 262.07/166.42 (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = err),
% 262.07/166.42 inference(transitivity,[status(thm)],[297, 316])).
% 262.07/166.42 tff(318,plain,
% 262.07/166.42 (d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) <=> d(err)),
% 262.07/166.42 inference(monotonicity,[status(thm)],[317])).
% 262.07/166.42 tff(319,plain,
% 262.07/166.42 (d(err) <=> d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.07/166.42 inference(symmetry,[status(thm)],[318])).
% 262.07/166.42 tff(320,plain,
% 262.07/166.42 (d(err) <=> d(err)),
% 262.07/166.42 inference(rewrite,[status(thm)],[])).
% 262.07/166.42 tff(321,plain,
% 262.07/166.42 (d(err)),
% 262.07/166.42 inference(and_elim,[status(thm)],[2])).
% 262.07/166.42 tff(322,plain,
% 262.07/166.42 (d(err)),
% 262.07/166.42 inference(modus_ponens,[status(thm)],[321, 320])).
% 262.07/166.42 tff(323,plain,
% 262.07/166.42 (d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.07/166.42 inference(modus_ponens,[status(thm)],[322, 319])).
% 262.07/166.42 tff(324,plain,
% 262.07/166.42 ($false),
% 262.07/166.42 inference(unit_resolution,[status(thm)],[301, 323])).
% 262.07/166.42 tff(325,plain,(d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) | (~(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(P!8)))), inference(lemma,lemma(discharge,[]))).
% 262.07/166.42 tff(326,plain,
% 262.07/166.42 (d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.07/166.42 inference(unit_resolution,[status(thm)],[325, 297])).
% 262.07/166.42 tff(327,plain,
% 262.07/166.42 (d(phi(P!8))),
% 262.07/166.42 inference(modus_ponens,[status(thm)],[326, 300])).
% 262.07/166.42 tff(328,plain,
% 262.07/166.42 ((d(phi(P!8)) | (~(phi(phi(P!8)) = err))) | (~d(phi(P!8)))),
% 262.07/166.42 inference(tautology,[status(thm)],[])).
% 262.07/166.42 tff(329,plain,
% 262.07/166.42 (d(phi(P!8)) | (~(phi(phi(P!8)) = err))),
% 262.07/166.42 inference(unit_resolution,[status(thm)],[328, 327])).
% 262.07/166.42 tff(330,plain,
% 262.07/166.42 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(phi(P!8))) | (~(phi(phi(P!8)) = phi(P!8))))) | (~(d(phi(P!8)) | (~(phi(phi(P!8)) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(phi(P!8))) | (~(phi(phi(P!8)) = phi(P!8))))) | (~(d(phi(P!8)) | (~(phi(phi(P!8)) = err)))))),
% 262.07/166.42 inference(rewrite,[status(thm)],[])).
% 262.07/166.42 tff(331,plain,
% 262.07/166.42 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(phi(P!8))) | (~(phi(phi(P!8)) = phi(P!8))))) | (~(d(phi(P!8)) | (~(phi(phi(P!8)) = err)))))),
% 262.07/166.42 inference(quant_inst,[status(thm)],[])).
% 262.07/166.42 tff(332,plain,
% 262.07/166.42 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(phi(P!8))) | (~(phi(phi(P!8)) = phi(P!8))))) | (~(d(phi(P!8)) | (~(phi(phi(P!8)) = err))))),
% 262.07/166.42 inference(modus_ponens,[status(thm)],[331, 330])).
% 262.07/166.42 tff(333,plain,
% 262.07/166.42 ((~((~d(phi(P!8))) | (~(phi(phi(P!8)) = phi(P!8))))) | (~(d(phi(P!8)) | (~(phi(phi(P!8)) = err))))),
% 262.07/166.42 inference(unit_resolution,[status(thm)],[332, 17])).
% 262.07/166.42 tff(334,plain,
% 262.07/166.42 (~((~d(phi(P!8))) | (~(phi(phi(P!8)) = phi(P!8))))),
% 262.07/166.42 inference(unit_resolution,[status(thm)],[333, 329])).
% 262.07/166.42 tff(335,plain,
% 262.07/166.42 (((~d(phi(P!8))) | (~(phi(phi(P!8)) = phi(P!8)))) | (phi(phi(P!8)) = phi(P!8))),
% 262.07/166.42 inference(tautology,[status(thm)],[])).
% 262.07/166.42 tff(336,plain,
% 262.07/166.42 (phi(phi(P!8)) = phi(P!8)),
% 262.07/166.42 inference(unit_resolution,[status(thm)],[335, 334])).
% 262.07/166.42 tff(337,plain,
% 262.07/166.42 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), phi(P!8)) = phi(phi(P!8)))),
% 262.07/166.42 inference(quant_inst,[status(thm)],[])).
% 262.07/166.42 tff(338,plain,
% 262.07/166.42 (lazy_impl(not1(false), phi(P!8)) = phi(phi(P!8))),
% 262.07/166.42 inference(unit_resolution,[status(thm)],[337, 33])).
% 262.07/166.42 tff(339,plain,
% 262.07/166.42 (phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = phi(phi(P!8))),
% 262.07/166.42 inference(monotonicity,[status(thm)],[297])).
% 262.07/166.42 tff(340,assumption,(impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))), introduced(assumption)).
% 262.07/166.42 tff(341,plain,
% 262.07/166.42 (impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)) = phi(P!8)),
% 262.07/166.42 inference(transitivity,[status(thm)],[340, 339, 336])).
% 262.07/166.42 tff(342,assumption,(prop(tptp_fun_R_0(Q!7, P!8)) = not1(false)), introduced(assumption)).
% 262.07/166.42 tff(343,plain,
% 262.07/166.42 (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(not1(false), phi(P!8))),
% 262.07/166.42 inference(monotonicity,[status(thm)],[342, 341])).
% 262.07/166.42 tff(344,plain,
% 262.07/166.42 (f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.07/166.42 inference(transitivity,[status(thm)],[176, 343, 338, 336, 298])).
% 262.07/166.42 tff(345,plain,
% 262.07/166.42 (phi(f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.07/166.42 inference(monotonicity,[status(thm)],[344])).
% 262.07/166.42 tff(346,plain,
% 262.07/166.42 (phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = phi(f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.07/166.42 inference(symmetry,[status(thm)],[345])).
% 262.07/166.42 tff(347,plain,
% 262.07/166.42 (phi(phi(P!8)) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.07/166.42 inference(symmetry,[status(thm)],[339])).
% 262.07/166.42 tff(348,plain,
% 262.07/166.42 (phi(P!8) = phi(phi(P!8))),
% 262.07/166.42 inference(symmetry,[status(thm)],[336])).
% 262.07/166.42 tff(349,assumption,(and1(P!8, Q!7) = phi(P!8)), introduced(assumption)).
% 262.07/166.42 tff(350,plain,
% 262.07/166.42 (and1(P!8, Q!7) = and2(P!8, Q!7)),
% 262.07/166.42 inference(transitivity,[status(thm)],[349, 348, 347, 346, 296])).
% 262.07/166.42 tff(351,plain,
% 262.07/166.42 ((~![P: $i, Q: $i] : (and1(P, Q) = and2(P, Q))) <=> (~![P: $i, Q: $i] : (and1(P, Q) = and2(P, Q)))),
% 262.07/166.42 inference(rewrite,[status(thm)],[])).
% 262.07/166.42 tff(352,axiom,(~![P: $i, Q: $i] : (and1(P, Q) = and2(P, Q))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','and1_and2')).
% 262.07/166.42 tff(353,plain,
% 262.07/166.42 (~![P: $i, Q: $i] : (and1(P, Q) = and2(P, Q))),
% 262.07/166.42 inference(modus_ponens,[status(thm)],[352, 351])).
% 262.07/166.42 tff(354,plain,
% 262.07/166.42 (~![P: $i, Q: $i] : (and1(P, Q) = and2(P, Q))),
% 262.07/166.42 inference(modus_ponens,[status(thm)],[353, 351])).
% 262.07/166.42 tff(355,plain,
% 262.07/166.42 (~![P: $i, Q: $i] : (and1(P, Q) = and2(P, Q))),
% 262.07/166.42 inference(modus_ponens,[status(thm)],[354, 351])).
% 262.07/166.42 tff(356,plain,
% 262.07/166.42 (~![P: $i, Q: $i] : (and1(P, Q) = and2(P, Q))),
% 262.07/166.42 inference(modus_ponens,[status(thm)],[355, 351])).
% 262.07/166.42 tff(357,plain,
% 262.07/166.42 (~![P: $i, Q: $i] : (and1(P, Q) = and2(P, Q))),
% 262.07/166.42 inference(modus_ponens,[status(thm)],[356, 351])).
% 262.07/166.42 tff(358,plain,
% 262.07/166.42 (~![P: $i, Q: $i] : (and1(P, Q) = and2(P, Q))),
% 262.07/166.42 inference(modus_ponens,[status(thm)],[357, 351])).
% 262.07/166.42 tff(359,plain,
% 262.07/166.42 (~![P: $i, Q: $i] : (and1(P, Q) = and2(P, Q))),
% 262.07/166.42 inference(modus_ponens,[status(thm)],[358, 351])).
% 262.07/166.42 tff(360,plain,
% 262.07/166.42 (~![P: $i, Q: $i] : (and1(P, Q) = and2(P, Q))),
% 262.07/166.42 inference(modus_ponens,[status(thm)],[359, 351])).
% 262.07/166.42 tff(361,plain,(
% 262.07/166.42 ~(and1(P!8, Q!7) = and2(P!8, Q!7))),
% 262.07/166.42 inference(skolemize,[status(sab)],[360])).
% 262.07/166.42 tff(362,plain,
% 262.07/166.42 ($false),
% 262.07/166.42 inference(unit_resolution,[status(thm)],[361, 350])).
% 262.07/166.42 tff(363,plain,((~(prop(tptp_fun_R_0(Q!7, P!8)) = not1(false))) | (~(and1(P!8, Q!7) = phi(P!8))) | (~(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(P!8))) | (~(impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))), inference(lemma,lemma(discharge,[]))).
% 262.07/166.42 tff(364,plain,
% 262.07/166.42 (~(prop(tptp_fun_R_0(Q!7, P!8)) = not1(false))),
% 262.07/166.42 inference(unit_resolution,[status(thm)],[363, 263, 193, 278])).
% 262.07/166.42 tff(365,plain,
% 262.07/166.42 ((~![X: $i] : ((prop(X) = not1(false)) <=> bool(X))) | ((prop(tptp_fun_R_0(Q!7, P!8)) = not1(false)) <=> bool(tptp_fun_R_0(Q!7, P!8)))),
% 262.07/166.42 inference(quant_inst,[status(thm)],[])).
% 262.07/166.42 tff(366,plain,
% 262.07/166.42 ((prop(tptp_fun_R_0(Q!7, P!8)) = not1(false)) <=> bool(tptp_fun_R_0(Q!7, P!8))),
% 262.07/166.42 inference(unit_resolution,[status(thm)],[365, 144])).
% 262.07/166.42 tff(367,plain,
% 262.07/166.42 ((~((prop(tptp_fun_R_0(Q!7, P!8)) = not1(false)) <=> bool(tptp_fun_R_0(Q!7, P!8)))) | (prop(tptp_fun_R_0(Q!7, P!8)) = not1(false)) | (~bool(tptp_fun_R_0(Q!7, P!8)))),
% 262.07/166.42 inference(tautology,[status(thm)],[])).
% 262.07/166.42 tff(368,plain,
% 262.07/166.42 ((prop(tptp_fun_R_0(Q!7, P!8)) = not1(false)) | (~bool(tptp_fun_R_0(Q!7, P!8)))),
% 262.07/166.42 inference(unit_resolution,[status(thm)],[367, 366])).
% 262.07/166.42 tff(369,plain,
% 262.07/166.42 (~bool(tptp_fun_R_0(Q!7, P!8))),
% 262.07/166.42 inference(unit_resolution,[status(thm)],[368, 364])).
% 262.07/166.42 tff(370,plain,
% 262.07/166.42 (^[X: $i] : refl(((prop(X) = false) <=> (~bool(X))) <=> ((prop(X) = false) <=> (~bool(X))))),
% 262.07/166.42 inference(bind,[status(th)],[])).
% 262.07/166.42 tff(371,plain,
% 262.07/166.42 (![X: $i] : ((prop(X) = false) <=> (~bool(X))) <=> ![X: $i] : ((prop(X) = false) <=> (~bool(X)))),
% 262.07/166.42 inference(quant_intro,[status(thm)],[370])).
% 262.07/166.42 tff(372,plain,
% 262.07/166.42 (![X: $i] : ((prop(X) = false) <=> (~bool(X))) <=> ![X: $i] : ((prop(X) = false) <=> (~bool(X)))),
% 262.07/166.42 inference(rewrite,[status(thm)],[])).
% 262.07/166.42 tff(373,axiom,(![X: $i] : ((prop(X) = false) <=> (~bool(X)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','prop_false')).
% 262.07/166.42 tff(374,plain,
% 262.07/166.42 (![X: $i] : ((prop(X) = false) <=> (~bool(X)))),
% 262.07/166.42 inference(modus_ponens,[status(thm)],[373, 372])).
% 262.07/166.42 tff(375,plain,(
% 262.07/166.42 ![X: $i] : ((prop(X) = false) <=> (~bool(X)))),
% 262.07/166.42 inference(skolemize,[status(sab)],[374])).
% 262.07/166.42 tff(376,plain,
% 262.07/166.42 (![X: $i] : ((prop(X) = false) <=> (~bool(X)))),
% 262.07/166.42 inference(modus_ponens,[status(thm)],[375, 371])).
% 262.07/166.42 tff(377,plain,
% 262.07/166.42 ((~![X: $i] : ((prop(X) = false) <=> (~bool(X)))) | ((prop(tptp_fun_R_0(Q!7, P!8)) = false) <=> (~bool(tptp_fun_R_0(Q!7, P!8))))),
% 262.07/166.42 inference(quant_inst,[status(thm)],[])).
% 262.07/166.42 tff(378,plain,
% 262.07/166.42 ((prop(tptp_fun_R_0(Q!7, P!8)) = false) <=> (~bool(tptp_fun_R_0(Q!7, P!8)))),
% 262.07/166.42 inference(unit_resolution,[status(thm)],[377, 376])).
% 262.07/166.42 tff(379,plain,
% 262.07/166.42 ((~((prop(tptp_fun_R_0(Q!7, P!8)) = false) <=> (~bool(tptp_fun_R_0(Q!7, P!8))))) | (prop(tptp_fun_R_0(Q!7, P!8)) = false) | bool(tptp_fun_R_0(Q!7, P!8))),
% 262.07/166.42 inference(tautology,[status(thm)],[])).
% 262.07/166.42 tff(380,plain,
% 262.07/166.42 ((prop(tptp_fun_R_0(Q!7, P!8)) = false) | bool(tptp_fun_R_0(Q!7, P!8))),
% 262.07/166.42 inference(unit_resolution,[status(thm)],[379, 378])).
% 262.07/166.42 tff(381,plain,
% 262.07/166.42 (prop(tptp_fun_R_0(Q!7, P!8)) = false),
% 262.07/166.42 inference(unit_resolution,[status(thm)],[380, 369])).
% 262.07/166.42 tff(382,plain,
% 262.07/166.42 (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(false, phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))),
% 262.07/166.42 inference(monotonicity,[status(thm)],[381, 263])).
% 262.07/166.42 tff(383,plain,
% 262.07/166.42 (lazy_impl(false, phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))),
% 262.07/166.42 inference(symmetry,[status(thm)],[382])).
% 262.07/166.42 tff(384,plain,
% 262.07/166.42 (^[B: $i] : refl((lazy_impl(false, B) = not1(false)) <=> (lazy_impl(false, B) = not1(false)))),
% 262.07/166.42 inference(bind,[status(th)],[])).
% 262.07/166.42 tff(385,plain,
% 262.07/166.42 (![B: $i] : (lazy_impl(false, B) = not1(false)) <=> ![B: $i] : (lazy_impl(false, B) = not1(false))),
% 262.07/166.42 inference(quant_intro,[status(thm)],[384])).
% 262.07/166.42 tff(386,plain,
% 262.07/166.42 (^[B: $i] : rewrite((lazy_impl(false, B) = true) <=> (lazy_impl(false, B) = not1(false)))),
% 262.07/166.42 inference(bind,[status(th)],[])).
% 262.07/166.42 tff(387,plain,
% 262.07/166.42 (![B: $i] : (lazy_impl(false, B) = true) <=> ![B: $i] : (lazy_impl(false, B) = not1(false))),
% 262.07/166.42 inference(quant_intro,[status(thm)],[386])).
% 262.07/166.42 tff(388,plain,
% 262.07/166.42 (![B: $i] : (lazy_impl(false, B) = true) <=> ![B: $i] : (lazy_impl(false, B) = true)),
% 262.07/166.42 inference(rewrite,[status(thm)],[])).
% 262.07/166.42 tff(389,axiom,(![B: $i] : (lazy_impl(false, B) = true)), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','lazy_impl_axiom2')).
% 262.07/166.42 tff(390,plain,
% 262.07/166.42 (![B: $i] : (lazy_impl(false, B) = true)),
% 262.07/166.42 inference(modus_ponens,[status(thm)],[389, 388])).
% 262.07/166.42 tff(391,plain,
% 262.07/166.42 (![B: $i] : (lazy_impl(false, B) = not1(false))),
% 262.07/166.42 inference(modus_ponens,[status(thm)],[390, 387])).
% 262.07/166.42 tff(392,plain,(
% 262.07/166.42 ![B: $i] : (lazy_impl(false, B) = not1(false))),
% 262.07/166.42 inference(skolemize,[status(sab)],[391])).
% 262.07/166.42 tff(393,plain,
% 262.07/166.42 (![B: $i] : (lazy_impl(false, B) = not1(false))),
% 262.07/166.42 inference(modus_ponens,[status(thm)],[392, 385])).
% 262.07/166.42 tff(394,plain,
% 262.07/166.42 ((~![B: $i] : (lazy_impl(false, B) = not1(false))) | (lazy_impl(false, phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) = not1(false))),
% 262.07/166.42 inference(quant_inst,[status(thm)],[])).
% 262.07/166.42 tff(395,plain,
% 262.07/166.42 (lazy_impl(false, phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) = not1(false)),
% 262.07/166.42 inference(unit_resolution,[status(thm)],[394, 393])).
% 262.07/166.42 tff(396,plain,
% 262.07/166.42 (not1(false) = lazy_impl(false, phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))),
% 262.07/166.42 inference(symmetry,[status(thm)],[395])).
% 262.07/166.42 tff(397,plain,
% 262.07/166.42 (not1(false) = f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))),
% 262.07/166.42 inference(transitivity,[status(thm)],[396, 383, 177])).
% 262.07/166.42 tff(398,plain,
% 262.07/166.42 (not1(false) = impl(false, not1(false))),
% 262.07/166.42 inference(symmetry,[status(thm)],[165])).
% 262.07/166.42 tff(399,plain,
% 262.07/166.42 (impl(P!8, not1(false)) = impl(P!8, impl(false, not1(false)))),
% 262.07/166.42 inference(monotonicity,[status(thm)],[398])).
% 262.07/166.42 tff(400,plain,
% 262.07/166.42 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(P!8) | (impl(P!8, not1(false)) = phi(P!8)))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(P!8) | (impl(P!8, not1(false)) = phi(P!8)))),
% 262.07/166.42 inference(rewrite,[status(thm)],[])).
% 262.07/166.42 tff(401,plain,
% 262.07/166.42 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(P!8) | (impl(P!8, not1(false)) = phi(P!8)))),
% 262.07/166.42 inference(quant_inst,[status(thm)],[])).
% 262.07/166.42 tff(402,plain,
% 262.07/166.42 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(P!8) | (impl(P!8, not1(false)) = phi(P!8))),
% 262.07/166.42 inference(modus_ponens,[status(thm)],[401, 400])).
% 262.07/166.42 tff(403,plain,
% 262.07/166.42 (bool(P!8) | (impl(P!8, not1(false)) = phi(P!8))),
% 262.07/166.42 inference(unit_resolution,[status(thm)],[402, 188])).
% 262.07/166.42 tff(404,plain,
% 262.07/166.42 (impl(P!8, not1(false)) = phi(P!8)),
% 262.07/166.42 inference(unit_resolution,[status(thm)],[403, 178])).
% 262.07/166.42 tff(405,plain,
% 262.07/166.42 (phi(P!8) = impl(P!8, not1(false))),
% 262.07/166.42 inference(symmetry,[status(thm)],[404])).
% 262.07/166.42 tff(406,plain,
% 262.07/166.42 (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = impl(P!8, impl(false, not1(false)))),
% 262.07/166.42 inference(transitivity,[status(thm)],[193, 405, 399])).
% 262.07/166.42 tff(407,plain,
% 262.07/166.42 (bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) <=> bool(impl(P!8, impl(false, not1(false))))),
% 262.07/166.42 inference(monotonicity,[status(thm)],[406])).
% 262.07/166.42 tff(408,plain,
% 262.07/166.42 ((~bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) <=> (~bool(impl(P!8, impl(false, not1(false)))))),
% 262.07/166.42 inference(monotonicity,[status(thm)],[407])).
% 262.07/166.42 tff(409,plain,
% 262.07/166.42 (~bool(impl(P!8, impl(false, not1(false))))),
% 262.07/166.42 inference(modus_ponens,[status(thm)],[258, 408])).
% 262.07/166.42 tff(410,plain,
% 262.07/166.42 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(P!8, impl(false, not1(false)))) | (impl(impl(P!8, impl(false, not1(false))), not1(false)) = phi(impl(P!8, impl(false, not1(false))))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(P!8, impl(false, not1(false)))) | (impl(impl(P!8, impl(false, not1(false))), not1(false)) = phi(impl(P!8, impl(false, not1(false))))))),
% 262.07/166.43 inference(rewrite,[status(thm)],[])).
% 262.07/166.43 tff(411,plain,
% 262.07/166.43 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(P!8, impl(false, not1(false)))) | (impl(impl(P!8, impl(false, not1(false))), not1(false)) = phi(impl(P!8, impl(false, not1(false))))))),
% 262.07/166.43 inference(quant_inst,[status(thm)],[])).
% 262.07/166.43 tff(412,plain,
% 262.07/166.43 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(P!8, impl(false, not1(false)))) | (impl(impl(P!8, impl(false, not1(false))), not1(false)) = phi(impl(P!8, impl(false, not1(false)))))),
% 262.07/166.43 inference(modus_ponens,[status(thm)],[411, 410])).
% 262.07/166.43 tff(413,plain,
% 262.07/166.43 (bool(impl(P!8, impl(false, not1(false)))) | (impl(impl(P!8, impl(false, not1(false))), not1(false)) = phi(impl(P!8, impl(false, not1(false)))))),
% 262.07/166.43 inference(unit_resolution,[status(thm)],[412, 188])).
% 262.07/166.43 tff(414,plain,
% 262.07/166.43 (impl(impl(P!8, impl(false, not1(false))), not1(false)) = phi(impl(P!8, impl(false, not1(false))))),
% 262.07/166.43 inference(unit_resolution,[status(thm)],[413, 409])).
% 262.07/166.43 tff(415,plain,
% 262.07/166.43 (phi(impl(P!8, impl(false, not1(false)))) = impl(impl(P!8, impl(false, not1(false))), not1(false))),
% 262.07/166.43 inference(symmetry,[status(thm)],[414])).
% 262.07/166.43 tff(416,plain,
% 262.07/166.43 (impl(P!8, impl(false, not1(false))) = impl(P!8, not1(false))),
% 262.07/166.43 inference(symmetry,[status(thm)],[399])).
% 262.07/166.43 tff(417,plain,
% 262.07/166.43 (impl(P!8, impl(false, not1(false))) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.07/166.43 inference(transitivity,[status(thm)],[416, 404, 194])).
% 262.07/166.43 tff(418,plain,
% 262.07/166.43 (d(impl(P!8, impl(false, not1(false)))) <=> d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.07/166.43 inference(monotonicity,[status(thm)],[417])).
% 262.07/166.43 tff(419,plain,
% 262.07/166.43 (d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) <=> d(impl(P!8, impl(false, not1(false))))),
% 262.07/166.43 inference(symmetry,[status(thm)],[418])).
% 262.07/166.43 tff(420,plain,
% 262.07/166.43 (d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.07/166.43 inference(unit_resolution,[status(thm)],[325, 193])).
% 262.07/166.43 tff(421,plain,
% 262.07/166.43 (d(impl(P!8, impl(false, not1(false))))),
% 262.07/166.43 inference(modus_ponens,[status(thm)],[420, 419])).
% 262.07/166.43 tff(422,plain,
% 262.07/166.43 ((d(impl(P!8, impl(false, not1(false)))) | (~(phi(impl(P!8, impl(false, not1(false)))) = err))) | (~d(impl(P!8, impl(false, not1(false)))))),
% 262.07/166.43 inference(tautology,[status(thm)],[])).
% 262.07/166.43 tff(423,plain,
% 262.07/166.43 (d(impl(P!8, impl(false, not1(false)))) | (~(phi(impl(P!8, impl(false, not1(false)))) = err))),
% 262.07/166.43 inference(unit_resolution,[status(thm)],[422, 421])).
% 262.07/166.43 tff(424,plain,
% 262.07/166.43 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(P!8, impl(false, not1(false))))) | (~(phi(impl(P!8, impl(false, not1(false)))) = impl(P!8, impl(false, not1(false))))))) | (~(d(impl(P!8, impl(false, not1(false)))) | (~(phi(impl(P!8, impl(false, not1(false)))) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(impl(P!8, impl(false, not1(false))))) | (~(phi(impl(P!8, impl(false, not1(false)))) = impl(P!8, impl(false, not1(false))))))) | (~(d(impl(P!8, impl(false, not1(false)))) | (~(phi(impl(P!8, impl(false, not1(false)))) = err)))))),
% 262.07/166.43 inference(rewrite,[status(thm)],[])).
% 262.07/166.43 tff(425,plain,
% 262.07/166.43 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(P!8, impl(false, not1(false))))) | (~(phi(impl(P!8, impl(false, not1(false)))) = impl(P!8, impl(false, not1(false))))))) | (~(d(impl(P!8, impl(false, not1(false)))) | (~(phi(impl(P!8, impl(false, not1(false)))) = err)))))),
% 262.07/166.43 inference(quant_inst,[status(thm)],[])).
% 262.07/166.43 tff(426,plain,
% 262.07/166.43 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(impl(P!8, impl(false, not1(false))))) | (~(phi(impl(P!8, impl(false, not1(false)))) = impl(P!8, impl(false, not1(false))))))) | (~(d(impl(P!8, impl(false, not1(false)))) | (~(phi(impl(P!8, impl(false, not1(false)))) = err))))),
% 262.07/166.43 inference(modus_ponens,[status(thm)],[425, 424])).
% 262.07/166.43 tff(427,plain,
% 262.07/166.43 ((~((~d(impl(P!8, impl(false, not1(false))))) | (~(phi(impl(P!8, impl(false, not1(false)))) = impl(P!8, impl(false, not1(false))))))) | (~(d(impl(P!8, impl(false, not1(false)))) | (~(phi(impl(P!8, impl(false, not1(false)))) = err))))),
% 262.07/166.43 inference(unit_resolution,[status(thm)],[426, 17])).
% 262.07/166.43 tff(428,plain,
% 262.07/166.43 (~((~d(impl(P!8, impl(false, not1(false))))) | (~(phi(impl(P!8, impl(false, not1(false)))) = impl(P!8, impl(false, not1(false))))))),
% 262.07/166.43 inference(unit_resolution,[status(thm)],[427, 423])).
% 262.07/166.43 tff(429,plain,
% 262.07/166.43 (((~d(impl(P!8, impl(false, not1(false))))) | (~(phi(impl(P!8, impl(false, not1(false)))) = impl(P!8, impl(false, not1(false)))))) | (phi(impl(P!8, impl(false, not1(false)))) = impl(P!8, impl(false, not1(false))))),
% 262.07/166.43 inference(tautology,[status(thm)],[])).
% 262.07/166.43 tff(430,plain,
% 262.07/166.43 (phi(impl(P!8, impl(false, not1(false)))) = impl(P!8, impl(false, not1(false)))),
% 262.07/166.43 inference(unit_resolution,[status(thm)],[429, 428])).
% 262.07/166.43 tff(431,plain,
% 262.07/166.43 (impl(P!8, impl(false, not1(false))) = phi(impl(P!8, impl(false, not1(false))))),
% 262.07/166.43 inference(symmetry,[status(thm)],[430])).
% 262.07/166.43 tff(432,plain,
% 262.07/166.43 (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = impl(impl(P!8, impl(false, not1(false))), not1(false))),
% 262.07/166.43 inference(transitivity,[status(thm)],[193, 405, 399, 431, 415])).
% 262.07/166.43 tff(433,plain,
% 262.07/166.43 (d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) <=> d(impl(impl(P!8, impl(false, not1(false))), not1(false)))),
% 262.07/166.43 inference(monotonicity,[status(thm)],[432])).
% 262.07/166.43 tff(434,plain,
% 262.07/166.43 (d(impl(impl(P!8, impl(false, not1(false))), not1(false)))),
% 262.07/166.43 inference(modus_ponens,[status(thm)],[420, 433])).
% 262.07/166.43 tff(435,plain,
% 262.07/166.43 (impl(P!8, impl(false, not1(false))) = impl(impl(P!8, impl(false, not1(false))), not1(false))),
% 262.07/166.43 inference(transitivity,[status(thm)],[431, 415])).
% 262.07/166.43 tff(436,plain,
% 262.07/166.43 (bool(impl(P!8, impl(false, not1(false)))) <=> bool(impl(impl(P!8, impl(false, not1(false))), not1(false)))),
% 262.07/166.43 inference(monotonicity,[status(thm)],[435])).
% 262.07/166.43 tff(437,plain,
% 262.07/166.43 ((~bool(impl(P!8, impl(false, not1(false))))) <=> (~bool(impl(impl(P!8, impl(false, not1(false))), not1(false))))),
% 262.07/166.43 inference(monotonicity,[status(thm)],[436])).
% 262.07/166.43 tff(438,plain,
% 262.07/166.43 (~bool(impl(impl(P!8, impl(false, not1(false))), not1(false)))),
% 262.07/166.43 inference(modus_ponens,[status(thm)],[409, 437])).
% 262.07/166.43 tff(439,assumption,(prop(tptp_fun_R_0(Q!7, P!8)) = false), introduced(assumption)).
% 262.07/166.43 tff(440,plain,
% 262.07/166.43 (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(false, phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))),
% 262.07/166.43 inference(monotonicity,[status(thm)],[439, 340])).
% 262.07/166.43 tff(441,plain,
% 262.07/166.43 (lazy_impl(false, phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))),
% 262.07/166.43 inference(symmetry,[status(thm)],[440])).
% 262.07/166.43 tff(442,plain,
% 262.07/166.43 (not1(false) = f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))),
% 262.07/166.43 inference(transitivity,[status(thm)],[396, 441, 177])).
% 262.07/166.43 tff(443,assumption,(Q!7 = not1(false)), introduced(assumption)).
% 262.07/166.43 tff(444,plain,
% 262.07/166.43 (f1(P!8, Q!7, not1(false)) = f1(P!8, not1(false), not1(false))),
% 262.07/166.43 inference(monotonicity,[status(thm)],[443])).
% 262.07/166.43 tff(445,plain,
% 262.07/166.43 (f1(P!8, not1(false), not1(false)) = f1(P!8, Q!7, not1(false))),
% 262.07/166.43 inference(symmetry,[status(thm)],[444])).
% 262.07/166.43 tff(446,plain,
% 262.07/166.43 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(P!8, not1(false), not1(false)) = lazy_impl(prop(not1(false)), impl(impl(P!8, impl(not1(false), not1(false))), not1(false))))),
% 262.07/166.43 inference(quant_inst,[status(thm)],[])).
% 262.07/166.43 tff(447,plain,
% 262.07/166.43 (f1(P!8, not1(false), not1(false)) = lazy_impl(prop(not1(false)), impl(impl(P!8, impl(not1(false), not1(false))), not1(false)))),
% 262.07/166.43 inference(unit_resolution,[status(thm)],[446, 159])).
% 262.07/166.43 tff(448,plain,
% 262.07/166.43 (lazy_impl(prop(not1(false)), impl(impl(P!8, impl(not1(false), not1(false))), not1(false))) = f1(P!8, not1(false), not1(false))),
% 262.07/166.43 inference(symmetry,[status(thm)],[447])).
% 262.07/166.43 tff(449,plain,
% 262.07/166.43 (impl(not1(false), not1(false)) = impl(false, not1(false))),
% 262.07/166.43 inference(transitivity,[status(thm)],[98, 398])).
% 262.07/166.43 tff(450,plain,
% 262.07/166.43 (impl(P!8, impl(not1(false), not1(false))) = impl(P!8, impl(false, not1(false)))),
% 262.07/166.44 inference(monotonicity,[status(thm)],[449])).
% 262.07/166.44 tff(451,plain,
% 262.07/166.44 (impl(impl(P!8, impl(not1(false), not1(false))), not1(false)) = impl(impl(P!8, impl(false, not1(false))), not1(false))),
% 262.07/166.44 inference(monotonicity,[status(thm)],[450])).
% 262.07/166.44 tff(452,plain,
% 262.07/166.44 (lazy_impl(prop(not1(false)), impl(impl(P!8, impl(not1(false), not1(false))), not1(false))) = lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false)))),
% 262.07/166.44 inference(monotonicity,[status(thm)],[451])).
% 262.07/166.44 tff(453,plain,
% 262.07/166.44 (lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))) = lazy_impl(prop(not1(false)), impl(impl(P!8, impl(not1(false), not1(false))), not1(false)))),
% 262.07/166.44 inference(symmetry,[status(thm)],[452])).
% 262.07/166.44 tff(454,plain,
% 262.07/166.44 ((~![X: $i] : ((prop(X) = not1(false)) <=> bool(X))) | ((prop(not1(false)) = not1(false)) <=> bool(not1(false)))),
% 262.07/166.44 inference(quant_inst,[status(thm)],[])).
% 262.07/166.44 tff(455,plain,
% 262.07/166.44 ((prop(not1(false)) = not1(false)) <=> bool(not1(false))),
% 262.07/166.44 inference(unit_resolution,[status(thm)],[454, 144])).
% 262.07/166.44 tff(456,plain,
% 262.07/166.44 ((~((prop(not1(false)) = not1(false)) <=> bool(not1(false)))) | (prop(not1(false)) = not1(false)) | (~bool(not1(false)))),
% 262.07/166.44 inference(tautology,[status(thm)],[])).
% 262.07/166.44 tff(457,plain,
% 262.07/166.44 ((~((prop(not1(false)) = not1(false)) <=> bool(not1(false)))) | (prop(not1(false)) = not1(false))),
% 262.07/166.44 inference(unit_resolution,[status(thm)],[456, 81])).
% 262.07/166.44 tff(458,plain,
% 262.07/166.44 (prop(not1(false)) = not1(false)),
% 262.07/166.44 inference(unit_resolution,[status(thm)],[457, 455])).
% 262.07/166.44 tff(459,plain,
% 262.07/166.44 (lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))) = lazy_impl(not1(false), impl(impl(P!8, impl(false, not1(false))), not1(false)))),
% 262.07/166.44 inference(monotonicity,[status(thm)],[458])).
% 262.07/166.44 tff(460,plain,
% 262.07/166.44 (lazy_impl(not1(false), impl(impl(P!8, impl(false, not1(false))), not1(false))) = lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false)))),
% 262.07/166.44 inference(symmetry,[status(thm)],[459])).
% 262.07/166.44 tff(461,plain,
% 262.07/166.44 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), impl(impl(P!8, impl(false, not1(false))), not1(false))) = phi(impl(impl(P!8, impl(false, not1(false))), not1(false))))),
% 262.07/166.44 inference(quant_inst,[status(thm)],[])).
% 262.07/166.44 tff(462,plain,
% 262.07/166.44 (lazy_impl(not1(false), impl(impl(P!8, impl(false, not1(false))), not1(false))) = phi(impl(impl(P!8, impl(false, not1(false))), not1(false)))),
% 262.07/166.44 inference(unit_resolution,[status(thm)],[461, 33])).
% 262.07/166.44 tff(463,plain,
% 262.07/166.44 (phi(impl(impl(P!8, impl(false, not1(false))), not1(false))) = lazy_impl(not1(false), impl(impl(P!8, impl(false, not1(false))), not1(false)))),
% 262.07/166.44 inference(symmetry,[status(thm)],[462])).
% 262.07/166.44 tff(464,assumption,(phi(impl(P!8, impl(false, not1(false)))) = impl(P!8, impl(false, not1(false)))), introduced(assumption)).
% 262.07/166.44 tff(465,assumption,(impl(impl(P!8, impl(false, not1(false))), not1(false)) = phi(impl(P!8, impl(false, not1(false))))), introduced(assumption)).
% 262.07/166.44 tff(466,plain,
% 262.07/166.44 (impl(impl(P!8, impl(false, not1(false))), not1(false)) = impl(P!8, impl(false, not1(false)))),
% 262.07/166.44 inference(transitivity,[status(thm)],[465, 464])).
% 262.07/166.44 tff(467,plain,
% 262.07/166.44 (phi(impl(impl(P!8, impl(false, not1(false))), not1(false))) = phi(impl(P!8, impl(false, not1(false))))),
% 262.07/166.44 inference(monotonicity,[status(thm)],[466])).
% 262.07/166.44 tff(468,plain,
% 262.07/166.44 (phi(impl(P!8, impl(false, not1(false)))) = phi(impl(impl(P!8, impl(false, not1(false))), not1(false)))),
% 262.07/166.44 inference(symmetry,[status(thm)],[467])).
% 262.07/166.44 tff(469,plain,
% 262.07/166.44 (impl(impl(P!8, impl(false, not1(false))), not1(false)) = f1(P!8, Q!7, not1(false))),
% 262.07/166.44 inference(transitivity,[status(thm)],[465, 468, 463, 460, 453, 448, 445])).
% 262.07/166.44 tff(470,plain,
% 262.07/166.44 (forallprefers(impl(impl(P!8, impl(false, not1(false))), not1(false)), not1(false)) <=> forallprefers(f1(P!8, Q!7, not1(false)), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.07/166.44 inference(monotonicity,[status(thm)],[469, 442])).
% 262.07/166.44 tff(471,plain,
% 262.07/166.44 (forallprefers(f1(P!8, Q!7, not1(false)), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))) <=> forallprefers(impl(impl(P!8, impl(false, not1(false))), not1(false)), not1(false))),
% 262.07/166.44 inference(symmetry,[status(thm)],[470])).
% 262.07/166.44 tff(472,plain,
% 262.07/166.44 ((~forallprefers(f1(P!8, Q!7, not1(false)), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))) <=> (~forallprefers(impl(impl(P!8, impl(false, not1(false))), not1(false)), not1(false)))),
% 262.07/166.44 inference(monotonicity,[status(thm)],[471])).
% 262.07/166.44 tff(473,plain,
% 262.07/166.44 (((~(and2(P!8, Q!7) = phi(f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~![R1: $i] : (~forallprefers(f1(P!8, Q!7, R1), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))))) | ![R1: $i] : (~forallprefers(f1(P!8, Q!7, R1), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.07/166.44 inference(tautology,[status(thm)],[])).
% 262.07/166.44 tff(474,plain,
% 262.07/166.44 (![R1: $i] : (~forallprefers(f1(P!8, Q!7, R1), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.07/166.44 inference(unit_resolution,[status(thm)],[473, 293])).
% 262.07/166.44 tff(475,plain,
% 262.07/166.44 ((~![R1: $i] : (~forallprefers(f1(P!8, Q!7, R1), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~forallprefers(f1(P!8, Q!7, not1(false)), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.07/166.44 inference(quant_inst,[status(thm)],[])).
% 262.07/166.44 tff(476,plain,
% 262.07/166.44 (~forallprefers(f1(P!8, Q!7, not1(false)), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.07/166.44 inference(unit_resolution,[status(thm)],[475, 474])).
% 262.07/166.44 tff(477,plain,
% 262.07/166.44 (~forallprefers(impl(impl(P!8, impl(false, not1(false))), not1(false)), not1(false))),
% 262.07/166.44 inference(modus_ponens,[status(thm)],[476, 472])).
% 262.07/166.44 tff(478,plain,
% 262.07/166.44 (^[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))))))))),
% 262.07/166.44 inference(bind,[status(th)],[])).
% 262.07/166.44 tff(479,plain,
% 262.07/166.44 (![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)))))))),
% 262.07/166.44 inference(quant_intro,[status(thm)],[478])).
% 262.07/166.44 tff(480,plain,
% 262.07/166.44 (^[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))))))))),
% 262.07/166.44 inference(bind,[status(th)],[])).
% 262.07/166.44 tff(481,plain,
% 262.07/166.44 (![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)))))))),
% 262.07/166.44 inference(quant_intro,[status(thm)],[480])).
% 262.07/166.44 tff(482,plain,
% 262.07/166.44 (^[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))))))),
% 262.07/166.44 inference(bind,[status(th)],[])).
% 262.07/166.44 tff(483,plain,
% 262.07/166.44 (![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)))))),
% 262.07/166.44 inference(quant_intro,[status(thm)],[482])).
% 262.07/166.44 tff(484,plain,
% 262.07/166.44 (![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))))),
% 262.07/166.44 inference(rewrite,[status(thm)],[])).
% 262.07/166.44 tff(485,plain,
% 262.07/166.44 (^[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)))))),
% 262.11/166.44 inference(bind,[status(th)],[])).
% 262.11/166.44 tff(486,plain,
% 262.11/166.44 (![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))))),
% 262.11/166.44 inference(quant_intro,[status(thm)],[485])).
% 262.11/166.44 tff(487,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')).
% 262.11/166.44 tff(488,plain,
% 262.11/166.44 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 262.11/166.44 inference(modus_ponens,[status(thm)],[487, 486])).
% 262.11/166.44 tff(489,plain,
% 262.11/166.44 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 262.11/166.44 inference(modus_ponens,[status(thm)],[488, 484])).
% 262.11/166.44 tff(490,plain,
% 262.11/166.44 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)) | ((X = false) & (Y = not1(false)))))),
% 262.11/166.44 inference(modus_ponens,[status(thm)],[489, 483])).
% 262.11/166.44 tff(491,plain,(
% 262.11/166.44 ![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)) | ((X = false) & (Y = not1(false)))))),
% 262.11/166.44 inference(skolemize,[status(sab)],[490])).
% 262.11/166.44 tff(492,plain,
% 262.11/166.44 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))),
% 262.11/166.44 inference(modus_ponens,[status(thm)],[491, 481])).
% 262.11/166.44 tff(493,plain,
% 262.11/166.44 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))),
% 262.11/166.44 inference(modus_ponens,[status(thm)],[492, 479])).
% 262.11/166.44 tff(494,plain,
% 262.11/166.44 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(impl(P!8, impl(false, not1(false))), not1(false)), not1(false)) <=> ((~((~d(not1(false))) | d(impl(impl(P!8, impl(false, not1(false))), not1(false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(impl(impl(P!8, impl(false, not1(false))), not1(false))) | (~d(impl(impl(P!8, impl(false, not1(false))), not1(false)))))) | (impl(impl(P!8, impl(false, 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(impl(impl(P!8, impl(false, not1(false))), not1(false)), not1(false)) <=> ((~((~d(not1(false))) | d(impl(impl(P!8, impl(false, not1(false))), not1(false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(impl(impl(P!8, impl(false, not1(false))), not1(false))) | (~d(impl(impl(P!8, impl(false, not1(false))), not1(false)))))) | (impl(impl(P!8, impl(false, not1(false))), not1(false)) = false))))),
% 262.11/166.44 inference(rewrite,[status(thm)],[])).
% 262.11/166.44 tff(495,plain,
% 262.11/166.44 ((forallprefers(impl(impl(P!8, impl(false, not1(false))), not1(false)), not1(false)) <=> ((~(d(impl(impl(P!8, impl(false, not1(false))), not1(false))) | (~d(not1(false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(impl(impl(P!8, impl(false, not1(false))), not1(false))) | (~d(impl(impl(P!8, impl(false, not1(false))), not1(false)))))) | (~((~(impl(impl(P!8, impl(false, not1(false))), not1(false)) = false)) | (~(not1(false) = not1(false))))))) <=> (forallprefers(impl(impl(P!8, impl(false, not1(false))), not1(false)), not1(false)) <=> ((~((~d(not1(false))) | d(impl(impl(P!8, impl(false, not1(false))), not1(false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(impl(impl(P!8, impl(false, not1(false))), not1(false))) | (~d(impl(impl(P!8, impl(false, not1(false))), not1(false)))))) | (impl(impl(P!8, impl(false, not1(false))), not1(false)) = false)))),
% 262.11/166.45 inference(rewrite,[status(thm)],[])).
% 262.11/166.45 tff(496,plain,
% 262.11/166.45 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(impl(P!8, impl(false, not1(false))), not1(false)), not1(false)) <=> ((~(d(impl(impl(P!8, impl(false, not1(false))), not1(false))) | (~d(not1(false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(impl(impl(P!8, impl(false, not1(false))), not1(false))) | (~d(impl(impl(P!8, impl(false, not1(false))), not1(false)))))) | (~((~(impl(impl(P!8, impl(false, not1(false))), not1(false)) = false)) | (~(not1(false) = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(impl(P!8, impl(false, not1(false))), not1(false)), not1(false)) <=> ((~((~d(not1(false))) | d(impl(impl(P!8, impl(false, not1(false))), not1(false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(impl(impl(P!8, impl(false, not1(false))), not1(false))) | (~d(impl(impl(P!8, impl(false, not1(false))), not1(false)))))) | (impl(impl(P!8, impl(false, not1(false))), not1(false)) = false))))),
% 262.11/166.45 inference(monotonicity,[status(thm)],[495])).
% 262.11/166.45 tff(497,plain,
% 262.11/166.45 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(impl(P!8, impl(false, not1(false))), not1(false)), not1(false)) <=> ((~(d(impl(impl(P!8, impl(false, not1(false))), not1(false))) | (~d(not1(false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(impl(impl(P!8, impl(false, not1(false))), not1(false))) | (~d(impl(impl(P!8, impl(false, not1(false))), not1(false)))))) | (~((~(impl(impl(P!8, impl(false, not1(false))), not1(false)) = false)) | (~(not1(false) = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(impl(P!8, impl(false, not1(false))), not1(false)), not1(false)) <=> ((~((~d(not1(false))) | d(impl(impl(P!8, impl(false, not1(false))), not1(false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(impl(impl(P!8, impl(false, not1(false))), not1(false))) | (~d(impl(impl(P!8, impl(false, not1(false))), not1(false)))))) | (impl(impl(P!8, impl(false, not1(false))), not1(false)) = false))))),
% 262.11/166.45 inference(transitivity,[status(thm)],[496, 494])).
% 262.11/166.45 tff(498,plain,
% 262.11/166.45 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(impl(P!8, impl(false, not1(false))), not1(false)), not1(false)) <=> ((~(d(impl(impl(P!8, impl(false, not1(false))), not1(false))) | (~d(not1(false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(impl(impl(P!8, impl(false, not1(false))), not1(false))) | (~d(impl(impl(P!8, impl(false, not1(false))), not1(false)))))) | (~((~(impl(impl(P!8, impl(false, not1(false))), not1(false)) = false)) | (~(not1(false) = not1(false)))))))),
% 262.11/166.45 inference(quant_inst,[status(thm)],[])).
% 262.11/166.45 tff(499,plain,
% 262.11/166.45 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(impl(impl(P!8, impl(false, not1(false))), not1(false)), not1(false)) <=> ((~((~d(not1(false))) | d(impl(impl(P!8, impl(false, not1(false))), not1(false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(impl(impl(P!8, impl(false, not1(false))), not1(false))) | (~d(impl(impl(P!8, impl(false, not1(false))), not1(false)))))) | (impl(impl(P!8, impl(false, not1(false))), not1(false)) = false)))),
% 262.11/166.45 inference(modus_ponens,[status(thm)],[498, 497])).
% 262.11/166.45 tff(500,plain,
% 262.11/166.45 (forallprefers(impl(impl(P!8, impl(false, not1(false))), not1(false)), not1(false)) <=> ((~((~d(not1(false))) | d(impl(impl(P!8, impl(false, not1(false))), not1(false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(impl(impl(P!8, impl(false, not1(false))), not1(false))) | (~d(impl(impl(P!8, impl(false, not1(false))), not1(false)))))) | (impl(impl(P!8, impl(false, not1(false))), not1(false)) = false))),
% 262.11/166.45 inference(unit_resolution,[status(thm)],[499, 493])).
% 262.11/166.45 tff(501,assumption,(d(impl(impl(P!8, impl(false, not1(false))), not1(false)))), introduced(assumption)).
% 262.11/166.45 tff(502,assumption,(~bool(impl(impl(P!8, impl(false, not1(false))), not1(false)))), introduced(assumption)).
% 262.11/166.45 tff(503,plain,
% 262.11/166.45 ((~((~d(not1(false))) | (~bool(not1(false))) | bool(impl(impl(P!8, impl(false, not1(false))), not1(false))) | (~d(impl(impl(P!8, impl(false, not1(false))), not1(false)))))) | (~d(not1(false))) | (~bool(not1(false))) | bool(impl(impl(P!8, impl(false, not1(false))), not1(false))) | (~d(impl(impl(P!8, impl(false, not1(false))), not1(false))))),
% 262.11/166.45 inference(tautology,[status(thm)],[])).
% 262.11/166.45 tff(504,plain,
% 262.11/166.45 (~((~d(not1(false))) | (~bool(not1(false))) | bool(impl(impl(P!8, impl(false, not1(false))), not1(false))) | (~d(impl(impl(P!8, impl(false, not1(false))), not1(false)))))),
% 262.11/166.45 inference(unit_resolution,[status(thm)],[503, 41, 81, 502, 501])).
% 262.11/166.45 tff(505,plain,
% 262.11/166.45 (((~((~d(not1(false))) | d(impl(impl(P!8, impl(false, not1(false))), not1(false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(impl(impl(P!8, impl(false, not1(false))), not1(false))) | (~d(impl(impl(P!8, impl(false, not1(false))), not1(false)))))) | (impl(impl(P!8, impl(false, not1(false))), not1(false)) = false)) | ((~d(not1(false))) | (~bool(not1(false))) | bool(impl(impl(P!8, impl(false, not1(false))), not1(false))) | (~d(impl(impl(P!8, impl(false, not1(false))), not1(false)))))),
% 262.11/166.45 inference(tautology,[status(thm)],[])).
% 262.11/166.45 tff(506,plain,
% 262.11/166.45 ((~((~d(not1(false))) | d(impl(impl(P!8, impl(false, not1(false))), not1(false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(impl(impl(P!8, impl(false, not1(false))), not1(false))) | (~d(impl(impl(P!8, impl(false, not1(false))), not1(false)))))) | (impl(impl(P!8, impl(false, not1(false))), not1(false)) = false)),
% 262.11/166.45 inference(unit_resolution,[status(thm)],[505, 504])).
% 262.11/166.45 tff(507,plain,
% 262.11/166.45 ((~(forallprefers(impl(impl(P!8, impl(false, not1(false))), not1(false)), not1(false)) <=> ((~((~d(not1(false))) | d(impl(impl(P!8, impl(false, not1(false))), not1(false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(impl(impl(P!8, impl(false, not1(false))), not1(false))) | (~d(impl(impl(P!8, impl(false, not1(false))), not1(false)))))) | (impl(impl(P!8, impl(false, not1(false))), not1(false)) = false)))) | forallprefers(impl(impl(P!8, impl(false, not1(false))), not1(false)), not1(false)) | (~((~((~d(not1(false))) | d(impl(impl(P!8, impl(false, not1(false))), not1(false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(impl(impl(P!8, impl(false, not1(false))), not1(false))) | (~d(impl(impl(P!8, impl(false, not1(false))), not1(false)))))) | (impl(impl(P!8, impl(false, not1(false))), not1(false)) = false)))),
% 262.11/166.45 inference(tautology,[status(thm)],[])).
% 262.11/166.45 tff(508,plain,
% 262.11/166.45 ((~(forallprefers(impl(impl(P!8, impl(false, not1(false))), not1(false)), not1(false)) <=> ((~((~d(not1(false))) | d(impl(impl(P!8, impl(false, not1(false))), not1(false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(impl(impl(P!8, impl(false, not1(false))), not1(false))) | (~d(impl(impl(P!8, impl(false, not1(false))), not1(false)))))) | (impl(impl(P!8, impl(false, not1(false))), not1(false)) = false)))) | forallprefers(impl(impl(P!8, impl(false, not1(false))), not1(false)), not1(false))),
% 262.11/166.45 inference(unit_resolution,[status(thm)],[507, 506])).
% 262.11/166.45 tff(509,plain,
% 262.11/166.45 (forallprefers(impl(impl(P!8, impl(false, not1(false))), not1(false)), not1(false))),
% 262.11/166.45 inference(unit_resolution,[status(thm)],[508, 500])).
% 262.11/166.45 tff(510,plain,
% 262.11/166.45 ($false),
% 262.11/166.45 inference(unit_resolution,[status(thm)],[509, 477])).
% 262.11/166.45 tff(511,plain,((~(Q!7 = not1(false))) | (~(impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))) | (~(prop(tptp_fun_R_0(Q!7, P!8)) = false)) | (~(impl(impl(P!8, impl(false, not1(false))), not1(false)) = phi(impl(P!8, impl(false, not1(false)))))) | (~(phi(impl(P!8, impl(false, not1(false)))) = impl(P!8, impl(false, not1(false))))) | bool(impl(impl(P!8, impl(false, not1(false))), not1(false))) | (~d(impl(impl(P!8, impl(false, not1(false))), not1(false))))), inference(lemma,lemma(discharge,[]))).
% 262.11/166.45 tff(512,plain,
% 262.11/166.45 (~(Q!7 = not1(false))),
% 262.11/166.45 inference(unit_resolution,[status(thm)],[511, 263, 381, 414, 430, 438, 434])).
% 262.11/166.45 tff(513,plain,
% 262.11/166.45 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), impl(Q!7, err)) = phi(impl(Q!7, err)))),
% 262.11/166.45 inference(quant_inst,[status(thm)],[])).
% 262.11/166.45 tff(514,plain,
% 262.11/166.45 (lazy_impl(not1(false), impl(Q!7, err)) = phi(impl(Q!7, err))),
% 262.11/166.45 inference(unit_resolution,[status(thm)],[513, 33])).
% 262.11/166.45 tff(515,plain,
% 262.11/166.45 (phi(impl(Q!7, err)) = lazy_impl(not1(false), impl(Q!7, err))),
% 262.11/166.45 inference(symmetry,[status(thm)],[514])).
% 262.11/166.45 tff(516,assumption,(~bool(Q!7)), introduced(assumption)).
% 262.11/166.45 tff(517,plain,
% 262.11/166.45 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(Q!7) | (impl(Q!7, false) = phi(Q!7)))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(Q!7) | (impl(Q!7, false) = phi(Q!7)))),
% 262.11/166.45 inference(rewrite,[status(thm)],[])).
% 262.11/166.45 tff(518,plain,
% 262.11/166.45 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(Q!7) | (impl(Q!7, false) = phi(Q!7)))),
% 262.11/166.45 inference(quant_inst,[status(thm)],[])).
% 262.11/166.45 tff(519,plain,
% 262.11/166.45 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(Q!7) | (impl(Q!7, false) = phi(Q!7))),
% 262.11/166.45 inference(modus_ponens,[status(thm)],[518, 517])).
% 262.11/166.45 tff(520,plain,
% 262.11/166.45 (bool(Q!7) | (impl(Q!7, false) = phi(Q!7))),
% 262.11/166.45 inference(unit_resolution,[status(thm)],[519, 188])).
% 262.11/166.45 tff(521,plain,
% 262.11/166.45 (impl(Q!7, false) = phi(Q!7)),
% 262.11/166.45 inference(unit_resolution,[status(thm)],[520, 516])).
% 262.11/166.45 tff(522,plain,
% 262.11/166.45 (phi(Q!7) = impl(Q!7, false)),
% 262.11/166.45 inference(symmetry,[status(thm)],[521])).
% 262.11/166.45 tff(523,plain,
% 262.11/166.45 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(Q!7) | (impl(Q!7, err) = phi(Q!7)))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(Q!7) | (impl(Q!7, err) = phi(Q!7)))),
% 262.11/166.45 inference(rewrite,[status(thm)],[])).
% 262.11/166.45 tff(524,plain,
% 262.11/166.45 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(Q!7) | (impl(Q!7, err) = phi(Q!7)))),
% 262.11/166.45 inference(quant_inst,[status(thm)],[])).
% 262.11/166.45 tff(525,plain,
% 262.11/166.45 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(Q!7) | (impl(Q!7, err) = phi(Q!7))),
% 262.11/166.45 inference(modus_ponens,[status(thm)],[524, 523])).
% 262.11/166.45 tff(526,plain,
% 262.11/166.45 (bool(Q!7) | (impl(Q!7, err) = phi(Q!7))),
% 262.11/166.45 inference(unit_resolution,[status(thm)],[525, 188])).
% 262.11/166.45 tff(527,plain,
% 262.11/166.45 (impl(Q!7, err) = phi(Q!7)),
% 262.11/166.45 inference(unit_resolution,[status(thm)],[526, 516])).
% 262.11/166.45 tff(528,plain,
% 262.11/166.45 (impl(Q!7, err) = impl(Q!7, false)),
% 262.11/166.45 inference(transitivity,[status(thm)],[527, 522])).
% 262.11/166.45 tff(529,plain,
% 262.11/166.45 (phi(impl(Q!7, err)) = phi(impl(Q!7, false))),
% 262.11/166.45 inference(monotonicity,[status(thm)],[528])).
% 262.11/166.45 tff(530,plain,
% 262.11/166.45 (phi(impl(Q!7, false)) = phi(impl(Q!7, err))),
% 262.11/166.45 inference(symmetry,[status(thm)],[529])).
% 262.11/166.45 tff(531,plain,
% 262.11/166.45 (lazy_impl(prop(false), false) = lazy_impl(not1(false), false)),
% 262.11/166.45 inference(monotonicity,[status(thm)],[149])).
% 262.11/166.45 tff(532,plain,
% 262.11/166.45 (^[P: $i] : refl((f7(P) = lazy_impl(prop(P), P)) <=> (f7(P) = lazy_impl(prop(P), P)))),
% 262.11/166.45 inference(bind,[status(th)],[])).
% 262.11/166.45 tff(533,plain,
% 262.11/166.45 (![P: $i] : (f7(P) = lazy_impl(prop(P), P)) <=> ![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 262.11/166.45 inference(quant_intro,[status(thm)],[532])).
% 262.11/166.45 tff(534,plain,
% 262.11/166.45 (![P: $i] : (f7(P) = lazy_impl(prop(P), P)) <=> ![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 262.11/166.45 inference(rewrite,[status(thm)],[])).
% 262.11/166.45 tff(535,axiom,(![P: $i] : (f7(P) = lazy_impl(prop(P), P))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','def_f7')).
% 262.11/166.45 tff(536,plain,
% 262.11/166.45 (![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 262.11/166.45 inference(modus_ponens,[status(thm)],[535, 534])).
% 262.11/166.45 tff(537,plain,(
% 262.11/166.45 ![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 262.11/166.45 inference(skolemize,[status(sab)],[536])).
% 262.11/166.46 tff(538,plain,
% 262.11/166.46 (![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 262.11/166.46 inference(modus_ponens,[status(thm)],[537, 533])).
% 262.11/166.46 tff(539,plain,
% 262.11/166.46 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(false) = lazy_impl(prop(false), false))),
% 262.11/166.46 inference(quant_inst,[status(thm)],[])).
% 262.11/166.46 tff(540,plain,
% 262.11/166.46 (f7(false) = lazy_impl(prop(false), false)),
% 262.11/166.46 inference(unit_resolution,[status(thm)],[539, 538])).
% 262.11/166.46 tff(541,plain,
% 262.11/166.46 ((~![B: $i] : (lazy_impl(false, B) = not1(false))) | (lazy_impl(false, P!6) = not1(false))),
% 262.11/166.46 inference(quant_inst,[status(thm)],[])).
% 262.11/166.46 tff(542,plain,
% 262.11/166.46 (lazy_impl(false, P!6) = not1(false)),
% 262.11/166.46 inference(unit_resolution,[status(thm)],[541, 393])).
% 262.11/166.46 tff(543,assumption,(prop(P!6) = false), introduced(assumption)).
% 262.11/166.46 tff(544,plain,
% 262.11/166.46 (lazy_impl(prop(P!6), P!6) = lazy_impl(false, P!6)),
% 262.11/166.46 inference(monotonicity,[status(thm)],[543])).
% 262.11/166.46 tff(545,plain,
% 262.11/166.46 (lazy_impl(prop(P!6), P!6) = not1(false)),
% 262.11/166.46 inference(transitivity,[status(thm)],[544, 542])).
% 262.11/166.46 tff(546,plain,
% 262.11/166.46 (((~![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)))))),
% 262.11/166.46 inference(rewrite,[status(thm)],[])).
% 262.11/166.46 tff(547,plain,
% 262.11/166.46 ((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))))),
% 262.11/166.46 inference(rewrite,[status(thm)],[])).
% 262.11/166.46 tff(548,plain,
% 262.11/166.46 (((~![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)))))),
% 262.11/166.46 inference(monotonicity,[status(thm)],[547])).
% 262.11/166.46 tff(549,plain,
% 262.11/166.46 (((~![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)))))),
% 262.11/166.46 inference(transitivity,[status(thm)],[548, 546])).
% 262.11/166.46 tff(550,plain,
% 262.11/166.46 ((~![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)))))))),
% 262.11/166.46 inference(quant_inst,[status(thm)],[])).
% 262.11/166.46 tff(551,plain,
% 262.11/166.46 ((~![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))))),
% 262.11/166.46 inference(modus_ponens,[status(thm)],[550, 549])).
% 262.11/166.46 tff(552,plain,
% 262.11/166.46 (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)))),
% 262.11/166.46 inference(unit_resolution,[status(thm)],[551, 493])).
% 262.11/166.46 tff(553,plain,
% 262.11/166.46 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(P!6) = lazy_impl(prop(P!6), P!6))),
% 262.11/166.46 inference(quant_inst,[status(thm)],[])).
% 262.11/166.46 tff(554,plain,
% 262.11/166.46 (f7(P!6) = lazy_impl(prop(P!6), P!6)),
% 262.11/166.46 inference(unit_resolution,[status(thm)],[553, 538])).
% 262.11/166.46 tff(555,plain,
% 262.11/166.46 (lazy_impl(prop(P!6), P!6) = f7(P!6)),
% 262.11/166.46 inference(symmetry,[status(thm)],[554])).
% 262.11/166.46 tff(556,plain,
% 262.11/166.46 (lazy_impl(prop(false), false) = f7(false)),
% 262.11/166.46 inference(symmetry,[status(thm)],[540])).
% 262.11/166.46 tff(557,plain,
% 262.11/166.46 (lazy_impl(not1(false), false) = lazy_impl(prop(false), false)),
% 262.11/166.46 inference(symmetry,[status(thm)],[531])).
% 262.11/166.46 tff(558,plain,
% 262.11/166.46 (phi(false) = lazy_impl(not1(false), false)),
% 262.11/166.46 inference(symmetry,[status(thm)],[35])).
% 262.11/166.46 tff(559,plain,
% 262.11/166.46 (false = phi(false)),
% 262.11/166.46 inference(symmetry,[status(thm)],[23])).
% 262.11/166.46 tff(560,plain,
% 262.11/166.46 (false = f7(false)),
% 262.11/166.46 inference(transitivity,[status(thm)],[559, 558, 557, 556])).
% 262.11/166.46 tff(561,plain,
% 262.11/166.46 (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> forallprefers(f7(false), f7(P!6))),
% 262.11/166.46 inference(monotonicity,[status(thm)],[560, 555])).
% 262.11/166.46 tff(562,plain,
% 262.11/166.46 (forallprefers(f7(false), f7(P!6)) <=> forallprefers(false, lazy_impl(prop(P!6), P!6))),
% 262.11/166.46 inference(symmetry,[status(thm)],[561])).
% 262.11/166.46 tff(563,plain,
% 262.11/166.46 ((~forallprefers(f7(false), f7(P!6))) <=> (~forallprefers(false, lazy_impl(prop(P!6), P!6)))),
% 262.11/166.46 inference(monotonicity,[status(thm)],[562])).
% 262.11/166.46 tff(564,plain,
% 262.11/166.46 (^[P1: $i] : refl((~forallprefers(f7(P1), f7(P!6))) <=> (~forallprefers(f7(P1), f7(P!6))))),
% 262.11/166.46 inference(bind,[status(th)],[])).
% 262.11/166.46 tff(565,plain,
% 262.11/166.46 (![P1: $i] : (~forallprefers(f7(P1), f7(P!6))) <=> ![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 262.11/166.46 inference(quant_intro,[status(thm)],[564])).
% 262.11/166.46 tff(566,plain,
% 262.11/166.46 (((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))))),
% 262.11/166.46 inference(rewrite,[status(thm)],[])).
% 262.11/166.46 tff(567,plain,
% 262.11/166.46 (?[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))))),
% 262.11/166.46 inference(rewrite,[status(thm)],[])).
% 262.11/166.46 tff(568,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')).
% 262.11/166.46 tff(569,plain,
% 262.11/166.46 (?[P: $i] : ((false2 = phi(f7(P))) & (~?[P1: $i] : forallprefers(f7(P1), f7(P))))),
% 262.11/166.46 inference(modus_ponens,[status(thm)],[568, 567])).
% 262.11/166.46 tff(570,plain,
% 262.11/166.46 ((false2 = phi(f7(P!6))) & ![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 262.11/166.46 inference(modus_ponens,[status(thm)],[569, 566])).
% 262.11/166.46 tff(571,plain,
% 262.11/166.46 (![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 262.11/166.46 inference(and_elim,[status(thm)],[570])).
% 262.11/166.46 tff(572,plain,
% 262.11/166.46 (![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 262.11/166.46 inference(modus_ponens,[status(thm)],[571, 565])).
% 262.11/166.46 tff(573,plain,
% 262.11/166.46 ((~![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))) | (~forallprefers(f7(false), f7(P!6)))),
% 262.11/166.46 inference(quant_inst,[status(thm)],[])).
% 262.11/166.46 tff(574,plain,
% 262.11/166.46 (~forallprefers(f7(false), f7(P!6))),
% 262.11/166.46 inference(unit_resolution,[status(thm)],[573, 572])).
% 262.11/166.46 tff(575,plain,
% 262.11/166.46 (~forallprefers(false, lazy_impl(prop(P!6), P!6))),
% 262.11/166.46 inference(modus_ponens,[status(thm)],[574, 563])).
% 262.11/166.46 tff(576,plain,
% 262.11/166.46 ((~(forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))) | (lazy_impl(prop(P!6), P!6) = not1(false))))) | forallprefers(false, lazy_impl(prop(P!6), P!6)) | (~((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))) | (lazy_impl(prop(P!6), P!6) = not1(false))))),
% 262.11/166.46 inference(tautology,[status(thm)],[])).
% 262.11/166.46 tff(577,plain,
% 262.11/166.46 (~((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))) | (lazy_impl(prop(P!6), P!6) = not1(false)))),
% 262.11/166.46 inference(unit_resolution,[status(thm)],[576, 575, 552])).
% 262.11/166.46 tff(578,plain,
% 262.11/166.46 (((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))) | (lazy_impl(prop(P!6), P!6) = not1(false))) | (~(lazy_impl(prop(P!6), P!6) = not1(false)))),
% 262.11/166.46 inference(tautology,[status(thm)],[])).
% 262.11/166.46 tff(579,plain,
% 262.11/166.46 (~(lazy_impl(prop(P!6), P!6) = not1(false))),
% 262.11/166.46 inference(unit_resolution,[status(thm)],[578, 577])).
% 262.11/166.46 tff(580,plain,
% 262.11/166.46 ($false),
% 262.11/166.46 inference(unit_resolution,[status(thm)],[579, 545])).
% 262.11/166.46 tff(581,plain,(~(prop(P!6) = false)), inference(lemma,lemma(discharge,[]))).
% 262.11/166.46 tff(582,plain,
% 262.11/166.46 ((~![X: $i] : ((prop(X) = false) <=> (~bool(X)))) | ((prop(P!6) = false) <=> (~bool(P!6)))),
% 262.11/166.46 inference(quant_inst,[status(thm)],[])).
% 262.11/166.46 tff(583,plain,
% 262.11/166.46 ((prop(P!6) = false) <=> (~bool(P!6))),
% 262.11/166.46 inference(unit_resolution,[status(thm)],[582, 376])).
% 262.11/166.46 tff(584,plain,
% 262.11/166.46 ((~((prop(P!6) = false) <=> (~bool(P!6)))) | (prop(P!6) = false) | bool(P!6)),
% 262.11/166.46 inference(tautology,[status(thm)],[])).
% 262.11/166.46 tff(585,plain,
% 262.11/166.46 ((prop(P!6) = false) | bool(P!6)),
% 262.11/166.46 inference(unit_resolution,[status(thm)],[584, 583])).
% 262.11/166.46 tff(586,plain,
% 262.11/166.46 (bool(P!6)),
% 262.11/166.46 inference(unit_resolution,[status(thm)],[585, 581])).
% 262.11/166.46 tff(587,plain,
% 262.11/166.46 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(P!6) <=> ((P!6 = false) | (P!6 = not1(false))))),
% 262.11/166.46 inference(quant_inst,[status(thm)],[])).
% 262.11/166.46 tff(588,plain,
% 262.11/166.46 (bool(P!6) <=> ((P!6 = false) | (P!6 = not1(false)))),
% 262.11/166.46 inference(unit_resolution,[status(thm)],[587, 229])).
% 262.11/166.46 tff(589,plain,
% 262.11/166.46 ((~(bool(P!6) <=> ((P!6 = false) | (P!6 = not1(false))))) | (~bool(P!6)) | ((P!6 = false) | (P!6 = not1(false)))),
% 262.11/166.46 inference(tautology,[status(thm)],[])).
% 262.11/166.46 tff(590,plain,
% 262.11/166.46 ((~bool(P!6)) | ((P!6 = false) | (P!6 = not1(false)))),
% 262.11/166.46 inference(unit_resolution,[status(thm)],[589, 588])).
% 262.11/166.46 tff(591,plain,
% 262.11/166.46 ((P!6 = false) | (P!6 = not1(false))),
% 262.11/166.46 inference(unit_resolution,[status(thm)],[590, 586])).
% 262.11/166.46 tff(592,plain,
% 262.11/166.46 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), not1(false)) = phi(not1(false)))),
% 262.11/166.46 inference(quant_inst,[status(thm)],[])).
% 262.11/166.46 tff(593,plain,
% 262.11/166.46 (lazy_impl(not1(false), not1(false)) = phi(not1(false))),
% 262.11/166.46 inference(unit_resolution,[status(thm)],[592, 33])).
% 262.11/166.46 tff(594,plain,
% 262.11/166.46 (lazy_impl(prop(not1(false)), not1(false)) = lazy_impl(not1(false), not1(false))),
% 262.11/166.46 inference(monotonicity,[status(thm)],[458])).
% 262.11/166.47 tff(595,plain,
% 262.11/166.47 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(not1(false)) = lazy_impl(prop(not1(false)), not1(false)))),
% 262.11/166.47 inference(quant_inst,[status(thm)],[])).
% 262.11/166.47 tff(596,plain,
% 262.11/166.47 (f7(not1(false)) = lazy_impl(prop(not1(false)), not1(false))),
% 262.11/166.47 inference(unit_resolution,[status(thm)],[595, 538])).
% 262.11/166.47 tff(597,assumption,(P!6 = not1(false)), introduced(assumption)).
% 262.11/166.47 tff(598,plain,
% 262.11/166.47 (f7(P!6) = f7(not1(false))),
% 262.11/166.47 inference(monotonicity,[status(thm)],[597])).
% 262.11/166.47 tff(599,plain,
% 262.11/166.47 (lazy_impl(prop(P!6), P!6) = not1(false)),
% 262.11/166.47 inference(transitivity,[status(thm)],[555, 598, 596, 594, 593, 49])).
% 262.11/166.47 tff(600,plain,
% 262.11/166.47 ($false),
% 262.11/166.47 inference(unit_resolution,[status(thm)],[579, 599])).
% 262.11/166.47 tff(601,plain,(~(P!6 = not1(false))), inference(lemma,lemma(discharge,[]))).
% 262.11/166.47 tff(602,plain,
% 262.11/166.47 ((~((P!6 = false) | (P!6 = not1(false)))) | (P!6 = false) | (P!6 = not1(false))),
% 262.11/166.47 inference(tautology,[status(thm)],[])).
% 262.11/166.47 tff(603,plain,
% 262.11/166.47 (P!6 = false),
% 262.11/166.47 inference(unit_resolution,[status(thm)],[602, 601, 591])).
% 262.11/166.47 tff(604,plain,
% 262.11/166.47 (f7(P!6) = f7(false)),
% 262.11/166.47 inference(monotonicity,[status(thm)],[603])).
% 262.11/166.47 tff(605,plain,
% 262.11/166.47 (f7(P!6) = false),
% 262.11/166.47 inference(transitivity,[status(thm)],[604, 540, 531, 35, 23])).
% 262.11/166.47 tff(606,plain,
% 262.11/166.47 (phi(f7(P!6)) = phi(false)),
% 262.11/166.47 inference(monotonicity,[status(thm)],[605])).
% 262.11/166.47 tff(607,plain,
% 262.11/166.47 (false2 = phi(f7(P!6))),
% 262.11/166.47 inference(and_elim,[status(thm)],[570])).
% 262.11/166.47 tff(608,plain,
% 262.11/166.47 (false2 = false),
% 262.11/166.47 inference(transitivity,[status(thm)],[607, 606, 23])).
% 262.11/166.47 tff(609,plain,
% 262.11/166.47 (impl(Q!7, impl(not1(false), false)) = impl(Q!7, false)),
% 262.11/166.47 inference(monotonicity,[status(thm)],[132])).
% 262.11/166.47 tff(610,plain,
% 262.11/166.47 (impl(Q!7, false) = impl(Q!7, impl(not1(false), false))),
% 262.11/166.47 inference(symmetry,[status(thm)],[609])).
% 262.11/166.47 tff(611,plain,
% 262.11/166.47 (impl(Q!7, false2) = impl(Q!7, false)),
% 262.11/166.47 inference(monotonicity,[status(thm)],[608])).
% 262.11/166.47 tff(612,plain,
% 262.11/166.47 (impl(Q!7, false2) = impl(Q!7, impl(not1(false), false))),
% 262.11/166.47 inference(transitivity,[status(thm)],[611, 610])).
% 262.11/166.47 tff(613,plain,
% 262.11/166.47 (impl(impl(Q!7, false2), false2) = impl(impl(Q!7, impl(not1(false), false)), false)),
% 262.11/166.47 inference(monotonicity,[status(thm)],[612, 608])).
% 262.11/166.47 tff(614,plain,
% 262.11/166.47 (impl(impl(Q!7, impl(not1(false), false)), false) = impl(impl(Q!7, false2), false2)),
% 262.11/166.47 inference(symmetry,[status(thm)],[613])).
% 262.11/166.47 tff(615,plain,
% 262.11/166.47 (impl(Q!7, false) = impl(Q!7, false2)),
% 262.11/166.47 inference(symmetry,[status(thm)],[611])).
% 262.11/166.47 tff(616,plain,
% 262.11/166.47 (impl(Q!7, impl(not1(false), false)) = impl(Q!7, false2)),
% 262.11/166.47 inference(transitivity,[status(thm)],[609, 615])).
% 262.11/166.47 tff(617,plain,
% 262.11/166.47 (impl(impl(Q!7, impl(not1(false), false)), false) = impl(impl(Q!7, false2), false)),
% 262.11/166.47 inference(monotonicity,[status(thm)],[616])).
% 262.11/166.47 tff(618,plain,
% 262.11/166.47 (impl(impl(Q!7, false2), false) = impl(impl(Q!7, impl(not1(false), false)), false)),
% 262.11/166.47 inference(symmetry,[status(thm)],[617])).
% 262.11/166.47 tff(619,plain,
% 262.11/166.47 (impl(Q!7, false2) = phi(Q!7)),
% 262.11/166.47 inference(transitivity,[status(thm)],[611, 521])).
% 262.11/166.47 tff(620,plain,
% 262.11/166.47 ((impl(Q!7, false2) = false) <=> (phi(Q!7) = false)),
% 262.11/166.47 inference(monotonicity,[status(thm)],[619])).
% 262.11/166.47 tff(621,plain,
% 262.11/166.47 ((phi(Q!7) = false) <=> (impl(Q!7, false2) = false)),
% 262.11/166.47 inference(symmetry,[status(thm)],[620])).
% 262.11/166.47 tff(622,plain,
% 262.11/166.47 ((~(phi(Q!7) = false)) <=> (~(impl(Q!7, false2) = false))),
% 262.11/166.47 inference(monotonicity,[status(thm)],[621])).
% 262.11/166.47 tff(623,plain,
% 262.11/166.47 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(Q!7) <=> ((Q!7 = false) | (Q!7 = not1(false))))),
% 262.11/166.47 inference(quant_inst,[status(thm)],[])).
% 262.11/166.47 tff(624,plain,
% 262.11/166.47 (bool(Q!7) <=> ((Q!7 = false) | (Q!7 = not1(false)))),
% 262.11/166.47 inference(unit_resolution,[status(thm)],[623, 229])).
% 262.11/166.47 tff(625,plain,
% 262.11/166.47 ((~(bool(Q!7) <=> ((Q!7 = false) | (Q!7 = not1(false))))) | bool(Q!7) | (~((Q!7 = false) | (Q!7 = not1(false))))),
% 262.11/166.47 inference(tautology,[status(thm)],[])).
% 262.11/166.47 tff(626,plain,
% 262.11/166.47 (bool(Q!7) | (~((Q!7 = false) | (Q!7 = not1(false))))),
% 262.11/166.47 inference(unit_resolution,[status(thm)],[625, 624])).
% 262.11/166.47 tff(627,plain,
% 262.11/166.47 (~((Q!7 = false) | (Q!7 = not1(false)))),
% 262.11/166.47 inference(unit_resolution,[status(thm)],[626, 516])).
% 262.11/166.47 tff(628,plain,
% 262.11/166.47 (((Q!7 = false) | (Q!7 = not1(false))) | (~(Q!7 = false))),
% 262.11/166.47 inference(tautology,[status(thm)],[])).
% 262.11/166.47 tff(629,plain,
% 262.11/166.47 (~(Q!7 = false)),
% 262.11/166.47 inference(unit_resolution,[status(thm)],[628, 627])).
% 262.11/166.47 tff(630,plain,
% 262.11/166.47 ((false = Q!7) <=> (Q!7 = false)),
% 262.11/166.47 inference(commutativity,[status(thm)],[])).
% 262.11/166.47 tff(631,assumption,(phi(Q!7) = false), introduced(assumption)).
% 262.11/166.47 tff(632,plain,
% 262.11/166.47 ((phi(Q!7) = Q!7) <=> (false = Q!7)),
% 262.11/166.47 inference(monotonicity,[status(thm)],[631])).
% 262.11/166.47 tff(633,plain,
% 262.11/166.47 ((phi(Q!7) = Q!7) <=> (Q!7 = false)),
% 262.11/166.47 inference(transitivity,[status(thm)],[632, 630])).
% 262.11/166.47 tff(634,plain,
% 262.11/166.47 ((Q!7 = false) <=> (phi(Q!7) = Q!7)),
% 262.11/166.47 inference(symmetry,[status(thm)],[633])).
% 262.11/166.47 tff(635,plain,
% 262.11/166.47 ((~(Q!7 = false)) <=> (~(phi(Q!7) = Q!7))),
% 262.11/166.47 inference(monotonicity,[status(thm)],[634])).
% 262.11/166.47 tff(636,assumption,(~(Q!7 = false)), introduced(assumption)).
% 262.11/166.47 tff(637,plain,
% 262.11/166.47 (~(phi(Q!7) = Q!7)),
% 262.11/166.47 inference(modus_ponens,[status(thm)],[636, 635])).
% 262.11/166.47 tff(638,plain,
% 262.11/166.47 (((~d(Q!7)) | (~(phi(Q!7) = Q!7))) | (phi(Q!7) = Q!7)),
% 262.11/166.47 inference(tautology,[status(thm)],[])).
% 262.11/166.47 tff(639,plain,
% 262.11/166.47 ((~d(Q!7)) | (~(phi(Q!7) = Q!7))),
% 262.11/166.47 inference(unit_resolution,[status(thm)],[638, 637])).
% 262.11/166.47 tff(640,plain,
% 262.11/166.47 ((phi(Q!7) = err) <=> (false = err)),
% 262.11/166.47 inference(monotonicity,[status(thm)],[631])).
% 262.11/166.47 tff(641,plain,
% 262.11/166.47 ((false = err) <=> (phi(Q!7) = err)),
% 262.11/166.47 inference(symmetry,[status(thm)],[640])).
% 262.11/166.47 tff(642,plain,
% 262.11/166.47 ((~(false = err)) <=> (~(phi(Q!7) = err))),
% 262.11/166.47 inference(monotonicity,[status(thm)],[641])).
% 262.11/166.47 tff(643,plain,
% 262.11/166.47 (~(phi(Q!7) = err)),
% 262.11/166.47 inference(modus_ponens,[status(thm)],[239, 642])).
% 262.11/166.47 tff(644,plain,
% 262.11/166.47 ((d(Q!7) | (~(phi(Q!7) = err))) | (phi(Q!7) = err)),
% 262.11/166.47 inference(tautology,[status(thm)],[])).
% 262.11/166.47 tff(645,plain,
% 262.11/166.47 (d(Q!7) | (~(phi(Q!7) = err))),
% 262.11/166.47 inference(unit_resolution,[status(thm)],[644, 643])).
% 262.11/166.47 tff(646,plain,
% 262.11/166.47 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(Q!7)) | (~(phi(Q!7) = Q!7)))) | (~(d(Q!7) | (~(phi(Q!7) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(Q!7)) | (~(phi(Q!7) = Q!7)))) | (~(d(Q!7) | (~(phi(Q!7) = err)))))),
% 262.11/166.47 inference(rewrite,[status(thm)],[])).
% 262.11/166.47 tff(647,plain,
% 262.11/166.47 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(Q!7)) | (~(phi(Q!7) = Q!7)))) | (~(d(Q!7) | (~(phi(Q!7) = err)))))),
% 262.11/166.47 inference(quant_inst,[status(thm)],[])).
% 262.11/166.47 tff(648,plain,
% 262.11/166.47 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(Q!7)) | (~(phi(Q!7) = Q!7)))) | (~(d(Q!7) | (~(phi(Q!7) = err))))),
% 262.11/166.47 inference(modus_ponens,[status(thm)],[647, 646])).
% 262.11/166.47 tff(649,plain,
% 262.11/166.47 ((~((~d(Q!7)) | (~(phi(Q!7) = Q!7)))) | (~(d(Q!7) | (~(phi(Q!7) = err))))),
% 262.11/166.47 inference(unit_resolution,[status(thm)],[648, 17])).
% 262.11/166.47 tff(650,plain,
% 262.11/166.47 ($false),
% 262.11/166.47 inference(unit_resolution,[status(thm)],[649, 645, 639])).
% 262.11/166.47 tff(651,plain,((~(phi(Q!7) = false)) | (Q!7 = false)), inference(lemma,lemma(discharge,[]))).
% 262.11/166.47 tff(652,plain,
% 262.11/166.47 (~(phi(Q!7) = false)),
% 262.11/166.47 inference(unit_resolution,[status(thm)],[651, 629])).
% 262.11/166.47 tff(653,plain,
% 262.11/166.47 (~(impl(Q!7, false2) = false)),
% 262.11/166.47 inference(modus_ponens,[status(thm)],[652, 622])).
% 262.11/166.47 tff(654,plain,
% 262.11/166.47 (^[A: $i, B: $i] : refl((bool(B) | (~bool(A)) | (impl(A, B) = phi(B))) <=> (bool(B) | (~bool(A)) | (impl(A, B) = phi(B))))),
% 262.11/166.47 inference(bind,[status(th)],[])).
% 262.11/166.47 tff(655,plain,
% 262.11/166.47 (![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B))) <=> ![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))),
% 262.11/166.47 inference(quant_intro,[status(thm)],[654])).
% 262.11/166.47 tff(656,plain,
% 262.11/166.47 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((bool(A) & (~bool(B))) <=> (~(bool(B) | (~bool(A))))), ((~(bool(A) & (~bool(B)))) <=> (~(~(bool(B) | (~bool(A))))))), rewrite((~(~(bool(B) | (~bool(A))))) <=> (bool(B) | (~bool(A)))), ((~(bool(A) & (~bool(B)))) <=> (bool(B) | (~bool(A))))), (((~(bool(A) & (~bool(B)))) | (impl(A, B) = phi(B))) <=> ((bool(B) | (~bool(A))) | (impl(A, B) = phi(B))))), rewrite(((bool(B) | (~bool(A))) | (impl(A, B) = phi(B))) <=> (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))), (((~(bool(A) & (~bool(B)))) | (impl(A, B) = phi(B))) <=> (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))))),
% 262.11/166.47 inference(bind,[status(th)],[])).
% 262.11/166.47 tff(657,plain,
% 262.11/166.47 (![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (impl(A, B) = phi(B))) <=> ![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))),
% 262.11/166.47 inference(quant_intro,[status(thm)],[656])).
% 262.11/166.47 tff(658,plain,
% 262.11/166.47 (![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (impl(A, B) = phi(B))) <=> ![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (impl(A, B) = phi(B)))),
% 262.11/166.47 inference(rewrite,[status(thm)],[])).
% 262.11/166.47 tff(659,plain,
% 262.11/166.47 (^[A: $i, B: $i] : rewrite(((bool(A) & (~bool(B))) => (impl(A, B) = phi(B))) <=> ((~(bool(A) & (~bool(B)))) | (impl(A, B) = phi(B))))),
% 262.11/166.47 inference(bind,[status(th)],[])).
% 262.11/166.47 tff(660,plain,
% 262.11/166.47 (![A: $i, B: $i] : ((bool(A) & (~bool(B))) => (impl(A, B) = phi(B))) <=> ![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (impl(A, B) = phi(B)))),
% 262.11/166.47 inference(quant_intro,[status(thm)],[659])).
% 262.11/166.47 tff(661,axiom,(![A: $i, B: $i] : ((bool(A) & (~bool(B))) => (impl(A, B) = phi(B)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','impl_axiom2')).
% 262.11/166.47 tff(662,plain,
% 262.11/166.47 (![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (impl(A, B) = phi(B)))),
% 262.11/166.47 inference(modus_ponens,[status(thm)],[661, 660])).
% 262.11/166.47 tff(663,plain,
% 262.11/166.47 (![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (impl(A, B) = phi(B)))),
% 262.11/166.47 inference(modus_ponens,[status(thm)],[662, 658])).
% 262.11/166.47 tff(664,plain,(
% 262.11/166.47 ![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (impl(A, B) = phi(B)))),
% 262.11/166.47 inference(skolemize,[status(sab)],[663])).
% 262.11/166.47 tff(665,plain,
% 262.11/166.47 (![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))),
% 262.11/166.47 inference(modus_ponens,[status(thm)],[664, 657])).
% 262.11/166.47 tff(666,plain,
% 262.11/166.47 (![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))),
% 262.11/166.47 inference(modus_ponens,[status(thm)],[665, 655])).
% 262.11/166.47 tff(667,plain,
% 262.11/166.47 (((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | (bool(Q!7) | (~bool(not1(false))) | (impl(not1(false), Q!7) = phi(Q!7)))) <=> ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | bool(Q!7) | (~bool(not1(false))) | (impl(not1(false), Q!7) = phi(Q!7)))),
% 262.11/166.47 inference(rewrite,[status(thm)],[])).
% 262.11/166.47 tff(668,plain,
% 262.11/166.47 ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | (bool(Q!7) | (~bool(not1(false))) | (impl(not1(false), Q!7) = phi(Q!7)))),
% 262.11/166.47 inference(quant_inst,[status(thm)],[])).
% 262.11/166.47 tff(669,plain,
% 262.11/166.47 ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | bool(Q!7) | (~bool(not1(false))) | (impl(not1(false), Q!7) = phi(Q!7))),
% 262.11/166.47 inference(modus_ponens,[status(thm)],[668, 667])).
% 262.11/166.47 tff(670,plain,
% 262.11/166.47 (bool(Q!7) | (impl(not1(false), Q!7) = phi(Q!7))),
% 262.11/166.47 inference(unit_resolution,[status(thm)],[669, 666, 81])).
% 262.11/166.47 tff(671,plain,
% 262.11/166.47 (impl(not1(false), Q!7) = phi(Q!7)),
% 262.11/166.47 inference(unit_resolution,[status(thm)],[670, 516])).
% 262.11/166.47 tff(672,plain,
% 262.11/166.47 (((Q!7 = false) | (Q!7 = not1(false))) | (~(Q!7 = not1(false)))),
% 262.11/166.47 inference(tautology,[status(thm)],[])).
% 262.11/166.47 tff(673,plain,
% 262.11/166.47 (~(Q!7 = not1(false))),
% 262.11/166.47 inference(unit_resolution,[status(thm)],[672, 627])).
% 262.11/166.47 tff(674,plain,
% 262.11/166.47 ((d(err) | (~(phi(err) = err))) | (~d(err))),
% 262.11/166.47 inference(tautology,[status(thm)],[])).
% 262.11/166.47 tff(675,plain,
% 262.11/166.47 (d(err) | (~(phi(err) = err))),
% 262.11/166.47 inference(unit_resolution,[status(thm)],[674, 322])).
% 262.11/166.47 tff(676,plain,
% 262.11/166.47 (((~![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)))))),
% 262.11/166.47 inference(rewrite,[status(thm)],[])).
% 262.11/166.47 tff(677,plain,
% 262.11/166.47 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(err)) | (~(phi(err) = err)))) | (~(d(err) | (~(phi(err) = err)))))),
% 262.11/166.47 inference(quant_inst,[status(thm)],[])).
% 262.11/166.47 tff(678,plain,
% 262.11/166.47 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(err)) | (~(phi(err) = err)))) | (~(d(err) | (~(phi(err) = err))))),
% 262.11/166.47 inference(modus_ponens,[status(thm)],[677, 676])).
% 262.11/166.47 tff(679,plain,
% 262.11/166.47 (~((~d(err)) | (~(phi(err) = err)))),
% 262.11/166.47 inference(unit_resolution,[status(thm)],[678, 17, 675])).
% 262.11/166.47 tff(680,plain,
% 262.11/166.47 (((~d(err)) | (~(phi(err) = err))) | (phi(err) = err)),
% 262.11/166.47 inference(tautology,[status(thm)],[])).
% 262.11/166.47 tff(681,plain,
% 262.11/166.47 (phi(err) = err),
% 262.11/166.47 inference(unit_resolution,[status(thm)],[680, 679])).
% 262.11/166.47 tff(682,plain,
% 262.11/166.47 (err = phi(err)),
% 262.11/166.47 inference(symmetry,[status(thm)],[681])).
% 262.11/166.47 tff(683,assumption,(impl(Q!7, err) = phi(Q!7)), introduced(assumption)).
% 262.11/166.47 tff(684,plain,
% 262.11/166.47 (phi(Q!7) = impl(Q!7, err)),
% 262.11/166.47 inference(symmetry,[status(thm)],[683])).
% 262.11/166.47 tff(685,plain,
% 262.11/166.47 ((phi(Q!7) = err) <=> (impl(Q!7, err) = phi(err))),
% 262.11/166.47 inference(monotonicity,[status(thm)],[684, 682])).
% 262.11/166.47 tff(686,plain,
% 262.11/166.47 ((impl(Q!7, err) = phi(err)) <=> (phi(Q!7) = err)),
% 262.11/166.47 inference(symmetry,[status(thm)],[685])).
% 262.11/166.47 tff(687,assumption,(impl(Q!7, false2) = not1(false)), introduced(assumption)).
% 262.11/166.47 tff(688,plain,
% 262.11/166.47 (phi(f7(P!6)) = false2),
% 262.11/166.47 inference(symmetry,[status(thm)],[607])).
% 262.11/166.47 tff(689,plain,
% 262.11/166.47 (phi(false) = phi(f7(P!6))),
% 262.11/166.47 inference(symmetry,[status(thm)],[606])).
% 262.11/166.47 tff(690,plain,
% 262.11/166.47 (false = false2),
% 262.11/166.47 inference(transitivity,[status(thm)],[559, 689, 688])).
% 262.11/166.47 tff(691,plain,
% 262.11/166.47 (impl(Q!7, false) = impl(Q!7, false2)),
% 262.11/166.47 inference(monotonicity,[status(thm)],[690])).
% 262.11/166.47 tff(692,assumption,(impl(Q!7, false) = phi(Q!7)), introduced(assumption)).
% 262.11/166.47 tff(693,plain,
% 262.11/166.47 (phi(Q!7) = impl(Q!7, false)),
% 262.11/166.47 inference(symmetry,[status(thm)],[692])).
% 262.11/166.47 tff(694,plain,
% 262.11/166.47 (impl(Q!7, err) = not1(false)),
% 262.11/166.47 inference(transitivity,[status(thm)],[683, 693, 691, 687])).
% 262.11/166.47 tff(695,plain,
% 262.11/166.47 ((impl(Q!7, err) = phi(err)) <=> (not1(false) = err)),
% 262.11/166.47 inference(monotonicity,[status(thm)],[694, 681])).
% 262.11/166.47 tff(696,plain,
% 262.11/166.47 ((not1(false) = err) <=> (impl(Q!7, err) = phi(err))),
% 262.11/166.47 inference(symmetry,[status(thm)],[695])).
% 262.11/166.47 tff(697,plain,
% 262.11/166.47 ((not1(false) = err) <=> (phi(Q!7) = err)),
% 262.11/166.47 inference(transitivity,[status(thm)],[696, 686])).
% 262.11/166.47 tff(698,plain,
% 262.11/166.47 ((~(not1(false) = err)) <=> (~(phi(Q!7) = err))),
% 262.11/166.47 inference(monotonicity,[status(thm)],[697])).
% 262.11/166.47 tff(699,plain,
% 262.11/166.47 (~(phi(Q!7) = err)),
% 262.11/166.47 inference(modus_ponens,[status(thm)],[248, 698])).
% 262.11/166.47 tff(700,plain,
% 262.11/166.47 (d(Q!7) | (~(phi(Q!7) = err))),
% 262.11/166.47 inference(unit_resolution,[status(thm)],[644, 699])).
% 262.11/166.47 tff(701,assumption,(impl(not1(false), Q!7) = phi(Q!7)), introduced(assumption)).
% 262.11/166.47 tff(702,plain,
% 262.11/166.47 (phi(Q!7) = impl(not1(false), Q!7)),
% 262.11/166.47 inference(symmetry,[status(thm)],[701])).
% 262.11/166.47 tff(703,plain,
% 262.11/166.47 ((phi(Q!7) = Q!7) <=> (impl(not1(false), Q!7) = Q!7)),
% 262.11/166.47 inference(monotonicity,[status(thm)],[702])).
% 262.11/166.47 tff(704,plain,
% 262.11/166.47 ((impl(not1(false), Q!7) = Q!7) <=> (phi(Q!7) = Q!7)),
% 262.11/166.47 inference(symmetry,[status(thm)],[703])).
% 262.11/166.47 tff(705,plain,
% 262.11/166.47 ((Q!7 = impl(not1(false), Q!7)) <=> (impl(not1(false), Q!7) = Q!7)),
% 262.11/166.47 inference(commutativity,[status(thm)],[])).
% 262.11/166.47 tff(706,plain,
% 262.11/166.47 (impl(Q!7, false2) = impl(Q!7, false)),
% 262.11/166.47 inference(symmetry,[status(thm)],[691])).
% 262.11/166.47 tff(707,plain,
% 262.11/166.47 (not1(false) = impl(Q!7, false2)),
% 262.11/166.47 inference(symmetry,[status(thm)],[687])).
% 262.11/166.47 tff(708,plain,
% 262.11/166.47 (not1(false) = impl(not1(false), Q!7)),
% 262.11/166.47 inference(transitivity,[status(thm)],[707, 706, 692, 702])).
% 262.11/166.47 tff(709,plain,
% 262.11/166.47 ((Q!7 = not1(false)) <=> (Q!7 = impl(not1(false), Q!7))),
% 262.11/166.47 inference(monotonicity,[status(thm)],[708])).
% 262.11/166.47 tff(710,plain,
% 262.11/166.47 ((Q!7 = not1(false)) <=> (impl(not1(false), Q!7) = Q!7)),
% 262.11/166.47 inference(transitivity,[status(thm)],[709, 705])).
% 262.11/166.47 tff(711,plain,
% 262.11/166.47 ((Q!7 = not1(false)) <=> (phi(Q!7) = Q!7)),
% 262.11/166.47 inference(transitivity,[status(thm)],[710, 704])).
% 262.11/166.47 tff(712,plain,
% 262.11/166.47 ((~(Q!7 = not1(false))) <=> (~(phi(Q!7) = Q!7))),
% 262.11/166.47 inference(monotonicity,[status(thm)],[711])).
% 262.11/166.47 tff(713,assumption,(~(Q!7 = not1(false))), introduced(assumption)).
% 262.11/166.47 tff(714,plain,
% 262.11/166.47 (~(phi(Q!7) = Q!7)),
% 262.11/166.47 inference(modus_ponens,[status(thm)],[713, 712])).
% 262.11/166.47 tff(715,plain,
% 262.11/166.47 ((~d(Q!7)) | (~(phi(Q!7) = Q!7))),
% 262.11/166.47 inference(unit_resolution,[status(thm)],[638, 714])).
% 262.11/166.47 tff(716,plain,
% 262.11/166.47 ($false),
% 262.11/166.47 inference(unit_resolution,[status(thm)],[649, 715, 700])).
% 262.11/166.48 tff(717,plain,((~(impl(Q!7, false2) = not1(false))) | (Q!7 = not1(false)) | (~(impl(not1(false), Q!7) = phi(Q!7))) | (~(impl(Q!7, false) = phi(Q!7))) | (~(impl(Q!7, err) = phi(Q!7)))), inference(lemma,lemma(discharge,[]))).
% 262.11/166.48 tff(718,plain,
% 262.11/166.48 (~(impl(Q!7, false2) = not1(false))),
% 262.11/166.48 inference(unit_resolution,[status(thm)],[717, 673, 671, 521, 527])).
% 262.11/166.48 tff(719,plain,
% 262.11/166.48 ((~((impl(Q!7, false2) = false) | (impl(Q!7, false2) = not1(false)))) | (impl(Q!7, false2) = false) | (impl(Q!7, false2) = not1(false))),
% 262.11/166.48 inference(tautology,[status(thm)],[])).
% 262.11/166.48 tff(720,plain,
% 262.11/166.48 (~((impl(Q!7, false2) = false) | (impl(Q!7, false2) = not1(false)))),
% 262.11/166.48 inference(unit_resolution,[status(thm)],[719, 718, 653])).
% 262.11/166.48 tff(721,assumption,(~(bool(impl(Q!7, false2)) <=> ((impl(Q!7, false2) = false) | (impl(Q!7, false2) = not1(false))))), introduced(assumption)).
% 262.11/166.48 tff(722,plain,
% 262.11/166.48 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(impl(Q!7, false2)) <=> ((impl(Q!7, false2) = false) | (impl(Q!7, false2) = not1(false))))),
% 262.11/166.48 inference(quant_inst,[status(thm)],[])).
% 262.11/166.48 tff(723,plain,
% 262.11/166.48 ($false),
% 262.11/166.48 inference(unit_resolution,[status(thm)],[722, 229, 721])).
% 262.11/166.48 tff(724,plain,(bool(impl(Q!7, false2)) <=> ((impl(Q!7, false2) = false) | (impl(Q!7, false2) = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 262.11/166.48 tff(725,plain,
% 262.11/166.48 ((~(bool(impl(Q!7, false2)) <=> ((impl(Q!7, false2) = false) | (impl(Q!7, false2) = not1(false))))) | (~bool(impl(Q!7, false2))) | ((impl(Q!7, false2) = false) | (impl(Q!7, false2) = not1(false)))),
% 262.11/166.48 inference(tautology,[status(thm)],[])).
% 262.11/166.48 tff(726,plain,
% 262.11/166.48 ((~bool(impl(Q!7, false2))) | ((impl(Q!7, false2) = false) | (impl(Q!7, false2) = not1(false)))),
% 262.11/166.48 inference(unit_resolution,[status(thm)],[725, 724])).
% 262.11/166.48 tff(727,plain,
% 262.11/166.48 (~bool(impl(Q!7, false2))),
% 262.11/166.48 inference(unit_resolution,[status(thm)],[726, 720])).
% 262.11/166.48 tff(728,plain,
% 262.11/166.48 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(Q!7, false2)) | (impl(impl(Q!7, false2), false) = phi(impl(Q!7, false2))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(Q!7, false2)) | (impl(impl(Q!7, false2), false) = phi(impl(Q!7, false2))))),
% 262.11/166.48 inference(rewrite,[status(thm)],[])).
% 262.11/166.48 tff(729,plain,
% 262.11/166.48 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(Q!7, false2)) | (impl(impl(Q!7, false2), false) = phi(impl(Q!7, false2))))),
% 262.11/166.48 inference(quant_inst,[status(thm)],[])).
% 262.11/166.48 tff(730,plain,
% 262.11/166.48 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(Q!7, false2)) | (impl(impl(Q!7, false2), false) = phi(impl(Q!7, false2)))),
% 262.11/166.48 inference(modus_ponens,[status(thm)],[729, 728])).
% 262.11/166.48 tff(731,plain,
% 262.11/166.48 (bool(impl(Q!7, false2)) | (impl(impl(Q!7, false2), false) = phi(impl(Q!7, false2)))),
% 262.11/166.48 inference(unit_resolution,[status(thm)],[730, 188])).
% 262.11/166.48 tff(732,plain,
% 262.11/166.48 (impl(impl(Q!7, false2), false) = phi(impl(Q!7, false2))),
% 262.11/166.48 inference(unit_resolution,[status(thm)],[731, 727])).
% 262.11/166.48 tff(733,plain,
% 262.11/166.48 (phi(impl(Q!7, false2)) = impl(impl(Q!7, false2), false)),
% 262.11/166.48 inference(symmetry,[status(thm)],[732])).
% 262.11/166.48 tff(734,plain,
% 262.11/166.48 (phi(impl(Q!7, false2)) = phi(impl(Q!7, false))),
% 262.11/166.48 inference(monotonicity,[status(thm)],[611])).
% 262.11/166.48 tff(735,plain,
% 262.11/166.48 (phi(impl(Q!7, false)) = phi(impl(Q!7, false2))),
% 262.11/166.48 inference(symmetry,[status(thm)],[734])).
% 262.11/166.48 tff(736,plain,
% 262.11/166.48 (phi(impl(Q!7, false)) = impl(impl(Q!7, false2), false2)),
% 262.11/166.48 inference(transitivity,[status(thm)],[735, 733, 618, 614])).
% 262.11/166.48 tff(737,plain,
% 262.11/166.48 (d(phi(impl(Q!7, false))) <=> d(impl(impl(Q!7, false2), false2))),
% 262.11/166.48 inference(monotonicity,[status(thm)],[736])).
% 262.11/166.48 tff(738,plain,
% 262.11/166.48 (d(impl(impl(Q!7, false2), false2)) <=> d(phi(impl(Q!7, false)))),
% 262.11/166.48 inference(symmetry,[status(thm)],[737])).
% 262.11/166.48 tff(739,plain,
% 262.11/166.48 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(Q!7) | (impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = phi(Q!7)))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(Q!7) | (impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = phi(Q!7)))),
% 262.11/166.48 inference(rewrite,[status(thm)],[])).
% 262.11/166.48 tff(740,plain,
% 262.11/166.48 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(Q!7) | (impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = phi(Q!7)))),
% 262.11/166.48 inference(quant_inst,[status(thm)],[])).
% 262.11/166.48 tff(741,plain,
% 262.11/166.48 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(Q!7) | (impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = phi(Q!7))),
% 262.11/166.48 inference(modus_ponens,[status(thm)],[740, 739])).
% 262.11/166.48 tff(742,plain,
% 262.11/166.48 (bool(Q!7) | (impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = phi(Q!7))),
% 262.11/166.48 inference(unit_resolution,[status(thm)],[741, 188])).
% 262.11/166.48 tff(743,plain,
% 262.11/166.48 (impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = phi(Q!7)),
% 262.11/166.48 inference(unit_resolution,[status(thm)],[742, 516])).
% 262.11/166.48 tff(744,plain,
% 262.11/166.48 (impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = impl(Q!7, false)),
% 262.11/166.48 inference(transitivity,[status(thm)],[743, 522])).
% 262.11/166.48 tff(745,plain,
% 262.11/166.48 (phi(impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(impl(Q!7, false))),
% 262.11/166.48 inference(monotonicity,[status(thm)],[744])).
% 262.11/166.48 tff(746,plain,
% 262.11/166.48 ((~![X: $i] : ((prop(X) = false) <=> (~bool(X)))) | ((prop(Q!7) = false) <=> (~bool(Q!7)))),
% 262.11/166.48 inference(quant_inst,[status(thm)],[])).
% 262.11/166.48 tff(747,plain,
% 262.11/166.48 ((prop(Q!7) = false) <=> (~bool(Q!7))),
% 262.11/166.48 inference(unit_resolution,[status(thm)],[746, 376])).
% 262.11/166.48 tff(748,plain,
% 262.11/166.48 ((~((prop(Q!7) = false) <=> (~bool(Q!7)))) | (prop(Q!7) = false) | bool(Q!7)),
% 262.11/166.48 inference(tautology,[status(thm)],[])).
% 262.11/166.48 tff(749,plain,
% 262.11/166.48 ((prop(Q!7) = false) | bool(Q!7)),
% 262.11/166.48 inference(unit_resolution,[status(thm)],[748, 747])).
% 262.11/166.48 tff(750,plain,
% 262.11/166.48 (prop(Q!7) = false),
% 262.11/166.48 inference(unit_resolution,[status(thm)],[749, 516])).
% 262.11/166.48 tff(751,assumption,(impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = phi(Q!7)), introduced(assumption)).
% 262.11/166.48 tff(752,plain,
% 262.11/166.48 (phi(Q!7) = impl(Q!7, tptp_fun_R_0(Q!7, P!8))),
% 262.11/166.48 inference(symmetry,[status(thm)],[751])).
% 262.11/166.48 tff(753,plain,
% 262.11/166.48 (impl(Q!7, false) = impl(Q!7, tptp_fun_R_0(Q!7, P!8))),
% 262.11/166.48 inference(transitivity,[status(thm)],[692, 752])).
% 262.11/166.48 tff(754,plain,
% 262.11/166.48 (impl(P!8, impl(Q!7, false)) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.11/166.48 inference(monotonicity,[status(thm)],[753])).
% 262.11/166.48 tff(755,plain,
% 262.11/166.48 (impl(impl(P!8, impl(Q!7, false)), false) = impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), false2)),
% 262.11/166.48 inference(monotonicity,[status(thm)],[754, 690])).
% 262.11/166.48 tff(756,plain,
% 262.11/166.48 (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = impl(P!8, impl(Q!7, false))),
% 262.11/166.48 inference(symmetry,[status(thm)],[754])).
% 262.11/166.48 tff(757,plain,
% 262.11/166.48 (impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), false) = impl(impl(P!8, impl(Q!7, false)), false)),
% 262.11/166.48 inference(monotonicity,[status(thm)],[756])).
% 262.11/166.48 tff(758,plain,
% 262.11/166.48 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) | (impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), false) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) | (impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), false) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))),
% 262.11/166.48 inference(rewrite,[status(thm)],[])).
% 262.11/166.48 tff(759,plain,
% 262.11/166.48 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) | (impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), false) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))),
% 262.11/166.48 inference(quant_inst,[status(thm)],[])).
% 262.11/166.48 tff(760,plain,
% 262.11/166.48 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) | (impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), false) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))),
% 262.11/166.48 inference(modus_ponens,[status(thm)],[759, 758])).
% 262.11/166.48 tff(761,plain,
% 262.11/166.48 (bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) | (impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), false) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))),
% 262.11/166.48 inference(unit_resolution,[status(thm)],[760, 188])).
% 262.11/166.48 tff(762,plain,
% 262.11/166.48 (impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), false) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.11/166.48 inference(unit_resolution,[status(thm)],[761, 258])).
% 262.11/166.48 tff(763,plain,
% 262.11/166.48 (phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), false)),
% 262.11/166.49 inference(symmetry,[status(thm)],[762])).
% 262.11/166.49 tff(764,plain,
% 262.11/166.49 ((d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) | (~(phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = err))) | (~d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))),
% 262.11/166.49 inference(tautology,[status(thm)],[])).
% 262.11/166.49 tff(765,plain,
% 262.11/166.49 (d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) | (~(phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = err))),
% 262.11/166.49 inference(unit_resolution,[status(thm)],[764, 420])).
% 262.11/166.49 tff(766,plain,
% 262.11/166.49 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~(phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))) | (~(d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) | (~(phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~(phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))) | (~(d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) | (~(phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = err)))))),
% 262.11/166.49 inference(rewrite,[status(thm)],[])).
% 262.11/166.49 tff(767,plain,
% 262.11/166.49 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~(phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))) | (~(d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) | (~(phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = err)))))),
% 262.11/166.49 inference(quant_inst,[status(thm)],[])).
% 262.11/166.49 tff(768,plain,
% 262.11/166.49 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~(phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))) | (~(d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) | (~(phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = err))))),
% 262.11/166.49 inference(modus_ponens,[status(thm)],[767, 766])).
% 262.11/166.49 tff(769,plain,
% 262.11/166.49 (~((~d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~(phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))),
% 262.11/166.49 inference(unit_resolution,[status(thm)],[768, 17, 765])).
% 262.11/166.49 tff(770,plain,
% 262.11/166.49 (((~d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~(phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))) | (phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.11/166.49 inference(tautology,[status(thm)],[])).
% 262.11/166.49 tff(771,plain,
% 262.11/166.49 (phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.11/166.49 inference(unit_resolution,[status(thm)],[770, 769])).
% 262.11/166.49 tff(772,plain,
% 262.11/166.49 (impl(impl(P!8, impl(Q!7, false)), false) = impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), false)),
% 262.11/166.49 inference(symmetry,[status(thm)],[757])).
% 262.11/166.49 tff(773,plain,
% 262.11/166.49 (impl(impl(P!8, impl(Q!7, false)), false) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.11/166.49 inference(transitivity,[status(thm)],[772, 762, 771])).
% 262.11/166.49 tff(774,plain,
% 262.11/166.49 (phi(impl(impl(P!8, impl(Q!7, false)), false)) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.11/166.49 inference(monotonicity,[status(thm)],[773])).
% 262.11/166.49 tff(775,plain,
% 262.11/166.49 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), impl(impl(P!8, impl(Q!7, false)), false)) = phi(impl(impl(P!8, impl(Q!7, false)), false)))),
% 262.11/166.49 inference(quant_inst,[status(thm)],[])).
% 262.11/166.49 tff(776,plain,
% 262.11/166.49 (lazy_impl(not1(false), impl(impl(P!8, impl(Q!7, false)), false)) = phi(impl(impl(P!8, impl(Q!7, false)), false))),
% 262.11/166.49 inference(unit_resolution,[status(thm)],[775, 33])).
% 262.11/166.49 tff(777,plain,
% 262.11/166.49 (lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)) = lazy_impl(not1(false), impl(impl(P!8, impl(Q!7, false)), false))),
% 262.11/166.49 inference(monotonicity,[status(thm)],[149])).
% 262.11/166.49 tff(778,plain,
% 262.11/166.49 (lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)) = impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), false2)),
% 262.11/166.49 inference(transitivity,[status(thm)],[777, 776, 774, 763, 757, 755])).
% 262.11/166.49 tff(779,plain,
% 262.11/166.49 (bool(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) <=> bool(impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), false2))),
% 262.11/166.49 inference(monotonicity,[status(thm)],[778])).
% 262.11/166.49 tff(780,plain,
% 262.11/166.49 (bool(impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), false2)) <=> bool(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)))),
% 262.11/166.49 inference(symmetry,[status(thm)],[779])).
% 262.11/166.49 tff(781,plain,
% 262.11/166.49 ((~bool(impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), false2))) <=> (~bool(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))))),
% 262.11/166.49 inference(monotonicity,[status(thm)],[780])).
% 262.11/166.49 tff(782,plain,
% 262.11/166.49 (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.11/166.49 inference(symmetry,[status(thm)],[771])).
% 262.11/166.49 tff(783,plain,
% 262.11/166.49 (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), false2)),
% 262.11/166.49 inference(transitivity,[status(thm)],[782, 763, 757, 755])).
% 262.11/166.49 tff(784,plain,
% 262.11/166.49 (bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) <=> bool(impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), false2))),
% 262.11/166.49 inference(monotonicity,[status(thm)],[783])).
% 262.11/166.49 tff(785,plain,
% 262.11/166.49 ((~bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) <=> (~bool(impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), false2)))),
% 262.11/166.49 inference(monotonicity,[status(thm)],[784])).
% 262.11/166.49 tff(786,plain,
% 262.11/166.49 (~bool(impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), false2))),
% 262.11/166.49 inference(modus_ponens,[status(thm)],[258, 785])).
% 262.11/166.49 tff(787,plain,
% 262.11/166.49 (~bool(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)))),
% 262.11/166.49 inference(modus_ponens,[status(thm)],[786, 781])).
% 262.11/166.49 tff(788,plain,
% 262.11/166.49 (((~![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(impl(P!8, impl(Q!7, false)), false)), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))) <=> ((~((~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | (~bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = not1(false))))) | (~(d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))))))))) <=> ((~![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(impl(P!8, impl(Q!7, false)), false)), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))) <=> ((~((~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | (~bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = not1(false))))) | (~(d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))))))))),
% 262.11/166.50 inference(rewrite,[status(thm)],[])).
% 262.11/166.50 tff(789,plain,
% 262.11/166.50 ((forallprefers(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))) <=> ((~(d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | (~bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = not1(false))))))) <=> (forallprefers(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))) <=> ((~((~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | (~bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = not1(false))))) | (~(d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))))))))),
% 262.11/166.50 inference(rewrite,[status(thm)],[])).
% 262.11/166.50 tff(790,plain,
% 262.11/166.50 (((~![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(impl(P!8, impl(Q!7, false)), false)), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))) <=> ((~(d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | (~bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = 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(impl(P!8, impl(Q!7, false)), false)), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))) <=> ((~((~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | (~bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = not1(false))))) | (~(d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))))))))),
% 262.16/166.50 inference(monotonicity,[status(thm)],[789])).
% 262.16/166.50 tff(791,plain,
% 262.16/166.50 (((~![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(impl(P!8, impl(Q!7, false)), false)), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))) <=> ((~(d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | (~bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = 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(impl(P!8, impl(Q!7, false)), false)), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))) <=> ((~((~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | (~bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = not1(false))))) | (~(d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))))))))),
% 262.16/166.50 inference(transitivity,[status(thm)],[790, 788])).
% 262.16/166.50 tff(792,plain,
% 262.16/166.50 ((~![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(impl(P!8, impl(Q!7, false)), false)), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))) <=> ((~(d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | (~bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = not1(false)))))))),
% 262.16/166.50 inference(quant_inst,[status(thm)],[])).
% 262.16/166.50 tff(793,plain,
% 262.16/166.50 ((~![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(impl(P!8, impl(Q!7, false)), false)), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))) <=> ((~((~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | (~bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = not1(false))))) | (~(d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))))))))),
% 262.16/166.50 inference(modus_ponens,[status(thm)],[792, 791])).
% 262.16/166.50 tff(794,plain,
% 262.16/166.50 (forallprefers(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))) <=> ((~((~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | (~bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = not1(false))))) | (~(d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))))))),
% 262.16/166.50 inference(unit_resolution,[status(thm)],[793, 493])).
% 262.16/166.50 tff(795,plain,
% 262.16/166.50 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(P!8, Q!7, false) = lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)))),
% 262.16/166.50 inference(quant_inst,[status(thm)],[])).
% 262.16/166.50 tff(796,plain,
% 262.16/166.50 (f1(P!8, Q!7, false) = lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))),
% 262.16/166.50 inference(unit_resolution,[status(thm)],[795, 159])).
% 262.16/166.50 tff(797,plain,
% 262.16/166.50 (lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)) = f1(P!8, Q!7, false)),
% 262.16/166.50 inference(symmetry,[status(thm)],[796])).
% 262.16/166.50 tff(798,plain,
% 262.16/166.50 (forallprefers(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))) <=> forallprefers(f1(P!8, Q!7, false), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.16/166.50 inference(monotonicity,[status(thm)],[797, 177])).
% 262.16/166.50 tff(799,plain,
% 262.16/166.50 (forallprefers(f1(P!8, Q!7, false), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))) <=> forallprefers(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))),
% 262.16/166.50 inference(symmetry,[status(thm)],[798])).
% 262.16/166.50 tff(800,plain,
% 262.16/166.50 ((~forallprefers(f1(P!8, Q!7, false), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))) <=> (~forallprefers(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))))),
% 262.16/166.51 inference(monotonicity,[status(thm)],[799])).
% 262.16/166.51 tff(801,plain,
% 262.16/166.51 ((~![R1: $i] : (~forallprefers(f1(P!8, Q!7, R1), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~forallprefers(f1(P!8, Q!7, false), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.16/166.51 inference(quant_inst,[status(thm)],[])).
% 262.16/166.51 tff(802,plain,
% 262.16/166.51 (~forallprefers(f1(P!8, Q!7, false), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.16/166.51 inference(unit_resolution,[status(thm)],[801, 474])).
% 262.16/166.51 tff(803,plain,
% 262.16/166.51 (~forallprefers(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))),
% 262.16/166.51 inference(modus_ponens,[status(thm)],[802, 800])).
% 262.16/166.51 tff(804,plain,
% 262.16/166.51 ((~(forallprefers(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))) <=> ((~((~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | (~bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = not1(false))))) | (~(d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))))))))) | forallprefers(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))) | (~((~((~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | (~bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = not1(false))))) | (~(d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))))))))),
% 262.16/166.51 inference(tautology,[status(thm)],[])).
% 262.16/166.51 tff(805,plain,
% 262.16/166.51 (~((~((~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | (~bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = not1(false))))) | (~(d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))))))),
% 262.16/166.51 inference(unit_resolution,[status(thm)],[804, 803, 794])).
% 262.16/166.51 tff(806,plain,
% 262.16/166.51 (((~((~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | (~bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = not1(false))))) | (~(d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))))))) | ((~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | (~bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)))))),
% 262.16/166.51 inference(tautology,[status(thm)],[])).
% 262.16/166.51 tff(807,plain,
% 262.16/166.51 ((~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | (~bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))))),
% 262.16/166.51 inference(unit_resolution,[status(thm)],[806, 805])).
% 262.16/166.51 tff(808,plain,
% 262.16/166.51 (d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))) <=> d(f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.16/166.51 inference(monotonicity,[status(thm)],[177])).
% 262.16/166.51 tff(809,plain,
% 262.16/166.51 (d(f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))) <=> d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))),
% 262.16/166.51 inference(symmetry,[status(thm)],[808])).
% 262.16/166.51 tff(810,plain,
% 262.16/166.51 ((~![B: $i] : (lazy_impl(false, B) = not1(false))) | (lazy_impl(false, impl(impl(P!8, impl(not1(false), Q!7)), Q!7)) = not1(false))),
% 262.16/166.51 inference(quant_inst,[status(thm)],[])).
% 262.16/166.51 tff(811,plain,
% 262.16/166.51 (lazy_impl(false, impl(impl(P!8, impl(not1(false), Q!7)), Q!7)) = not1(false)),
% 262.16/166.51 inference(unit_resolution,[status(thm)],[810, 393])).
% 262.16/166.51 tff(812,assumption,(prop(Q!7) = false), introduced(assumption)).
% 262.16/166.51 tff(813,plain,
% 262.16/166.51 (lazy_impl(prop(Q!7), impl(impl(P!8, impl(not1(false), Q!7)), Q!7)) = lazy_impl(false, impl(impl(P!8, impl(not1(false), Q!7)), Q!7))),
% 262.16/166.51 inference(monotonicity,[status(thm)],[812])).
% 262.16/166.51 tff(814,plain,
% 262.16/166.51 (impl(not1(false), Q!7) = impl(Q!7, tptp_fun_R_0(Q!7, P!8))),
% 262.16/166.51 inference(transitivity,[status(thm)],[701, 752])).
% 262.16/166.51 tff(815,plain,
% 262.16/166.51 (impl(P!8, impl(not1(false), Q!7)) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.16/166.51 inference(monotonicity,[status(thm)],[814])).
% 262.16/166.51 tff(816,plain,
% 262.16/166.51 (impl(impl(P!8, impl(not1(false), Q!7)), Q!7) = impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), Q!7)),
% 262.16/166.51 inference(monotonicity,[status(thm)],[815])).
% 262.16/166.51 tff(817,plain,
% 262.16/166.51 (impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), Q!7) = impl(impl(P!8, impl(not1(false), Q!7)), Q!7)),
% 262.16/166.51 inference(symmetry,[status(thm)],[816])).
% 262.16/166.51 tff(818,plain,
% 262.16/166.51 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) | (impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), Q!7) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) | (impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), Q!7) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))),
% 262.16/166.51 inference(rewrite,[status(thm)],[])).
% 262.16/166.51 tff(819,plain,
% 262.16/166.51 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) | (impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), Q!7) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))),
% 262.16/166.51 inference(quant_inst,[status(thm)],[])).
% 262.16/166.52 tff(820,plain,
% 262.16/166.52 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) | (impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), Q!7) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))),
% 262.16/166.52 inference(modus_ponens,[status(thm)],[819, 818])).
% 262.16/166.52 tff(821,plain,
% 262.16/166.52 (bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) | (impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), Q!7) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))),
% 262.16/166.52 inference(unit_resolution,[status(thm)],[820, 188])).
% 262.16/166.52 tff(822,plain,
% 262.16/166.52 (impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), Q!7) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.16/166.52 inference(unit_resolution,[status(thm)],[821, 258])).
% 262.16/166.52 tff(823,plain,
% 262.16/166.52 (phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), Q!7)),
% 262.16/166.52 inference(symmetry,[status(thm)],[822])).
% 262.16/166.52 tff(824,plain,
% 262.16/166.52 (impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)) = impl(impl(P!8, impl(not1(false), Q!7)), Q!7)),
% 262.16/166.52 inference(transitivity,[status(thm)],[263, 823, 817])).
% 262.16/166.52 tff(825,plain,
% 262.16/166.52 (false = prop(Q!7)),
% 262.16/166.52 inference(symmetry,[status(thm)],[812])).
% 262.16/166.52 tff(826,assumption,(impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), false) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))), introduced(assumption)).
% 262.16/166.52 tff(827,plain,
% 262.16/166.52 (phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), false)),
% 262.16/166.52 inference(symmetry,[status(thm)],[826])).
% 262.16/166.52 tff(828,plain,
% 262.16/166.52 ((~((~d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~(phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))) | (~(d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) | (~(phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = err))))),
% 262.16/166.52 inference(unit_resolution,[status(thm)],[768, 17])).
% 262.16/166.52 tff(829,plain,
% 262.16/166.52 (~((~d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~(phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))),
% 262.16/166.52 inference(unit_resolution,[status(thm)],[828, 765])).
% 262.16/166.52 tff(830,plain,
% 262.16/166.52 (phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.16/166.52 inference(unit_resolution,[status(thm)],[770, 829])).
% 262.16/166.52 tff(831,plain,
% 262.16/166.52 (impl(impl(P!8, impl(Q!7, false)), false) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.16/166.52 inference(transitivity,[status(thm)],[772, 826, 830])).
% 262.16/166.52 tff(832,plain,
% 262.16/166.52 (phi(impl(impl(P!8, impl(Q!7, false)), false)) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.16/166.52 inference(monotonicity,[status(thm)],[831])).
% 262.16/166.52 tff(833,plain,
% 262.16/166.52 (impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)) = impl(impl(P!8, impl(Q!7, false)), false)),
% 262.16/166.52 inference(transitivity,[status(thm)],[340, 827, 757])).
% 262.16/166.52 tff(834,plain,
% 262.16/166.52 (prop(tptp_fun_R_0(Q!7, P!8)) = prop(false)),
% 262.16/166.52 inference(transitivity,[status(thm)],[342, 150])).
% 262.16/166.52 tff(835,plain,
% 262.16/166.52 (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))),
% 262.16/166.52 inference(monotonicity,[status(thm)],[834, 833])).
% 262.16/166.52 tff(836,plain,
% 262.16/166.52 (f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)) = impl(impl(P!8, impl(Q!7, false)), false)),
% 262.16/166.52 inference(transitivity,[status(thm)],[176, 835, 777, 776, 832, 827, 757])).
% 262.16/166.52 tff(837,plain,
% 262.16/166.52 (phi(f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(impl(impl(P!8, impl(Q!7, false)), false))),
% 262.16/166.52 inference(monotonicity,[status(thm)],[836])).
% 262.16/166.52 tff(838,plain,
% 262.16/166.52 (phi(impl(impl(P!8, impl(Q!7, false)), false)) = phi(f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.16/166.52 inference(symmetry,[status(thm)],[837])).
% 262.16/166.52 tff(839,plain,
% 262.16/166.52 (phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = phi(impl(impl(P!8, impl(Q!7, false)), false))),
% 262.16/166.52 inference(symmetry,[status(thm)],[832])).
% 262.16/166.52 tff(840,plain,
% 262.16/166.52 (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.16/166.52 inference(symmetry,[status(thm)],[830])).
% 262.16/166.52 tff(841,plain,
% 262.16/166.52 (and1(P!8, Q!7) = and2(P!8, Q!7)),
% 262.16/166.52 inference(transitivity,[status(thm)],[278, 194, 840, 839, 838, 296])).
% 262.16/166.52 tff(842,plain,
% 262.16/166.52 ($false),
% 262.16/166.52 inference(unit_resolution,[status(thm)],[361, 841])).
% 262.16/166.52 tff(843,plain,(bool(P!8) | (~(impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), false) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))) | (~(impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = phi(Q!7))) | (~(impl(Q!7, false) = phi(Q!7))) | (~(impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))) | (~(prop(tptp_fun_R_0(Q!7, P!8)) = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 262.16/166.52 tff(844,plain,
% 262.16/166.52 (~(prop(tptp_fun_R_0(Q!7, P!8)) = not1(false))),
% 262.16/166.52 inference(unit_resolution,[status(thm)],[843, 762, 751, 692, 178, 263])).
% 262.16/166.52 tff(845,plain,
% 262.16/166.52 (~bool(tptp_fun_R_0(Q!7, P!8))),
% 262.16/166.52 inference(unit_resolution,[status(thm)],[368, 844])).
% 262.16/166.52 tff(846,plain,
% 262.16/166.52 (prop(tptp_fun_R_0(Q!7, P!8)) = false),
% 262.16/166.52 inference(unit_resolution,[status(thm)],[380, 845])).
% 262.16/166.52 tff(847,plain,
% 262.16/166.52 (prop(tptp_fun_R_0(Q!7, P!8)) = prop(Q!7)),
% 262.16/166.52 inference(transitivity,[status(thm)],[846, 825])).
% 262.16/166.52 tff(848,plain,
% 262.16/166.52 (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(prop(Q!7), impl(impl(P!8, impl(not1(false), Q!7)), Q!7))),
% 262.16/166.52 inference(monotonicity,[status(thm)],[847, 824])).
% 262.16/166.52 tff(849,plain,
% 262.16/166.52 (f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)) = not1(false)),
% 262.16/166.52 inference(transitivity,[status(thm)],[176, 848, 813, 811])).
% 262.16/166.52 tff(850,plain,
% 262.16/166.52 (d(f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))) <=> d(not1(false))),
% 262.16/166.52 inference(monotonicity,[status(thm)],[849])).
% 262.16/166.52 tff(851,plain,
% 262.16/166.52 (d(not1(false)) <=> d(f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.16/166.52 inference(symmetry,[status(thm)],[850])).
% 262.16/166.52 tff(852,plain,
% 262.16/166.52 (d(not1(false)) <=> d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))),
% 262.16/166.52 inference(transitivity,[status(thm)],[851, 809])).
% 262.16/166.52 tff(853,plain,
% 262.16/166.52 (d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))),
% 262.16/166.52 inference(modus_ponens,[status(thm)],[41, 852])).
% 262.16/166.52 tff(854,plain,
% 262.16/166.52 (bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))) <=> bool(f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.16/166.52 inference(monotonicity,[status(thm)],[177])).
% 262.16/166.52 tff(855,plain,
% 262.16/166.52 (bool(f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))) <=> bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))),
% 262.16/166.52 inference(symmetry,[status(thm)],[854])).
% 262.16/166.52 tff(856,plain,
% 262.16/166.52 (bool(f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))) <=> bool(not1(false))),
% 262.16/166.52 inference(monotonicity,[status(thm)],[849])).
% 262.16/166.52 tff(857,plain,
% 262.16/166.52 (bool(not1(false)) <=> bool(f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.16/166.52 inference(symmetry,[status(thm)],[856])).
% 262.16/166.52 tff(858,plain,
% 262.16/166.52 (bool(not1(false)) <=> bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))),
% 262.16/166.52 inference(transitivity,[status(thm)],[857, 855])).
% 262.16/166.52 tff(859,plain,
% 262.16/166.52 (bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))),
% 262.16/166.52 inference(modus_ponens,[status(thm)],[81, 858])).
% 262.16/166.52 tff(860,plain,
% 262.16/166.52 (((~((~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | (~bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = not1(false))))) | (~(d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))))))) | (d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))))),
% 262.16/166.52 inference(tautology,[status(thm)],[])).
% 262.16/166.52 tff(861,plain,
% 262.16/166.52 (d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))))),
% 262.16/166.52 inference(unit_resolution,[status(thm)],[860, 805])).
% 262.16/166.52 tff(862,plain,
% 262.16/166.52 ((~(d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))))) | d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))))),
% 262.16/166.52 inference(tautology,[status(thm)],[])).
% 262.16/166.52 tff(863,plain,
% 262.16/166.52 (d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)))),
% 262.16/166.52 inference(unit_resolution,[status(thm)],[862, 853, 861])).
% 262.16/166.52 tff(864,plain,
% 262.16/166.52 ((~((~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | (~bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)))))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | (~bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))))),
% 262.16/166.52 inference(tautology,[status(thm)],[])).
% 262.16/166.52 tff(865,plain,
% 262.16/166.52 (bool(lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)))),
% 262.16/166.52 inference(unit_resolution,[status(thm)],[864, 863, 859, 853, 807])).
% 262.16/166.52 tff(866,plain,
% 262.16/166.52 ($false),
% 262.16/166.52 inference(unit_resolution,[status(thm)],[865, 787])).
% 262.16/166.52 tff(867,plain,(bool(P!8) | (~(impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = phi(Q!7))) | (~(impl(Q!7, false) = phi(Q!7))) | (~(prop(Q!7) = false)) | (~(impl(not1(false), Q!7) = phi(Q!7)))), inference(lemma,lemma(discharge,[]))).
% 262.16/166.52 tff(868,plain,
% 262.16/166.52 (bool(P!8)),
% 262.16/166.52 inference(unit_resolution,[status(thm)],[867, 743, 521, 750, 671])).
% 262.16/166.52 tff(869,plain,
% 262.16/166.52 (bool(impl(Q!7, false2)) <=> bool(impl(Q!7, false))),
% 262.16/166.52 inference(monotonicity,[status(thm)],[706])).
% 262.16/166.52 tff(870,plain,
% 262.16/166.52 (bool(impl(Q!7, false)) <=> bool(impl(Q!7, false2))),
% 262.16/166.52 inference(symmetry,[status(thm)],[869])).
% 262.16/166.52 tff(871,plain,
% 262.16/166.52 (impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = impl(Q!7, false)),
% 262.16/166.52 inference(transitivity,[status(thm)],[751, 693])).
% 262.16/166.52 tff(872,plain,
% 262.16/166.52 (bool(impl(Q!7, tptp_fun_R_0(Q!7, P!8))) <=> bool(impl(Q!7, false))),
% 262.16/166.52 inference(monotonicity,[status(thm)],[871])).
% 262.16/166.52 tff(873,plain,
% 262.16/166.52 (bool(impl(Q!7, tptp_fun_R_0(Q!7, P!8))) <=> bool(impl(Q!7, false2))),
% 262.16/166.52 inference(transitivity,[status(thm)],[872, 870])).
% 262.16/166.52 tff(874,assumption,(bool(impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), introduced(assumption)).
% 262.16/166.52 tff(875,plain,
% 262.16/166.52 (bool(impl(Q!7, false2))),
% 262.16/166.52 inference(modus_ponens,[status(thm)],[874, 873])).
% 262.16/166.52 tff(876,assumption,(~bool(impl(Q!7, false2))), introduced(assumption)).
% 262.16/166.52 tff(877,plain,
% 262.16/166.52 ($false),
% 262.16/166.52 inference(unit_resolution,[status(thm)],[876, 875])).
% 262.16/166.52 tff(878,plain,((~bool(impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) | bool(impl(Q!7, false2)) | (~(impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = phi(Q!7))) | (~(impl(Q!7, false) = phi(Q!7)))), inference(lemma,lemma(discharge,[]))).
% 262.16/166.52 tff(879,plain,
% 262.16/166.52 (~bool(impl(Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.16/166.52 inference(unit_resolution,[status(thm)],[878, 727, 743, 521])).
% 262.16/166.52 tff(880,plain,
% 262.16/166.52 (((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | ((~bool(P!8)) | bool(impl(Q!7, tptp_fun_R_0(Q!7, P!8))) | (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))) <=> ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | (~bool(P!8)) | bool(impl(Q!7, tptp_fun_R_0(Q!7, P!8))) | (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))),
% 262.16/166.53 inference(rewrite,[status(thm)],[])).
% 262.16/166.53 tff(881,plain,
% 262.16/166.53 ((bool(impl(Q!7, tptp_fun_R_0(Q!7, P!8))) | (~bool(P!8)) | (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) <=> ((~bool(P!8)) | bool(impl(Q!7, tptp_fun_R_0(Q!7, P!8))) | (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))),
% 262.16/166.53 inference(rewrite,[status(thm)],[])).
% 262.16/166.53 tff(882,plain,
% 262.16/166.53 (((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | (bool(impl(Q!7, tptp_fun_R_0(Q!7, P!8))) | (~bool(P!8)) | (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))) <=> ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | ((~bool(P!8)) | bool(impl(Q!7, tptp_fun_R_0(Q!7, P!8))) | (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))),
% 262.16/166.53 inference(monotonicity,[status(thm)],[881])).
% 262.16/166.53 tff(883,plain,
% 262.16/166.53 (((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | (bool(impl(Q!7, tptp_fun_R_0(Q!7, P!8))) | (~bool(P!8)) | (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))) <=> ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | (~bool(P!8)) | bool(impl(Q!7, tptp_fun_R_0(Q!7, P!8))) | (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))),
% 262.16/166.53 inference(transitivity,[status(thm)],[882, 880])).
% 262.16/166.53 tff(884,plain,
% 262.16/166.53 ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | (bool(impl(Q!7, tptp_fun_R_0(Q!7, P!8))) | (~bool(P!8)) | (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))),
% 262.16/166.53 inference(quant_inst,[status(thm)],[])).
% 262.16/166.53 tff(885,plain,
% 262.16/166.53 ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | (~bool(P!8)) | bool(impl(Q!7, tptp_fun_R_0(Q!7, P!8))) | (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.16/166.53 inference(modus_ponens,[status(thm)],[884, 883])).
% 262.16/166.53 tff(886,plain,
% 262.16/166.53 ((~bool(P!8)) | bool(impl(Q!7, tptp_fun_R_0(Q!7, P!8))) | (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.16/166.53 inference(unit_resolution,[status(thm)],[885, 666])).
% 262.16/166.53 tff(887,plain,
% 262.16/166.53 (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(impl(Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.16/166.53 inference(unit_resolution,[status(thm)],[886, 879, 868])).
% 262.16/166.53 tff(888,plain,
% 262.16/166.53 (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = impl(impl(Q!7, false2), false2)),
% 262.16/166.53 inference(transitivity,[status(thm)],[887, 745, 735, 733, 618, 614])).
% 262.16/166.53 tff(889,plain,
% 262.16/166.53 (d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) <=> d(impl(impl(Q!7, false2), false2))),
% 262.16/166.53 inference(monotonicity,[status(thm)],[888])).
% 262.16/166.53 tff(890,plain,
% 262.16/166.53 (d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) <=> d(phi(impl(Q!7, false)))),
% 262.16/166.53 inference(transitivity,[status(thm)],[889, 738])).
% 262.16/166.53 tff(891,assumption,(impl(impl(Q!7, false2), false) = phi(impl(Q!7, false2))), introduced(assumption)).
% 262.16/166.53 tff(892,plain,
% 262.16/166.53 (phi(impl(Q!7, false2)) = impl(impl(Q!7, false2), false)),
% 262.16/166.53 inference(symmetry,[status(thm)],[891])).
% 262.16/166.53 tff(893,assumption,(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), introduced(assumption)).
% 262.16/166.53 tff(894,plain,
% 262.16/166.53 (phi(impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(impl(Q!7, false))),
% 262.16/166.53 inference(monotonicity,[status(thm)],[871])).
% 262.16/166.53 tff(895,plain,
% 262.16/166.53 (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = impl(impl(Q!7, false2), false2)),
% 262.16/166.53 inference(transitivity,[status(thm)],[893, 894, 735, 892, 618, 614])).
% 262.16/166.53 tff(896,plain,
% 262.16/166.53 (d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) <=> d(impl(impl(Q!7, false2), false2))),
% 262.16/166.53 inference(monotonicity,[status(thm)],[895])).
% 262.16/166.53 tff(897,plain,
% 262.16/166.53 (d(impl(impl(Q!7, false2), false2)) <=> d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.16/166.53 inference(symmetry,[status(thm)],[896])).
% 262.16/166.53 tff(898,assumption,(~((~d(Q!7)) | (~(phi(Q!7) = Q!7)))), introduced(assumption)).
% 262.16/166.53 tff(899,plain,
% 262.16/166.53 (phi(Q!7) = Q!7),
% 262.16/166.53 inference(unit_resolution,[status(thm)],[638, 898])).
% 262.16/166.53 tff(900,plain,
% 262.16/166.53 (Q!7 = phi(Q!7)),
% 262.16/166.53 inference(symmetry,[status(thm)],[899])).
% 262.16/166.53 tff(901,plain,
% 262.16/166.53 (Q!7 = impl(Q!7, false)),
% 262.16/166.53 inference(transitivity,[status(thm)],[900, 693])).
% 262.16/166.53 tff(902,plain,
% 262.16/166.53 (phi(Q!7) = phi(impl(Q!7, false))),
% 262.16/166.53 inference(monotonicity,[status(thm)],[901])).
% 262.16/166.53 tff(903,plain,
% 262.16/166.53 (impl(Q!7, err) = impl(impl(Q!7, false2), false2)),
% 262.16/166.53 inference(transitivity,[status(thm)],[683, 902, 735, 892, 618, 614])).
% 262.16/166.53 tff(904,plain,
% 262.16/166.53 (d(impl(Q!7, err)) <=> d(impl(impl(Q!7, false2), false2))),
% 262.16/166.53 inference(monotonicity,[status(thm)],[903])).
% 262.16/166.53 tff(905,plain,
% 262.16/166.53 (d(impl(Q!7, err)) <=> d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.16/166.53 inference(transitivity,[status(thm)],[904, 897])).
% 262.16/166.53 tff(906,plain,
% 262.16/166.53 (Q!7 = impl(Q!7, err)),
% 262.16/166.53 inference(transitivity,[status(thm)],[900, 684])).
% 262.16/166.53 tff(907,plain,
% 262.16/166.53 (d(Q!7) <=> d(impl(Q!7, err))),
% 262.16/166.53 inference(monotonicity,[status(thm)],[906])).
% 262.16/166.53 tff(908,plain,
% 262.16/166.53 (((~d(Q!7)) | (~(phi(Q!7) = Q!7))) | d(Q!7)),
% 262.16/166.53 inference(tautology,[status(thm)],[])).
% 262.16/166.53 tff(909,plain,
% 262.16/166.53 (d(Q!7)),
% 262.16/166.53 inference(unit_resolution,[status(thm)],[908, 898])).
% 262.16/166.53 tff(910,plain,
% 262.16/166.53 (d(impl(Q!7, err))),
% 262.16/166.53 inference(modus_ponens,[status(thm)],[909, 907])).
% 262.16/166.53 tff(911,plain,
% 262.16/166.53 (d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.16/166.53 inference(modus_ponens,[status(thm)],[910, 905])).
% 262.16/166.53 tff(912,plain,
% 262.16/166.53 ($false),
% 262.16/166.53 inference(unit_resolution,[status(thm)],[301, 911])).
% 262.16/166.53 tff(913,plain,(((~d(Q!7)) | (~(phi(Q!7) = Q!7))) | d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) | (~(impl(Q!7, err) = phi(Q!7))) | (~(impl(impl(Q!7, false2), false) = phi(impl(Q!7, false2)))) | (~(impl(Q!7, false) = phi(Q!7))) | (~(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~(impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = phi(Q!7)))), inference(lemma,lemma(discharge,[]))).
% 262.16/166.53 tff(914,plain,
% 262.16/166.53 ((~d(Q!7)) | (~(phi(Q!7) = Q!7))),
% 262.16/166.53 inference(unit_resolution,[status(thm)],[913, 301, 683, 891, 692, 893, 751])).
% 262.16/166.53 tff(915,plain,
% 262.16/166.53 (~(d(Q!7) | (~(phi(Q!7) = err)))),
% 262.16/166.53 inference(unit_resolution,[status(thm)],[649, 914])).
% 262.16/166.53 tff(916,plain,
% 262.16/166.53 (phi(Q!7) = err),
% 262.16/166.53 inference(unit_resolution,[status(thm)],[644, 915])).
% 262.16/166.53 tff(917,plain,
% 262.16/166.53 (err = phi(Q!7)),
% 262.16/166.53 inference(symmetry,[status(thm)],[916])).
% 262.16/166.53 tff(918,plain,
% 262.16/166.53 (err = impl(Q!7, false)),
% 262.16/166.53 inference(transitivity,[status(thm)],[917, 693])).
% 262.16/166.53 tff(919,plain,
% 262.16/166.53 (phi(err) = phi(impl(Q!7, false))),
% 262.16/166.53 inference(monotonicity,[status(thm)],[918])).
% 262.16/166.53 tff(920,plain,
% 262.16/166.53 (impl(Q!7, err) = impl(impl(Q!7, false2), false2)),
% 262.16/166.53 inference(transitivity,[status(thm)],[683, 916, 682, 919, 735, 892, 618, 614])).
% 262.16/166.53 tff(921,plain,
% 262.16/166.53 (d(impl(Q!7, err)) <=> d(impl(impl(Q!7, false2), false2))),
% 262.16/166.53 inference(monotonicity,[status(thm)],[920])).
% 262.16/166.53 tff(922,plain,
% 262.16/166.53 (d(impl(impl(Q!7, false2), false2)) <=> d(impl(Q!7, err))),
% 262.16/166.53 inference(symmetry,[status(thm)],[921])).
% 262.16/166.53 tff(923,plain,
% 262.16/166.53 ((~d(impl(impl(Q!7, false2), false2))) <=> (~d(impl(Q!7, err)))),
% 262.16/166.53 inference(monotonicity,[status(thm)],[922])).
% 262.16/166.53 tff(924,plain,
% 262.16/166.53 ((~d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) <=> (~d(impl(impl(Q!7, false2), false2)))),
% 262.16/166.53 inference(monotonicity,[status(thm)],[896])).
% 262.16/166.53 tff(925,plain,
% 262.16/166.53 (~d(impl(impl(Q!7, false2), false2))),
% 262.16/166.53 inference(modus_ponens,[status(thm)],[301, 924])).
% 262.16/166.53 tff(926,plain,
% 262.16/166.53 (~d(impl(Q!7, err))),
% 262.16/166.53 inference(modus_ponens,[status(thm)],[925, 923])).
% 262.16/166.53 tff(927,plain,
% 262.16/166.53 (err = impl(Q!7, err)),
% 262.16/166.53 inference(transitivity,[status(thm)],[917, 684])).
% 262.16/166.53 tff(928,plain,
% 262.16/166.53 (d(err) <=> d(impl(Q!7, err))),
% 262.16/166.53 inference(monotonicity,[status(thm)],[927])).
% 262.16/166.53 tff(929,plain,
% 262.16/166.53 (d(impl(Q!7, err))),
% 262.16/166.53 inference(modus_ponens,[status(thm)],[322, 928])).
% 262.16/166.53 tff(930,plain,
% 262.16/166.53 ($false),
% 262.16/166.53 inference(unit_resolution,[status(thm)],[929, 926])).
% 262.16/166.54 tff(931,plain,(d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) | (~(impl(Q!7, err) = phi(Q!7))) | (~(impl(impl(Q!7, false2), false) = phi(impl(Q!7, false2)))) | (~(impl(Q!7, false) = phi(Q!7))) | (~(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~(impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = phi(Q!7)))), inference(lemma,lemma(discharge,[]))).
% 262.16/166.54 tff(932,plain,
% 262.16/166.54 (d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.16/166.54 inference(unit_resolution,[status(thm)],[931, 527, 732, 521, 887, 743])).
% 262.16/166.54 tff(933,plain,
% 262.16/166.54 (d(phi(impl(Q!7, false)))),
% 262.16/166.54 inference(modus_ponens,[status(thm)],[932, 890])).
% 262.16/166.54 tff(934,plain,
% 262.16/166.54 ((d(phi(impl(Q!7, false))) | (~(phi(phi(impl(Q!7, false))) = err))) | (~d(phi(impl(Q!7, false))))),
% 262.16/166.54 inference(tautology,[status(thm)],[])).
% 262.16/166.54 tff(935,plain,
% 262.16/166.54 (d(phi(impl(Q!7, false))) | (~(phi(phi(impl(Q!7, false))) = err))),
% 262.16/166.54 inference(unit_resolution,[status(thm)],[934, 933])).
% 262.16/166.54 tff(936,plain,
% 262.16/166.54 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(phi(impl(Q!7, false)))) | (~(phi(phi(impl(Q!7, false))) = phi(impl(Q!7, false)))))) | (~(d(phi(impl(Q!7, false))) | (~(phi(phi(impl(Q!7, false))) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(phi(impl(Q!7, false)))) | (~(phi(phi(impl(Q!7, false))) = phi(impl(Q!7, false)))))) | (~(d(phi(impl(Q!7, false))) | (~(phi(phi(impl(Q!7, false))) = err)))))),
% 262.16/166.54 inference(rewrite,[status(thm)],[])).
% 262.16/166.54 tff(937,plain,
% 262.16/166.54 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(phi(impl(Q!7, false)))) | (~(phi(phi(impl(Q!7, false))) = phi(impl(Q!7, false)))))) | (~(d(phi(impl(Q!7, false))) | (~(phi(phi(impl(Q!7, false))) = err)))))),
% 262.16/166.54 inference(quant_inst,[status(thm)],[])).
% 262.16/166.54 tff(938,plain,
% 262.16/166.54 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(phi(impl(Q!7, false)))) | (~(phi(phi(impl(Q!7, false))) = phi(impl(Q!7, false)))))) | (~(d(phi(impl(Q!7, false))) | (~(phi(phi(impl(Q!7, false))) = err))))),
% 262.16/166.54 inference(modus_ponens,[status(thm)],[937, 936])).
% 262.16/166.54 tff(939,plain,
% 262.16/166.54 ((~((~d(phi(impl(Q!7, false)))) | (~(phi(phi(impl(Q!7, false))) = phi(impl(Q!7, false)))))) | (~(d(phi(impl(Q!7, false))) | (~(phi(phi(impl(Q!7, false))) = err))))),
% 262.16/166.54 inference(unit_resolution,[status(thm)],[938, 17])).
% 262.16/166.54 tff(940,plain,
% 262.16/166.54 (~((~d(phi(impl(Q!7, false)))) | (~(phi(phi(impl(Q!7, false))) = phi(impl(Q!7, false)))))),
% 262.16/166.54 inference(unit_resolution,[status(thm)],[939, 935])).
% 262.16/166.54 tff(941,plain,
% 262.16/166.54 (((~d(phi(impl(Q!7, false)))) | (~(phi(phi(impl(Q!7, false))) = phi(impl(Q!7, false))))) | (phi(phi(impl(Q!7, false))) = phi(impl(Q!7, false)))),
% 262.16/166.54 inference(tautology,[status(thm)],[])).
% 262.16/166.54 tff(942,plain,
% 262.16/166.54 (phi(phi(impl(Q!7, false))) = phi(impl(Q!7, false))),
% 262.16/166.54 inference(unit_resolution,[status(thm)],[941, 940])).
% 262.16/166.54 tff(943,plain,
% 262.16/166.54 (lazy_impl(not1(false), impl(Q!7, err)) = phi(impl(Q!7, false))),
% 262.16/166.54 inference(transitivity,[status(thm)],[514, 529])).
% 262.16/166.54 tff(944,plain,
% 262.16/166.54 (phi(lazy_impl(not1(false), impl(Q!7, err))) = phi(phi(impl(Q!7, false)))),
% 262.16/166.54 inference(monotonicity,[status(thm)],[943])).
% 262.16/166.54 tff(945,plain,
% 262.16/166.54 (impl(impl(Q!7, impl(not1(false), false)), false) = lazy_impl(not1(false), impl(Q!7, err))),
% 262.16/166.54 inference(transitivity,[status(thm)],[617, 732, 734, 530, 515])).
% 262.16/166.54 tff(946,plain,
% 262.16/166.54 (phi(impl(impl(Q!7, impl(not1(false), false)), false)) = phi(lazy_impl(not1(false), impl(Q!7, err)))),
% 262.16/166.54 inference(monotonicity,[status(thm)],[945])).
% 262.16/166.54 tff(947,plain,
% 262.16/166.54 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), impl(impl(Q!7, impl(not1(false), false)), false)) = phi(impl(impl(Q!7, impl(not1(false), false)), false)))),
% 262.16/166.54 inference(quant_inst,[status(thm)],[])).
% 262.16/166.54 tff(948,plain,
% 262.16/166.54 (lazy_impl(not1(false), impl(impl(Q!7, impl(not1(false), false)), false)) = phi(impl(impl(Q!7, impl(not1(false), false)), false))),
% 262.16/166.54 inference(unit_resolution,[status(thm)],[947, 33])).
% 262.16/166.54 tff(949,plain,
% 262.16/166.54 (lazy_impl(prop(false), impl(impl(Q!7, impl(not1(false), false)), false)) = lazy_impl(not1(false), impl(impl(Q!7, impl(not1(false), false)), false))),
% 262.16/166.54 inference(monotonicity,[status(thm)],[149])).
% 262.16/166.54 tff(950,plain,
% 262.16/166.54 (bool(impl(Q!7, false2)) <=> bool(impl(Q!7, false))),
% 262.16/166.54 inference(monotonicity,[status(thm)],[611])).
% 262.16/166.54 tff(951,plain,
% 262.16/166.54 ((~bool(impl(Q!7, false2))) <=> (~bool(impl(Q!7, false)))),
% 262.16/166.54 inference(monotonicity,[status(thm)],[950])).
% 262.16/166.54 tff(952,plain,
% 262.16/166.54 (~bool(impl(Q!7, false))),
% 262.16/166.54 inference(modus_ponens,[status(thm)],[727, 951])).
% 262.16/166.54 tff(953,plain,
% 262.16/166.54 (((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | (bool(impl(Q!7, false)) | (~bool(false)) | (impl(false, impl(Q!7, false)) = phi(impl(Q!7, false))))) <=> ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | bool(impl(Q!7, false)) | (~bool(false)) | (impl(false, impl(Q!7, false)) = phi(impl(Q!7, false))))),
% 262.16/166.54 inference(rewrite,[status(thm)],[])).
% 262.16/166.54 tff(954,plain,
% 262.16/166.54 ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | (bool(impl(Q!7, false)) | (~bool(false)) | (impl(false, impl(Q!7, false)) = phi(impl(Q!7, false))))),
% 262.16/166.54 inference(quant_inst,[status(thm)],[])).
% 262.16/166.54 tff(955,plain,
% 262.16/166.54 ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | bool(impl(Q!7, false)) | (~bool(false)) | (impl(false, impl(Q!7, false)) = phi(impl(Q!7, false)))),
% 262.16/166.54 inference(modus_ponens,[status(thm)],[954, 953])).
% 262.16/166.54 tff(956,plain,
% 262.16/166.54 (bool(impl(Q!7, false)) | (impl(false, impl(Q!7, false)) = phi(impl(Q!7, false)))),
% 262.16/166.54 inference(unit_resolution,[status(thm)],[955, 666, 107])).
% 262.16/166.54 tff(957,plain,
% 262.16/166.54 (impl(false, impl(Q!7, false)) = phi(impl(Q!7, false))),
% 262.16/166.54 inference(unit_resolution,[status(thm)],[956, 952])).
% 262.16/166.54 tff(958,plain,
% 262.16/166.54 (impl(false, impl(Q!7, false)) = lazy_impl(not1(false), impl(Q!7, err))),
% 262.16/166.54 inference(transitivity,[status(thm)],[957, 530, 515])).
% 262.16/166.54 tff(959,plain,
% 262.16/166.54 (phi(impl(false, impl(Q!7, false))) = phi(lazy_impl(not1(false), impl(Q!7, err)))),
% 262.16/166.54 inference(monotonicity,[status(thm)],[958])).
% 262.16/166.54 tff(960,plain,
% 262.16/166.54 (bool(impl(false, impl(Q!7, false))) <=> bool(lazy_impl(not1(false), impl(Q!7, err)))),
% 262.16/166.54 inference(monotonicity,[status(thm)],[958])).
% 262.16/166.54 tff(961,plain,
% 262.16/166.54 (bool(lazy_impl(not1(false), impl(Q!7, err))) <=> bool(impl(false, impl(Q!7, false)))),
% 262.16/166.54 inference(symmetry,[status(thm)],[960])).
% 262.16/166.54 tff(962,plain,
% 262.16/166.54 ((impl(Q!7, err) = phi(impl(Q!7, err))) <=> (phi(impl(Q!7, err)) = impl(Q!7, err))),
% 262.16/166.54 inference(commutativity,[status(thm)],[])).
% 262.16/166.54 tff(963,assumption,(~(phi(impl(Q!7, err)) = impl(Q!7, err))), introduced(assumption)).
% 262.16/166.54 tff(964,plain,
% 262.16/166.54 (((~d(impl(Q!7, err))) | (~(phi(impl(Q!7, err)) = impl(Q!7, err)))) | (phi(impl(Q!7, err)) = impl(Q!7, err))),
% 262.16/166.54 inference(tautology,[status(thm)],[])).
% 262.16/166.54 tff(965,plain,
% 262.16/166.54 ((~d(impl(Q!7, err))) | (~(phi(impl(Q!7, err)) = impl(Q!7, err)))),
% 262.16/166.54 inference(unit_resolution,[status(thm)],[964, 963])).
% 262.16/166.54 tff(966,plain,
% 262.16/166.54 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(Q!7, err))) | (~(phi(impl(Q!7, err)) = impl(Q!7, err))))) | (~(d(impl(Q!7, err)) | (~(phi(impl(Q!7, err)) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(impl(Q!7, err))) | (~(phi(impl(Q!7, err)) = impl(Q!7, err))))) | (~(d(impl(Q!7, err)) | (~(phi(impl(Q!7, err)) = err)))))),
% 262.16/166.54 inference(rewrite,[status(thm)],[])).
% 262.16/166.54 tff(967,plain,
% 262.16/166.54 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(Q!7, err))) | (~(phi(impl(Q!7, err)) = impl(Q!7, err))))) | (~(d(impl(Q!7, err)) | (~(phi(impl(Q!7, err)) = err)))))),
% 262.16/166.54 inference(quant_inst,[status(thm)],[])).
% 262.16/166.54 tff(968,plain,
% 262.16/166.54 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(impl(Q!7, err))) | (~(phi(impl(Q!7, err)) = impl(Q!7, err))))) | (~(d(impl(Q!7, err)) | (~(phi(impl(Q!7, err)) = err))))),
% 262.16/166.54 inference(modus_ponens,[status(thm)],[967, 966])).
% 262.16/166.54 tff(969,plain,
% 262.16/166.54 ((~((~d(impl(Q!7, err))) | (~(phi(impl(Q!7, err)) = impl(Q!7, err))))) | (~(d(impl(Q!7, err)) | (~(phi(impl(Q!7, err)) = err))))),
% 262.16/166.54 inference(unit_resolution,[status(thm)],[968, 17])).
% 262.16/166.54 tff(970,plain,
% 262.16/166.54 (~(d(impl(Q!7, err)) | (~(phi(impl(Q!7, err)) = err)))),
% 262.16/166.54 inference(unit_resolution,[status(thm)],[969, 965])).
% 262.16/166.54 tff(971,plain,
% 262.16/166.54 ((d(impl(Q!7, err)) | (~(phi(impl(Q!7, err)) = err))) | (phi(impl(Q!7, err)) = err)),
% 262.16/166.54 inference(tautology,[status(thm)],[])).
% 262.16/166.54 tff(972,plain,
% 262.16/166.54 (phi(impl(Q!7, err)) = err),
% 262.16/166.54 inference(unit_resolution,[status(thm)],[971, 970])).
% 262.16/166.54 tff(973,plain,
% 262.16/166.54 (err = phi(impl(Q!7, err))),
% 262.16/166.54 inference(symmetry,[status(thm)],[972])).
% 262.16/166.54 tff(974,plain,
% 262.16/166.54 (phi(err) = phi(impl(Q!7, err))),
% 262.16/166.54 inference(transitivity,[status(thm)],[681, 973])).
% 262.16/166.54 tff(975,plain,
% 262.16/166.54 ((impl(Q!7, err) = phi(err)) <=> (impl(Q!7, err) = phi(impl(Q!7, err)))),
% 262.16/166.54 inference(monotonicity,[status(thm)],[974])).
% 262.16/166.54 tff(976,plain,
% 262.16/166.54 ((impl(Q!7, err) = phi(err)) <=> (phi(impl(Q!7, err)) = impl(Q!7, err))),
% 262.16/166.54 inference(transitivity,[status(thm)],[975, 962])).
% 262.16/166.54 tff(977,plain,
% 262.16/166.54 ((phi(impl(Q!7, err)) = impl(Q!7, err)) <=> (impl(Q!7, err) = phi(err))),
% 262.16/166.54 inference(symmetry,[status(thm)],[976])).
% 262.16/166.54 tff(978,plain,
% 262.16/166.54 ((phi(impl(Q!7, err)) = impl(Q!7, err)) <=> (phi(Q!7) = err)),
% 262.16/166.54 inference(transitivity,[status(thm)],[977, 686])).
% 262.16/166.54 tff(979,plain,
% 262.16/166.54 ((~(phi(impl(Q!7, err)) = impl(Q!7, err))) <=> (~(phi(Q!7) = err))),
% 262.16/166.54 inference(monotonicity,[status(thm)],[978])).
% 262.16/166.54 tff(980,plain,
% 262.16/166.54 (~(phi(Q!7) = err)),
% 262.16/166.54 inference(modus_ponens,[status(thm)],[963, 979])).
% 262.16/166.54 tff(981,plain,
% 262.16/166.54 (d(Q!7) | (~(phi(Q!7) = err))),
% 262.16/166.54 inference(unit_resolution,[status(thm)],[644, 980])).
% 262.16/166.54 tff(982,plain,
% 262.16/166.54 (~((~d(Q!7)) | (~(phi(Q!7) = Q!7)))),
% 262.16/166.54 inference(unit_resolution,[status(thm)],[649, 981])).
% 262.16/166.54 tff(983,plain,
% 262.16/166.54 (phi(Q!7) = Q!7),
% 262.16/166.54 inference(unit_resolution,[status(thm)],[638, 982])).
% 262.16/166.54 tff(984,plain,
% 262.16/166.54 (Q!7 = phi(Q!7)),
% 262.16/166.54 inference(symmetry,[status(thm)],[983])).
% 262.16/166.54 tff(985,plain,
% 262.16/166.54 (Q!7 = impl(Q!7, false)),
% 262.16/166.54 inference(transitivity,[status(thm)],[984, 693])).
% 262.16/166.54 tff(986,plain,
% 262.16/166.54 (phi(Q!7) = phi(impl(Q!7, false))),
% 262.16/166.54 inference(monotonicity,[status(thm)],[985])).
% 262.16/166.54 tff(987,plain,
% 262.16/166.54 (phi(impl(Q!7, false)) = phi(Q!7)),
% 262.16/166.54 inference(symmetry,[status(thm)],[986])).
% 262.16/166.54 tff(988,plain,
% 262.16/166.54 (impl(Q!7, err) = impl(Q!7, false)),
% 262.16/166.54 inference(transitivity,[status(thm)],[683, 693])).
% 262.16/166.54 tff(989,plain,
% 262.16/166.54 (phi(impl(Q!7, err)) = phi(impl(Q!7, false))),
% 262.16/166.54 inference(monotonicity,[status(thm)],[988])).
% 262.16/166.54 tff(990,plain,
% 262.16/166.54 (phi(impl(Q!7, err)) = impl(Q!7, err)),
% 262.16/166.54 inference(transitivity,[status(thm)],[989, 987, 684])).
% 262.16/166.54 tff(991,plain,
% 262.16/166.54 ($false),
% 262.16/166.54 inference(unit_resolution,[status(thm)],[963, 990])).
% 262.16/166.54 tff(992,plain,((phi(impl(Q!7, err)) = impl(Q!7, err)) | (~(impl(Q!7, err) = phi(Q!7))) | (~(impl(Q!7, false) = phi(Q!7)))), inference(lemma,lemma(discharge,[]))).
% 262.16/166.54 tff(993,plain,
% 262.16/166.54 (phi(impl(Q!7, err)) = impl(Q!7, err)),
% 262.16/166.54 inference(unit_resolution,[status(thm)],[992, 527, 521])).
% 262.16/166.54 tff(994,plain,
% 262.16/166.54 (impl(Q!7, err) = phi(impl(Q!7, err))),
% 262.16/166.54 inference(symmetry,[status(thm)],[993])).
% 262.16/166.54 tff(995,plain,
% 262.16/166.54 (phi(Q!7) = impl(Q!7, err)),
% 262.16/166.54 inference(symmetry,[status(thm)],[527])).
% 262.16/166.54 tff(996,plain,
% 262.16/166.54 (impl(Q!7, false) = lazy_impl(not1(false), impl(Q!7, err))),
% 262.16/166.54 inference(transitivity,[status(thm)],[521, 995, 994, 515])).
% 262.16/166.54 tff(997,plain,
% 262.16/166.54 (bool(impl(Q!7, false)) <=> bool(lazy_impl(not1(false), impl(Q!7, err)))),
% 262.16/166.54 inference(monotonicity,[status(thm)],[996])).
% 262.16/166.54 tff(998,plain,
% 262.16/166.54 (bool(impl(Q!7, false)) <=> bool(impl(false, impl(Q!7, false)))),
% 262.16/166.54 inference(transitivity,[status(thm)],[997, 961])).
% 262.16/166.54 tff(999,plain,
% 262.16/166.54 ((~bool(impl(Q!7, false))) <=> (~bool(impl(false, impl(Q!7, false))))),
% 262.16/166.54 inference(monotonicity,[status(thm)],[998])).
% 262.16/166.54 tff(1000,plain,
% 262.16/166.54 (~bool(impl(false, impl(Q!7, false)))),
% 262.16/166.54 inference(modus_ponens,[status(thm)],[952, 999])).
% 262.16/166.54 tff(1001,plain,
% 262.16/166.54 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(false, impl(Q!7, false))) | (impl(impl(false, impl(Q!7, false)), tptp_fun_R_0(Q!7, P!8)) = phi(impl(false, impl(Q!7, false)))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(false, impl(Q!7, false))) | (impl(impl(false, impl(Q!7, false)), tptp_fun_R_0(Q!7, P!8)) = phi(impl(false, impl(Q!7, false)))))),
% 262.16/166.55 inference(rewrite,[status(thm)],[])).
% 262.16/166.55 tff(1002,plain,
% 262.16/166.55 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(false, impl(Q!7, false))) | (impl(impl(false, impl(Q!7, false)), tptp_fun_R_0(Q!7, P!8)) = phi(impl(false, impl(Q!7, false)))))),
% 262.16/166.55 inference(quant_inst,[status(thm)],[])).
% 262.16/166.55 tff(1003,plain,
% 262.16/166.55 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(false, impl(Q!7, false))) | (impl(impl(false, impl(Q!7, false)), tptp_fun_R_0(Q!7, P!8)) = phi(impl(false, impl(Q!7, false))))),
% 262.16/166.55 inference(modus_ponens,[status(thm)],[1002, 1001])).
% 262.16/166.55 tff(1004,plain,
% 262.16/166.55 (bool(impl(false, impl(Q!7, false))) | (impl(impl(false, impl(Q!7, false)), tptp_fun_R_0(Q!7, P!8)) = phi(impl(false, impl(Q!7, false))))),
% 262.16/166.55 inference(unit_resolution,[status(thm)],[1003, 188])).
% 262.16/166.55 tff(1005,plain,
% 262.16/166.55 (impl(impl(false, impl(Q!7, false)), tptp_fun_R_0(Q!7, P!8)) = phi(impl(false, impl(Q!7, false)))),
% 262.16/166.55 inference(unit_resolution,[status(thm)],[1004, 1000])).
% 262.16/166.55 tff(1006,plain,
% 262.16/166.55 (impl(false, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = impl(false, impl(Q!7, false))),
% 262.16/166.55 inference(monotonicity,[status(thm)],[744])).
% 262.16/166.55 tff(1007,plain,
% 262.16/166.55 (impl(impl(false, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)) = impl(impl(false, impl(Q!7, false)), tptp_fun_R_0(Q!7, P!8))),
% 262.16/166.55 inference(monotonicity,[status(thm)],[1006])).
% 262.16/166.55 tff(1008,plain,
% 262.16/166.55 (impl(impl(false, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)) = impl(impl(Q!7, impl(not1(false), false)), false)),
% 262.16/166.55 inference(transitivity,[status(thm)],[1007, 1005, 959, 944, 942, 735, 733, 618])).
% 262.16/166.55 tff(1009,plain,
% 262.16/166.55 (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = lazy_impl(not1(false), impl(Q!7, err))),
% 262.16/166.55 inference(transitivity,[status(thm)],[887, 745, 530, 515])).
% 262.16/166.55 tff(1010,plain,
% 262.16/166.55 (bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) <=> bool(lazy_impl(not1(false), impl(Q!7, err)))),
% 262.16/166.55 inference(monotonicity,[status(thm)],[1009])).
% 262.16/166.55 tff(1011,plain,
% 262.16/166.55 (bool(lazy_impl(not1(false), impl(Q!7, err))) <=> bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.16/166.55 inference(symmetry,[status(thm)],[1010])).
% 262.16/166.55 tff(1012,plain,
% 262.16/166.55 (bool(impl(Q!7, false)) <=> bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.16/166.55 inference(transitivity,[status(thm)],[997, 1011])).
% 262.16/166.55 tff(1013,plain,
% 262.16/166.55 ((~bool(impl(Q!7, false))) <=> (~bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))),
% 262.16/166.55 inference(monotonicity,[status(thm)],[1012])).
% 262.16/166.55 tff(1014,plain,
% 262.16/166.55 (~bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.16/166.55 inference(modus_ponens,[status(thm)],[952, 1013])).
% 262.16/166.55 tff(1015,plain,
% 262.16/166.55 ((impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) <=> (phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.16/166.55 inference(commutativity,[status(thm)],[])).
% 262.16/166.55 tff(1016,plain,
% 262.16/166.55 (bool(impl(Q!7, tptp_fun_R_0(Q!7, P!8))) <=> bool(impl(Q!7, false))),
% 262.16/166.55 inference(monotonicity,[status(thm)],[744])).
% 262.16/166.55 tff(1017,plain,
% 262.16/166.55 ((~bool(impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) <=> (~bool(impl(Q!7, false)))),
% 262.16/166.55 inference(monotonicity,[status(thm)],[1016])).
% 262.16/166.55 tff(1018,assumption,(~bool(impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), introduced(assumption)).
% 262.16/166.55 tff(1019,plain,
% 262.16/166.55 (~bool(impl(Q!7, false))),
% 262.16/166.55 inference(modus_ponens,[status(thm)],[1018, 1017])).
% 262.16/166.55 tff(1020,plain,
% 262.16/166.55 (impl(false, impl(Q!7, false)) = phi(impl(Q!7, false))),
% 262.16/166.55 inference(unit_resolution,[status(thm)],[956, 1019])).
% 262.16/166.55 tff(1021,plain,
% 262.16/166.55 (phi(impl(Q!7, false)) = impl(false, impl(Q!7, false))),
% 262.16/166.55 inference(symmetry,[status(thm)],[1020])).
% 262.16/166.55 tff(1022,plain,
% 262.16/166.55 (phi(Q!7) = impl(Q!7, tptp_fun_R_0(Q!7, P!8))),
% 262.16/166.55 inference(symmetry,[status(thm)],[743])).
% 262.16/166.55 tff(1023,plain,
% 262.16/166.55 (impl(Q!7, false) = impl(Q!7, tptp_fun_R_0(Q!7, P!8))),
% 262.16/166.55 inference(transitivity,[status(thm)],[521, 1022])).
% 262.16/166.55 tff(1024,plain,
% 262.16/166.55 (phi(impl(Q!7, false)) = phi(impl(Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.16/166.55 inference(monotonicity,[status(thm)],[1023])).
% 262.16/166.55 tff(1025,plain,
% 262.16/166.55 (phi(impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(impl(Q!7, false))),
% 262.16/166.55 inference(symmetry,[status(thm)],[1024])).
% 262.16/166.55 tff(1026,plain,
% 262.16/166.55 (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = impl(false, impl(Q!7, false))),
% 262.16/166.55 inference(transitivity,[status(thm)],[893, 1025, 1021])).
% 262.16/166.55 tff(1027,plain,
% 262.16/166.55 (phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = phi(impl(false, impl(Q!7, false)))),
% 262.16/166.55 inference(monotonicity,[status(thm)],[1026])).
% 262.16/166.55 tff(1028,plain,
% 262.16/166.55 (phi(impl(false, impl(Q!7, false))) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.16/166.55 inference(symmetry,[status(thm)],[1027])).
% 262.16/166.55 tff(1029,plain,
% 262.16/166.55 (phi(impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.16/166.55 inference(symmetry,[status(thm)],[893])).
% 262.16/166.55 tff(1030,plain,
% 262.16/166.55 (impl(false, impl(Q!7, false)) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.16/166.55 inference(transitivity,[status(thm)],[1020, 1024, 1029])).
% 262.16/166.55 tff(1031,plain,
% 262.16/166.55 (bool(impl(false, impl(Q!7, false))) <=> bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.16/166.55 inference(monotonicity,[status(thm)],[1030])).
% 262.16/166.55 tff(1032,plain,
% 262.16/166.55 (bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) <=> bool(impl(false, impl(Q!7, false)))),
% 262.16/166.55 inference(symmetry,[status(thm)],[1031])).
% 262.16/166.55 tff(1033,plain,
% 262.16/166.55 ((~bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) <=> (~bool(impl(false, impl(Q!7, false))))),
% 262.16/166.55 inference(monotonicity,[status(thm)],[1032])).
% 262.16/166.55 tff(1034,assumption,(~bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))), introduced(assumption)).
% 262.16/166.55 tff(1035,plain,
% 262.16/166.55 (~bool(impl(false, impl(Q!7, false)))),
% 262.16/166.55 inference(modus_ponens,[status(thm)],[1034, 1033])).
% 262.16/166.55 tff(1036,plain,
% 262.16/166.55 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(false, impl(Q!7, false))) | (impl(impl(false, impl(Q!7, false)), false) = phi(impl(false, impl(Q!7, false)))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(false, impl(Q!7, false))) | (impl(impl(false, impl(Q!7, false)), false) = phi(impl(false, impl(Q!7, false)))))),
% 262.16/166.55 inference(rewrite,[status(thm)],[])).
% 262.16/166.55 tff(1037,plain,
% 262.16/166.55 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(false, impl(Q!7, false))) | (impl(impl(false, impl(Q!7, false)), false) = phi(impl(false, impl(Q!7, false)))))),
% 262.16/166.55 inference(quant_inst,[status(thm)],[])).
% 262.16/166.55 tff(1038,plain,
% 262.16/166.55 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(false, impl(Q!7, false))) | (impl(impl(false, impl(Q!7, false)), false) = phi(impl(false, impl(Q!7, false))))),
% 262.16/166.55 inference(modus_ponens,[status(thm)],[1037, 1036])).
% 262.16/166.55 tff(1039,plain,
% 262.16/166.55 (bool(impl(false, impl(Q!7, false))) | (impl(impl(false, impl(Q!7, false)), false) = phi(impl(false, impl(Q!7, false))))),
% 262.16/166.55 inference(unit_resolution,[status(thm)],[1038, 188])).
% 262.16/166.55 tff(1040,plain,
% 262.16/166.55 (impl(impl(false, impl(Q!7, false)), false) = phi(impl(false, impl(Q!7, false)))),
% 262.16/166.55 inference(unit_resolution,[status(thm)],[1039, 1035])).
% 262.16/166.55 tff(1041,plain,
% 262.16/166.55 (impl(Q!7, false2) = impl(Q!7, impl(not1(false), false))),
% 262.16/166.55 inference(transitivity,[status(thm)],[706, 610])).
% 262.16/166.55 tff(1042,plain,
% 262.16/166.55 (impl(impl(Q!7, false2), impl(not1(false), false)) = impl(impl(Q!7, impl(not1(false), false)), false)),
% 262.16/166.55 inference(monotonicity,[status(thm)],[1041, 132])).
% 262.16/166.55 tff(1043,plain,
% 262.16/166.55 (impl(impl(Q!7, impl(not1(false), false)), false) = impl(impl(Q!7, false2), impl(not1(false), false))),
% 262.16/166.55 inference(symmetry,[status(thm)],[1042])).
% 262.16/166.55 tff(1044,plain,
% 262.16/166.55 (impl(Q!7, impl(not1(false), false)) = impl(Q!7, false2)),
% 262.16/166.55 inference(transitivity,[status(thm)],[609, 691])).
% 262.16/166.55 tff(1045,plain,
% 262.16/166.55 (impl(impl(Q!7, impl(not1(false), false)), false) = impl(impl(Q!7, false2), false)),
% 262.16/166.55 inference(monotonicity,[status(thm)],[1044])).
% 262.16/166.55 tff(1046,plain,
% 262.16/166.55 (impl(impl(Q!7, false2), false) = impl(impl(Q!7, impl(not1(false), false)), false)),
% 262.16/166.55 inference(symmetry,[status(thm)],[1045])).
% 262.16/166.55 tff(1047,plain,
% 262.16/166.55 (bool(impl(Q!7, tptp_fun_R_0(Q!7, P!8))) <=> bool(impl(Q!7, false2))),
% 262.16/166.55 inference(transitivity,[status(thm)],[1016, 870])).
% 262.16/166.55 tff(1048,plain,
% 262.16/166.55 ((~bool(impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) <=> (~bool(impl(Q!7, false2)))),
% 262.16/166.55 inference(monotonicity,[status(thm)],[1047])).
% 262.16/166.55 tff(1049,plain,
% 262.16/166.55 (~bool(impl(Q!7, false2))),
% 262.22/166.55 inference(modus_ponens,[status(thm)],[1018, 1048])).
% 262.22/166.55 tff(1050,plain,
% 262.22/166.55 (impl(impl(Q!7, false2), false) = phi(impl(Q!7, false2))),
% 262.22/166.55 inference(unit_resolution,[status(thm)],[731, 1049])).
% 262.22/166.55 tff(1051,plain,
% 262.22/166.55 (phi(impl(Q!7, false2)) = impl(impl(Q!7, false2), false)),
% 262.22/166.55 inference(symmetry,[status(thm)],[1050])).
% 262.22/166.55 tff(1052,plain,
% 262.22/166.55 (phi(impl(Q!7, false2)) = phi(impl(Q!7, false))),
% 262.22/166.55 inference(monotonicity,[status(thm)],[706])).
% 262.22/166.55 tff(1053,plain,
% 262.22/166.55 (phi(impl(Q!7, false)) = phi(impl(Q!7, false2))),
% 262.22/166.55 inference(symmetry,[status(thm)],[1052])).
% 262.22/166.55 tff(1054,plain,
% 262.22/166.55 (impl(false, impl(Q!7, false)) = impl(impl(Q!7, false2), impl(not1(false), false))),
% 262.22/166.55 inference(transitivity,[status(thm)],[1020, 1053, 1051, 1046, 1043])).
% 262.22/166.55 tff(1055,plain,
% 262.22/166.55 (impl(impl(false, impl(Q!7, false)), false) = impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)),
% 262.22/166.55 inference(monotonicity,[status(thm)],[1054])).
% 262.22/166.55 tff(1056,plain,
% 262.22/166.55 (impl(impl(impl(Q!7, false2), impl(not1(false), false)), false) = impl(impl(false, impl(Q!7, false)), false)),
% 262.22/166.55 inference(symmetry,[status(thm)],[1055])).
% 262.22/166.55 tff(1057,plain,
% 262.22/166.55 (impl(impl(Q!7, false2), false2) = impl(impl(Q!7, impl(not1(false), false)), false)),
% 262.22/166.55 inference(monotonicity,[status(thm)],[1041, 608])).
% 262.22/166.55 tff(1058,plain,
% 262.22/166.55 (impl(impl(Q!7, impl(not1(false), false)), false) = impl(impl(Q!7, false2), false2)),
% 262.22/166.55 inference(symmetry,[status(thm)],[1057])).
% 262.22/166.55 tff(1059,plain,
% 262.22/166.55 (impl(impl(Q!7, false2), impl(not1(false), false)) = impl(impl(Q!7, false2), false2)),
% 262.22/166.55 inference(transitivity,[status(thm)],[1042, 1058])).
% 262.22/166.55 tff(1060,plain,
% 262.22/166.55 (impl(impl(impl(Q!7, false2), impl(not1(false), false)), false) = impl(impl(impl(Q!7, false2), false2), false2)),
% 262.22/166.55 inference(monotonicity,[status(thm)],[1059, 690])).
% 262.22/166.55 tff(1061,plain,
% 262.22/166.55 (impl(impl(impl(Q!7, false2), false2), false2) = impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)),
% 262.22/166.55 inference(symmetry,[status(thm)],[1060])).
% 262.22/166.55 tff(1062,plain,
% 262.22/166.55 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))) <=> ((lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = false) | (lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = not1(false))))),
% 262.22/166.55 inference(quant_inst,[status(thm)],[])).
% 262.22/166.55 tff(1063,plain,
% 262.22/166.55 (bool(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))) <=> ((lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = false) | (lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = not1(false)))),
% 262.22/166.55 inference(unit_resolution,[status(thm)],[1062, 229])).
% 262.22/166.55 tff(1064,plain,
% 262.22/166.55 (((~![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(impl(impl(Q!7, false2), impl(not1(false), false)), false)), not1(false)) <=> ((~((~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | (~d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)))) | bool(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))))) | (lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), 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(impl(impl(Q!7, false2), impl(not1(false), false)), false)), not1(false)) <=> ((~((~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | (~d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)))) | bool(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))))) | (lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = false))))),
% 262.22/166.56 inference(rewrite,[status(thm)],[])).
% 262.22/166.56 tff(1065,plain,
% 262.22/166.56 ((forallprefers(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)), not1(false)) <=> ((~(d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))) | (~d(not1(false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))) | (~d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)))))) | (~((~(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = false)) | (~(not1(false) = not1(false))))))) <=> (forallprefers(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)), not1(false)) <=> ((~((~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | (~d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)))) | bool(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))))) | (lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = false)))),
% 262.22/166.56 inference(rewrite,[status(thm)],[])).
% 262.22/166.56 tff(1066,plain,
% 262.22/166.56 (((~![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(impl(impl(Q!7, false2), impl(not1(false), false)), false)), not1(false)) <=> ((~(d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))) | (~d(not1(false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))) | (~d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)))))) | (~((~(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = false)) | (~(not1(false) = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)), not1(false)) <=> ((~((~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | (~d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)))) | bool(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))))) | (lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = false))))),
% 262.22/166.56 inference(monotonicity,[status(thm)],[1065])).
% 262.22/166.56 tff(1067,plain,
% 262.22/166.56 (((~![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(impl(impl(Q!7, false2), impl(not1(false), false)), false)), not1(false)) <=> ((~(d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))) | (~d(not1(false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))) | (~d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)))))) | (~((~(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = false)) | (~(not1(false) = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)), not1(false)) <=> ((~((~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | (~d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)))) | bool(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))))) | (lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = false))))),
% 262.22/166.56 inference(transitivity,[status(thm)],[1066, 1064])).
% 262.22/166.56 tff(1068,plain,
% 262.22/166.56 ((~![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(impl(impl(Q!7, false2), impl(not1(false), false)), false)), not1(false)) <=> ((~(d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))) | (~d(not1(false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))) | (~d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)))))) | (~((~(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = false)) | (~(not1(false) = not1(false)))))))),
% 262.22/166.56 inference(quant_inst,[status(thm)],[])).
% 262.22/166.56 tff(1069,plain,
% 262.22/166.56 ((~![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(impl(impl(Q!7, false2), impl(not1(false), false)), false)), not1(false)) <=> ((~((~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | (~d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)))) | bool(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))))) | (lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = false)))),
% 262.22/166.56 inference(modus_ponens,[status(thm)],[1068, 1067])).
% 262.22/166.56 tff(1070,plain,
% 262.22/166.56 (forallprefers(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)), not1(false)) <=> ((~((~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | (~d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)))) | bool(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))))) | (lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = false))),
% 262.22/166.56 inference(unit_resolution,[status(thm)],[1069, 493])).
% 262.22/166.56 tff(1071,plain,
% 262.22/166.56 (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(false, impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))),
% 262.22/166.56 inference(monotonicity,[status(thm)],[439])).
% 262.22/166.56 tff(1072,plain,
% 262.22/166.56 (lazy_impl(false, impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))),
% 262.22/166.56 inference(symmetry,[status(thm)],[1071])).
% 262.22/166.56 tff(1073,plain,
% 262.22/166.56 ((~![B: $i] : (lazy_impl(false, B) = not1(false))) | (lazy_impl(false, impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = not1(false))),
% 262.22/166.56 inference(quant_inst,[status(thm)],[])).
% 262.22/166.56 tff(1074,plain,
% 262.22/166.56 (lazy_impl(false, impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = not1(false)),
% 262.22/166.56 inference(unit_resolution,[status(thm)],[1073, 393])).
% 262.22/166.56 tff(1075,plain,
% 262.22/166.56 (not1(false) = lazy_impl(false, impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))),
% 262.22/166.56 inference(symmetry,[status(thm)],[1074])).
% 262.22/166.56 tff(1076,plain,
% 262.22/166.57 (not1(false) = f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))),
% 262.22/166.57 inference(transitivity,[status(thm)],[1075, 1072, 177])).
% 262.22/166.57 tff(1077,plain,
% 262.22/166.57 (impl(P!8, impl(Q!7, false)) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.22/166.57 inference(monotonicity,[status(thm)],[1023])).
% 262.22/166.57 tff(1078,plain,
% 262.22/166.57 (impl(P!8, impl(Q!7, false)) = impl(false, impl(Q!7, false))),
% 262.22/166.57 inference(transitivity,[status(thm)],[1077, 893, 1025, 1021])).
% 262.22/166.57 tff(1079,plain,
% 262.22/166.57 (impl(impl(P!8, impl(Q!7, false)), false) = impl(impl(false, impl(Q!7, false)), false)),
% 262.22/166.57 inference(monotonicity,[status(thm)],[1078])).
% 262.22/166.57 tff(1080,plain,
% 262.22/166.57 (impl(impl(P!8, impl(Q!7, false)), false) = impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)),
% 262.22/166.57 inference(transitivity,[status(thm)],[1079, 1055])).
% 262.22/166.57 tff(1081,plain,
% 262.22/166.57 (lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false)) = lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))),
% 262.22/166.57 inference(monotonicity,[status(thm)],[1080])).
% 262.22/166.57 tff(1082,plain,
% 262.22/166.57 (lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = lazy_impl(prop(false), impl(impl(P!8, impl(Q!7, false)), false))),
% 262.22/166.57 inference(symmetry,[status(thm)],[1081])).
% 262.22/166.57 tff(1083,plain,
% 262.22/166.57 (lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = f1(P!8, Q!7, false)),
% 262.22/166.57 inference(transitivity,[status(thm)],[1082, 797])).
% 262.22/166.57 tff(1084,plain,
% 262.22/166.57 (forallprefers(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)), not1(false)) <=> forallprefers(f1(P!8, Q!7, false), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.22/166.57 inference(monotonicity,[status(thm)],[1083, 1076])).
% 262.22/166.57 tff(1085,plain,
% 262.22/166.57 (forallprefers(f1(P!8, Q!7, false), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))) <=> forallprefers(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)), not1(false))),
% 262.22/166.57 inference(symmetry,[status(thm)],[1084])).
% 262.22/166.57 tff(1086,plain,
% 262.22/166.57 ((~forallprefers(f1(P!8, Q!7, false), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))) <=> (~forallprefers(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)), not1(false)))),
% 262.22/166.57 inference(monotonicity,[status(thm)],[1085])).
% 262.22/166.57 tff(1087,plain,
% 262.22/166.57 (~forallprefers(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)), not1(false))),
% 262.22/166.57 inference(modus_ponens,[status(thm)],[802, 1086])).
% 262.22/166.57 tff(1088,plain,
% 262.22/166.57 ((~(forallprefers(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)), not1(false)) <=> ((~((~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | (~d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)))) | bool(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))))) | (lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = false)))) | forallprefers(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)), not1(false)) | (~((~((~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | (~d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)))) | bool(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))))) | (lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = false)))),
% 262.22/166.57 inference(tautology,[status(thm)],[])).
% 262.22/166.57 tff(1089,plain,
% 262.22/166.57 (~((~((~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | (~d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)))) | bool(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))))) | (lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = false))),
% 262.22/166.57 inference(unit_resolution,[status(thm)],[1088, 1087, 1070])).
% 262.22/166.57 tff(1090,plain,
% 262.22/166.57 (((~((~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | (~d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)))) | bool(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))))) | (lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = false)) | ((~d(not1(false))) | (~bool(not1(false))) | (~d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)))) | bool(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))))),
% 262.22/166.57 inference(tautology,[status(thm)],[])).
% 262.22/166.57 tff(1091,plain,
% 262.22/166.57 ((~d(not1(false))) | (~bool(not1(false))) | (~d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)))) | bool(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)))),
% 262.22/166.57 inference(unit_resolution,[status(thm)],[1090, 1089])).
% 262.22/166.57 tff(1092,plain,
% 262.22/166.57 (((~((~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | (~d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)))) | bool(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))))) | (lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = false)) | ((~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))))),
% 262.22/166.57 inference(tautology,[status(thm)],[])).
% 262.22/166.57 tff(1093,plain,
% 262.22/166.57 ((~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)))),
% 262.22/166.57 inference(unit_resolution,[status(thm)],[1092, 1089])).
% 262.22/166.57 tff(1094,plain,
% 262.22/166.57 ((~((~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))))) | (~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)))),
% 262.22/166.57 inference(tautology,[status(thm)],[])).
% 262.22/166.57 tff(1095,plain,
% 262.22/166.57 ((~((~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))))) | d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)))),
% 262.22/166.57 inference(unit_resolution,[status(thm)],[1094, 41])).
% 262.22/166.57 tff(1096,plain,
% 262.22/166.57 (d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)))),
% 262.22/166.57 inference(unit_resolution,[status(thm)],[1095, 1093])).
% 262.22/166.57 tff(1097,plain,
% 262.22/166.57 ((~((~d(not1(false))) | (~bool(not1(false))) | (~d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)))) | bool(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))))) | (~d(not1(false))) | (~bool(not1(false))) | (~d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)))) | bool(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)))),
% 262.22/166.57 inference(tautology,[status(thm)],[])).
% 262.22/166.57 tff(1098,plain,
% 262.22/166.57 ((~((~d(not1(false))) | (~bool(not1(false))) | (~d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)))) | bool(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))))) | (~d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)))) | bool(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)))),
% 262.22/166.57 inference(unit_resolution,[status(thm)],[1097, 41, 81])).
% 262.22/166.57 tff(1099,plain,
% 262.22/166.57 (bool(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)))),
% 262.22/166.57 inference(unit_resolution,[status(thm)],[1098, 1096, 1091])).
% 262.22/166.57 tff(1100,plain,
% 262.22/166.57 ((~(bool(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))) <=> ((lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = false) | (lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = not1(false))))) | (~bool(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)))) | ((lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = false) | (lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = not1(false)))),
% 262.22/166.57 inference(tautology,[status(thm)],[])).
% 262.22/166.57 tff(1101,plain,
% 262.22/166.57 ((~(bool(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))) <=> ((lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = false) | (lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = not1(false))))) | ((lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = false) | (lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = not1(false)))),
% 262.22/166.57 inference(unit_resolution,[status(thm)],[1100, 1099])).
% 262.22/166.57 tff(1102,plain,
% 262.22/166.57 ((lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = false) | (lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = not1(false))),
% 262.22/166.57 inference(unit_resolution,[status(thm)],[1101, 1063])).
% 262.22/166.57 tff(1103,plain,
% 262.22/166.57 (((~((~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | (~d(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)))) | bool(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))))) | (lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = false)) | (~(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = false))),
% 262.22/166.57 inference(tautology,[status(thm)],[])).
% 262.22/166.57 tff(1104,plain,
% 262.22/166.57 (~(lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = false)),
% 262.22/166.57 inference(unit_resolution,[status(thm)],[1103, 1089])).
% 262.22/166.57 tff(1105,plain,
% 262.22/166.57 ((~((lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = false) | (lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = not1(false)))) | (lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = false) | (lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = not1(false))),
% 262.22/166.57 inference(tautology,[status(thm)],[])).
% 262.22/166.57 tff(1106,plain,
% 262.22/166.57 ((~((lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = false) | (lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = not1(false)))) | (lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = not1(false))),
% 262.22/166.57 inference(unit_resolution,[status(thm)],[1105, 1104])).
% 262.22/166.57 tff(1107,plain,
% 262.22/166.57 (lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = not1(false)),
% 262.22/166.57 inference(unit_resolution,[status(thm)],[1106, 1102])).
% 262.22/166.57 tff(1108,plain,
% 262.22/166.57 (lazy_impl(not1(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))),
% 262.22/166.57 inference(monotonicity,[status(thm)],[150])).
% 262.22/166.57 tff(1109,plain,
% 262.22/166.57 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = phi(impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)))),
% 262.22/166.57 inference(quant_inst,[status(thm)],[])).
% 262.22/166.57 tff(1110,plain,
% 262.22/166.57 (lazy_impl(not1(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = phi(impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))),
% 262.22/166.57 inference(unit_resolution,[status(thm)],[1109, 33])).
% 262.22/166.57 tff(1111,plain,
% 262.22/166.57 (phi(impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = lazy_impl(not1(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))),
% 262.22/166.58 inference(symmetry,[status(thm)],[1110])).
% 262.22/166.58 tff(1112,plain,
% 262.22/166.58 (phi(impl(impl(impl(Q!7, false2), false2), false2)) = phi(impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))),
% 262.22/166.58 inference(monotonicity,[status(thm)],[1061])).
% 262.22/166.58 tff(1113,plain,
% 262.22/166.58 (phi(impl(impl(impl(Q!7, false2), false2), false2)) = not1(false)),
% 262.22/166.58 inference(transitivity,[status(thm)],[1112, 1111, 1108, 1107])).
% 262.22/166.58 tff(1114,plain,
% 262.22/166.58 ((phi(impl(impl(impl(Q!7, false2), false2), false2)) = err) <=> (not1(false) = err)),
% 262.22/166.58 inference(monotonicity,[status(thm)],[1113])).
% 262.22/166.58 tff(1115,plain,
% 262.22/166.58 ((not1(false) = err) <=> (phi(impl(impl(impl(Q!7, false2), false2), false2)) = err)),
% 262.22/166.58 inference(symmetry,[status(thm)],[1114])).
% 262.22/166.58 tff(1116,plain,
% 262.22/166.58 ((~(not1(false) = err)) <=> (~(phi(impl(impl(impl(Q!7, false2), false2), false2)) = err))),
% 262.22/166.58 inference(monotonicity,[status(thm)],[1115])).
% 262.22/166.58 tff(1117,plain,
% 262.22/166.58 (~(phi(impl(impl(impl(Q!7, false2), false2), false2)) = err)),
% 262.22/166.58 inference(modus_ponens,[status(thm)],[248, 1116])).
% 262.22/166.58 tff(1118,plain,
% 262.22/166.58 ((d(impl(impl(impl(Q!7, false2), false2), false2)) | (~(phi(impl(impl(impl(Q!7, false2), false2), false2)) = err))) | (phi(impl(impl(impl(Q!7, false2), false2), false2)) = err)),
% 262.22/166.58 inference(tautology,[status(thm)],[])).
% 262.22/166.58 tff(1119,plain,
% 262.22/166.58 (d(impl(impl(impl(Q!7, false2), false2), false2)) | (~(phi(impl(impl(impl(Q!7, false2), false2), false2)) = err))),
% 262.22/166.58 inference(unit_resolution,[status(thm)],[1118, 1117])).
% 262.22/166.58 tff(1120,plain,
% 262.22/166.58 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(impl(impl(Q!7, false2), false2), false2))) | (~(phi(impl(impl(impl(Q!7, false2), false2), false2)) = impl(impl(impl(Q!7, false2), false2), false2))))) | (~(d(impl(impl(impl(Q!7, false2), false2), false2)) | (~(phi(impl(impl(impl(Q!7, false2), false2), false2)) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(impl(impl(impl(Q!7, false2), false2), false2))) | (~(phi(impl(impl(impl(Q!7, false2), false2), false2)) = impl(impl(impl(Q!7, false2), false2), false2))))) | (~(d(impl(impl(impl(Q!7, false2), false2), false2)) | (~(phi(impl(impl(impl(Q!7, false2), false2), false2)) = err)))))),
% 262.22/166.58 inference(rewrite,[status(thm)],[])).
% 262.22/166.58 tff(1121,plain,
% 262.22/166.58 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(impl(impl(Q!7, false2), false2), false2))) | (~(phi(impl(impl(impl(Q!7, false2), false2), false2)) = impl(impl(impl(Q!7, false2), false2), false2))))) | (~(d(impl(impl(impl(Q!7, false2), false2), false2)) | (~(phi(impl(impl(impl(Q!7, false2), false2), false2)) = err)))))),
% 262.22/166.58 inference(quant_inst,[status(thm)],[])).
% 262.22/166.58 tff(1122,plain,
% 262.22/166.58 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(impl(impl(impl(Q!7, false2), false2), false2))) | (~(phi(impl(impl(impl(Q!7, false2), false2), false2)) = impl(impl(impl(Q!7, false2), false2), false2))))) | (~(d(impl(impl(impl(Q!7, false2), false2), false2)) | (~(phi(impl(impl(impl(Q!7, false2), false2), false2)) = err))))),
% 262.22/166.58 inference(modus_ponens,[status(thm)],[1121, 1120])).
% 262.22/166.58 tff(1123,plain,
% 262.22/166.58 ((~((~d(impl(impl(impl(Q!7, false2), false2), false2))) | (~(phi(impl(impl(impl(Q!7, false2), false2), false2)) = impl(impl(impl(Q!7, false2), false2), false2))))) | (~(d(impl(impl(impl(Q!7, false2), false2), false2)) | (~(phi(impl(impl(impl(Q!7, false2), false2), false2)) = err))))),
% 262.22/166.58 inference(unit_resolution,[status(thm)],[1122, 17])).
% 262.22/166.58 tff(1124,plain,
% 262.22/166.58 (~((~d(impl(impl(impl(Q!7, false2), false2), false2))) | (~(phi(impl(impl(impl(Q!7, false2), false2), false2)) = impl(impl(impl(Q!7, false2), false2), false2))))),
% 262.22/166.58 inference(unit_resolution,[status(thm)],[1123, 1119])).
% 262.22/166.58 tff(1125,plain,
% 262.22/166.58 (((~d(impl(impl(impl(Q!7, false2), false2), false2))) | (~(phi(impl(impl(impl(Q!7, false2), false2), false2)) = impl(impl(impl(Q!7, false2), false2), false2)))) | (phi(impl(impl(impl(Q!7, false2), false2), false2)) = impl(impl(impl(Q!7, false2), false2), false2))),
% 262.22/166.58 inference(tautology,[status(thm)],[])).
% 262.22/166.58 tff(1126,plain,
% 262.22/166.58 (phi(impl(impl(impl(Q!7, false2), false2), false2)) = impl(impl(impl(Q!7, false2), false2), false2)),
% 262.22/166.58 inference(unit_resolution,[status(thm)],[1125, 1124])).
% 262.22/166.58 tff(1127,plain,
% 262.22/166.58 (phi(impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = phi(impl(impl(impl(Q!7, false2), false2), false2))),
% 262.22/166.58 inference(symmetry,[status(thm)],[1112])).
% 262.22/166.58 tff(1128,plain,
% 262.22/166.58 (lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false)) = lazy_impl(not1(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))),
% 262.22/166.58 inference(symmetry,[status(thm)],[1108])).
% 262.22/166.58 tff(1129,plain,
% 262.22/166.58 (not1(false) = lazy_impl(prop(false), impl(impl(impl(Q!7, false2), impl(not1(false), false)), false))),
% 262.22/166.58 inference(symmetry,[status(thm)],[1107])).
% 262.22/166.58 tff(1130,plain,
% 262.22/166.58 (not1(false) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.22/166.58 inference(transitivity,[status(thm)],[1129, 1128, 1110, 1127, 1126, 1061, 1056, 1040, 1028])).
% 262.22/166.58 tff(1131,plain,
% 262.22/166.58 ((impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = not1(false)) <=> (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))),
% 262.22/166.58 inference(monotonicity,[status(thm)],[1130])).
% 262.22/166.58 tff(1132,plain,
% 262.22/166.58 ((impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = not1(false)) <=> (phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.22/166.58 inference(transitivity,[status(thm)],[1131, 1015])).
% 262.22/166.58 tff(1133,plain,
% 262.22/166.58 ((~(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = not1(false))) <=> (~(phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))),
% 262.22/166.58 inference(monotonicity,[status(thm)],[1132])).
% 262.22/166.58 tff(1134,plain,
% 262.22/166.58 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) <=> ((impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = false) | (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = not1(false))))),
% 262.22/166.58 inference(quant_inst,[status(thm)],[])).
% 262.22/166.58 tff(1135,plain,
% 262.22/166.58 (bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) <=> ((impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = false) | (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = not1(false)))),
% 262.22/166.58 inference(unit_resolution,[status(thm)],[1134, 229])).
% 262.22/166.58 tff(1136,plain,
% 262.22/166.58 ((~(bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) <=> ((impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = false) | (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = not1(false))))) | bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) | (~((impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = false) | (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = not1(false))))),
% 262.22/166.58 inference(tautology,[status(thm)],[])).
% 262.22/166.58 tff(1137,plain,
% 262.22/166.58 ((~(bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) <=> ((impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = false) | (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = not1(false))))) | (~((impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = false) | (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = not1(false))))),
% 262.22/166.58 inference(unit_resolution,[status(thm)],[1136, 1034])).
% 262.22/166.58 tff(1138,plain,
% 262.22/166.58 (~((impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = false) | (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = not1(false)))),
% 262.22/166.58 inference(unit_resolution,[status(thm)],[1137, 1135])).
% 262.22/166.58 tff(1139,plain,
% 262.22/166.58 (((impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = false) | (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = not1(false))) | (~(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = not1(false)))),
% 262.22/166.58 inference(tautology,[status(thm)],[])).
% 262.22/166.58 tff(1140,plain,
% 262.22/166.58 (~(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = not1(false))),
% 262.22/166.58 inference(unit_resolution,[status(thm)],[1139, 1138])).
% 262.22/166.58 tff(1141,plain,
% 262.22/166.58 (~(phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.22/166.58 inference(modus_ponens,[status(thm)],[1140, 1133])).
% 262.22/166.58 tff(1142,plain,
% 262.22/166.58 ((~d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~(phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))),
% 262.22/166.59 inference(unit_resolution,[status(thm)],[770, 1141])).
% 262.22/166.59 tff(1143,plain,
% 262.22/166.59 (impl(impl(impl(Q!7, false2), false2), false2) = phi(impl(impl(impl(Q!7, false2), false2), false2))),
% 262.22/166.59 inference(symmetry,[status(thm)],[1126])).
% 262.22/166.59 tff(1144,plain,
% 262.22/166.59 (phi(impl(false, impl(Q!7, false))) = impl(impl(false, impl(Q!7, false)), false)),
% 262.22/166.59 inference(symmetry,[status(thm)],[1040])).
% 262.22/166.59 tff(1145,plain,
% 262.22/166.59 (phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = not1(false)),
% 262.22/166.59 inference(transitivity,[status(thm)],[1027, 1144, 1055, 1060, 1143, 1112, 1111, 1108, 1107])).
% 262.22/166.59 tff(1146,plain,
% 262.22/166.59 ((phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = err) <=> (not1(false) = err)),
% 262.22/166.59 inference(monotonicity,[status(thm)],[1145])).
% 262.22/166.59 tff(1147,plain,
% 262.22/166.59 ((not1(false) = err) <=> (phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = err)),
% 262.22/166.59 inference(symmetry,[status(thm)],[1146])).
% 262.22/166.59 tff(1148,plain,
% 262.22/166.59 ((~(not1(false) = err)) <=> (~(phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = err))),
% 262.22/166.59 inference(monotonicity,[status(thm)],[1147])).
% 262.22/166.59 tff(1149,plain,
% 262.22/166.59 (~(phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = err)),
% 262.22/166.59 inference(modus_ponens,[status(thm)],[248, 1148])).
% 262.22/166.59 tff(1150,plain,
% 262.22/166.59 ((d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) | (~(phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = err))) | (phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = err)),
% 262.22/166.59 inference(tautology,[status(thm)],[])).
% 262.22/166.59 tff(1151,plain,
% 262.22/166.59 (d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) | (~(phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = err))),
% 262.22/166.59 inference(unit_resolution,[status(thm)],[1150, 1149])).
% 262.22/166.59 tff(1152,plain,
% 262.22/166.59 ($false),
% 262.22/166.59 inference(unit_resolution,[status(thm)],[828, 1151, 1142])).
% 262.22/166.59 tff(1153,plain,(bool(Q!7) | (~(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~(prop(tptp_fun_R_0(Q!7, P!8)) = false)) | bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) | bool(impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), inference(lemma,lemma(discharge,[]))).
% 262.22/166.59 tff(1154,plain,
% 262.22/166.59 (~(prop(tptp_fun_R_0(Q!7, P!8)) = false)),
% 262.22/166.59 inference(unit_resolution,[status(thm)],[1153, 1014, 879, 516, 887])).
% 262.22/166.59 tff(1155,plain,
% 262.22/166.59 (bool(tptp_fun_R_0(Q!7, P!8))),
% 262.22/166.59 inference(unit_resolution,[status(thm)],[380, 1154])).
% 262.22/166.59 tff(1156,plain,
% 262.22/166.59 (prop(tptp_fun_R_0(Q!7, P!8)) = not1(false)),
% 262.22/166.59 inference(unit_resolution,[status(thm)],[368, 1155])).
% 262.22/166.59 tff(1157,plain,
% 262.22/166.59 (prop(tptp_fun_R_0(Q!7, P!8)) = prop(false)),
% 262.22/166.59 inference(transitivity,[status(thm)],[1156, 150])).
% 262.22/166.59 tff(1158,plain,
% 262.22/166.59 (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(false, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(prop(false), impl(impl(Q!7, impl(not1(false), false)), false))),
% 262.22/166.59 inference(monotonicity,[status(thm)],[1157, 1008])).
% 262.22/166.59 tff(1159,plain,
% 262.22/166.59 (impl(false, impl(Q!7, false)) = impl(false, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.22/166.59 inference(symmetry,[status(thm)],[1006])).
% 262.22/166.59 tff(1160,plain,
% 262.22/166.59 (phi(impl(Q!7, false)) = impl(false, impl(Q!7, false))),
% 262.22/166.59 inference(symmetry,[status(thm)],[957])).
% 262.22/166.59 tff(1161,plain,
% 262.22/166.59 (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = impl(false, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.22/166.59 inference(transitivity,[status(thm)],[887, 745, 1160, 1159])).
% 262.22/166.59 tff(1162,plain,
% 262.22/166.59 (impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)) = impl(impl(false, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))),
% 262.22/166.59 inference(monotonicity,[status(thm)],[1161])).
% 262.22/166.59 tff(1163,plain,
% 262.22/166.59 (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(false, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))),
% 262.22/166.59 inference(monotonicity,[status(thm)],[1162])).
% 262.22/166.59 tff(1164,plain,
% 262.22/166.59 (f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)) = lazy_impl(not1(false), impl(Q!7, err))),
% 262.22/166.59 inference(transitivity,[status(thm)],[176, 1163, 1158, 949, 948, 946, 944, 942, 530, 515])).
% 262.22/166.59 tff(1165,plain,
% 262.22/166.59 (phi(f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(lazy_impl(not1(false), impl(Q!7, err)))),
% 262.22/166.59 inference(monotonicity,[status(thm)],[1164])).
% 262.22/166.59 tff(1166,plain,
% 262.22/166.59 (phi(lazy_impl(not1(false), impl(Q!7, err))) = phi(f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.22/166.59 inference(symmetry,[status(thm)],[1165])).
% 262.22/166.59 tff(1167,plain,
% 262.22/166.59 (phi(phi(impl(Q!7, false))) = phi(lazy_impl(not1(false), impl(Q!7, err)))),
% 262.22/166.59 inference(symmetry,[status(thm)],[944])).
% 262.22/166.59 tff(1168,plain,
% 262.22/166.59 (phi(impl(Q!7, false)) = phi(phi(impl(Q!7, false)))),
% 262.22/166.59 inference(symmetry,[status(thm)],[942])).
% 262.22/166.59 tff(1169,plain,
% 262.22/166.59 (^[A: $i, B: $i] : refl((bool(B) | (~bool(A)) | (and1(A, B) = phi(B))) <=> (bool(B) | (~bool(A)) | (and1(A, B) = phi(B))))),
% 262.22/166.59 inference(bind,[status(th)],[])).
% 262.22/166.59 tff(1170,plain,
% 262.22/166.59 (![A: $i, B: $i] : (bool(B) | (~bool(A)) | (and1(A, B) = phi(B))) <=> ![A: $i, B: $i] : (bool(B) | (~bool(A)) | (and1(A, B) = phi(B)))),
% 262.22/166.59 inference(quant_intro,[status(thm)],[1169])).
% 262.22/166.59 tff(1171,plain,
% 262.22/166.59 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((bool(A) & (~bool(B))) <=> (~(bool(B) | (~bool(A))))), ((~(bool(A) & (~bool(B)))) <=> (~(~(bool(B) | (~bool(A))))))), rewrite((~(~(bool(B) | (~bool(A))))) <=> (bool(B) | (~bool(A)))), ((~(bool(A) & (~bool(B)))) <=> (bool(B) | (~bool(A))))), (((~(bool(A) & (~bool(B)))) | (and1(A, B) = phi(B))) <=> ((bool(B) | (~bool(A))) | (and1(A, B) = phi(B))))), rewrite(((bool(B) | (~bool(A))) | (and1(A, B) = phi(B))) <=> (bool(B) | (~bool(A)) | (and1(A, B) = phi(B)))), (((~(bool(A) & (~bool(B)))) | (and1(A, B) = phi(B))) <=> (bool(B) | (~bool(A)) | (and1(A, B) = phi(B)))))),
% 262.22/166.59 inference(bind,[status(th)],[])).
% 262.22/166.59 tff(1172,plain,
% 262.22/166.59 (![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (and1(A, B) = phi(B))) <=> ![A: $i, B: $i] : (bool(B) | (~bool(A)) | (and1(A, B) = phi(B)))),
% 262.22/166.59 inference(quant_intro,[status(thm)],[1171])).
% 262.22/166.59 tff(1173,plain,
% 262.22/166.59 (![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (and1(A, B) = phi(B))) <=> ![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (and1(A, B) = phi(B)))),
% 262.22/166.59 inference(rewrite,[status(thm)],[])).
% 262.22/166.59 tff(1174,plain,
% 262.22/166.59 (^[A: $i, B: $i] : rewrite(((bool(A) & (~bool(B))) => (and1(A, B) = phi(B))) <=> ((~(bool(A) & (~bool(B)))) | (and1(A, B) = phi(B))))),
% 262.22/166.59 inference(bind,[status(th)],[])).
% 262.22/166.59 tff(1175,plain,
% 262.22/166.59 (![A: $i, B: $i] : ((bool(A) & (~bool(B))) => (and1(A, B) = phi(B))) <=> ![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (and1(A, B) = phi(B)))),
% 262.22/166.59 inference(quant_intro,[status(thm)],[1174])).
% 262.22/166.59 tff(1176,axiom,(![A: $i, B: $i] : ((bool(A) & (~bool(B))) => (and1(A, B) = phi(B)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','and1_axiom2')).
% 262.22/166.59 tff(1177,plain,
% 262.22/166.59 (![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (and1(A, B) = phi(B)))),
% 262.22/166.59 inference(modus_ponens,[status(thm)],[1176, 1175])).
% 262.22/166.59 tff(1178,plain,
% 262.22/166.59 (![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (and1(A, B) = phi(B)))),
% 262.22/166.59 inference(modus_ponens,[status(thm)],[1177, 1173])).
% 262.22/166.59 tff(1179,plain,(
% 262.22/166.59 ![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (and1(A, B) = phi(B)))),
% 262.22/166.59 inference(skolemize,[status(sab)],[1178])).
% 262.22/166.59 tff(1180,plain,
% 262.22/166.59 (![A: $i, B: $i] : (bool(B) | (~bool(A)) | (and1(A, B) = phi(B)))),
% 262.22/166.59 inference(modus_ponens,[status(thm)],[1179, 1172])).
% 262.22/166.59 tff(1181,plain,
% 262.22/166.59 (![A: $i, B: $i] : (bool(B) | (~bool(A)) | (and1(A, B) = phi(B)))),
% 262.22/166.59 inference(modus_ponens,[status(thm)],[1180, 1170])).
% 262.22/166.59 tff(1182,plain,
% 262.22/166.59 (((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (and1(A, B) = phi(B)))) | (bool(Q!7) | (~bool(P!8)) | (and1(P!8, Q!7) = phi(Q!7)))) <=> ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (and1(A, B) = phi(B)))) | bool(Q!7) | (~bool(P!8)) | (and1(P!8, Q!7) = phi(Q!7)))),
% 262.22/166.59 inference(rewrite,[status(thm)],[])).
% 262.22/166.59 tff(1183,plain,
% 262.22/166.59 ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (and1(A, B) = phi(B)))) | (bool(Q!7) | (~bool(P!8)) | (and1(P!8, Q!7) = phi(Q!7)))),
% 262.22/166.59 inference(quant_inst,[status(thm)],[])).
% 262.22/166.59 tff(1184,plain,
% 262.22/166.59 ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (and1(A, B) = phi(B)))) | bool(Q!7) | (~bool(P!8)) | (and1(P!8, Q!7) = phi(Q!7))),
% 262.22/166.59 inference(modus_ponens,[status(thm)],[1183, 1182])).
% 262.22/166.59 tff(1185,plain,
% 262.22/166.59 (bool(Q!7) | (~bool(P!8)) | (and1(P!8, Q!7) = phi(Q!7))),
% 262.22/166.59 inference(unit_resolution,[status(thm)],[1184, 1181])).
% 262.22/166.59 tff(1186,plain,
% 262.22/166.59 (and1(P!8, Q!7) = phi(Q!7)),
% 262.22/166.59 inference(unit_resolution,[status(thm)],[1185, 868, 516])).
% 262.22/166.59 tff(1187,plain,
% 262.22/166.59 (and1(P!8, Q!7) = and2(P!8, Q!7)),
% 262.22/166.59 inference(transitivity,[status(thm)],[1186, 995, 994, 529, 1168, 1167, 1166, 296])).
% 262.22/166.59 tff(1188,plain,
% 262.22/166.59 ($false),
% 262.22/166.59 inference(unit_resolution,[status(thm)],[361, 1187])).
% 262.22/166.59 tff(1189,plain,(bool(Q!7)), inference(lemma,lemma(discharge,[]))).
% 262.22/166.59 tff(1190,plain,
% 262.22/166.59 ((~(bool(Q!7) <=> ((Q!7 = false) | (Q!7 = not1(false))))) | (~bool(Q!7)) | ((Q!7 = false) | (Q!7 = not1(false)))),
% 262.22/166.59 inference(tautology,[status(thm)],[])).
% 262.22/166.59 tff(1191,plain,
% 262.22/166.59 ((~bool(Q!7)) | ((Q!7 = false) | (Q!7 = not1(false)))),
% 262.22/166.59 inference(unit_resolution,[status(thm)],[1190, 624])).
% 262.22/166.59 tff(1192,plain,
% 262.22/166.59 ((Q!7 = false) | (Q!7 = not1(false))),
% 262.22/166.59 inference(unit_resolution,[status(thm)],[1191, 1189])).
% 262.22/166.59 tff(1193,plain,
% 262.22/166.59 ((~((Q!7 = false) | (Q!7 = not1(false)))) | (Q!7 = false) | (Q!7 = not1(false))),
% 262.22/166.59 inference(tautology,[status(thm)],[])).
% 262.22/166.59 tff(1194,plain,
% 262.22/166.59 ((Q!7 = false) | (Q!7 = not1(false))),
% 262.22/166.59 inference(unit_resolution,[status(thm)],[1193, 1192])).
% 262.22/166.59 tff(1195,plain,
% 262.22/166.59 (Q!7 = false),
% 262.22/166.59 inference(unit_resolution,[status(thm)],[1194, 512])).
% 262.22/166.59 tff(1196,plain,
% 262.22/166.59 (f1(P!8, Q!7, not1(false)) = f1(P!8, false, not1(false))),
% 262.22/166.59 inference(monotonicity,[status(thm)],[1195])).
% 262.22/166.59 tff(1197,plain,
% 262.22/166.59 (f1(P!8, false, not1(false)) = f1(P!8, Q!7, not1(false))),
% 262.22/166.59 inference(symmetry,[status(thm)],[1196])).
% 262.22/166.59 tff(1198,plain,
% 262.22/166.59 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(P!8, false, not1(false)) = lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))),
% 262.22/166.59 inference(quant_inst,[status(thm)],[])).
% 262.22/166.59 tff(1199,plain,
% 262.22/166.59 (f1(P!8, false, not1(false)) = lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false)))),
% 262.22/166.59 inference(unit_resolution,[status(thm)],[1198, 159])).
% 262.22/166.59 tff(1200,plain,
% 262.22/166.59 (lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))) = f1(P!8, false, not1(false))),
% 262.22/166.59 inference(symmetry,[status(thm)],[1199])).
% 262.22/166.59 tff(1201,plain,
% 262.22/166.59 (impl(impl(P!8, impl(false, not1(false))), not1(false)) = impl(P!8, impl(false, not1(false)))),
% 262.22/166.59 inference(transitivity,[status(thm)],[414, 430])).
% 262.22/166.59 tff(1202,plain,
% 262.22/166.59 (phi(impl(impl(P!8, impl(false, not1(false))), not1(false))) = phi(impl(P!8, impl(false, not1(false))))),
% 262.22/166.59 inference(monotonicity,[status(thm)],[1201])).
% 262.22/166.59 tff(1203,plain,
% 262.22/166.59 (phi(impl(P!8, impl(false, not1(false)))) = phi(impl(impl(P!8, impl(false, not1(false))), not1(false)))),
% 262.22/166.59 inference(symmetry,[status(thm)],[1202])).
% 262.22/166.59 tff(1204,plain,
% 262.22/166.59 (impl(impl(P!8, impl(false, not1(false))), not1(false)) = f1(P!8, Q!7, not1(false))),
% 262.22/166.59 inference(transitivity,[status(thm)],[414, 1203, 463, 460, 1200, 1197])).
% 262.22/166.59 tff(1205,plain,
% 262.22/166.59 (forallprefers(impl(impl(P!8, impl(false, not1(false))), not1(false)), not1(false)) <=> forallprefers(f1(P!8, Q!7, not1(false)), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.22/166.59 inference(monotonicity,[status(thm)],[1204, 397])).
% 262.22/166.59 tff(1206,plain,
% 262.22/166.59 (forallprefers(f1(P!8, Q!7, not1(false)), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))) <=> forallprefers(impl(impl(P!8, impl(false, not1(false))), not1(false)), not1(false))),
% 262.22/166.59 inference(symmetry,[status(thm)],[1205])).
% 262.22/166.59 tff(1207,plain,
% 262.22/166.59 ((~forallprefers(f1(P!8, Q!7, not1(false)), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))) <=> (~forallprefers(impl(impl(P!8, impl(false, not1(false))), not1(false)), not1(false)))),
% 262.22/166.59 inference(monotonicity,[status(thm)],[1206])).
% 262.22/166.59 tff(1208,plain,
% 262.22/166.59 (~forallprefers(impl(impl(P!8, impl(false, not1(false))), not1(false)), not1(false))),
% 262.22/166.59 inference(modus_ponens,[status(thm)],[476, 1207])).
% 262.22/166.59 tff(1209,plain,
% 262.22/166.59 (~((~d(not1(false))) | (~bool(not1(false))) | bool(impl(impl(P!8, impl(false, not1(false))), not1(false))) | (~d(impl(impl(P!8, impl(false, not1(false))), not1(false)))))),
% 262.22/166.59 inference(unit_resolution,[status(thm)],[503, 41, 81, 438, 434])).
% 262.22/166.59 tff(1210,plain,
% 262.22/166.59 ((~((~d(not1(false))) | d(impl(impl(P!8, impl(false, not1(false))), not1(false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(impl(impl(P!8, impl(false, not1(false))), not1(false))) | (~d(impl(impl(P!8, impl(false, not1(false))), not1(false)))))) | (impl(impl(P!8, impl(false, not1(false))), not1(false)) = false)),
% 262.22/166.59 inference(unit_resolution,[status(thm)],[505, 1209])).
% 262.22/166.59 tff(1211,plain,
% 262.22/166.59 ((~(forallprefers(impl(impl(P!8, impl(false, not1(false))), not1(false)), not1(false)) <=> ((~((~d(not1(false))) | d(impl(impl(P!8, impl(false, not1(false))), not1(false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(impl(impl(P!8, impl(false, not1(false))), not1(false))) | (~d(impl(impl(P!8, impl(false, not1(false))), not1(false)))))) | (impl(impl(P!8, impl(false, not1(false))), not1(false)) = false)))) | forallprefers(impl(impl(P!8, impl(false, not1(false))), not1(false)), not1(false))),
% 262.22/166.59 inference(unit_resolution,[status(thm)],[507, 1210])).
% 262.22/166.59 tff(1212,plain,
% 262.22/166.59 (forallprefers(impl(impl(P!8, impl(false, not1(false))), not1(false)), not1(false))),
% 262.22/166.59 inference(unit_resolution,[status(thm)],[1211, 500])).
% 262.22/166.59 tff(1213,plain,
% 262.22/166.59 ($false),
% 262.22/166.59 inference(unit_resolution,[status(thm)],[1212, 1208])).
% 262.22/166.59 tff(1214,plain,(bool(P!8)), inference(lemma,lemma(discharge,[]))).
% 262.22/166.59 tff(1215,plain,
% 262.22/166.59 ((~![X: $i] : ((prop(X) = not1(false)) <=> bool(X))) | ((prop(P!8) = not1(false)) <=> bool(P!8))),
% 262.22/166.59 inference(quant_inst,[status(thm)],[])).
% 262.22/166.59 tff(1216,plain,
% 262.22/166.59 ((prop(P!8) = not1(false)) <=> bool(P!8)),
% 262.22/166.59 inference(unit_resolution,[status(thm)],[1215, 144])).
% 262.22/166.59 tff(1217,plain,
% 262.22/166.59 ((~((prop(P!8) = not1(false)) <=> bool(P!8))) | (prop(P!8) = not1(false)) | (~bool(P!8))),
% 262.22/166.59 inference(tautology,[status(thm)],[])).
% 262.22/166.59 tff(1218,plain,
% 262.22/166.59 ((prop(P!8) = not1(false)) | (~bool(P!8))),
% 262.22/166.59 inference(unit_resolution,[status(thm)],[1217, 1216])).
% 262.22/166.59 tff(1219,plain,
% 262.22/166.59 (prop(P!8) = not1(false)),
% 262.22/166.59 inference(unit_resolution,[status(thm)],[1218, 1214])).
% 262.22/166.59 tff(1220,plain,
% 262.22/166.59 (lazy_impl(prop(P!8), P!8) = lazy_impl(not1(false), P!8)),
% 262.22/166.59 inference(monotonicity,[status(thm)],[1219])).
% 262.22/166.60 tff(1221,plain,
% 262.22/166.60 (lazy_impl(not1(false), P!8) = lazy_impl(prop(P!8), P!8)),
% 262.22/166.60 inference(symmetry,[status(thm)],[1220])).
% 262.22/166.60 tff(1222,plain,
% 262.22/166.60 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), P!8) = phi(P!8))),
% 262.22/166.60 inference(quant_inst,[status(thm)],[])).
% 262.22/166.60 tff(1223,plain,
% 262.22/166.60 (lazy_impl(not1(false), P!8) = phi(P!8)),
% 262.22/166.60 inference(unit_resolution,[status(thm)],[1222, 33])).
% 262.22/166.60 tff(1224,plain,
% 262.22/166.60 (phi(P!8) = lazy_impl(not1(false), P!8)),
% 262.22/166.60 inference(symmetry,[status(thm)],[1223])).
% 262.22/166.60 tff(1225,assumption,(prop(P!8) = not1(false)), introduced(assumption)).
% 262.22/166.60 tff(1226,plain,
% 262.22/166.60 (not1(false) = prop(P!8)),
% 262.22/166.60 inference(symmetry,[status(thm)],[1225])).
% 262.22/166.60 tff(1227,plain,
% 262.22/166.60 (lazy_impl(not1(false), P!8) = lazy_impl(prop(P!8), P!8)),
% 262.22/166.60 inference(monotonicity,[status(thm)],[1226])).
% 262.22/166.60 tff(1228,assumption,(phi(P!8) = err), introduced(assumption)).
% 262.22/166.60 tff(1229,plain,
% 262.22/166.60 (err = phi(P!8)),
% 262.22/166.60 inference(symmetry,[status(thm)],[1228])).
% 262.22/166.60 tff(1230,plain,
% 262.22/166.60 (err = lazy_impl(prop(P!8), P!8)),
% 262.22/166.60 inference(transitivity,[status(thm)],[1229, 1224, 1227])).
% 262.22/166.60 tff(1231,plain,
% 262.22/166.60 (bool(err) <=> bool(lazy_impl(prop(P!8), P!8))),
% 262.22/166.60 inference(monotonicity,[status(thm)],[1230])).
% 262.22/166.60 tff(1232,plain,
% 262.22/166.60 (bool(lazy_impl(prop(P!8), P!8)) <=> bool(err)),
% 262.22/166.60 inference(symmetry,[status(thm)],[1231])).
% 262.22/166.60 tff(1233,plain,
% 262.22/166.60 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(P!8), P!8), false) <=> ((~((~d(false)) | d(lazy_impl(prop(P!8), P!8)))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(P!8), P!8) = false)))) | (~((~d(false)) | (~bool(false)) | (~d(lazy_impl(prop(P!8), P!8))) | bool(lazy_impl(prop(P!8), P!8))))))) <=> ((~![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(P!8), P!8), false) <=> ((~((~d(false)) | d(lazy_impl(prop(P!8), P!8)))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(P!8), P!8) = false)))) | (~((~d(false)) | (~bool(false)) | (~d(lazy_impl(prop(P!8), P!8))) | bool(lazy_impl(prop(P!8), P!8)))))))),
% 262.22/166.60 inference(rewrite,[status(thm)],[])).
% 262.22/166.60 tff(1234,plain,
% 262.22/166.60 ((forallprefers(lazy_impl(prop(P!8), P!8), false) <=> ((~(d(lazy_impl(prop(P!8), P!8)) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!8), P!8)) | (~d(lazy_impl(prop(P!8), P!8))))) | (~((~(lazy_impl(prop(P!8), P!8) = false)) | (~(false = not1(false))))))) <=> (forallprefers(lazy_impl(prop(P!8), P!8), false) <=> ((~((~d(false)) | d(lazy_impl(prop(P!8), P!8)))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(P!8), P!8) = false)))) | (~((~d(false)) | (~bool(false)) | (~d(lazy_impl(prop(P!8), P!8))) | bool(lazy_impl(prop(P!8), P!8))))))),
% 262.22/166.60 inference(rewrite,[status(thm)],[])).
% 262.22/166.60 tff(1235,plain,
% 262.22/166.60 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(P!8), P!8), false) <=> ((~(d(lazy_impl(prop(P!8), P!8)) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!8), P!8)) | (~d(lazy_impl(prop(P!8), P!8))))) | (~((~(lazy_impl(prop(P!8), P!8) = 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(P!8), P!8), false) <=> ((~((~d(false)) | d(lazy_impl(prop(P!8), P!8)))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(P!8), P!8) = false)))) | (~((~d(false)) | (~bool(false)) | (~d(lazy_impl(prop(P!8), P!8))) | bool(lazy_impl(prop(P!8), P!8)))))))),
% 262.22/166.60 inference(monotonicity,[status(thm)],[1234])).
% 262.22/166.60 tff(1236,plain,
% 262.22/166.60 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(P!8), P!8), false) <=> ((~(d(lazy_impl(prop(P!8), P!8)) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!8), P!8)) | (~d(lazy_impl(prop(P!8), P!8))))) | (~((~(lazy_impl(prop(P!8), P!8) = 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(P!8), P!8), false) <=> ((~((~d(false)) | d(lazy_impl(prop(P!8), P!8)))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(P!8), P!8) = false)))) | (~((~d(false)) | (~bool(false)) | (~d(lazy_impl(prop(P!8), P!8))) | bool(lazy_impl(prop(P!8), P!8)))))))),
% 262.22/166.60 inference(transitivity,[status(thm)],[1235, 1233])).
% 262.22/166.60 tff(1237,plain,
% 262.22/166.60 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(P!8), P!8), false) <=> ((~(d(lazy_impl(prop(P!8), P!8)) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!8), P!8)) | (~d(lazy_impl(prop(P!8), P!8))))) | (~((~(lazy_impl(prop(P!8), P!8) = false)) | (~(false = not1(false)))))))),
% 262.22/166.60 inference(quant_inst,[status(thm)],[])).
% 262.22/166.60 tff(1238,plain,
% 262.22/166.60 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(P!8), P!8), false) <=> ((~((~d(false)) | d(lazy_impl(prop(P!8), P!8)))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(P!8), P!8) = false)))) | (~((~d(false)) | (~bool(false)) | (~d(lazy_impl(prop(P!8), P!8))) | bool(lazy_impl(prop(P!8), P!8))))))),
% 262.22/166.60 inference(modus_ponens,[status(thm)],[1237, 1236])).
% 262.22/166.60 tff(1239,plain,
% 262.22/166.60 (forallprefers(lazy_impl(prop(P!8), P!8), false) <=> ((~((~d(false)) | d(lazy_impl(prop(P!8), P!8)))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(P!8), P!8) = false)))) | (~((~d(false)) | (~bool(false)) | (~d(lazy_impl(prop(P!8), P!8))) | bool(lazy_impl(prop(P!8), P!8)))))),
% 262.22/166.60 inference(unit_resolution,[status(thm)],[1238, 493])).
% 262.22/166.60 tff(1240,plain,
% 262.22/166.60 (f7(false) = f7(P!6)),
% 262.22/166.60 inference(symmetry,[status(thm)],[604])).
% 262.22/166.60 tff(1241,plain,
% 262.22/166.60 (false = f7(P!6)),
% 262.22/166.60 inference(transitivity,[status(thm)],[559, 558, 557, 556, 1240])).
% 262.22/166.60 tff(1242,plain,
% 262.22/166.60 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(P!8) = lazy_impl(prop(P!8), P!8))),
% 262.22/166.60 inference(quant_inst,[status(thm)],[])).
% 262.22/166.60 tff(1243,plain,
% 262.22/166.60 (f7(P!8) = lazy_impl(prop(P!8), P!8)),
% 262.22/166.60 inference(unit_resolution,[status(thm)],[1242, 538])).
% 262.22/166.60 tff(1244,plain,
% 262.22/166.60 (lazy_impl(prop(P!8), P!8) = f7(P!8)),
% 262.22/166.60 inference(symmetry,[status(thm)],[1243])).
% 262.22/166.60 tff(1245,plain,
% 262.22/166.60 (forallprefers(lazy_impl(prop(P!8), P!8), false) <=> forallprefers(f7(P!8), f7(P!6))),
% 262.22/166.60 inference(monotonicity,[status(thm)],[1244, 1241])).
% 262.22/166.60 tff(1246,plain,
% 262.22/166.60 (forallprefers(f7(P!8), f7(P!6)) <=> forallprefers(lazy_impl(prop(P!8), P!8), false)),
% 262.22/166.60 inference(symmetry,[status(thm)],[1245])).
% 262.22/166.60 tff(1247,plain,
% 262.22/166.60 ((~forallprefers(f7(P!8), f7(P!6))) <=> (~forallprefers(lazy_impl(prop(P!8), P!8), false))),
% 262.22/166.60 inference(monotonicity,[status(thm)],[1246])).
% 262.22/166.60 tff(1248,plain,
% 262.22/166.60 ((~![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))) | (~forallprefers(f7(P!8), f7(P!6)))),
% 262.22/166.60 inference(quant_inst,[status(thm)],[])).
% 262.22/166.60 tff(1249,plain,
% 262.22/166.60 (~forallprefers(f7(P!8), f7(P!6))),
% 262.22/166.60 inference(unit_resolution,[status(thm)],[1248, 572])).
% 262.22/166.60 tff(1250,plain,
% 262.22/166.60 (~forallprefers(lazy_impl(prop(P!8), P!8), false)),
% 262.22/166.60 inference(modus_ponens,[status(thm)],[1249, 1247])).
% 262.22/166.60 tff(1251,plain,
% 262.22/166.60 ((~(forallprefers(lazy_impl(prop(P!8), P!8), false) <=> ((~((~d(false)) | d(lazy_impl(prop(P!8), P!8)))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(P!8), P!8) = false)))) | (~((~d(false)) | (~bool(false)) | (~d(lazy_impl(prop(P!8), P!8))) | bool(lazy_impl(prop(P!8), P!8))))))) | forallprefers(lazy_impl(prop(P!8), P!8), false) | (~((~((~d(false)) | d(lazy_impl(prop(P!8), P!8)))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(P!8), P!8) = false)))) | (~((~d(false)) | (~bool(false)) | (~d(lazy_impl(prop(P!8), P!8))) | bool(lazy_impl(prop(P!8), P!8))))))),
% 262.22/166.60 inference(tautology,[status(thm)],[])).
% 262.22/166.60 tff(1252,plain,
% 262.22/166.60 (~((~((~d(false)) | d(lazy_impl(prop(P!8), P!8)))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(P!8), P!8) = false)))) | (~((~d(false)) | (~bool(false)) | (~d(lazy_impl(prop(P!8), P!8))) | bool(lazy_impl(prop(P!8), P!8)))))),
% 262.22/166.60 inference(unit_resolution,[status(thm)],[1251, 1250, 1239])).
% 262.22/166.60 tff(1253,plain,
% 262.22/166.60 (((~((~d(false)) | d(lazy_impl(prop(P!8), P!8)))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(P!8), P!8) = false)))) | (~((~d(false)) | (~bool(false)) | (~d(lazy_impl(prop(P!8), P!8))) | bool(lazy_impl(prop(P!8), P!8))))) | ((~d(false)) | (~bool(false)) | (~d(lazy_impl(prop(P!8), P!8))) | bool(lazy_impl(prop(P!8), P!8)))),
% 262.22/166.60 inference(tautology,[status(thm)],[])).
% 262.22/166.60 tff(1254,plain,
% 262.22/166.60 ((~d(false)) | (~bool(false)) | (~d(lazy_impl(prop(P!8), P!8))) | bool(lazy_impl(prop(P!8), P!8))),
% 262.22/166.60 inference(unit_resolution,[status(thm)],[1253, 1252])).
% 262.22/166.60 tff(1255,plain,
% 262.22/166.60 (((~((~d(false)) | d(lazy_impl(prop(P!8), P!8)))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(P!8), P!8) = false)))) | (~((~d(false)) | (~bool(false)) | (~d(lazy_impl(prop(P!8), P!8))) | bool(lazy_impl(prop(P!8), P!8))))) | ((~d(false)) | d(lazy_impl(prop(P!8), P!8)))),
% 262.22/166.60 inference(tautology,[status(thm)],[])).
% 262.22/166.60 tff(1256,plain,
% 262.22/166.60 ((~d(false)) | d(lazy_impl(prop(P!8), P!8))),
% 262.22/166.60 inference(unit_resolution,[status(thm)],[1255, 1252])).
% 262.22/166.60 tff(1257,plain,
% 262.22/166.60 ((~((~d(false)) | d(lazy_impl(prop(P!8), P!8)))) | (~d(false)) | d(lazy_impl(prop(P!8), P!8))),
% 262.22/166.60 inference(tautology,[status(thm)],[])).
% 262.22/166.60 tff(1258,plain,
% 262.22/166.60 ((~((~d(false)) | d(lazy_impl(prop(P!8), P!8)))) | d(lazy_impl(prop(P!8), P!8))),
% 262.22/166.60 inference(unit_resolution,[status(thm)],[1257, 5])).
% 262.22/166.60 tff(1259,plain,
% 262.22/166.60 (d(lazy_impl(prop(P!8), P!8))),
% 262.22/166.60 inference(unit_resolution,[status(thm)],[1258, 1256])).
% 262.22/166.60 tff(1260,plain,
% 262.22/166.60 ((~((~d(false)) | (~bool(false)) | (~d(lazy_impl(prop(P!8), P!8))) | bool(lazy_impl(prop(P!8), P!8)))) | (~d(false)) | (~bool(false)) | (~d(lazy_impl(prop(P!8), P!8))) | bool(lazy_impl(prop(P!8), P!8))),
% 262.22/166.61 inference(tautology,[status(thm)],[])).
% 262.22/166.61 tff(1261,plain,
% 262.22/166.61 ((~((~d(false)) | (~bool(false)) | (~d(lazy_impl(prop(P!8), P!8))) | bool(lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(P!8), P!8))) | bool(lazy_impl(prop(P!8), P!8))),
% 262.22/166.61 inference(unit_resolution,[status(thm)],[1260, 5, 107])).
% 262.22/166.61 tff(1262,plain,
% 262.22/166.61 (bool(lazy_impl(prop(P!8), P!8))),
% 262.22/166.61 inference(unit_resolution,[status(thm)],[1261, 1259, 1254])).
% 262.22/166.61 tff(1263,plain,
% 262.22/166.61 (bool(err)),
% 262.22/166.61 inference(modus_ponens,[status(thm)],[1262, 1232])).
% 262.22/166.61 tff(1264,plain,
% 262.22/166.61 ($false),
% 262.22/166.61 inference(unit_resolution,[status(thm)],[255, 1263])).
% 262.22/166.61 tff(1265,plain,((~(phi(P!8) = err)) | (~(prop(P!8) = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 262.22/166.61 tff(1266,plain,
% 262.22/166.61 (~(phi(P!8) = err)),
% 262.22/166.61 inference(unit_resolution,[status(thm)],[1265, 1219])).
% 262.22/166.61 tff(1267,plain,
% 262.22/166.61 (d(P!8) | (~(phi(P!8) = err))),
% 262.22/166.61 inference(unit_resolution,[status(thm)],[212, 1266])).
% 262.22/166.61 tff(1268,plain,
% 262.22/166.61 (~((~d(P!8)) | (~(phi(P!8) = P!8)))),
% 262.22/166.61 inference(unit_resolution,[status(thm)],[209, 17, 1267])).
% 262.22/166.61 tff(1269,plain,
% 262.22/166.61 (phi(P!8) = P!8),
% 262.22/166.61 inference(unit_resolution,[status(thm)],[205, 1268])).
% 262.22/166.61 tff(1270,plain,
% 262.22/166.61 (P!8 = phi(P!8)),
% 262.22/166.61 inference(symmetry,[status(thm)],[1269])).
% 262.22/166.61 tff(1271,assumption,(P!8 = false), introduced(assumption)).
% 262.22/166.61 tff(1272,plain,
% 262.22/166.61 (false = P!8),
% 262.22/166.61 inference(symmetry,[status(thm)],[1271])).
% 262.22/166.61 tff(1273,plain,
% 262.22/166.61 (false = lazy_impl(prop(P!8), P!8)),
% 262.22/166.61 inference(transitivity,[status(thm)],[1272, 1270, 1224, 1221])).
% 262.22/166.61 tff(1274,plain,
% 262.22/166.61 (f1(false, false, false) = f1(P!8, false, lazy_impl(prop(P!8), P!8))),
% 262.22/166.61 inference(monotonicity,[status(thm)],[1272, 1273])).
% 262.22/166.61 tff(1275,plain,
% 262.22/166.61 (f1(P!8, false, lazy_impl(prop(P!8), P!8)) = f1(false, false, false)),
% 262.22/166.61 inference(symmetry,[status(thm)],[1274])).
% 262.22/166.61 tff(1276,plain,
% 262.22/166.61 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(P!8, false, lazy_impl(prop(P!8), P!8)) = lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))),
% 262.22/166.61 inference(quant_inst,[status(thm)],[])).
% 262.22/166.61 tff(1277,plain,
% 262.22/166.61 (f1(P!8, false, lazy_impl(prop(P!8), P!8)) = lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))),
% 262.22/166.61 inference(unit_resolution,[status(thm)],[1276, 159])).
% 262.22/166.61 tff(1278,plain,
% 262.22/166.61 (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = f1(P!8, false, lazy_impl(prop(P!8), P!8))),
% 262.22/166.61 inference(symmetry,[status(thm)],[1277])).
% 262.22/166.61 tff(1279,plain,
% 262.22/166.61 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) <=> ((lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = not1(false))))),
% 262.22/166.61 inference(quant_inst,[status(thm)],[])).
% 262.22/166.61 tff(1280,plain,
% 262.22/166.61 (bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) <=> ((lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = not1(false)))),
% 262.22/166.61 inference(unit_resolution,[status(thm)],[1279, 229])).
% 262.22/166.61 tff(1281,plain,
% 262.22/166.61 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), not1(false)) <=> ((~((~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = 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(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), not1(false)) <=> ((~((~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false))))),
% 262.22/166.61 inference(rewrite,[status(thm)],[])).
% 262.22/166.61 tff(1282,plain,
% 262.22/166.61 ((forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), not1(false)) <=> ((~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(not1(false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(not1(false) = not1(false))))))) <=> (forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), not1(false)) <=> ((~((~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)))),
% 262.22/166.61 inference(rewrite,[status(thm)],[])).
% 262.22/166.61 tff(1283,plain,
% 262.22/166.61 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), not1(false)) <=> ((~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(not1(false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(not1(false) = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), not1(false)) <=> ((~((~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false))))),
% 262.22/166.61 inference(monotonicity,[status(thm)],[1282])).
% 262.22/166.61 tff(1284,plain,
% 262.22/166.61 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), not1(false)) <=> ((~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(not1(false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(not1(false) = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), not1(false)) <=> ((~((~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false))))),
% 262.22/166.61 inference(transitivity,[status(thm)],[1283, 1281])).
% 262.22/166.61 tff(1285,plain,
% 262.22/166.61 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), not1(false)) <=> ((~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(not1(false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(not1(false) = not1(false)))))))),
% 262.22/166.62 inference(quant_inst,[status(thm)],[])).
% 262.22/166.62 tff(1286,plain,
% 262.22/166.62 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), not1(false)) <=> ((~((~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)))),
% 262.22/166.62 inference(modus_ponens,[status(thm)],[1285, 1284])).
% 262.22/166.62 tff(1287,plain,
% 262.22/166.62 (forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), not1(false)) <=> ((~((~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false))),
% 262.22/166.62 inference(unit_resolution,[status(thm)],[1286, 493])).
% 262.22/166.62 tff(1288,plain,
% 262.22/166.62 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)), lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))) <=> ((~((~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))) | (~bool(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~(d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = 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(impl(P!8, impl(false, false)), false)), lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))) <=> ((~((~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))) | (~bool(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~(d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false))))))))),
% 262.22/166.62 inference(rewrite,[status(thm)],[])).
% 262.22/166.62 tff(1289,plain,
% 262.22/166.62 ((forallprefers(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)), lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))) <=> ((~(d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~((~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~bool(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false))))))) <=> (forallprefers(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)), lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))) <=> ((~((~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))) | (~bool(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~(d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false)))))))),
% 262.22/166.63 inference(rewrite,[status(thm)],[])).
% 262.22/166.63 tff(1290,plain,
% 262.22/166.63 (((~![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(impl(P!8, impl(false, false)), false)), lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))) <=> ((~(d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~((~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~bool(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = 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(impl(P!8, impl(false, false)), false)), lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))) <=> ((~((~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))) | (~bool(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~(d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false))))))))),
% 262.22/166.63 inference(monotonicity,[status(thm)],[1289])).
% 262.22/166.63 tff(1291,plain,
% 262.22/166.63 (((~![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(impl(P!8, impl(false, false)), false)), lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))) <=> ((~(d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~((~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~bool(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = 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(impl(P!8, impl(false, false)), false)), lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))) <=> ((~((~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))) | (~bool(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~(d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false))))))))),
% 262.22/166.64 inference(transitivity,[status(thm)],[1290, 1288])).
% 262.22/166.64 tff(1292,plain,
% 262.22/166.64 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)), lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))) <=> ((~(d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~((~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~bool(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false)))))))),
% 262.22/166.64 inference(quant_inst,[status(thm)],[])).
% 262.22/166.64 tff(1293,plain,
% 262.22/166.64 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)), lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))) <=> ((~((~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))) | (~bool(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~(d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false)))))))),
% 262.22/166.64 inference(modus_ponens,[status(thm)],[1292, 1291])).
% 262.22/166.64 tff(1294,plain,
% 262.22/166.64 (forallprefers(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)), lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))) <=> ((~((~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))) | (~bool(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~(d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false))))))),
% 262.22/166.64 inference(unit_resolution,[status(thm)],[1293, 493])).
% 262.22/166.64 tff(1295,plain,
% 262.22/166.64 (not1(false) = prop(tptp_fun_R_0(Q!7, P!8))),
% 262.22/166.64 inference(symmetry,[status(thm)],[342])).
% 262.22/166.64 tff(1296,plain,
% 262.22/166.64 (lazy_impl(not1(false), tptp_fun_R_0(Q!7, P!8)) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))),
% 262.22/166.64 inference(monotonicity,[status(thm)],[1295])).
% 262.22/166.64 tff(1297,plain,
% 262.22/166.64 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), tptp_fun_R_0(Q!7, P!8)) = phi(tptp_fun_R_0(Q!7, P!8)))),
% 262.22/166.64 inference(quant_inst,[status(thm)],[])).
% 262.22/166.64 tff(1298,plain,
% 262.22/166.64 (lazy_impl(not1(false), tptp_fun_R_0(Q!7, P!8)) = phi(tptp_fun_R_0(Q!7, P!8))),
% 262.22/166.64 inference(unit_resolution,[status(thm)],[1297, 33])).
% 262.22/166.64 tff(1299,plain,
% 262.22/166.64 (phi(tptp_fun_R_0(Q!7, P!8)) = lazy_impl(not1(false), tptp_fun_R_0(Q!7, P!8))),
% 262.22/166.64 inference(symmetry,[status(thm)],[1298])).
% 262.22/166.64 tff(1300,assumption,(phi(tptp_fun_R_0(Q!7, P!8)) = err), introduced(assumption)).
% 262.22/166.64 tff(1301,plain,
% 262.22/166.64 (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = lazy_impl(not1(false), tptp_fun_R_0(Q!7, P!8))),
% 262.22/166.64 inference(monotonicity,[status(thm)],[342])).
% 262.22/166.64 tff(1302,plain,
% 262.22/166.64 (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = err),
% 262.22/166.64 inference(transitivity,[status(thm)],[1301, 1298, 1300])).
% 262.22/166.64 tff(1303,plain,
% 262.22/166.64 (bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) <=> bool(err)),
% 262.22/166.64 inference(monotonicity,[status(thm)],[1302])).
% 262.22/166.64 tff(1304,plain,
% 262.22/166.64 (bool(err) <=> bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.22/166.64 inference(symmetry,[status(thm)],[1303])).
% 262.22/166.64 tff(1305,plain,
% 262.22/166.64 ((~bool(err)) <=> (~bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))),
% 262.22/166.64 inference(monotonicity,[status(thm)],[1304])).
% 262.22/166.64 tff(1306,plain,
% 262.22/166.64 (~bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.22/166.64 inference(modus_ponens,[status(thm)],[255, 1305])).
% 262.22/166.64 tff(1307,plain,
% 262.22/166.64 (d(lazy_impl(prop(P!6), P!6)) <=> d(f7(P!6))),
% 262.22/166.64 inference(monotonicity,[status(thm)],[555])).
% 262.22/166.64 tff(1308,plain,
% 262.22/166.64 (d(f7(P!6)) <=> d(lazy_impl(prop(P!6), P!6))),
% 262.22/166.64 inference(symmetry,[status(thm)],[1307])).
% 262.22/166.64 tff(1309,plain,
% 262.22/166.64 (d(f7(P!6)) <=> d(false)),
% 262.22/166.64 inference(monotonicity,[status(thm)],[605])).
% 262.22/166.64 tff(1310,plain,
% 262.22/166.64 (d(false) <=> d(f7(P!6))),
% 262.22/166.64 inference(symmetry,[status(thm)],[1309])).
% 262.22/166.64 tff(1311,plain,
% 262.22/166.64 (d(false) <=> d(lazy_impl(prop(P!6), P!6))),
% 262.22/166.64 inference(transitivity,[status(thm)],[1310, 1308])).
% 262.22/166.64 tff(1312,plain,
% 262.22/166.64 (d(lazy_impl(prop(P!6), P!6))),
% 262.22/166.64 inference(modus_ponens,[status(thm)],[5, 1311])).
% 262.22/166.64 tff(1313,plain,
% 262.22/166.64 (bool(lazy_impl(prop(P!6), P!6)) <=> bool(f7(P!6))),
% 262.22/166.64 inference(monotonicity,[status(thm)],[555])).
% 262.22/166.64 tff(1314,plain,
% 262.22/166.64 (bool(f7(P!6)) <=> bool(lazy_impl(prop(P!6), P!6))),
% 262.22/166.64 inference(symmetry,[status(thm)],[1313])).
% 262.22/166.64 tff(1315,plain,
% 262.22/166.64 (bool(f7(P!6)) <=> bool(false)),
% 262.22/166.64 inference(monotonicity,[status(thm)],[605])).
% 262.22/166.64 tff(1316,plain,
% 262.22/166.64 (bool(false) <=> bool(f7(P!6))),
% 262.22/166.64 inference(symmetry,[status(thm)],[1315])).
% 262.22/166.64 tff(1317,plain,
% 262.22/166.64 (bool(false) <=> bool(lazy_impl(prop(P!6), P!6))),
% 262.22/166.64 inference(transitivity,[status(thm)],[1316, 1314])).
% 262.22/166.64 tff(1318,plain,
% 262.22/166.64 (bool(lazy_impl(prop(P!6), P!6))),
% 262.22/166.64 inference(modus_ponens,[status(thm)],[107, 1317])).
% 262.22/166.64 tff(1319,plain,
% 262.22/166.64 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~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_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~((~(lazy_impl(prop(P!6), P!6) = not1(false))) | (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = 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_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~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_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~((~(lazy_impl(prop(P!6), P!6) = not1(false))) | (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = false)))))))),
% 262.22/166.64 inference(rewrite,[status(thm)],[])).
% 262.22/166.64 tff(1320,plain,
% 262.22/166.64 ((forallprefers(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~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_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~((~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = false)) | (~(lazy_impl(prop(P!6), P!6) = not1(false))))))) <=> (forallprefers(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~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_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~((~(lazy_impl(prop(P!6), P!6) = not1(false))) | (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = false))))))),
% 262.22/166.64 inference(rewrite,[status(thm)],[])).
% 262.22/166.64 tff(1321,plain,
% 262.22/166.64 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~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_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~((~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = 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_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~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_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~((~(lazy_impl(prop(P!6), P!6) = not1(false))) | (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = false)))))))),
% 262.22/166.65 inference(monotonicity,[status(thm)],[1320])).
% 262.22/166.65 tff(1322,plain,
% 262.22/166.65 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~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_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~((~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = 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_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~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_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~((~(lazy_impl(prop(P!6), P!6) = not1(false))) | (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = false)))))))),
% 262.22/166.65 inference(transitivity,[status(thm)],[1321, 1319])).
% 262.22/166.65 tff(1323,plain,
% 262.22/166.65 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~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_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~((~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = false)) | (~(lazy_impl(prop(P!6), P!6) = not1(false)))))))),
% 262.22/166.65 inference(quant_inst,[status(thm)],[])).
% 262.22/166.65 tff(1324,plain,
% 262.22/166.65 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~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_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~((~(lazy_impl(prop(P!6), P!6) = not1(false))) | (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = false))))))),
% 262.32/166.65 inference(modus_ponens,[status(thm)],[1323, 1322])).
% 262.32/166.65 tff(1325,plain,
% 262.32/166.65 (forallprefers(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~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_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~((~(lazy_impl(prop(P!6), P!6) = not1(false))) | (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = false)))))),
% 262.32/166.65 inference(unit_resolution,[status(thm)],[1324, 493])).
% 262.32/166.65 tff(1326,plain,
% 262.32/166.65 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(tptp_fun_R_0(Q!7, P!8)) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.32/166.65 inference(quant_inst,[status(thm)],[])).
% 262.32/166.65 tff(1327,plain,
% 262.32/166.65 (f7(tptp_fun_R_0(Q!7, P!8)) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))),
% 262.32/166.65 inference(unit_resolution,[status(thm)],[1326, 538])).
% 262.32/166.65 tff(1328,plain,
% 262.32/166.65 (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = f7(tptp_fun_R_0(Q!7, P!8))),
% 262.32/166.65 inference(symmetry,[status(thm)],[1327])).
% 262.32/166.65 tff(1329,plain,
% 262.32/166.65 (forallprefers(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)), lazy_impl(prop(P!6), P!6)) <=> forallprefers(f7(tptp_fun_R_0(Q!7, P!8)), f7(P!6))),
% 262.32/166.65 inference(monotonicity,[status(thm)],[1328, 555])).
% 262.32/166.65 tff(1330,plain,
% 262.32/166.65 (forallprefers(f7(tptp_fun_R_0(Q!7, P!8)), f7(P!6)) <=> forallprefers(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)), lazy_impl(prop(P!6), P!6))),
% 262.32/166.65 inference(symmetry,[status(thm)],[1329])).
% 262.32/166.65 tff(1331,plain,
% 262.32/166.65 ((~forallprefers(f7(tptp_fun_R_0(Q!7, P!8)), f7(P!6))) <=> (~forallprefers(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)), lazy_impl(prop(P!6), P!6)))),
% 262.32/166.65 inference(monotonicity,[status(thm)],[1330])).
% 262.32/166.65 tff(1332,plain,
% 262.32/166.65 ((~![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))) | (~forallprefers(f7(tptp_fun_R_0(Q!7, P!8)), f7(P!6)))),
% 262.32/166.65 inference(quant_inst,[status(thm)],[])).
% 262.32/166.65 tff(1333,plain,
% 262.32/166.65 (~forallprefers(f7(tptp_fun_R_0(Q!7, P!8)), f7(P!6))),
% 262.32/166.65 inference(unit_resolution,[status(thm)],[1332, 572])).
% 262.32/166.65 tff(1334,plain,
% 262.32/166.65 (~forallprefers(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)), lazy_impl(prop(P!6), P!6))),
% 262.32/166.65 inference(modus_ponens,[status(thm)],[1333, 1331])).
% 262.32/166.65 tff(1335,plain,
% 262.32/166.65 ((~(forallprefers(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~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_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~((~(lazy_impl(prop(P!6), P!6) = not1(false))) | (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = false))))))) | forallprefers(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)), lazy_impl(prop(P!6), P!6)) | (~((~(d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~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_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~((~(lazy_impl(prop(P!6), P!6) = not1(false))) | (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = false))))))),
% 262.32/166.65 inference(tautology,[status(thm)],[])).
% 262.32/166.65 tff(1336,plain,
% 262.32/166.65 (~((~(d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~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_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~((~(lazy_impl(prop(P!6), P!6) = not1(false))) | (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = false)))))),
% 262.32/166.66 inference(unit_resolution,[status(thm)],[1335, 1334, 1325])).
% 262.32/166.66 tff(1337,plain,
% 262.32/166.66 (((~(d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~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_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~((~(lazy_impl(prop(P!6), P!6) = not1(false))) | (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = false))))) | (d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~d(lazy_impl(prop(P!6), P!6))))),
% 262.32/166.66 inference(tautology,[status(thm)],[])).
% 262.32/166.66 tff(1338,plain,
% 262.32/166.66 (d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~d(lazy_impl(prop(P!6), P!6)))),
% 262.32/166.66 inference(unit_resolution,[status(thm)],[1337, 1336])).
% 262.32/166.66 tff(1339,plain,
% 262.32/166.66 ((~(d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~d(lazy_impl(prop(P!6), P!6))))) | d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~d(lazy_impl(prop(P!6), P!6)))),
% 262.32/166.66 inference(tautology,[status(thm)],[])).
% 262.32/166.66 tff(1340,plain,
% 262.32/166.66 (d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~d(lazy_impl(prop(P!6), P!6)))),
% 262.32/166.66 inference(unit_resolution,[status(thm)],[1339, 1338])).
% 262.32/166.66 tff(1341,plain,
% 262.32/166.66 (d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.32/166.66 inference(unit_resolution,[status(thm)],[1340, 1312])).
% 262.32/166.66 tff(1342,plain,
% 262.32/166.66 (((~(d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~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_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~((~(lazy_impl(prop(P!6), P!6) = not1(false))) | (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = false))))) | ((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))),
% 262.32/166.66 inference(tautology,[status(thm)],[])).
% 262.32/166.66 tff(1343,plain,
% 262.32/166.66 ((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))),
% 262.32/166.66 inference(unit_resolution,[status(thm)],[1342, 1336])).
% 262.32/166.66 tff(1344,plain,
% 262.32/166.66 ((~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))),
% 262.32/166.66 inference(tautology,[status(thm)],[])).
% 262.32/166.66 tff(1345,plain,
% 262.32/166.66 ((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))),
% 262.32/166.66 inference(unit_resolution,[status(thm)],[1344, 1343])).
% 262.32/166.66 tff(1346,plain,
% 262.32/166.66 (bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.32/166.66 inference(unit_resolution,[status(thm)],[1345, 1341, 1318, 1312])).
% 262.32/166.66 tff(1347,plain,
% 262.32/166.66 ($false),
% 262.32/166.66 inference(unit_resolution,[status(thm)],[1346, 1306])).
% 262.32/166.66 tff(1348,plain,((~(phi(tptp_fun_R_0(Q!7, P!8)) = err)) | (~(prop(tptp_fun_R_0(Q!7, P!8)) = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 262.32/166.66 tff(1349,plain,
% 262.32/166.66 (~(phi(tptp_fun_R_0(Q!7, P!8)) = err)),
% 262.32/166.66 inference(unit_resolution,[status(thm)],[1348, 342])).
% 262.32/166.66 tff(1350,plain,
% 262.32/166.66 ((d(tptp_fun_R_0(Q!7, P!8)) | (~(phi(tptp_fun_R_0(Q!7, P!8)) = err))) | (phi(tptp_fun_R_0(Q!7, P!8)) = err)),
% 262.32/166.66 inference(tautology,[status(thm)],[])).
% 262.32/166.66 tff(1351,plain,
% 262.32/166.66 (d(tptp_fun_R_0(Q!7, P!8)) | (~(phi(tptp_fun_R_0(Q!7, P!8)) = err))),
% 262.32/166.66 inference(unit_resolution,[status(thm)],[1350, 1349])).
% 262.32/166.66 tff(1352,plain,
% 262.32/166.66 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(tptp_fun_R_0(Q!7, P!8))) | (~(phi(tptp_fun_R_0(Q!7, P!8)) = tptp_fun_R_0(Q!7, P!8))))) | (~(d(tptp_fun_R_0(Q!7, P!8)) | (~(phi(tptp_fun_R_0(Q!7, P!8)) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(tptp_fun_R_0(Q!7, P!8))) | (~(phi(tptp_fun_R_0(Q!7, P!8)) = tptp_fun_R_0(Q!7, P!8))))) | (~(d(tptp_fun_R_0(Q!7, P!8)) | (~(phi(tptp_fun_R_0(Q!7, P!8)) = err)))))),
% 262.32/166.66 inference(rewrite,[status(thm)],[])).
% 262.32/166.66 tff(1353,plain,
% 262.32/166.66 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(tptp_fun_R_0(Q!7, P!8))) | (~(phi(tptp_fun_R_0(Q!7, P!8)) = tptp_fun_R_0(Q!7, P!8))))) | (~(d(tptp_fun_R_0(Q!7, P!8)) | (~(phi(tptp_fun_R_0(Q!7, P!8)) = err)))))),
% 262.32/166.66 inference(quant_inst,[status(thm)],[])).
% 262.32/166.66 tff(1354,plain,
% 262.32/166.66 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(tptp_fun_R_0(Q!7, P!8))) | (~(phi(tptp_fun_R_0(Q!7, P!8)) = tptp_fun_R_0(Q!7, P!8))))) | (~(d(tptp_fun_R_0(Q!7, P!8)) | (~(phi(tptp_fun_R_0(Q!7, P!8)) = err))))),
% 262.32/166.66 inference(modus_ponens,[status(thm)],[1353, 1352])).
% 262.32/166.66 tff(1355,plain,
% 262.32/166.66 ((~((~d(tptp_fun_R_0(Q!7, P!8))) | (~(phi(tptp_fun_R_0(Q!7, P!8)) = tptp_fun_R_0(Q!7, P!8))))) | (~(d(tptp_fun_R_0(Q!7, P!8)) | (~(phi(tptp_fun_R_0(Q!7, P!8)) = err))))),
% 262.32/166.66 inference(unit_resolution,[status(thm)],[1354, 17])).
% 262.32/166.66 tff(1356,plain,
% 262.32/166.66 (~((~d(tptp_fun_R_0(Q!7, P!8))) | (~(phi(tptp_fun_R_0(Q!7, P!8)) = tptp_fun_R_0(Q!7, P!8))))),
% 262.32/166.66 inference(unit_resolution,[status(thm)],[1355, 1351])).
% 262.32/166.66 tff(1357,plain,
% 262.32/166.66 (((~d(tptp_fun_R_0(Q!7, P!8))) | (~(phi(tptp_fun_R_0(Q!7, P!8)) = tptp_fun_R_0(Q!7, P!8)))) | (phi(tptp_fun_R_0(Q!7, P!8)) = tptp_fun_R_0(Q!7, P!8))),
% 262.32/166.66 inference(tautology,[status(thm)],[])).
% 262.32/166.66 tff(1358,plain,
% 262.32/166.66 (phi(tptp_fun_R_0(Q!7, P!8)) = tptp_fun_R_0(Q!7, P!8)),
% 262.32/166.66 inference(unit_resolution,[status(thm)],[1357, 1356])).
% 262.32/166.66 tff(1359,plain,
% 262.32/166.66 (tptp_fun_R_0(Q!7, P!8) = phi(tptp_fun_R_0(Q!7, P!8))),
% 262.32/166.66 inference(symmetry,[status(thm)],[1358])).
% 262.32/166.66 tff(1360,plain,
% 262.32/166.66 (tptp_fun_R_0(Q!7, P!8) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))),
% 262.32/166.66 inference(transitivity,[status(thm)],[1359, 1299, 1296])).
% 262.32/166.66 tff(1361,plain,
% 262.32/166.66 (((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | ((~bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) | (impl(not1(false), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))) <=> ((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | (~bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) | (impl(not1(false), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))),
% 262.32/166.66 inference(rewrite,[status(thm)],[])).
% 262.32/166.66 tff(1362,plain,
% 262.32/166.66 ((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | ((~bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) | (impl(not1(false), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))),
% 262.32/166.66 inference(quant_inst,[status(thm)],[])).
% 262.32/166.66 tff(1363,plain,
% 262.32/166.66 ((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | (~bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) | (impl(not1(false), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.32/166.66 inference(modus_ponens,[status(thm)],[1362, 1361])).
% 262.32/166.66 tff(1364,plain,
% 262.32/166.66 (impl(not1(false), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))),
% 262.32/166.66 inference(unit_resolution,[status(thm)],[1363, 94, 1346])).
% 262.32/166.66 tff(1365,plain,
% 262.32/166.66 (impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = impl(not1(false), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.32/166.66 inference(monotonicity,[status(thm)],[443, 1360])).
% 262.32/166.66 tff(1366,plain,
% 262.32/166.66 (impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))),
% 262.32/166.66 inference(transitivity,[status(thm)],[1365, 1364])).
% 262.32/166.66 tff(1367,plain,
% 262.32/166.66 ((impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = not1(false)) <=> (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = not1(false))),
% 262.32/166.66 inference(monotonicity,[status(thm)],[1366])).
% 262.32/166.66 tff(1368,plain,
% 262.32/166.66 (phi(Q!7) = phi(not1(false))),
% 262.32/166.66 inference(monotonicity,[status(thm)],[443])).
% 262.32/166.66 tff(1369,plain,
% 262.32/166.66 (phi(Q!7) = not1(false)),
% 262.32/166.66 inference(transitivity,[status(thm)],[1368, 49])).
% 262.32/166.66 tff(1370,plain,
% 262.32/166.66 ((impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = phi(Q!7)) <=> (impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = not1(false))),
% 262.32/166.66 inference(monotonicity,[status(thm)],[1369])).
% 262.32/166.66 tff(1371,plain,
% 262.32/166.66 (impl(false, impl(not1(false), false)) = impl(false, false)),
% 262.32/166.66 inference(monotonicity,[status(thm)],[132])).
% 262.32/166.66 tff(1372,plain,
% 262.32/166.66 (impl(false, impl(not1(false), false)) = not1(false)),
% 262.32/166.66 inference(transitivity,[status(thm)],[1371, 124])).
% 262.32/166.66 tff(1373,plain,
% 262.32/166.66 (impl(impl(false, impl(not1(false), false)), false) = impl(not1(false), false)),
% 262.32/166.66 inference(monotonicity,[status(thm)],[1372])).
% 262.32/166.66 tff(1374,plain,
% 262.32/166.66 (impl(impl(false, impl(not1(false), false)), false) = false),
% 262.32/166.66 inference(transitivity,[status(thm)],[1373, 132])).
% 262.32/166.66 tff(1375,plain,
% 262.32/166.66 (lazy_impl(prop(false), impl(impl(false, impl(not1(false), false)), false)) = lazy_impl(not1(false), false)),
% 262.32/166.66 inference(monotonicity,[status(thm)],[149, 1374])).
% 262.32/166.66 tff(1376,plain,
% 262.32/166.66 ((~![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)))),
% 262.32/166.66 inference(quant_inst,[status(thm)],[])).
% 262.32/166.66 tff(1377,plain,
% 262.32/166.66 (f1(false, not1(false), false) = lazy_impl(prop(false), impl(impl(false, impl(not1(false), false)), false))),
% 262.32/166.66 inference(unit_resolution,[status(thm)],[1376, 159])).
% 262.32/166.66 tff(1378,plain,
% 262.32/166.66 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(P!8) <=> ((P!8 = false) | (P!8 = not1(false))))),
% 262.32/166.66 inference(quant_inst,[status(thm)],[])).
% 262.32/166.66 tff(1379,plain,
% 262.32/166.66 (bool(P!8) <=> ((P!8 = false) | (P!8 = not1(false)))),
% 262.32/166.66 inference(unit_resolution,[status(thm)],[1378, 229])).
% 262.32/166.66 tff(1380,plain,
% 262.32/166.66 ((~(bool(P!8) <=> ((P!8 = false) | (P!8 = not1(false))))) | (~bool(P!8)) | ((P!8 = false) | (P!8 = not1(false)))),
% 262.32/166.66 inference(tautology,[status(thm)],[])).
% 262.32/166.66 tff(1381,plain,
% 262.32/166.66 ((~bool(P!8)) | ((P!8 = false) | (P!8 = not1(false)))),
% 262.32/166.66 inference(unit_resolution,[status(thm)],[1380, 1379])).
% 262.32/166.66 tff(1382,plain,
% 262.32/166.66 ((P!8 = false) | (P!8 = not1(false))),
% 262.32/166.66 inference(unit_resolution,[status(thm)],[1381, 1214])).
% 262.32/166.66 tff(1383,plain,
% 262.32/166.66 ((~(impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = phi(Q!7))) <=> (~(impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = not1(false)))),
% 262.32/166.66 inference(monotonicity,[status(thm)],[1370])).
% 262.32/166.66 tff(1384,assumption,(~(impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = phi(Q!7))), introduced(assumption)).
% 262.32/166.66 tff(1385,plain,
% 262.32/166.66 (~(impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = not1(false))),
% 262.32/166.66 inference(modus_ponens,[status(thm)],[1384, 1383])).
% 262.32/166.66 tff(1386,plain,
% 262.32/166.66 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(impl(Q!7, tptp_fun_R_0(Q!7, P!8))) <=> ((impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = false) | (impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = not1(false))))),
% 262.32/166.66 inference(quant_inst,[status(thm)],[])).
% 262.32/166.66 tff(1387,plain,
% 262.32/166.66 (bool(impl(Q!7, tptp_fun_R_0(Q!7, P!8))) <=> ((impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = false) | (impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = not1(false)))),
% 262.32/166.66 inference(unit_resolution,[status(thm)],[1386, 229])).
% 262.32/166.66 tff(1388,plain,
% 262.32/166.66 (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = lazy_impl(not1(false), tptp_fun_R_0(Q!7, P!8))),
% 262.32/166.66 inference(symmetry,[status(thm)],[1296])).
% 262.32/166.66 tff(1389,plain,
% 262.32/166.66 (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = tptp_fun_R_0(Q!7, P!8)),
% 262.32/166.66 inference(transitivity,[status(thm)],[1388, 1298, 1358])).
% 262.32/166.67 tff(1390,plain,
% 262.32/166.67 (not1(false) = Q!7),
% 262.32/166.67 inference(symmetry,[status(thm)],[443])).
% 262.32/166.67 tff(1391,plain,
% 262.32/166.67 (impl(not1(false), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = impl(Q!7, tptp_fun_R_0(Q!7, P!8))),
% 262.32/166.67 inference(monotonicity,[status(thm)],[1390, 1389])).
% 262.32/166.67 tff(1392,plain,
% 262.32/166.67 (impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = impl(not1(false), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.32/166.67 inference(symmetry,[status(thm)],[1391])).
% 262.32/166.67 tff(1393,plain,
% 262.32/166.67 (impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))),
% 262.32/166.67 inference(transitivity,[status(thm)],[1392, 1364])).
% 262.32/166.67 tff(1394,plain,
% 262.32/166.67 (bool(impl(Q!7, tptp_fun_R_0(Q!7, P!8))) <=> bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.32/166.67 inference(monotonicity,[status(thm)],[1393])).
% 262.32/166.67 tff(1395,plain,
% 262.32/166.67 (bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) <=> bool(impl(Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.32/166.67 inference(symmetry,[status(thm)],[1394])).
% 262.32/166.67 tff(1396,plain,
% 262.32/166.67 (bool(impl(Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.32/166.67 inference(modus_ponens,[status(thm)],[1346, 1395])).
% 262.32/166.67 tff(1397,plain,
% 262.32/166.67 ((~(bool(impl(Q!7, tptp_fun_R_0(Q!7, P!8))) <=> ((impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = false) | (impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = not1(false))))) | (~bool(impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) | ((impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = false) | (impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = not1(false)))),
% 262.32/166.67 inference(tautology,[status(thm)],[])).
% 262.32/166.67 tff(1398,plain,
% 262.32/166.67 ((impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = false) | (impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = not1(false))),
% 262.32/166.67 inference(unit_resolution,[status(thm)],[1397, 1396, 1387])).
% 262.32/166.67 tff(1399,plain,
% 262.32/166.67 ((~((impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = false) | (impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = not1(false)))) | (impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = false) | (impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = not1(false))),
% 262.32/166.67 inference(tautology,[status(thm)],[])).
% 262.32/166.67 tff(1400,plain,
% 262.32/166.67 (impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = false),
% 262.32/166.67 inference(unit_resolution,[status(thm)],[1399, 1398, 1385])).
% 262.32/166.67 tff(1401,plain,
% 262.32/166.67 (impl(not1(false), impl(not1(false), false)) = impl(not1(false), false)),
% 262.32/166.67 inference(monotonicity,[status(thm)],[132])).
% 262.32/166.67 tff(1402,plain,
% 262.32/166.67 (impl(not1(false), impl(not1(false), false)) = false),
% 262.32/166.67 inference(transitivity,[status(thm)],[1401, 132])).
% 262.32/166.67 tff(1403,plain,
% 262.32/166.67 (impl(impl(not1(false), impl(not1(false), false)), false) = impl(false, false)),
% 262.32/166.67 inference(monotonicity,[status(thm)],[1402])).
% 262.32/166.67 tff(1404,plain,
% 262.32/166.67 (impl(impl(not1(false), impl(not1(false), false)), false) = not1(false)),
% 262.32/166.67 inference(transitivity,[status(thm)],[1403, 124])).
% 262.32/166.67 tff(1405,plain,
% 262.32/166.67 (lazy_impl(prop(false), impl(impl(not1(false), impl(not1(false), false)), false)) = lazy_impl(not1(false), not1(false))),
% 262.32/166.67 inference(monotonicity,[status(thm)],[149, 1404])).
% 262.32/166.67 tff(1406,plain,
% 262.32/166.67 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(not1(false), not1(false), false) = lazy_impl(prop(false), impl(impl(not1(false), impl(not1(false), false)), false)))),
% 262.32/166.67 inference(quant_inst,[status(thm)],[])).
% 262.32/166.67 tff(1407,plain,
% 262.32/166.67 (f1(not1(false), not1(false), false) = lazy_impl(prop(false), impl(impl(not1(false), impl(not1(false), false)), false))),
% 262.32/166.67 inference(unit_resolution,[status(thm)],[1406, 159])).
% 262.32/166.67 tff(1408,assumption,(P!8 = not1(false)), introduced(assumption)).
% 262.32/166.67 tff(1409,plain,
% 262.32/166.67 (f1(P!8, not1(false), false) = f1(not1(false), not1(false), false)),
% 262.32/166.67 inference(monotonicity,[status(thm)],[1408])).
% 262.32/166.67 tff(1410,assumption,(impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = false), introduced(assumption)).
% 262.32/166.67 tff(1411,plain,
% 262.32/166.67 (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = impl(not1(false), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.32/166.67 inference(symmetry,[status(thm)],[1364])).
% 262.32/166.67 tff(1412,plain,
% 262.32/166.67 (tptp_fun_R_0(Q!7, P!8) = false),
% 262.32/166.67 inference(transitivity,[status(thm)],[1359, 1299, 1296, 1411, 1391, 1410])).
% 262.32/166.67 tff(1413,plain,
% 262.32/166.67 (f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)) = f1(P!8, not1(false), false)),
% 262.32/166.67 inference(monotonicity,[status(thm)],[443, 1412])).
% 262.32/166.67 tff(1414,plain,
% 262.32/166.67 (f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)) = not1(false)),
% 262.32/166.67 inference(transitivity,[status(thm)],[1413, 1409, 1407, 1405, 593, 49])).
% 262.32/166.67 tff(1415,plain,
% 262.32/166.67 (phi(f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(not1(false))),
% 262.32/166.67 inference(monotonicity,[status(thm)],[1414])).
% 262.32/166.67 tff(1416,plain,
% 262.32/166.67 (phi(not1(false)) = phi(f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.32/166.67 inference(symmetry,[status(thm)],[1415])).
% 262.32/166.67 tff(1417,plain,
% 262.32/166.67 (not1(false) = phi(not1(false))),
% 262.32/166.67 inference(symmetry,[status(thm)],[49])).
% 262.32/166.67 tff(1418,plain,
% 262.32/166.67 (^[B: $i] : refl(((~bool(B)) | (and1(not1(false), B) = B)) <=> ((~bool(B)) | (and1(not1(false), B) = B)))),
% 262.32/166.67 inference(bind,[status(th)],[])).
% 262.32/166.67 tff(1419,plain,
% 262.32/166.67 (![B: $i] : ((~bool(B)) | (and1(not1(false), B) = B)) <=> ![B: $i] : ((~bool(B)) | (and1(not1(false), B) = B))),
% 262.32/166.67 inference(quant_intro,[status(thm)],[1418])).
% 262.32/166.67 tff(1420,plain,
% 262.32/166.67 (^[B: $i] : rewrite(((~bool(B)) | (and1(true, B) = B)) <=> ((~bool(B)) | (and1(not1(false), B) = B)))),
% 262.32/166.67 inference(bind,[status(th)],[])).
% 262.32/166.67 tff(1421,plain,
% 262.32/166.67 (![B: $i] : ((~bool(B)) | (and1(true, B) = B)) <=> ![B: $i] : ((~bool(B)) | (and1(not1(false), B) = B))),
% 262.32/166.67 inference(quant_intro,[status(thm)],[1420])).
% 262.32/166.67 tff(1422,plain,
% 262.32/166.67 (![B: $i] : ((~bool(B)) | (and1(true, B) = B)) <=> ![B: $i] : ((~bool(B)) | (and1(true, B) = B))),
% 262.32/166.67 inference(rewrite,[status(thm)],[])).
% 262.32/166.67 tff(1423,plain,
% 262.32/166.67 (^[B: $i] : rewrite((bool(B) => (and1(true, B) = B)) <=> ((~bool(B)) | (and1(true, B) = B)))),
% 262.32/166.67 inference(bind,[status(th)],[])).
% 262.32/166.67 tff(1424,plain,
% 262.32/166.67 (![B: $i] : (bool(B) => (and1(true, B) = B)) <=> ![B: $i] : ((~bool(B)) | (and1(true, B) = B))),
% 262.32/166.67 inference(quant_intro,[status(thm)],[1423])).
% 262.32/166.67 tff(1425,axiom,(![B: $i] : (bool(B) => (and1(true, B) = B))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','and1_axiom4')).
% 262.32/166.67 tff(1426,plain,
% 262.32/166.67 (![B: $i] : ((~bool(B)) | (and1(true, B) = B))),
% 262.32/166.67 inference(modus_ponens,[status(thm)],[1425, 1424])).
% 262.32/166.67 tff(1427,plain,
% 262.32/166.67 (![B: $i] : ((~bool(B)) | (and1(true, B) = B))),
% 262.32/166.67 inference(modus_ponens,[status(thm)],[1426, 1422])).
% 262.32/166.67 tff(1428,plain,
% 262.32/166.67 (![B: $i] : ((~bool(B)) | (and1(not1(false), B) = B))),
% 262.32/166.67 inference(modus_ponens,[status(thm)],[1427, 1421])).
% 262.32/166.67 tff(1429,plain,(
% 262.32/166.67 ![B: $i] : ((~bool(B)) | (and1(not1(false), B) = B))),
% 262.32/166.67 inference(skolemize,[status(sab)],[1428])).
% 262.32/166.67 tff(1430,plain,
% 262.32/166.67 (![B: $i] : ((~bool(B)) | (and1(not1(false), B) = B))),
% 262.32/166.67 inference(modus_ponens,[status(thm)],[1429, 1419])).
% 262.32/166.67 tff(1431,plain,
% 262.32/166.67 (((~![B: $i] : ((~bool(B)) | (and1(not1(false), B) = B))) | ((~bool(not1(false))) | (and1(not1(false), not1(false)) = not1(false)))) <=> ((~![B: $i] : ((~bool(B)) | (and1(not1(false), B) = B))) | (~bool(not1(false))) | (and1(not1(false), not1(false)) = not1(false)))),
% 262.32/166.67 inference(rewrite,[status(thm)],[])).
% 262.32/166.67 tff(1432,plain,
% 262.32/166.67 ((~![B: $i] : ((~bool(B)) | (and1(not1(false), B) = B))) | ((~bool(not1(false))) | (and1(not1(false), not1(false)) = not1(false)))),
% 262.32/166.67 inference(quant_inst,[status(thm)],[])).
% 262.32/166.67 tff(1433,plain,
% 262.32/166.67 ((~![B: $i] : ((~bool(B)) | (and1(not1(false), B) = B))) | (~bool(not1(false))) | (and1(not1(false), not1(false)) = not1(false))),
% 262.32/166.67 inference(modus_ponens,[status(thm)],[1432, 1431])).
% 262.32/166.67 tff(1434,plain,
% 262.32/166.67 (and1(not1(false), not1(false)) = not1(false)),
% 262.32/166.67 inference(unit_resolution,[status(thm)],[1433, 1430, 81])).
% 262.32/166.67 tff(1435,plain,
% 262.32/166.67 (and1(P!8, Q!7) = and1(not1(false), not1(false))),
% 262.32/166.67 inference(monotonicity,[status(thm)],[1408, 443])).
% 262.32/166.67 tff(1436,plain,
% 262.32/166.67 (and1(P!8, Q!7) = and2(P!8, Q!7)),
% 262.32/166.67 inference(transitivity,[status(thm)],[1435, 1434, 1417, 1416, 296])).
% 262.32/166.67 tff(1437,plain,
% 262.32/166.67 ($false),
% 262.32/166.67 inference(unit_resolution,[status(thm)],[361, 1436])).
% 262.32/166.67 tff(1438,plain,((~(P!8 = not1(false))) | (~(impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = false)) | (~(prop(tptp_fun_R_0(Q!7, P!8)) = not1(false))) | (~(Q!7 = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 262.32/166.67 tff(1439,plain,
% 262.32/166.67 (~(P!8 = not1(false))),
% 262.32/166.67 inference(unit_resolution,[status(thm)],[1438, 1400, 342, 443])).
% 262.32/166.67 tff(1440,plain,
% 262.32/166.67 ((~((P!8 = false) | (P!8 = not1(false)))) | (P!8 = false) | (P!8 = not1(false))),
% 262.32/166.67 inference(tautology,[status(thm)],[])).
% 262.32/166.67 tff(1441,plain,
% 262.32/166.67 (P!8 = false),
% 262.32/166.67 inference(unit_resolution,[status(thm)],[1440, 1439, 1382])).
% 262.32/166.67 tff(1442,plain,
% 262.32/166.67 (f1(P!8, not1(false), false) = f1(false, not1(false), false)),
% 262.32/166.67 inference(monotonicity,[status(thm)],[1441])).
% 262.32/166.67 tff(1443,plain,
% 262.32/166.67 (tptp_fun_R_0(Q!7, P!8) = false),
% 262.32/166.67 inference(transitivity,[status(thm)],[1359, 1299, 1296, 1411, 1391, 1400])).
% 262.32/166.67 tff(1444,plain,
% 262.32/166.67 (f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)) = f1(P!8, not1(false), false)),
% 262.32/166.67 inference(monotonicity,[status(thm)],[443, 1443])).
% 262.32/166.67 tff(1445,plain,
% 262.32/166.67 (f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)) = false),
% 262.32/166.67 inference(transitivity,[status(thm)],[1444, 1442, 1377, 1375, 35, 23])).
% 262.32/166.67 tff(1446,plain,
% 262.32/166.67 (phi(f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(false)),
% 262.32/166.67 inference(monotonicity,[status(thm)],[1445])).
% 262.32/166.67 tff(1447,plain,
% 262.32/166.67 (phi(false) = phi(f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.32/166.67 inference(symmetry,[status(thm)],[1446])).
% 262.32/166.67 tff(1448,plain,
% 262.32/166.67 (^[B: $i] : refl(((~bool(B)) | (and1(false, B) = false)) <=> ((~bool(B)) | (and1(false, B) = false)))),
% 262.32/166.67 inference(bind,[status(th)],[])).
% 262.32/166.67 tff(1449,plain,
% 262.32/166.67 (![B: $i] : ((~bool(B)) | (and1(false, B) = false)) <=> ![B: $i] : ((~bool(B)) | (and1(false, B) = false))),
% 262.32/166.67 inference(quant_intro,[status(thm)],[1448])).
% 262.32/166.67 tff(1450,plain,
% 262.32/166.67 (![B: $i] : ((~bool(B)) | (and1(false, B) = false)) <=> ![B: $i] : ((~bool(B)) | (and1(false, B) = false))),
% 262.32/166.67 inference(rewrite,[status(thm)],[])).
% 262.32/166.67 tff(1451,plain,
% 262.32/166.67 (^[B: $i] : rewrite((bool(B) => (and1(false, B) = false)) <=> ((~bool(B)) | (and1(false, B) = false)))),
% 262.32/166.67 inference(bind,[status(th)],[])).
% 262.32/166.67 tff(1452,plain,
% 262.32/166.67 (![B: $i] : (bool(B) => (and1(false, B) = false)) <=> ![B: $i] : ((~bool(B)) | (and1(false, B) = false))),
% 262.32/166.67 inference(quant_intro,[status(thm)],[1451])).
% 262.32/166.67 tff(1453,axiom,(![B: $i] : (bool(B) => (and1(false, B) = false))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','and1_axiom3')).
% 262.32/166.67 tff(1454,plain,
% 262.32/166.67 (![B: $i] : ((~bool(B)) | (and1(false, B) = false))),
% 262.32/166.67 inference(modus_ponens,[status(thm)],[1453, 1452])).
% 262.32/166.67 tff(1455,plain,
% 262.32/166.67 (![B: $i] : ((~bool(B)) | (and1(false, B) = false))),
% 262.32/166.67 inference(modus_ponens,[status(thm)],[1454, 1450])).
% 262.32/166.67 tff(1456,plain,(
% 262.32/166.67 ![B: $i] : ((~bool(B)) | (and1(false, B) = false))),
% 262.32/166.67 inference(skolemize,[status(sab)],[1455])).
% 262.32/166.67 tff(1457,plain,
% 262.32/166.67 (![B: $i] : ((~bool(B)) | (and1(false, B) = false))),
% 262.32/166.67 inference(modus_ponens,[status(thm)],[1456, 1449])).
% 262.32/166.67 tff(1458,plain,
% 262.32/166.67 (((~![B: $i] : ((~bool(B)) | (and1(false, B) = false))) | ((~bool(not1(false))) | (and1(false, not1(false)) = false))) <=> ((~![B: $i] : ((~bool(B)) | (and1(false, B) = false))) | (~bool(not1(false))) | (and1(false, not1(false)) = false))),
% 262.32/166.67 inference(rewrite,[status(thm)],[])).
% 262.32/166.67 tff(1459,plain,
% 262.32/166.67 ((~![B: $i] : ((~bool(B)) | (and1(false, B) = false))) | ((~bool(not1(false))) | (and1(false, not1(false)) = false))),
% 262.32/166.67 inference(quant_inst,[status(thm)],[])).
% 262.32/166.67 tff(1460,plain,
% 262.32/166.67 ((~![B: $i] : ((~bool(B)) | (and1(false, B) = false))) | (~bool(not1(false))) | (and1(false, not1(false)) = false)),
% 262.32/166.67 inference(modus_ponens,[status(thm)],[1459, 1458])).
% 262.32/166.67 tff(1461,plain,
% 262.32/166.67 (and1(false, not1(false)) = false),
% 262.32/166.67 inference(unit_resolution,[status(thm)],[1460, 1457, 81])).
% 262.32/166.67 tff(1462,plain,
% 262.32/166.67 (and1(P!8, Q!7) = and1(false, not1(false))),
% 262.32/166.67 inference(monotonicity,[status(thm)],[1441, 443])).
% 262.32/166.67 tff(1463,plain,
% 262.32/166.67 (and1(P!8, Q!7) = and2(P!8, Q!7)),
% 262.32/166.67 inference(transitivity,[status(thm)],[1462, 1461, 559, 1447, 296])).
% 262.32/166.67 tff(1464,plain,
% 262.32/166.67 ($false),
% 262.32/166.67 inference(unit_resolution,[status(thm)],[361, 1463])).
% 262.32/166.67 tff(1465,plain,((~(Q!7 = not1(false))) | (~(prop(tptp_fun_R_0(Q!7, P!8)) = not1(false))) | (impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = phi(Q!7))), inference(lemma,lemma(discharge,[]))).
% 262.32/166.67 tff(1466,plain,
% 262.32/166.67 (impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = phi(Q!7)),
% 262.32/166.67 inference(unit_resolution,[status(thm)],[1465, 443, 342])).
% 262.32/166.67 tff(1467,plain,
% 262.32/166.67 (impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = not1(false)),
% 262.32/166.68 inference(modus_ponens,[status(thm)],[1466, 1370])).
% 262.32/166.68 tff(1468,plain,
% 262.32/166.68 (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = not1(false)),
% 262.32/166.68 inference(modus_ponens,[status(thm)],[1467, 1367])).
% 262.32/166.68 tff(1469,plain,
% 262.32/166.68 (tptp_fun_R_0(Q!7, P!8) = not1(false)),
% 262.32/166.68 inference(transitivity,[status(thm)],[1359, 1299, 1296, 1468])).
% 262.32/166.68 tff(1470,plain,
% 262.32/166.68 (f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)) = f1(P!8, not1(false), not1(false))),
% 262.32/166.68 inference(monotonicity,[status(thm)],[443, 1469])).
% 262.32/166.68 tff(1471,plain,
% 262.32/166.68 (f1(P!8, not1(false), not1(false)) = f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))),
% 262.32/166.68 inference(symmetry,[status(thm)],[1470])).
% 262.32/166.68 tff(1472,plain,
% 262.32/166.68 (lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))),
% 262.32/166.68 inference(transitivity,[status(thm)],[453, 448, 1471, 176])).
% 262.32/166.68 tff(1473,plain,
% 262.32/166.68 ((lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))) = not1(false)) <=> (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = not1(false))),
% 262.32/166.68 inference(monotonicity,[status(thm)],[1472])).
% 262.32/166.68 tff(1474,plain,
% 262.32/166.68 ((~(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))) = not1(false))) <=> (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = not1(false)))),
% 262.32/166.68 inference(monotonicity,[status(thm)],[1473])).
% 262.32/166.68 tff(1475,plain,
% 262.32/166.68 (((~![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(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false)))) <=> ((~(bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))) | (~bool(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))) | (~d(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))))) | (~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))) = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false)))) <=> ((~(bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))) | (~bool(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))) | (~d(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))))) | (~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))) = not1(false))))))))),
% 262.32/166.68 inference(rewrite,[status(thm)],[])).
% 262.32/166.68 tff(1476,plain,
% 262.32/166.68 ((forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false)))) <=> ((~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))))) | (~((~d(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))) | (~bool(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))) = not1(false))))))) <=> (forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false)))) <=> ((~(bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))) | (~bool(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))) | (~d(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))))) | (~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))) = not1(false)))))))),
% 262.32/166.68 inference(rewrite,[status(thm)],[])).
% 262.32/166.68 tff(1477,plain,
% 262.32/166.68 (((~![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(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false)))) <=> ((~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))))) | (~((~d(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))) | (~bool(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))) = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false)))) <=> ((~(bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))) | (~bool(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))) | (~d(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))))) | (~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))) = not1(false))))))))),
% 262.32/166.68 inference(monotonicity,[status(thm)],[1476])).
% 262.32/166.68 tff(1478,plain,
% 262.32/166.68 (((~![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(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false)))) <=> ((~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))))) | (~((~d(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))) | (~bool(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))) = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false)))) <=> ((~(bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))) | (~bool(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))) | (~d(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))))) | (~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))) = not1(false))))))))),
% 262.32/166.69 inference(transitivity,[status(thm)],[1477, 1475])).
% 262.32/166.69 tff(1479,plain,
% 262.32/166.69 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false)))) <=> ((~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))))) | (~((~d(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))) | (~bool(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))) = not1(false)))))))),
% 262.32/166.69 inference(quant_inst,[status(thm)],[])).
% 262.32/166.69 tff(1480,plain,
% 262.32/166.69 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false)))) <=> ((~(bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))) | (~bool(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))) | (~d(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))))) | (~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))) = not1(false)))))))),
% 262.32/166.69 inference(modus_ponens,[status(thm)],[1479, 1478])).
% 262.32/166.69 tff(1481,plain,
% 262.32/166.69 (forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false)))) <=> ((~(bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))) | (~bool(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))) | (~d(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))))) | (~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))) = not1(false))))))),
% 262.32/166.69 inference(unit_resolution,[status(thm)],[1480, 493])).
% 262.32/166.69 tff(1482,plain,
% 262.32/166.69 (lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))) = f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))),
% 262.32/166.69 inference(transitivity,[status(thm)],[453, 448, 1471])).
% 262.32/166.69 tff(1483,plain,
% 262.32/166.69 (P!8 = lazy_impl(prop(P!8), P!8)),
% 262.32/166.69 inference(transitivity,[status(thm)],[1270, 1224, 1221])).
% 262.32/166.69 tff(1484,plain,
% 262.32/166.69 (f1(P!8, Q!7, lazy_impl(prop(P!8), P!8)) = f1(lazy_impl(prop(P!8), P!8), not1(false), lazy_impl(prop(P!8), P!8))),
% 262.32/166.69 inference(monotonicity,[status(thm)],[1483, 443])).
% 262.32/166.69 tff(1485,plain,
% 262.32/166.69 (f1(lazy_impl(prop(P!8), P!8), not1(false), lazy_impl(prop(P!8), P!8)) = f1(P!8, Q!7, lazy_impl(prop(P!8), P!8))),
% 262.32/166.69 inference(symmetry,[status(thm)],[1484])).
% 262.32/166.69 tff(1486,plain,
% 262.32/166.69 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(lazy_impl(prop(P!8), P!8), not1(false), lazy_impl(prop(P!8), P!8)) = lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))),
% 262.32/166.69 inference(quant_inst,[status(thm)],[])).
% 262.32/166.69 tff(1487,plain,
% 262.32/166.69 (f1(lazy_impl(prop(P!8), P!8), not1(false), lazy_impl(prop(P!8), P!8)) = lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))),
% 262.32/166.69 inference(unit_resolution,[status(thm)],[1486, 159])).
% 262.32/166.69 tff(1488,plain,
% 262.32/166.69 (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = f1(lazy_impl(prop(P!8), P!8), not1(false), lazy_impl(prop(P!8), P!8))),
% 262.32/166.69 inference(symmetry,[status(thm)],[1487])).
% 262.32/166.69 tff(1489,plain,
% 262.32/166.69 (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = f1(P!8, Q!7, lazy_impl(prop(P!8), P!8))),
% 262.32/166.69 inference(transitivity,[status(thm)],[1488, 1485])).
% 262.32/166.69 tff(1490,plain,
% 262.32/166.69 (forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false)))) <=> forallprefers(f1(P!8, Q!7, lazy_impl(prop(P!8), P!8)), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.32/166.69 inference(monotonicity,[status(thm)],[1489, 1482])).
% 262.32/166.69 tff(1491,plain,
% 262.32/166.69 (forallprefers(f1(P!8, Q!7, lazy_impl(prop(P!8), P!8)), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))) <=> forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))),
% 262.36/166.70 inference(symmetry,[status(thm)],[1490])).
% 262.36/166.70 tff(1492,plain,
% 262.36/166.70 ((~forallprefers(f1(P!8, Q!7, lazy_impl(prop(P!8), P!8)), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))) <=> (~forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false)))))),
% 262.36/166.70 inference(monotonicity,[status(thm)],[1491])).
% 262.36/166.70 tff(1493,plain,
% 262.36/166.70 ((~![R1: $i] : (~forallprefers(f1(P!8, Q!7, R1), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~forallprefers(f1(P!8, Q!7, lazy_impl(prop(P!8), P!8)), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.36/166.70 inference(quant_inst,[status(thm)],[])).
% 262.36/166.70 tff(1494,plain,
% 262.36/166.70 (~forallprefers(f1(P!8, Q!7, lazy_impl(prop(P!8), P!8)), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.36/166.70 inference(unit_resolution,[status(thm)],[1493, 474])).
% 262.36/166.70 tff(1495,plain,
% 262.36/166.70 (~forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))),
% 262.36/166.70 inference(modus_ponens,[status(thm)],[1494, 1492])).
% 262.36/166.70 tff(1496,plain,
% 262.36/166.70 ((~(forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false)))) <=> ((~(bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))) | (~bool(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))) | (~d(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))))) | (~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))) = not1(false)))))))) | forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false)))) | (~((~(bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))) | (~bool(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))) | (~d(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))))) | (~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))) = not1(false)))))))),
% 262.36/166.70 inference(tautology,[status(thm)],[])).
% 262.36/166.70 tff(1497,plain,
% 262.36/166.70 (~((~(bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))) | (~bool(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))) | (~d(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))))) | (~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))) = not1(false))))))),
% 262.36/166.70 inference(unit_resolution,[status(thm)],[1496, 1495, 1481])).
% 262.36/166.70 tff(1498,plain,
% 262.36/166.70 (((~(bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))) | (~bool(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))) | (~d(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))))) | (~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))) = not1(false)))))) | ((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))) = not1(false))))),
% 262.36/166.70 inference(tautology,[status(thm)],[])).
% 262.36/166.70 tff(1499,plain,
% 262.36/166.70 ((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))) = not1(false)))),
% 262.36/166.70 inference(unit_resolution,[status(thm)],[1498, 1497])).
% 262.36/166.70 tff(1500,plain,
% 262.36/166.70 (impl(not1(false), impl(false, not1(false))) = impl(not1(false), not1(false))),
% 262.36/166.70 inference(monotonicity,[status(thm)],[165])).
% 262.36/166.70 tff(1501,plain,
% 262.36/166.70 (impl(not1(false), impl(false, not1(false))) = not1(false)),
% 262.36/166.70 inference(transitivity,[status(thm)],[1500, 98])).
% 262.36/166.70 tff(1502,plain,
% 262.36/166.70 (impl(impl(not1(false), impl(false, not1(false))), not1(false)) = impl(not1(false), not1(false))),
% 262.36/166.70 inference(monotonicity,[status(thm)],[1501])).
% 262.36/166.70 tff(1503,plain,
% 262.36/166.70 (impl(impl(not1(false), impl(false, not1(false))), not1(false)) = not1(false)),
% 262.36/166.70 inference(transitivity,[status(thm)],[1502, 98])).
% 262.36/166.70 tff(1504,plain,
% 262.36/166.70 (lazy_impl(prop(not1(false)), impl(impl(not1(false), impl(false, not1(false))), not1(false))) = lazy_impl(not1(false), not1(false))),
% 262.36/166.70 inference(monotonicity,[status(thm)],[458, 1503])).
% 262.36/166.70 tff(1505,plain,
% 262.36/166.70 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(not1(false), false, not1(false)) = lazy_impl(prop(not1(false)), impl(impl(not1(false), impl(false, not1(false))), not1(false))))),
% 262.36/166.70 inference(quant_inst,[status(thm)],[])).
% 262.36/166.71 tff(1506,plain,
% 262.36/166.71 (f1(not1(false), false, not1(false)) = lazy_impl(prop(not1(false)), impl(impl(not1(false), impl(false, not1(false))), not1(false)))),
% 262.36/166.71 inference(unit_resolution,[status(thm)],[1505, 159])).
% 262.36/166.71 tff(1507,plain,
% 262.36/166.71 (f1(P!8, false, not1(false)) = f1(not1(false), false, not1(false))),
% 262.36/166.71 inference(monotonicity,[status(thm)],[1408])).
% 262.36/166.71 tff(1508,plain,
% 262.36/166.71 (f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)) = not1(false)),
% 262.36/166.71 inference(transitivity,[status(thm)],[1470, 447, 452, 1200, 1507, 1506, 1504, 593, 49])).
% 262.36/166.71 tff(1509,plain,
% 262.36/166.71 (phi(f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(not1(false))),
% 262.36/166.71 inference(monotonicity,[status(thm)],[1508])).
% 262.36/166.71 tff(1510,plain,
% 262.36/166.71 (phi(not1(false)) = phi(f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.36/166.71 inference(symmetry,[status(thm)],[1509])).
% 262.36/166.71 tff(1511,plain,
% 262.36/166.71 (and1(P!8, Q!7) = and2(P!8, Q!7)),
% 262.36/166.71 inference(transitivity,[status(thm)],[1435, 1434, 1417, 1510, 296])).
% 262.36/166.71 tff(1512,plain,
% 262.36/166.71 ($false),
% 262.36/166.71 inference(unit_resolution,[status(thm)],[361, 1511])).
% 262.36/166.71 tff(1513,plain,((~(P!8 = not1(false))) | (~(prop(tptp_fun_R_0(Q!7, P!8)) = not1(false))) | (~(Q!7 = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 262.36/166.71 tff(1514,plain,
% 262.36/166.71 (~(P!8 = not1(false))),
% 262.36/166.71 inference(unit_resolution,[status(thm)],[1513, 443, 342])).
% 262.36/166.71 tff(1515,plain,
% 262.36/166.71 (P!8 = false),
% 262.36/166.71 inference(unit_resolution,[status(thm)],[1440, 1514, 1382])).
% 262.36/166.71 tff(1516,plain,
% 262.36/166.71 (lazy_impl(prop(P!8), P!8) = false),
% 262.36/166.71 inference(transitivity,[status(thm)],[1220, 1223, 1269, 1515])).
% 262.36/166.71 tff(1517,plain,
% 262.36/166.71 (f1(lazy_impl(prop(P!8), P!8), not1(false), lazy_impl(prop(P!8), P!8)) = f1(false, not1(false), false)),
% 262.36/166.71 inference(monotonicity,[status(thm)],[1516, 1516])).
% 262.36/166.71 tff(1518,plain,
% 262.36/166.71 (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false),
% 262.36/166.71 inference(transitivity,[status(thm)],[1488, 1517, 1377, 1375, 35, 23])).
% 262.36/166.71 tff(1519,plain,
% 262.36/166.71 ((~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))) = not1(false))))) | (~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))) = not1(false)))),
% 262.36/166.71 inference(tautology,[status(thm)],[])).
% 262.36/166.71 tff(1520,plain,
% 262.36/166.71 (~(lazy_impl(prop(not1(false)), impl(impl(P!8, impl(false, not1(false))), not1(false))) = not1(false))),
% 262.36/166.71 inference(unit_resolution,[status(thm)],[1519, 1518, 1499])).
% 262.36/166.71 tff(1521,plain,
% 262.36/166.71 (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = not1(false))),
% 262.36/166.71 inference(modus_ponens,[status(thm)],[1520, 1474])).
% 262.36/166.71 tff(1522,plain,
% 262.36/166.71 (impl(false, impl(false, not1(false))) = impl(false, not1(false))),
% 262.36/166.71 inference(monotonicity,[status(thm)],[165])).
% 262.36/166.71 tff(1523,plain,
% 262.36/166.71 (impl(false, impl(false, not1(false))) = not1(false)),
% 262.36/166.71 inference(transitivity,[status(thm)],[1522, 165])).
% 262.36/166.71 tff(1524,plain,
% 262.36/166.71 (impl(impl(false, impl(false, not1(false))), not1(false)) = impl(not1(false), not1(false))),
% 262.36/166.71 inference(monotonicity,[status(thm)],[1523])).
% 262.36/166.71 tff(1525,plain,
% 262.36/166.71 (impl(impl(false, impl(false, not1(false))), not1(false)) = not1(false)),
% 262.36/166.71 inference(transitivity,[status(thm)],[1524, 98])).
% 262.36/166.71 tff(1526,plain,
% 262.36/166.71 (lazy_impl(prop(not1(false)), impl(impl(false, impl(false, not1(false))), not1(false))) = lazy_impl(not1(false), not1(false))),
% 262.36/166.71 inference(monotonicity,[status(thm)],[458, 1525])).
% 262.36/166.71 tff(1527,plain,
% 262.36/166.71 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(false, false, not1(false)) = lazy_impl(prop(not1(false)), impl(impl(false, impl(false, not1(false))), not1(false))))),
% 262.36/166.71 inference(quant_inst,[status(thm)],[])).
% 262.36/166.71 tff(1528,plain,
% 262.36/166.71 (f1(false, false, not1(false)) = lazy_impl(prop(not1(false)), impl(impl(false, impl(false, not1(false))), not1(false)))),
% 262.36/166.71 inference(unit_resolution,[status(thm)],[1527, 159])).
% 262.36/166.71 tff(1529,plain,
% 262.36/166.71 (f1(P!8, false, not1(false)) = f1(false, false, not1(false))),
% 262.36/166.71 inference(monotonicity,[status(thm)],[1515])).
% 262.36/166.71 tff(1530,plain,
% 262.36/166.71 (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = not1(false)),
% 262.36/166.71 inference(transitivity,[status(thm)],[177, 1470, 447, 452, 1200, 1529, 1528, 1526, 593, 49])).
% 262.36/166.71 tff(1531,plain,
% 262.36/166.71 ($false),
% 262.36/166.71 inference(unit_resolution,[status(thm)],[1530, 1521])).
% 262.36/166.71 tff(1532,plain,((~(Q!7 = not1(false))) | (~(prop(tptp_fun_R_0(Q!7, P!8)) = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 262.36/166.71 tff(1533,plain,
% 262.36/166.71 (~(Q!7 = not1(false))),
% 262.36/166.71 inference(unit_resolution,[status(thm)],[1532, 342])).
% 262.36/166.71 tff(1534,plain,
% 262.36/166.71 (Q!7 = false),
% 262.36/166.71 inference(unit_resolution,[status(thm)],[1194, 1533])).
% 262.36/166.71 tff(1535,plain,
% 262.36/166.71 (f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)) = f1(P!8, false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.36/166.71 inference(monotonicity,[status(thm)],[1534, 1360])).
% 262.36/166.71 tff(1536,plain,
% 262.36/166.71 (f1(P!8, false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))),
% 262.36/166.71 inference(symmetry,[status(thm)],[1535])).
% 262.36/166.71 tff(1537,plain,
% 262.36/166.71 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(P!8, false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))),
% 262.36/166.71 inference(quant_inst,[status(thm)],[])).
% 262.36/166.71 tff(1538,plain,
% 262.36/166.71 (f1(P!8, false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))),
% 262.36/166.71 inference(unit_resolution,[status(thm)],[1537, 159])).
% 262.36/166.71 tff(1539,plain,
% 262.36/166.71 (lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = f1(P!8, false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.36/166.71 inference(symmetry,[status(thm)],[1538])).
% 262.36/166.71 tff(1540,plain,
% 262.36/166.71 (lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))),
% 262.36/166.71 inference(transitivity,[status(thm)],[1539, 1536])).
% 262.36/166.71 tff(1541,plain,
% 262.36/166.71 (f1(P!8, Q!7, false) = f1(P!8, false, false)),
% 262.36/166.71 inference(monotonicity,[status(thm)],[1534])).
% 262.36/166.71 tff(1542,plain,
% 262.36/166.71 (f1(P!8, false, false) = f1(P!8, Q!7, false)),
% 262.36/166.71 inference(symmetry,[status(thm)],[1541])).
% 262.36/166.71 tff(1543,plain,
% 262.36/166.71 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(P!8, false, false) = lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))),
% 262.36/166.71 inference(quant_inst,[status(thm)],[])).
% 262.36/166.71 tff(1544,plain,
% 262.36/166.71 (f1(P!8, false, false) = lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))),
% 262.36/166.71 inference(unit_resolution,[status(thm)],[1543, 159])).
% 262.36/166.71 tff(1545,plain,
% 262.36/166.71 (lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = f1(P!8, false, false)),
% 262.36/166.71 inference(symmetry,[status(thm)],[1544])).
% 262.36/166.71 tff(1546,plain,
% 262.36/166.71 (lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = f1(P!8, Q!7, false)),
% 262.36/166.71 inference(transitivity,[status(thm)],[1545, 1542])).
% 262.36/166.71 tff(1547,plain,
% 262.36/166.71 (forallprefers(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)), lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))) <=> forallprefers(f1(P!8, Q!7, false), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.36/166.71 inference(monotonicity,[status(thm)],[1546, 1540])).
% 262.36/166.71 tff(1548,plain,
% 262.36/166.71 (forallprefers(f1(P!8, Q!7, false), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))) <=> forallprefers(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)), lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))),
% 262.36/166.71 inference(symmetry,[status(thm)],[1547])).
% 262.36/166.71 tff(1549,plain,
% 262.36/166.71 ((~forallprefers(f1(P!8, Q!7, false), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))) <=> (~forallprefers(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)), lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))))),
% 262.36/166.71 inference(monotonicity,[status(thm)],[1548])).
% 262.36/166.71 tff(1550,plain,
% 262.36/166.71 (~forallprefers(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)), lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))),
% 262.36/166.71 inference(modus_ponens,[status(thm)],[802, 1549])).
% 262.36/166.71 tff(1551,plain,
% 262.36/166.71 ((~(forallprefers(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)), lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))) <=> ((~((~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))) | (~bool(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~(d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false)))))))) | forallprefers(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)), lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))) | (~((~((~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))) | (~bool(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~(d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false)))))))),
% 262.36/166.72 inference(tautology,[status(thm)],[])).
% 262.36/166.72 tff(1552,plain,
% 262.36/166.72 (~((~((~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))) | (~bool(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~(d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false))))))),
% 262.36/166.72 inference(unit_resolution,[status(thm)],[1551, 1550, 1294])).
% 262.36/166.72 tff(1553,plain,
% 262.36/166.72 (((~((~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))) | (~bool(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~(d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false)))))) | ((~(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false))))),
% 262.36/166.72 inference(tautology,[status(thm)],[])).
% 262.36/166.72 tff(1554,plain,
% 262.36/166.72 ((~(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false)))),
% 262.36/166.72 inference(unit_resolution,[status(thm)],[1553, 1552])).
% 262.36/166.72 tff(1555,plain,
% 262.36/166.72 (impl(impl(not1(false), impl(false, false)), false) = false),
% 262.36/166.72 inference(transitivity,[status(thm)],[127, 132])).
% 262.36/166.72 tff(1556,plain,
% 262.36/166.72 (lazy_impl(prop(false), impl(impl(not1(false), impl(false, false)), false)) = lazy_impl(not1(false), false)),
% 262.36/166.72 inference(monotonicity,[status(thm)],[149, 1555])).
% 262.36/166.72 tff(1557,plain,
% 262.36/166.72 (((~![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(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))) <=> ((~(bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~bool(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = 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(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))) <=> ((~(bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~bool(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false))))))))),
% 262.36/166.73 inference(rewrite,[status(thm)],[])).
% 262.36/166.73 tff(1558,plain,
% 262.36/166.73 ((forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))) <=> ((~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~((~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~bool(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false))))))) <=> (forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))) <=> ((~(bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~bool(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false)))))))),
% 262.36/166.73 inference(rewrite,[status(thm)],[])).
% 262.36/166.73 tff(1559,plain,
% 262.36/166.73 (((~![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(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))) <=> ((~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~((~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~bool(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = 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(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))) <=> ((~(bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~bool(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false))))))))),
% 262.36/166.74 inference(monotonicity,[status(thm)],[1558])).
% 262.36/166.74 tff(1560,plain,
% 262.36/166.74 (((~![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(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))) <=> ((~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~((~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~bool(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = 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(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))) <=> ((~(bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~bool(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false))))))))),
% 262.36/166.74 inference(transitivity,[status(thm)],[1559, 1557])).
% 262.36/166.74 tff(1561,plain,
% 262.36/166.74 ((~![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(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))) <=> ((~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~((~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~bool(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false)))))))),
% 262.36/166.74 inference(quant_inst,[status(thm)],[])).
% 262.36/166.74 tff(1562,plain,
% 262.36/166.74 ((~![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(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))) <=> ((~(bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~bool(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false)))))))),
% 262.41/166.74 inference(modus_ponens,[status(thm)],[1561, 1560])).
% 262.41/166.74 tff(1563,plain,
% 262.41/166.74 (forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))) <=> ((~(bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~bool(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false))))))),
% 262.41/166.74 inference(unit_resolution,[status(thm)],[1562, 493])).
% 262.41/166.74 tff(1564,plain,
% 262.41/166.74 (f1(P!8, Q!7, lazy_impl(prop(P!8), P!8)) = f1(P!8, false, lazy_impl(prop(P!8), P!8))),
% 262.41/166.74 inference(monotonicity,[status(thm)],[1534])).
% 262.41/166.74 tff(1565,plain,
% 262.41/166.74 (f1(P!8, false, lazy_impl(prop(P!8), P!8)) = f1(P!8, Q!7, lazy_impl(prop(P!8), P!8))),
% 262.41/166.74 inference(symmetry,[status(thm)],[1564])).
% 262.41/166.75 tff(1566,plain,
% 262.41/166.75 (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = f1(P!8, Q!7, lazy_impl(prop(P!8), P!8))),
% 262.41/166.75 inference(transitivity,[status(thm)],[1278, 1565])).
% 262.41/166.75 tff(1567,plain,
% 262.41/166.75 (forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))) <=> forallprefers(f1(P!8, Q!7, lazy_impl(prop(P!8), P!8)), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.41/166.75 inference(monotonicity,[status(thm)],[1566, 1540])).
% 262.41/166.75 tff(1568,plain,
% 262.41/166.75 (forallprefers(f1(P!8, Q!7, lazy_impl(prop(P!8), P!8)), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))) <=> forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))),
% 262.41/166.75 inference(symmetry,[status(thm)],[1567])).
% 262.41/166.75 tff(1569,plain,
% 262.41/166.75 ((~forallprefers(f1(P!8, Q!7, lazy_impl(prop(P!8), P!8)), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))) <=> (~forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))))),
% 262.41/166.75 inference(monotonicity,[status(thm)],[1568])).
% 262.41/166.75 tff(1570,plain,
% 262.41/166.75 (~forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))),
% 262.41/166.75 inference(modus_ponens,[status(thm)],[1494, 1569])).
% 262.41/166.75 tff(1571,plain,
% 262.41/166.75 ((~(forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))) <=> ((~(bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~bool(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false)))))))) | forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))) | (~((~(bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~bool(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false)))))))),
% 262.41/166.75 inference(tautology,[status(thm)],[])).
% 262.41/166.75 tff(1572,plain,
% 262.41/166.75 (~((~(bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~bool(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false))))))),
% 262.41/166.75 inference(unit_resolution,[status(thm)],[1571, 1570, 1563])).
% 262.41/166.75 tff(1573,plain,
% 262.41/166.75 (((~(bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~bool(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false)))))) | ((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false))))),
% 262.41/166.76 inference(tautology,[status(thm)],[])).
% 262.41/166.76 tff(1574,plain,
% 262.41/166.76 ((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false)))),
% 262.41/166.76 inference(unit_resolution,[status(thm)],[1573, 1572])).
% 262.41/166.76 tff(1575,plain,
% 262.41/166.76 (impl(impl(false, impl(false, false)), false) = false),
% 262.41/166.76 inference(transitivity,[status(thm)],[168, 132])).
% 262.41/166.76 tff(1576,plain,
% 262.41/166.76 (lazy_impl(prop(false), impl(impl(false, impl(false, false)), false)) = lazy_impl(not1(false), false)),
% 262.41/166.76 inference(monotonicity,[status(thm)],[149, 1575])).
% 262.41/166.76 tff(1577,plain,
% 262.41/166.76 (lazy_impl(prop(P!8), P!8) = false),
% 262.41/166.76 inference(transitivity,[status(thm)],[1220, 1223, 1269, 1271])).
% 262.41/166.76 tff(1578,plain,
% 262.41/166.76 (f1(P!8, false, lazy_impl(prop(P!8), P!8)) = f1(false, false, false)),
% 262.41/166.76 inference(monotonicity,[status(thm)],[1271, 1577])).
% 262.41/166.76 tff(1579,plain,
% 262.41/166.76 (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false),
% 262.41/166.76 inference(transitivity,[status(thm)],[1278, 1578, 174, 1576, 35, 23])).
% 262.41/166.76 tff(1580,plain,
% 262.41/166.76 (lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))),
% 262.41/166.76 inference(transitivity,[status(thm)],[1539, 1536, 176])).
% 262.41/166.76 tff(1581,plain,
% 262.41/166.76 ((lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false)) <=> (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = not1(false))),
% 262.41/166.76 inference(monotonicity,[status(thm)],[1580])).
% 262.41/166.76 tff(1582,plain,
% 262.41/166.76 ((lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = not1(false)) <=> (lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false))),
% 262.41/166.76 inference(symmetry,[status(thm)],[1581])).
% 262.41/166.76 tff(1583,plain,
% 262.41/166.76 ((d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~(phi(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = err))) | (~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))),
% 262.41/166.76 inference(tautology,[status(thm)],[])).
% 262.41/166.76 tff(1584,plain,
% 262.41/166.76 (d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~(phi(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = err))),
% 262.41/166.76 inference(unit_resolution,[status(thm)],[1583, 1341])).
% 262.41/166.76 tff(1585,plain,
% 262.41/166.76 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) | (~(phi(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~(d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~(phi(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) | (~(phi(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~(d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~(phi(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = err)))))),
% 262.41/166.76 inference(rewrite,[status(thm)],[])).
% 262.41/166.76 tff(1586,plain,
% 262.41/166.76 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) | (~(phi(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~(d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~(phi(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = err)))))),
% 262.41/166.76 inference(quant_inst,[status(thm)],[])).
% 262.41/166.76 tff(1587,plain,
% 262.41/166.76 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) | (~(phi(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))) | (~(d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) | (~(phi(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = err))))),
% 262.41/166.76 inference(modus_ponens,[status(thm)],[1586, 1585])).
% 262.41/166.76 tff(1588,plain,
% 262.41/166.76 (~((~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) | (~(phi(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))),
% 262.41/166.76 inference(unit_resolution,[status(thm)],[1587, 17, 1584])).
% 262.41/166.76 tff(1589,plain,
% 262.41/166.76 (((~d(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) | (~(phi(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))) | (phi(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.41/166.76 inference(tautology,[status(thm)],[])).
% 262.41/166.76 tff(1590,plain,
% 262.41/166.76 (phi(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))),
% 262.41/166.76 inference(unit_resolution,[status(thm)],[1589, 1588])).
% 262.41/166.76 tff(1591,plain,
% 262.41/166.76 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = phi(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))),
% 262.41/166.77 inference(quant_inst,[status(thm)],[])).
% 262.41/166.77 tff(1592,plain,
% 262.41/166.77 (lazy_impl(not1(false), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = phi(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.41/166.77 inference(unit_resolution,[status(thm)],[1591, 33])).
% 262.41/166.77 tff(1593,plain,
% 262.41/166.77 (((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | ((~bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) | (impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = not1(false)))) <=> ((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | (~bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) | (impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = not1(false)))),
% 262.41/166.77 inference(rewrite,[status(thm)],[])).
% 262.41/166.77 tff(1594,plain,
% 262.41/166.77 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | ((~bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) | (impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = not1(false)))),
% 262.41/166.77 inference(quant_inst,[status(thm)],[])).
% 262.41/166.77 tff(1595,plain,
% 262.41/166.77 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | (~bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) | (impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = not1(false))),
% 262.41/166.77 inference(modus_ponens,[status(thm)],[1594, 1593])).
% 262.41/166.77 tff(1596,plain,
% 262.41/166.77 (impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = not1(false)),
% 262.41/166.77 inference(unit_resolution,[status(thm)],[1595, 120, 1346])).
% 262.41/166.77 tff(1597,plain,
% 262.41/166.77 (impl(false, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = impl(false, not1(false))),
% 262.41/166.77 inference(monotonicity,[status(thm)],[1596])).
% 262.41/166.77 tff(1598,plain,
% 262.41/166.77 (impl(false, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false)),
% 262.41/166.77 inference(transitivity,[status(thm)],[1597, 165])).
% 262.41/166.77 tff(1599,plain,
% 262.41/166.77 (impl(impl(false, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = impl(not1(false), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.41/166.77 inference(monotonicity,[status(thm)],[1598])).
% 262.41/166.77 tff(1600,plain,
% 262.41/166.77 (impl(impl(false, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))),
% 262.41/166.77 inference(transitivity,[status(thm)],[1599, 1364])).
% 262.41/166.77 tff(1601,plain,
% 262.41/166.77 ((~![X: $i] : ((prop(X) = not1(false)) <=> bool(X))) | ((prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = not1(false)) <=> bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))),
% 262.41/166.77 inference(quant_inst,[status(thm)],[])).
% 262.41/166.77 tff(1602,plain,
% 262.41/166.77 ((prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = not1(false)) <=> bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.41/166.77 inference(unit_resolution,[status(thm)],[1601, 144])).
% 262.41/166.77 tff(1603,plain,
% 262.41/166.77 ((~((prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = not1(false)) <=> bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))) | (prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = not1(false)) | (~bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))),
% 262.41/166.77 inference(tautology,[status(thm)],[])).
% 262.41/166.77 tff(1604,plain,
% 262.41/166.77 ((~((prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = not1(false)) <=> bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))) | (prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = not1(false))),
% 262.41/166.77 inference(unit_resolution,[status(thm)],[1603, 1346])).
% 262.41/166.77 tff(1605,plain,
% 262.41/166.77 (prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = not1(false)),
% 262.41/166.77 inference(unit_resolution,[status(thm)],[1604, 1602])).
% 262.41/166.77 tff(1606,plain,
% 262.41/166.77 (lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(false, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = lazy_impl(not1(false), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.41/166.77 inference(monotonicity,[status(thm)],[1605, 1600])).
% 262.41/166.77 tff(1607,plain,
% 262.41/166.77 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(false, false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(false, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))),
% 262.41/166.77 inference(quant_inst,[status(thm)],[])).
% 262.41/166.77 tff(1608,plain,
% 262.41/166.77 (f1(false, false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(false, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))),
% 262.41/166.77 inference(unit_resolution,[status(thm)],[1607, 159])).
% 262.41/166.77 tff(1609,plain,
% 262.41/166.77 (f1(P!8, false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = f1(false, false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.41/166.77 inference(monotonicity,[status(thm)],[1271])).
% 262.41/166.77 tff(1610,plain,
% 262.41/166.77 (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))),
% 262.41/166.77 inference(transitivity,[status(thm)],[177, 1535, 1609, 1608, 1606, 1592, 1590])).
% 262.41/166.77 tff(1611,plain,
% 262.41/166.77 ((lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = not1(false)) <=> (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = not1(false))),
% 262.41/166.77 inference(monotonicity,[status(thm)],[1610])).
% 262.41/166.77 tff(1612,plain,
% 262.41/166.77 ((lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = not1(false)) <=> (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = not1(false))),
% 262.41/166.77 inference(symmetry,[status(thm)],[1611])).
% 262.41/166.77 tff(1613,plain,
% 262.41/166.77 ((lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = not1(false)) <=> (lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false))),
% 262.41/166.77 inference(transitivity,[status(thm)],[1612, 1582])).
% 262.41/166.77 tff(1614,plain,
% 262.41/166.77 (impl(P!8, impl(false, not1(false))) = impl(false, not1(false))),
% 262.41/166.77 inference(monotonicity,[status(thm)],[1271, 165])).
% 262.41/166.77 tff(1615,plain,
% 262.41/166.77 (impl(P!8, impl(false, not1(false))) = not1(false)),
% 262.41/166.77 inference(transitivity,[status(thm)],[1614, 165])).
% 262.41/166.77 tff(1616,plain,
% 262.41/166.77 (phi(impl(P!8, impl(false, not1(false)))) = phi(not1(false))),
% 262.41/166.77 inference(monotonicity,[status(thm)],[1615])).
% 262.41/166.77 tff(1617,plain,
% 262.41/166.77 (impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.41/166.77 inference(monotonicity,[status(thm)],[1534, 1360])).
% 262.41/166.77 tff(1618,plain,
% 262.41/166.77 (impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = impl(false, not1(false))),
% 262.41/166.77 inference(transitivity,[status(thm)],[1617, 1596, 398])).
% 262.41/166.77 tff(1619,plain,
% 262.41/166.77 (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = impl(P!8, impl(false, not1(false)))),
% 262.41/166.77 inference(monotonicity,[status(thm)],[1618])).
% 262.41/166.77 tff(1620,plain,
% 262.41/166.77 (phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = phi(impl(P!8, impl(false, not1(false))))),
% 262.41/166.77 inference(monotonicity,[status(thm)],[1619])).
% 262.41/166.77 tff(1621,assumption,(~(impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))), introduced(assumption)).
% 262.41/166.77 tff(1622,plain,
% 262.41/166.77 ((~![X: $i] : ((prop(X) = not1(false)) <=> bool(X))) | ((prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = not1(false)) <=> bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))),
% 262.41/166.77 inference(quant_inst,[status(thm)],[])).
% 262.41/166.77 tff(1623,plain,
% 262.41/166.77 ((prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = not1(false)) <=> bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.41/166.77 inference(unit_resolution,[status(thm)],[1622, 144])).
% 262.41/166.77 tff(1624,plain,
% 262.41/166.77 (bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.41/166.77 inference(unit_resolution,[status(thm)],[262, 1621])).
% 262.41/166.77 tff(1625,plain,
% 262.41/166.77 ((~((prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = not1(false)) <=> bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))) | (prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = not1(false)) | (~bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))),
% 262.41/166.77 inference(tautology,[status(thm)],[])).
% 262.41/166.77 tff(1626,plain,
% 262.41/166.77 ((~((prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = not1(false)) <=> bool(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))) | (prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = not1(false))),
% 262.41/166.77 inference(unit_resolution,[status(thm)],[1625, 1624])).
% 262.41/166.77 tff(1627,plain,
% 262.41/166.77 (prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = not1(false)),
% 262.41/166.77 inference(unit_resolution,[status(thm)],[1626, 1623])).
% 262.41/166.77 tff(1628,assumption,(phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = err), introduced(assumption)).
% 262.41/166.77 tff(1629,plain,
% 262.41/166.77 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))),
% 262.41/166.77 inference(quant_inst,[status(thm)],[])).
% 262.41/166.77 tff(1630,plain,
% 262.41/166.77 (lazy_impl(not1(false), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.41/166.77 inference(unit_resolution,[status(thm)],[1629, 33])).
% 262.41/166.77 tff(1631,assumption,(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = not1(false)), introduced(assumption)).
% 262.41/166.77 tff(1632,plain,
% 262.41/166.77 (lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = lazy_impl(not1(false), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.41/166.77 inference(monotonicity,[status(thm)],[1631])).
% 262.41/166.77 tff(1633,plain,
% 262.41/166.77 (lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = err),
% 262.41/166.77 inference(transitivity,[status(thm)],[1632, 1630, 1628])).
% 262.41/166.77 tff(1634,plain,
% 262.41/166.77 (bool(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) <=> bool(err)),
% 262.41/166.77 inference(monotonicity,[status(thm)],[1633])).
% 262.41/166.77 tff(1635,plain,
% 262.41/166.77 (bool(err) <=> bool(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))),
% 262.41/166.77 inference(symmetry,[status(thm)],[1634])).
% 262.41/166.77 tff(1636,plain,
% 262.41/166.77 ((~bool(err)) <=> (~bool(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))),
% 262.41/166.77 inference(monotonicity,[status(thm)],[1635])).
% 262.41/166.77 tff(1637,plain,
% 262.41/166.77 (~bool(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))),
% 262.41/166.77 inference(modus_ponens,[status(thm)],[255, 1636])).
% 262.41/166.77 tff(1638,plain,
% 262.41/166.77 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))))) | (~((~d(false)) | d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = 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(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))))) | (~((~d(false)) | d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = false)))))))),
% 262.41/166.78 inference(rewrite,[status(thm)],[])).
% 262.41/166.78 tff(1639,plain,
% 262.41/166.78 ((forallprefers(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), false) <=> ((~(d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))))) | (~((~(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = false)) | (~(false = not1(false))))))) <=> (forallprefers(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))))) | (~((~d(false)) | d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = false))))))),
% 262.41/166.78 inference(rewrite,[status(thm)],[])).
% 262.41/166.78 tff(1640,plain,
% 262.41/166.78 (((~![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(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), false) <=> ((~(d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))))) | (~((~(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = 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(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))))) | (~((~d(false)) | d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = false)))))))),
% 262.41/166.78 inference(monotonicity,[status(thm)],[1639])).
% 262.41/166.78 tff(1641,plain,
% 262.41/166.78 (((~![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(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), false) <=> ((~(d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))))) | (~((~(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = 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(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))))) | (~((~d(false)) | d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = false)))))))),
% 262.41/166.78 inference(transitivity,[status(thm)],[1640, 1638])).
% 262.41/166.78 tff(1642,plain,
% 262.41/166.78 ((~![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(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), false) <=> ((~(d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))))) | (~((~(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = false)) | (~(false = not1(false)))))))),
% 262.41/166.78 inference(quant_inst,[status(thm)],[])).
% 262.41/166.78 tff(1643,plain,
% 262.41/166.78 ((~![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(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))))) | (~((~d(false)) | d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = false))))))),
% 262.41/166.78 inference(modus_ponens,[status(thm)],[1642, 1641])).
% 262.41/166.78 tff(1644,plain,
% 262.41/166.78 (forallprefers(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))))) | (~((~d(false)) | d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = false)))))),
% 262.41/166.79 inference(unit_resolution,[status(thm)],[1643, 493])).
% 262.41/166.79 tff(1645,plain,
% 262.41/166.79 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))),
% 262.41/166.79 inference(quant_inst,[status(thm)],[])).
% 262.41/166.79 tff(1646,plain,
% 262.41/166.79 (f7(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.41/166.79 inference(unit_resolution,[status(thm)],[1645, 538])).
% 262.41/166.79 tff(1647,plain,
% 262.41/166.79 (lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = f7(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.41/166.79 inference(symmetry,[status(thm)],[1646])).
% 262.41/166.79 tff(1648,plain,
% 262.41/166.79 (forallprefers(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), false) <=> forallprefers(f7(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), f7(P!6))),
% 262.41/166.79 inference(monotonicity,[status(thm)],[1647, 1241])).
% 262.41/166.79 tff(1649,plain,
% 262.41/166.79 (forallprefers(f7(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), f7(P!6)) <=> forallprefers(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), false)),
% 262.41/166.79 inference(symmetry,[status(thm)],[1648])).
% 262.41/166.79 tff(1650,plain,
% 262.41/166.79 ((~forallprefers(f7(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), f7(P!6))) <=> (~forallprefers(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), false))),
% 262.41/166.79 inference(monotonicity,[status(thm)],[1649])).
% 262.41/166.79 tff(1651,plain,
% 262.41/166.79 ((~![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))) | (~forallprefers(f7(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), f7(P!6)))),
% 262.41/166.79 inference(quant_inst,[status(thm)],[])).
% 262.41/166.79 tff(1652,plain,
% 262.41/166.79 (~forallprefers(f7(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), f7(P!6))),
% 262.41/166.79 inference(unit_resolution,[status(thm)],[1651, 572])).
% 262.41/166.79 tff(1653,plain,
% 262.41/166.79 (~forallprefers(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), false)),
% 262.41/166.79 inference(modus_ponens,[status(thm)],[1652, 1650])).
% 262.41/166.79 tff(1654,plain,
% 262.41/166.79 ((~(forallprefers(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))))) | (~((~d(false)) | d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = false))))))) | forallprefers(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), false) | (~((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))))) | (~((~d(false)) | d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = false))))))),
% 262.41/166.79 inference(tautology,[status(thm)],[])).
% 262.41/166.79 tff(1655,plain,
% 262.41/166.79 (~((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))))) | (~((~d(false)) | d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = false)))))),
% 262.41/166.79 inference(unit_resolution,[status(thm)],[1654, 1653, 1644])).
% 262.41/166.79 tff(1656,plain,
% 262.41/166.79 (((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))))) | (~((~d(false)) | d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = false))))) | ((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))))),
% 262.41/166.79 inference(tautology,[status(thm)],[])).
% 262.41/166.79 tff(1657,plain,
% 262.41/166.79 ((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))),
% 262.41/166.79 inference(unit_resolution,[status(thm)],[1656, 1655])).
% 262.41/166.79 tff(1658,plain,
% 262.41/166.79 (((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))))) | (~((~d(false)) | d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))) | (~((~(false = not1(false))) | (~(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = false))))) | ((~d(false)) | d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))),
% 262.41/166.79 inference(tautology,[status(thm)],[])).
% 262.41/166.79 tff(1659,plain,
% 262.41/166.79 ((~d(false)) | d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))),
% 262.41/166.79 inference(unit_resolution,[status(thm)],[1658, 1655])).
% 262.41/166.79 tff(1660,plain,
% 262.41/166.79 ((~((~d(false)) | d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))) | (~d(false)) | d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))),
% 262.41/166.79 inference(tautology,[status(thm)],[])).
% 262.41/166.79 tff(1661,plain,
% 262.41/166.79 ((~((~d(false)) | d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))) | d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))),
% 262.41/166.79 inference(unit_resolution,[status(thm)],[1660, 5])).
% 262.41/166.79 tff(1662,plain,
% 262.41/166.79 (d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))),
% 262.41/166.79 inference(unit_resolution,[status(thm)],[1661, 1659])).
% 262.41/166.79 tff(1663,plain,
% 262.41/166.79 ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))))) | (~d(false)) | (~bool(false)) | bool(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))),
% 262.41/166.79 inference(tautology,[status(thm)],[])).
% 262.41/166.79 tff(1664,plain,
% 262.41/166.79 ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))))) | bool(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~d(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))),
% 262.41/166.79 inference(unit_resolution,[status(thm)],[1663, 5, 107])).
% 262.41/166.79 tff(1665,plain,
% 262.41/166.79 (bool(lazy_impl(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))),
% 262.41/166.79 inference(unit_resolution,[status(thm)],[1664, 1662, 1657])).
% 262.41/166.79 tff(1666,plain,
% 262.41/166.79 ($false),
% 262.41/166.79 inference(unit_resolution,[status(thm)],[1665, 1637])).
% 262.41/166.80 tff(1667,plain,((~(phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = err)) | (~(prop(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 262.41/166.80 tff(1668,plain,
% 262.41/166.80 (~(phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = err)),
% 262.41/166.80 inference(unit_resolution,[status(thm)],[1667, 1627])).
% 262.41/166.80 tff(1669,plain,
% 262.41/166.80 (d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) | (~(phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = err))),
% 262.41/166.80 inference(unit_resolution,[status(thm)],[1150, 1668])).
% 262.41/166.80 tff(1670,plain,
% 262.41/166.80 (~((~d(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~(phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))))),
% 262.41/166.80 inference(unit_resolution,[status(thm)],[768, 17, 1669])).
% 262.41/166.80 tff(1671,plain,
% 262.41/166.80 (phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.41/166.80 inference(unit_resolution,[status(thm)],[770, 1670])).
% 262.41/166.80 tff(1672,assumption,(Q!7 = false), introduced(assumption)).
% 262.41/166.80 tff(1673,plain,
% 262.41/166.80 (impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.41/166.80 inference(monotonicity,[status(thm)],[1672, 1360])).
% 262.41/166.80 tff(1674,plain,
% 262.41/166.80 (impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = impl(false, not1(false))),
% 262.41/166.80 inference(transitivity,[status(thm)],[1673, 1596, 398])).
% 262.41/166.80 tff(1675,plain,
% 262.41/166.80 (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = impl(P!8, impl(false, not1(false)))),
% 262.41/166.80 inference(monotonicity,[status(thm)],[1674])).
% 262.41/166.80 tff(1676,plain,
% 262.41/166.80 (impl(P!8, impl(false, not1(false))) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.41/166.80 inference(symmetry,[status(thm)],[1675])).
% 262.41/166.80 tff(1677,plain,
% 262.41/166.80 (phi(impl(P!8, impl(false, not1(false)))) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.41/166.80 inference(monotonicity,[status(thm)],[1676])).
% 262.41/166.80 tff(1678,plain,
% 262.41/166.80 (phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = phi(impl(P!8, impl(false, not1(false))))),
% 262.41/166.80 inference(symmetry,[status(thm)],[1677])).
% 262.41/166.80 tff(1679,plain,
% 262.41/166.80 (impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = impl(false, not1(false))),
% 262.41/166.80 inference(transitivity,[status(thm)],[1596, 398])).
% 262.41/166.80 tff(1680,plain,
% 262.41/166.80 (impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = impl(P!8, impl(false, not1(false)))),
% 262.41/166.80 inference(monotonicity,[status(thm)],[1679])).
% 262.41/166.80 tff(1681,plain,
% 262.41/166.80 (impl(P!8, impl(false, not1(false))) = impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))),
% 262.41/166.80 inference(symmetry,[status(thm)],[1680])).
% 262.41/166.80 tff(1682,plain,
% 262.41/166.80 (impl(impl(P!8, impl(false, not1(false))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.41/166.80 inference(monotonicity,[status(thm)],[1681])).
% 262.41/166.80 tff(1683,plain,
% 262.41/166.80 (impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = impl(impl(P!8, impl(false, not1(false))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.46/166.80 inference(symmetry,[status(thm)],[1682])).
% 262.46/166.80 tff(1684,plain,
% 262.46/166.80 (impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.46/166.80 inference(transitivity,[status(thm)],[1680, 1676])).
% 262.46/166.80 tff(1685,plain,
% 262.46/166.80 (impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))),
% 262.46/166.80 inference(monotonicity,[status(thm)],[1684, 1389])).
% 262.46/166.80 tff(1686,plain,
% 262.46/166.80 (impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)) = impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.46/166.80 inference(symmetry,[status(thm)],[1685])).
% 262.46/166.80 tff(1687,plain,
% 262.46/166.80 (impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)) = impl(impl(P!8, impl(false, not1(false))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.46/166.80 inference(transitivity,[status(thm)],[1686, 1683])).
% 262.46/166.80 tff(1688,plain,
% 262.46/166.80 ((impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) <=> (impl(impl(P!8, impl(false, not1(false))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = phi(impl(P!8, impl(false, not1(false)))))),
% 262.46/166.80 inference(monotonicity,[status(thm)],[1687, 1678])).
% 262.46/166.80 tff(1689,plain,
% 262.46/166.80 ((~(impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))) <=> (~(impl(impl(P!8, impl(false, not1(false))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = phi(impl(P!8, impl(false, not1(false))))))),
% 262.46/166.80 inference(monotonicity,[status(thm)],[1688])).
% 262.46/166.80 tff(1690,plain,
% 262.46/166.80 (~(impl(impl(P!8, impl(false, not1(false))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = phi(impl(P!8, impl(false, not1(false)))))),
% 262.46/166.80 inference(modus_ponens,[status(thm)],[1621, 1689])).
% 262.46/166.80 tff(1691,plain,
% 262.46/166.80 (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = not1(false)),
% 262.46/166.80 inference(transitivity,[status(thm)],[1675, 1614, 165])).
% 262.46/166.80 tff(1692,plain,
% 262.46/166.80 (impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)) = impl(not1(false), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.46/166.80 inference(monotonicity,[status(thm)],[1691, 1360])).
% 262.46/166.80 tff(1693,plain,
% 262.46/166.80 (impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))),
% 262.46/166.80 inference(transitivity,[status(thm)],[1685, 1692, 1364])).
% 262.46/166.80 tff(1694,plain,
% 262.46/166.80 ((impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = not1(false)) <=> (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = not1(false))),
% 262.46/166.80 inference(monotonicity,[status(thm)],[1693])).
% 262.46/166.80 tff(1695,plain,
% 262.46/166.80 ((~(impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = not1(false))) <=> (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = not1(false)))),
% 262.46/166.80 inference(monotonicity,[status(thm)],[1694])).
% 262.46/166.80 tff(1696,assumption,(phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))), introduced(assumption)).
% 262.46/166.80 tff(1697,plain,
% 262.46/166.80 (phi(impl(P!8, impl(false, not1(false)))) = not1(false)),
% 262.46/166.80 inference(transitivity,[status(thm)],[1677, 1696, 1675, 1614, 165])).
% 262.46/166.80 tff(1698,plain,
% 262.46/166.80 ((impl(impl(P!8, impl(false, not1(false))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = phi(impl(P!8, impl(false, not1(false))))) <=> (impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = not1(false))),
% 262.46/166.80 inference(monotonicity,[status(thm)],[1682, 1697])).
% 262.46/166.80 tff(1699,plain,
% 262.46/166.80 ((~(impl(impl(P!8, impl(false, not1(false))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = phi(impl(P!8, impl(false, not1(false)))))) <=> (~(impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = not1(false)))),
% 262.46/166.80 inference(monotonicity,[status(thm)],[1698])).
% 262.46/166.80 tff(1700,assumption,(~(impl(impl(P!8, impl(false, not1(false))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = phi(impl(P!8, impl(false, not1(false)))))), introduced(assumption)).
% 262.46/166.80 tff(1701,plain,
% 262.46/166.80 (~(impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = not1(false))),
% 262.46/166.80 inference(modus_ponens,[status(thm)],[1700, 1699])).
% 262.46/166.80 tff(1702,plain,
% 262.46/166.80 (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = not1(false))),
% 262.46/166.80 inference(modus_ponens,[status(thm)],[1701, 1695])).
% 262.46/166.80 tff(1703,plain,
% 262.46/166.80 ((false = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) <=> (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = false)),
% 262.46/166.80 inference(commutativity,[status(thm)],[])).
% 262.46/166.80 tff(1704,plain,
% 262.46/166.80 (f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)) = f1(P!8, false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.46/166.80 inference(monotonicity,[status(thm)],[1672, 1360])).
% 262.46/166.80 tff(1705,plain,
% 262.46/166.80 (f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))),
% 262.46/166.80 inference(transitivity,[status(thm)],[1704, 1609, 1608, 1606, 1592, 1590])).
% 262.46/166.80 tff(1706,plain,
% 262.46/166.80 (phi(f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.46/166.80 inference(monotonicity,[status(thm)],[1705])).
% 262.46/166.80 tff(1707,plain,
% 262.46/166.80 (and2(P!8, Q!7) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))),
% 262.46/166.80 inference(transitivity,[status(thm)],[295, 1706, 1590])).
% 262.46/166.80 tff(1708,plain,
% 262.46/166.80 (((~![B: $i] : ((~bool(B)) | (and1(false, B) = false))) | ((~bool(false)) | (and1(false, false) = false))) <=> ((~![B: $i] : ((~bool(B)) | (and1(false, B) = false))) | (~bool(false)) | (and1(false, false) = false))),
% 262.46/166.80 inference(rewrite,[status(thm)],[])).
% 262.46/166.80 tff(1709,plain,
% 262.46/166.80 ((~![B: $i] : ((~bool(B)) | (and1(false, B) = false))) | ((~bool(false)) | (and1(false, false) = false))),
% 262.46/166.80 inference(quant_inst,[status(thm)],[])).
% 262.46/166.80 tff(1710,plain,
% 262.46/166.80 ((~![B: $i] : ((~bool(B)) | (and1(false, B) = false))) | (~bool(false)) | (and1(false, false) = false)),
% 262.46/166.80 inference(modus_ponens,[status(thm)],[1709, 1708])).
% 262.46/166.80 tff(1711,plain,
% 262.46/166.80 (and1(false, false) = false),
% 262.46/166.80 inference(unit_resolution,[status(thm)],[1710, 1457, 107])).
% 262.46/166.80 tff(1712,plain,
% 262.46/166.80 (and1(P!8, Q!7) = and1(false, false)),
% 262.46/166.80 inference(monotonicity,[status(thm)],[1271, 1672])).
% 262.46/166.80 tff(1713,plain,
% 262.46/166.80 (and1(P!8, Q!7) = false),
% 262.46/166.80 inference(transitivity,[status(thm)],[1712, 1711])).
% 262.46/166.80 tff(1714,plain,
% 262.46/166.80 ((and1(P!8, Q!7) = and2(P!8, Q!7)) <=> (false = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.46/166.80 inference(monotonicity,[status(thm)],[1713, 1707])).
% 262.46/166.80 tff(1715,plain,
% 262.46/166.80 ((and1(P!8, Q!7) = and2(P!8, Q!7)) <=> (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = false)),
% 262.46/166.80 inference(transitivity,[status(thm)],[1714, 1703])).
% 262.46/166.80 tff(1716,plain,
% 262.46/166.80 ((~(and1(P!8, Q!7) = and2(P!8, Q!7))) <=> (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = false))),
% 262.46/166.80 inference(monotonicity,[status(thm)],[1715])).
% 262.46/166.80 tff(1717,plain,
% 262.46/166.80 (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = false)),
% 262.46/166.80 inference(modus_ponens,[status(thm)],[361, 1716])).
% 262.46/166.80 tff(1718,plain,
% 262.46/166.80 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) <=> ((lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = false) | (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = not1(false))))),
% 262.46/166.81 inference(quant_inst,[status(thm)],[])).
% 262.46/166.81 tff(1719,plain,
% 262.46/166.81 (bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) <=> ((lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = false) | (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = not1(false)))),
% 262.46/166.81 inference(unit_resolution,[status(thm)],[1718, 229])).
% 262.46/166.81 tff(1720,plain,
% 262.46/166.81 ((~(bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) <=> ((lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = false) | (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = not1(false))))) | (~bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) | ((lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = false) | (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = not1(false)))),
% 262.46/166.81 inference(tautology,[status(thm)],[])).
% 262.46/166.81 tff(1721,plain,
% 262.46/166.81 ((~(bool(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) <=> ((lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = false) | (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = not1(false))))) | ((lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = false) | (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = not1(false)))),
% 262.46/166.81 inference(unit_resolution,[status(thm)],[1720, 1346])).
% 262.46/166.81 tff(1722,plain,
% 262.46/166.81 ((lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = false) | (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = not1(false))),
% 262.46/166.81 inference(unit_resolution,[status(thm)],[1721, 1719])).
% 262.46/166.81 tff(1723,plain,
% 262.46/166.81 ((~((lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = false) | (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = not1(false)))) | (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = false) | (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = not1(false))),
% 262.46/166.81 inference(tautology,[status(thm)],[])).
% 262.46/166.81 tff(1724,plain,
% 262.46/166.81 ((lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = false) | (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = not1(false))),
% 262.46/166.81 inference(unit_resolution,[status(thm)],[1723, 1722])).
% 262.46/166.81 tff(1725,plain,
% 262.46/166.81 ($false),
% 262.46/166.81 inference(unit_resolution,[status(thm)],[1724, 1717, 1702])).
% 262.46/166.81 tff(1726,plain,((~(P!8 = false)) | (~(prop(tptp_fun_R_0(Q!7, P!8)) = not1(false))) | (~(Q!7 = false)) | (impl(impl(P!8, impl(false, not1(false))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = phi(impl(P!8, impl(false, not1(false))))) | (~(phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))), inference(lemma,lemma(discharge,[]))).
% 262.46/166.81 tff(1727,plain,
% 262.46/166.81 (~(P!8 = false)),
% 262.46/166.81 inference(unit_resolution,[status(thm)],[1726, 1690, 342, 1672, 1671])).
% 262.46/166.81 tff(1728,plain,
% 262.46/166.81 (P!8 = not1(false)),
% 262.46/166.81 inference(unit_resolution,[status(thm)],[1440, 1727, 1382])).
% 262.46/166.81 tff(1729,plain,
% 262.46/166.81 (impl(P!8, impl(false, not1(false))) = impl(not1(false), not1(false))),
% 262.46/166.81 inference(monotonicity,[status(thm)],[1728, 165])).
% 262.46/166.81 tff(1730,plain,
% 262.46/166.81 (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = not1(false)),
% 262.46/166.81 inference(transitivity,[status(thm)],[1675, 1729, 98])).
% 262.46/166.81 tff(1731,plain,
% 262.46/166.81 (impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)) = impl(not1(false), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.46/166.81 inference(monotonicity,[status(thm)],[1730, 1360])).
% 262.46/166.81 tff(1732,plain,
% 262.46/166.81 (impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))),
% 262.46/166.81 inference(transitivity,[status(thm)],[1685, 1731, 1364])).
% 262.46/166.81 tff(1733,plain,
% 262.46/166.81 ((impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = not1(false)) <=> (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = not1(false))),
% 262.46/166.81 inference(monotonicity,[status(thm)],[1732])).
% 262.46/166.81 tff(1734,plain,
% 262.46/166.81 ((~(impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = not1(false))) <=> (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = not1(false)))),
% 262.46/166.81 inference(monotonicity,[status(thm)],[1733])).
% 262.46/166.81 tff(1735,plain,
% 262.46/166.81 (phi(impl(P!8, impl(false, not1(false)))) = not1(false)),
% 262.46/166.81 inference(transitivity,[status(thm)],[1677, 1671, 1675, 1729, 98])).
% 262.46/166.81 tff(1736,plain,
% 262.46/166.81 ((impl(impl(P!8, impl(false, not1(false))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = phi(impl(P!8, impl(false, not1(false))))) <=> (impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = not1(false))),
% 262.46/166.81 inference(monotonicity,[status(thm)],[1682, 1735])).
% 262.46/166.81 tff(1737,plain,
% 262.46/166.81 ((~(impl(impl(P!8, impl(false, not1(false))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = phi(impl(P!8, impl(false, not1(false)))))) <=> (~(impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = not1(false)))),
% 262.46/166.81 inference(monotonicity,[status(thm)],[1736])).
% 262.46/166.81 tff(1738,plain,
% 262.46/166.81 (~(impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = not1(false))),
% 262.46/166.81 inference(modus_ponens,[status(thm)],[1690, 1737])).
% 262.46/166.81 tff(1739,plain,
% 262.46/166.81 (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = not1(false))),
% 262.46/166.81 inference(modus_ponens,[status(thm)],[1738, 1734])).
% 262.46/166.81 tff(1740,plain,
% 262.46/166.81 (impl(not1(false), impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = impl(not1(false), not1(false))),
% 262.46/166.81 inference(monotonicity,[status(thm)],[1596])).
% 262.46/166.81 tff(1741,plain,
% 262.46/166.81 (impl(not1(false), impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false)),
% 262.46/166.81 inference(transitivity,[status(thm)],[1740, 98])).
% 262.46/166.81 tff(1742,plain,
% 262.46/166.81 (impl(impl(not1(false), impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = impl(not1(false), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.46/166.81 inference(monotonicity,[status(thm)],[1741])).
% 262.46/166.81 tff(1743,plain,
% 262.46/166.81 (impl(impl(not1(false), impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))),
% 262.46/166.81 inference(transitivity,[status(thm)],[1742, 1364])).
% 262.46/166.81 tff(1744,plain,
% 262.46/166.81 (lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(not1(false), impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = lazy_impl(not1(false), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.46/166.81 inference(monotonicity,[status(thm)],[1605, 1743])).
% 262.46/166.81 tff(1745,plain,
% 262.46/166.81 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(not1(false), false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(not1(false), impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))))),
% 262.46/166.81 inference(quant_inst,[status(thm)],[])).
% 262.46/166.81 tff(1746,plain,
% 262.46/166.81 (f1(not1(false), false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(not1(false), impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))),
% 262.46/166.81 inference(unit_resolution,[status(thm)],[1745, 159])).
% 262.46/166.81 tff(1747,plain,
% 262.46/166.81 (f1(P!8, false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = f1(not1(false), false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.46/166.81 inference(monotonicity,[status(thm)],[1728])).
% 262.46/166.81 tff(1748,plain,
% 262.46/166.81 (f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))),
% 262.46/166.81 inference(transitivity,[status(thm)],[1704, 1747, 1746, 1744, 1592, 1590])).
% 262.46/166.81 tff(1749,plain,
% 262.46/166.81 (phi(f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.46/166.81 inference(monotonicity,[status(thm)],[1748])).
% 262.46/166.81 tff(1750,plain,
% 262.46/166.81 (and2(P!8, Q!7) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))),
% 262.46/166.81 inference(transitivity,[status(thm)],[295, 1749, 1590])).
% 262.46/166.81 tff(1751,plain,
% 262.46/166.81 (((~![B: $i] : ((~bool(B)) | (and1(not1(false), B) = B))) | ((~bool(false)) | (and1(not1(false), false) = false))) <=> ((~![B: $i] : ((~bool(B)) | (and1(not1(false), B) = B))) | (~bool(false)) | (and1(not1(false), false) = false))),
% 262.46/166.81 inference(rewrite,[status(thm)],[])).
% 262.46/166.81 tff(1752,plain,
% 262.46/166.81 ((~![B: $i] : ((~bool(B)) | (and1(not1(false), B) = B))) | ((~bool(false)) | (and1(not1(false), false) = false))),
% 262.46/166.81 inference(quant_inst,[status(thm)],[])).
% 262.46/166.81 tff(1753,plain,
% 262.46/166.81 ((~![B: $i] : ((~bool(B)) | (and1(not1(false), B) = B))) | (~bool(false)) | (and1(not1(false), false) = false)),
% 262.46/166.81 inference(modus_ponens,[status(thm)],[1752, 1751])).
% 262.46/166.81 tff(1754,plain,
% 262.46/166.81 (and1(not1(false), false) = false),
% 262.46/166.81 inference(unit_resolution,[status(thm)],[1753, 1430, 107])).
% 262.46/166.81 tff(1755,plain,
% 262.46/166.81 (and1(P!8, Q!7) = and1(not1(false), false)),
% 262.46/166.81 inference(monotonicity,[status(thm)],[1728, 1672])).
% 262.46/166.81 tff(1756,plain,
% 262.46/166.81 (and1(P!8, Q!7) = false),
% 262.46/166.81 inference(transitivity,[status(thm)],[1755, 1754])).
% 262.46/166.81 tff(1757,plain,
% 262.46/166.81 ((and1(P!8, Q!7) = and2(P!8, Q!7)) <=> (false = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.46/166.81 inference(monotonicity,[status(thm)],[1756, 1750])).
% 262.46/166.81 tff(1758,plain,
% 262.46/166.81 ((and1(P!8, Q!7) = and2(P!8, Q!7)) <=> (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = false)),
% 262.46/166.81 inference(transitivity,[status(thm)],[1757, 1703])).
% 262.46/166.81 tff(1759,plain,
% 262.46/166.81 ((~(and1(P!8, Q!7) = and2(P!8, Q!7))) <=> (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = false))),
% 262.46/166.81 inference(monotonicity,[status(thm)],[1758])).
% 262.46/166.81 tff(1760,plain,
% 262.46/166.81 (~(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = false)),
% 262.46/166.81 inference(modus_ponens,[status(thm)],[361, 1759])).
% 262.46/166.81 tff(1761,plain,
% 262.46/166.81 ($false),
% 262.46/166.81 inference(unit_resolution,[status(thm)],[1724, 1760, 1739])).
% 262.46/166.81 tff(1762,plain,((~(Q!7 = false)) | (~(prop(tptp_fun_R_0(Q!7, P!8)) = not1(false))) | (impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))), inference(lemma,lemma(discharge,[]))).
% 262.46/166.81 tff(1763,plain,
% 262.46/166.81 (~(Q!7 = false)),
% 262.46/166.81 inference(unit_resolution,[status(thm)],[1762, 1621, 342])).
% 262.46/166.81 tff(1764,plain,
% 262.46/166.81 (Q!7 = not1(false)),
% 262.46/166.81 inference(unit_resolution,[status(thm)],[1194, 1763])).
% 262.46/166.81 tff(1765,plain,
% 262.46/166.81 (phi(Q!7) = phi(not1(false))),
% 262.46/166.81 inference(monotonicity,[status(thm)],[1764])).
% 262.46/166.81 tff(1766,plain,
% 262.46/166.81 (phi(Q!7) = not1(false)),
% 262.46/166.81 inference(transitivity,[status(thm)],[1765, 49])).
% 262.46/166.81 tff(1767,plain,
% 262.46/166.81 ((impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = phi(Q!7)) <=> (impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = not1(false))),
% 262.46/166.81 inference(monotonicity,[status(thm)],[1766])).
% 262.46/166.81 tff(1768,plain,
% 262.46/166.81 (impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = phi(Q!7)),
% 262.46/166.81 inference(unit_resolution,[status(thm)],[1465, 1764, 342])).
% 262.46/166.81 tff(1769,plain,
% 262.46/166.81 (impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = not1(false)),
% 262.46/166.81 inference(modus_ponens,[status(thm)],[1768, 1767])).
% 262.46/166.81 tff(1770,plain,
% 262.46/166.81 (not1(false) = Q!7),
% 262.46/166.81 inference(symmetry,[status(thm)],[1764])).
% 262.46/166.81 tff(1771,plain,
% 262.46/166.81 (impl(not1(false), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = impl(Q!7, tptp_fun_R_0(Q!7, P!8))),
% 262.46/166.82 inference(monotonicity,[status(thm)],[1770, 1389])).
% 262.46/166.82 tff(1772,plain,
% 262.46/166.82 (tptp_fun_R_0(Q!7, P!8) = not1(false)),
% 262.46/166.82 inference(transitivity,[status(thm)],[1359, 1299, 1296, 1411, 1771, 1769])).
% 262.46/166.82 tff(1773,plain,
% 262.46/166.82 (impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = impl(false, not1(false))),
% 262.46/166.82 inference(transitivity,[status(thm)],[1769, 398])).
% 262.46/166.82 tff(1774,plain,
% 262.46/166.82 (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = impl(P!8, impl(false, not1(false)))),
% 262.46/166.82 inference(monotonicity,[status(thm)],[1773])).
% 262.46/166.82 tff(1775,plain,
% 262.46/166.82 (impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))) = not1(false)),
% 262.46/166.82 inference(transitivity,[status(thm)],[1774, 1614, 165])).
% 262.46/166.82 tff(1776,plain,
% 262.46/166.82 (impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)) = impl(not1(false), not1(false))),
% 262.46/166.82 inference(monotonicity,[status(thm)],[1775, 1772])).
% 262.46/166.82 tff(1777,plain,
% 262.46/166.82 (impl(Q!7, tptp_fun_R_0(Q!7, P!8)) = impl(not1(false), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.46/166.82 inference(symmetry,[status(thm)],[1771])).
% 262.46/166.82 tff(1778,plain,
% 262.46/166.82 (not1(false) = impl(Q!7, tptp_fun_R_0(Q!7, P!8))),
% 262.46/166.82 inference(symmetry,[status(thm)],[1769])).
% 262.46/166.82 tff(1779,plain,
% 262.46/166.82 (not1(false) = tptp_fun_R_0(Q!7, P!8)),
% 262.46/166.82 inference(transitivity,[status(thm)],[1778, 1777, 1364, 1388, 1298, 1358])).
% 262.46/166.82 tff(1780,plain,
% 262.46/166.82 (impl(P!8, impl(false, not1(false))) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.46/166.82 inference(symmetry,[status(thm)],[1774])).
% 262.46/166.82 tff(1781,plain,
% 262.46/166.82 (impl(impl(P!8, impl(false, not1(false))), not1(false)) = impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))),
% 262.46/166.82 inference(monotonicity,[status(thm)],[1780, 1779])).
% 262.46/166.82 tff(1782,plain,
% 262.46/166.82 (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = not1(false)),
% 262.46/166.82 inference(transitivity,[status(thm)],[1411, 1771, 1769])).
% 262.46/166.82 tff(1783,plain,
% 262.46/166.82 (impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = impl(impl(P!8, impl(false, not1(false))), not1(false))),
% 262.46/166.82 inference(monotonicity,[status(thm)],[1680, 1782])).
% 262.46/166.82 tff(1784,plain,
% 262.46/166.82 (impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = not1(false)),
% 262.46/166.82 inference(transitivity,[status(thm)],[1783, 1781, 1776, 98])).
% 262.46/166.82 tff(1785,plain,
% 262.46/166.82 (phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))) = not1(false)),
% 262.46/166.82 inference(transitivity,[status(thm)],[1671, 1774, 1614, 165])).
% 262.46/166.82 tff(1786,plain,
% 262.46/166.82 (impl(impl(P!8, impl(false, not1(false))), not1(false)) = impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.46/166.82 inference(symmetry,[status(thm)],[1783])).
% 262.46/166.82 tff(1787,plain,
% 262.46/166.82 (impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)) = impl(impl(P!8, impl(false, not1(false))), not1(false))),
% 262.46/166.82 inference(symmetry,[status(thm)],[1781])).
% 262.46/166.82 tff(1788,plain,
% 262.46/166.82 (impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)) = impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.46/166.82 inference(transitivity,[status(thm)],[1787, 1786])).
% 262.46/166.82 tff(1789,plain,
% 262.46/166.82 ((impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) <=> (impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = not1(false))),
% 262.46/166.82 inference(monotonicity,[status(thm)],[1788, 1785])).
% 262.46/166.82 tff(1790,plain,
% 262.46/166.82 ((~(impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))) <=> (~(impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = not1(false)))),
% 262.46/166.82 inference(monotonicity,[status(thm)],[1789])).
% 262.46/166.82 tff(1791,plain,
% 262.46/166.82 (~(impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = not1(false))),
% 262.46/166.82 inference(modus_ponens,[status(thm)],[1621, 1790])).
% 262.46/166.82 tff(1792,plain,
% 262.46/166.82 ($false),
% 262.46/166.82 inference(unit_resolution,[status(thm)],[1791, 1784])).
% 262.46/166.82 tff(1793,plain,((~(P!8 = false)) | (~(prop(tptp_fun_R_0(Q!7, P!8)) = not1(false))) | (impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))))), inference(lemma,lemma(discharge,[]))).
% 262.46/166.82 tff(1794,plain,
% 262.46/166.82 (~(P!8 = false)),
% 262.46/166.82 inference(unit_resolution,[status(thm)],[1793, 1621, 342])).
% 262.46/166.82 tff(1795,plain,
% 262.46/166.82 (P!8 = not1(false)),
% 262.46/166.82 inference(unit_resolution,[status(thm)],[1440, 1794, 1382])).
% 262.46/166.82 tff(1796,plain,
% 262.46/166.82 (f1(P!8, false, not1(false)) = f1(not1(false), false, not1(false))),
% 262.46/166.82 inference(monotonicity,[status(thm)],[1795])).
% 262.46/166.82 tff(1797,plain,
% 262.46/166.82 (f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)) = f1(P!8, not1(false), not1(false))),
% 262.46/166.82 inference(monotonicity,[status(thm)],[1764, 1772])).
% 262.46/166.82 tff(1798,plain,
% 262.46/166.82 (f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)) = not1(false)),
% 262.46/166.82 inference(transitivity,[status(thm)],[1797, 447, 452, 1200, 1796, 1506, 1504, 593, 49])).
% 262.46/166.82 tff(1799,plain,
% 262.46/166.82 (phi(f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(not1(false))),
% 262.46/166.82 inference(monotonicity,[status(thm)],[1798])).
% 262.46/166.82 tff(1800,plain,
% 262.46/166.82 (phi(not1(false)) = phi(f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.46/166.82 inference(symmetry,[status(thm)],[1799])).
% 262.46/166.82 tff(1801,plain,
% 262.46/166.82 (and1(P!8, Q!7) = and1(not1(false), not1(false))),
% 262.46/166.82 inference(monotonicity,[status(thm)],[1795, 1764])).
% 262.46/166.82 tff(1802,plain,
% 262.46/166.82 (and1(P!8, Q!7) = and2(P!8, Q!7)),
% 262.46/166.82 inference(transitivity,[status(thm)],[1801, 1434, 1417, 1800, 296])).
% 262.46/166.82 tff(1803,plain,
% 262.46/166.82 ($false),
% 262.46/166.82 inference(unit_resolution,[status(thm)],[361, 1802])).
% 262.46/166.82 tff(1804,plain,((impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))) | (~(prop(tptp_fun_R_0(Q!7, P!8)) = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 262.46/166.82 tff(1805,plain,
% 262.46/166.82 (impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)) = phi(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))))),
% 262.46/166.82 inference(unit_resolution,[status(thm)],[1804, 342])).
% 262.46/166.82 tff(1806,plain,
% 262.46/166.82 (impl(P!8, impl(false, not1(false))) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.46/166.82 inference(symmetry,[status(thm)],[1619])).
% 262.46/166.82 tff(1807,plain,
% 262.46/166.82 (impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.46/166.82 inference(transitivity,[status(thm)],[1680, 1806])).
% 262.46/166.82 tff(1808,plain,
% 262.46/166.82 (impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))),
% 262.46/166.82 inference(monotonicity,[status(thm)],[1807, 1389])).
% 262.46/166.82 tff(1809,plain,
% 262.46/166.82 (impl(false, not1(false)) = impl(P!8, impl(false, not1(false)))),
% 262.46/166.82 inference(symmetry,[status(thm)],[1614])).
% 262.46/166.82 tff(1810,plain,
% 262.46/166.82 (not1(false) = impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))),
% 262.46/166.82 inference(transitivity,[status(thm)],[398, 1809, 1681])).
% 262.46/166.82 tff(1811,plain,
% 262.46/166.82 (impl(not1(false), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.46/166.82 inference(monotonicity,[status(thm)],[1810])).
% 262.46/166.82 tff(1812,plain,
% 262.46/166.82 (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = not1(false)),
% 262.46/166.82 inference(transitivity,[status(thm)],[1411, 1811, 1808, 1805, 1620, 1616, 49])).
% 262.46/166.82 tff(1813,plain,
% 262.46/166.82 (lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false)),
% 262.46/166.82 inference(modus_ponens,[status(thm)],[1812, 1613])).
% 262.46/166.82 tff(1814,plain,
% 262.46/166.82 ((~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false))))) | (~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false)))),
% 262.46/166.82 inference(tautology,[status(thm)],[])).
% 262.46/166.82 tff(1815,plain,
% 262.46/166.82 ($false),
% 262.46/166.82 inference(unit_resolution,[status(thm)],[1814, 1813, 1579, 1574])).
% 262.46/166.82 tff(1816,plain,((~(P!8 = false)) | (~(prop(tptp_fun_R_0(Q!7, P!8)) = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 262.46/166.82 tff(1817,plain,
% 262.46/166.82 (~(P!8 = false)),
% 262.46/166.82 inference(unit_resolution,[status(thm)],[1816, 342])).
% 262.46/166.82 tff(1818,plain,
% 262.46/166.82 (P!8 = not1(false)),
% 262.46/166.82 inference(unit_resolution,[status(thm)],[1440, 1817, 1382])).
% 262.46/166.82 tff(1819,plain,
% 262.46/166.82 (f1(P!8, false, false) = f1(not1(false), false, false)),
% 262.46/166.82 inference(monotonicity,[status(thm)],[1818])).
% 262.46/166.82 tff(1820,plain,
% 262.46/166.82 (lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false),
% 262.46/166.82 inference(transitivity,[status(thm)],[1545, 1819, 161, 1556, 35, 23])).
% 262.46/166.82 tff(1821,plain,
% 262.46/166.82 (f1(P!8, false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = f1(not1(false), false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.46/166.82 inference(monotonicity,[status(thm)],[1818])).
% 262.46/166.82 tff(1822,plain,
% 262.46/166.82 (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))),
% 262.46/166.82 inference(transitivity,[status(thm)],[177, 1535, 1821, 1746, 1744, 1592, 1590])).
% 262.46/166.82 tff(1823,plain,
% 262.46/166.82 ((lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = not1(false)) <=> (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = not1(false))),
% 262.46/166.82 inference(monotonicity,[status(thm)],[1822])).
% 262.46/166.82 tff(1824,plain,
% 262.46/166.82 ((lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = not1(false)) <=> (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = not1(false))),
% 262.46/166.82 inference(symmetry,[status(thm)],[1823])).
% 262.46/166.82 tff(1825,plain,
% 262.46/166.82 ((lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = not1(false)) <=> (lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false))),
% 262.46/166.82 inference(transitivity,[status(thm)],[1824, 1582])).
% 262.46/166.82 tff(1826,plain,
% 262.46/166.82 (impl(P!8, impl(false, not1(false))) = impl(not1(false), not1(false))),
% 262.46/166.82 inference(monotonicity,[status(thm)],[1818, 165])).
% 262.46/166.82 tff(1827,plain,
% 262.46/166.82 (impl(P!8, impl(false, not1(false))) = not1(false)),
% 262.46/166.82 inference(transitivity,[status(thm)],[1826, 98])).
% 262.46/166.82 tff(1828,plain,
% 262.46/166.82 (phi(impl(P!8, impl(false, not1(false)))) = phi(not1(false))),
% 262.46/166.82 inference(monotonicity,[status(thm)],[1827])).
% 262.46/166.82 tff(1829,plain,
% 262.46/166.82 (impl(not1(false), not1(false)) = impl(P!8, impl(false, not1(false)))),
% 262.46/166.82 inference(symmetry,[status(thm)],[1826])).
% 262.46/166.82 tff(1830,plain,
% 262.46/166.82 (not1(false) = impl(not1(false), not1(false))),
% 262.46/166.82 inference(symmetry,[status(thm)],[98])).
% 262.46/166.82 tff(1831,plain,
% 262.46/166.82 (not1(false) = impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))))),
% 262.46/166.83 inference(transitivity,[status(thm)],[1830, 1829, 1681])).
% 262.46/166.83 tff(1832,plain,
% 262.46/166.83 (impl(not1(false), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))) = impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))),
% 262.46/166.83 inference(monotonicity,[status(thm)],[1831])).
% 262.46/166.83 tff(1833,plain,
% 262.46/166.83 (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)) = not1(false)),
% 262.46/166.83 inference(transitivity,[status(thm)],[1411, 1832, 1808, 1805, 1620, 1828, 49])).
% 262.46/166.83 tff(1834,plain,
% 262.46/166.83 (lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false)),
% 262.46/166.83 inference(modus_ponens,[status(thm)],[1833, 1825])).
% 262.46/166.83 tff(1835,plain,
% 262.46/166.83 ((~((~(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false))))) | (~(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false)) | (~(lazy_impl(prop(lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8))), impl(impl(P!8, impl(false, lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))), lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), tptp_fun_R_0(Q!7, P!8)))) = not1(false)))),
% 262.46/166.83 inference(tautology,[status(thm)],[])).
% 262.46/166.83 tff(1836,plain,
% 262.46/166.83 ($false),
% 262.46/166.83 inference(unit_resolution,[status(thm)],[1835, 1834, 1820, 1554])).
% 262.46/166.83 tff(1837,plain,(~(prop(tptp_fun_R_0(Q!7, P!8)) = not1(false))), inference(lemma,lemma(discharge,[]))).
% 262.46/166.83 tff(1838,plain,
% 262.46/166.83 (~bool(tptp_fun_R_0(Q!7, P!8))),
% 262.46/166.83 inference(unit_resolution,[status(thm)],[368, 1837])).
% 262.46/166.83 tff(1839,plain,
% 262.46/166.83 (prop(tptp_fun_R_0(Q!7, P!8)) = false),
% 262.46/166.83 inference(unit_resolution,[status(thm)],[380, 1838])).
% 262.46/166.83 tff(1840,plain,
% 262.46/166.83 (lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(false, impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))),
% 262.46/166.83 inference(monotonicity,[status(thm)],[1839])).
% 262.46/166.83 tff(1841,plain,
% 262.46/166.83 (lazy_impl(false, impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8))) = lazy_impl(prop(tptp_fun_R_0(Q!7, P!8)), impl(impl(P!8, impl(Q!7, tptp_fun_R_0(Q!7, P!8))), tptp_fun_R_0(Q!7, P!8)))),
% 262.46/166.83 inference(symmetry,[status(thm)],[1840])).
% 262.46/166.83 tff(1842,plain,
% 262.46/166.83 (not1(false) = f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))),
% 262.46/166.83 inference(transitivity,[status(thm)],[1075, 1841, 177])).
% 262.46/166.83 tff(1843,plain,
% 262.46/166.83 (impl(not1(false), false) = impl(impl(false, impl(not1(false), false)), false)),
% 262.46/166.83 inference(symmetry,[status(thm)],[1373])).
% 262.46/166.83 tff(1844,plain,
% 262.46/166.83 (false = impl(impl(false, impl(not1(false), false)), false)),
% 262.46/166.83 inference(transitivity,[status(thm)],[133, 1843])).
% 262.46/166.83 tff(1845,plain,
% 262.46/166.83 (lazy_impl(not1(false), false) = lazy_impl(prop(false), impl(impl(false, impl(not1(false), false)), false))),
% 262.46/166.83 inference(monotonicity,[status(thm)],[150, 1844])).
% 262.46/166.83 tff(1846,plain,
% 262.46/166.83 (lazy_impl(prop(false), impl(impl(false, impl(not1(false), false)), false)) = lazy_impl(not1(false), false)),
% 262.46/166.83 inference(symmetry,[status(thm)],[1845])).
% 262.46/166.83 tff(1847,plain,
% 262.46/166.83 (f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)) = not1(false)),
% 262.46/166.83 inference(transitivity,[status(thm)],[176, 1840, 1074])).
% 262.46/166.83 tff(1848,plain,
% 262.46/166.83 (phi(f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))) = phi(not1(false))),
% 262.46/166.83 inference(monotonicity,[status(thm)],[1847])).
% 262.46/166.83 tff(1849,plain,
% 262.46/166.83 (phi(not1(false)) = phi(f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.46/166.83 inference(symmetry,[status(thm)],[1848])).
% 262.46/166.83 tff(1850,plain,
% 262.46/166.83 (and1(P!8, Q!7) = and2(P!8, Q!7)),
% 262.46/166.83 inference(transitivity,[status(thm)],[1435, 1434, 1417, 1849, 296])).
% 262.46/166.83 tff(1851,plain,
% 262.46/166.83 ($false),
% 262.46/166.83 inference(unit_resolution,[status(thm)],[361, 1850])).
% 262.46/166.83 tff(1852,plain,((~(P!8 = not1(false))) | (~(Q!7 = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 262.46/166.83 tff(1853,plain,
% 262.46/166.83 (~(P!8 = not1(false))),
% 262.46/166.83 inference(unit_resolution,[status(thm)],[1852, 443])).
% 262.46/166.83 tff(1854,plain,
% 262.46/166.83 ((P!8 = false) | (P!8 = not1(false))),
% 262.46/166.83 inference(unit_resolution,[status(thm)],[1440, 1382])).
% 262.46/166.83 tff(1855,plain,
% 262.46/166.83 (P!8 = false),
% 262.46/166.83 inference(unit_resolution,[status(thm)],[1854, 1853])).
% 262.46/166.83 tff(1856,plain,
% 262.46/166.83 (false = P!8),
% 262.46/166.83 inference(symmetry,[status(thm)],[1855])).
% 262.46/166.83 tff(1857,plain,
% 262.46/166.83 (false = lazy_impl(prop(P!8), P!8)),
% 262.46/166.83 inference(transitivity,[status(thm)],[1856, 1270, 1224, 1221])).
% 262.46/166.83 tff(1858,plain,
% 262.46/166.83 (f1(false, not1(false), false) = f1(lazy_impl(prop(P!8), P!8), not1(false), lazy_impl(prop(P!8), P!8))),
% 262.46/166.83 inference(monotonicity,[status(thm)],[1857, 1857])).
% 262.46/166.83 tff(1859,plain,
% 262.46/166.83 (f1(lazy_impl(prop(P!8), P!8), not1(false), lazy_impl(prop(P!8), P!8)) = f1(false, not1(false), false)),
% 262.46/166.83 inference(symmetry,[status(thm)],[1858])).
% 262.46/166.83 tff(1860,plain,
% 262.46/166.83 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) <=> ((lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = not1(false))))),
% 262.46/166.83 inference(quant_inst,[status(thm)],[])).
% 262.46/166.83 tff(1861,plain,
% 262.46/166.83 (bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) <=> ((lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = not1(false)))),
% 262.46/166.83 inference(unit_resolution,[status(thm)],[1860, 229])).
% 262.46/166.83 tff(1862,plain,
% 262.46/166.83 (((~![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(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), not1(false)) <=> ((~((~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = 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(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), not1(false)) <=> ((~((~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false))))),
% 262.46/166.84 inference(rewrite,[status(thm)],[])).
% 262.46/166.84 tff(1863,plain,
% 262.46/166.84 ((forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), not1(false)) <=> ((~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(not1(false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(not1(false) = not1(false))))))) <=> (forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), not1(false)) <=> ((~((~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)))),
% 262.46/166.84 inference(rewrite,[status(thm)],[])).
% 262.46/166.84 tff(1864,plain,
% 262.46/166.84 (((~![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(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), not1(false)) <=> ((~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(not1(false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(not1(false) = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), not1(false)) <=> ((~((~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false))))),
% 262.46/166.84 inference(monotonicity,[status(thm)],[1863])).
% 262.46/166.84 tff(1865,plain,
% 262.46/166.84 (((~![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(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), not1(false)) <=> ((~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(not1(false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(not1(false) = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), not1(false)) <=> ((~((~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false))))),
% 262.46/166.84 inference(transitivity,[status(thm)],[1864, 1862])).
% 262.46/166.84 tff(1866,plain,
% 262.46/166.84 ((~![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(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), not1(false)) <=> ((~(d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(not1(false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (~((~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(not1(false) = not1(false)))))))),
% 262.46/166.84 inference(quant_inst,[status(thm)],[])).
% 262.46/166.84 tff(1867,plain,
% 262.46/166.84 ((~![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(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), not1(false)) <=> ((~((~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)))),
% 262.46/166.84 inference(modus_ponens,[status(thm)],[1866, 1865])).
% 262.46/166.84 tff(1868,plain,
% 262.46/166.84 (forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), not1(false)) <=> ((~((~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false))),
% 262.46/166.84 inference(unit_resolution,[status(thm)],[1867, 493])).
% 262.46/166.84 tff(1869,plain,
% 262.46/166.84 (forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), not1(false)) <=> forallprefers(f1(P!8, Q!7, lazy_impl(prop(P!8), P!8)), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.46/166.84 inference(monotonicity,[status(thm)],[1489, 1842])).
% 262.46/166.84 tff(1870,plain,
% 262.46/166.84 (forallprefers(f1(P!8, Q!7, lazy_impl(prop(P!8), P!8)), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))) <=> forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), not1(false))),
% 262.46/166.84 inference(symmetry,[status(thm)],[1869])).
% 262.46/166.84 tff(1871,plain,
% 262.46/166.84 ((~forallprefers(f1(P!8, Q!7, lazy_impl(prop(P!8), P!8)), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))) <=> (~forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), not1(false)))),
% 262.46/166.84 inference(monotonicity,[status(thm)],[1870])).
% 262.46/166.84 tff(1872,plain,
% 262.46/166.84 (~forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), not1(false))),
% 262.46/166.84 inference(modus_ponens,[status(thm)],[1494, 1871])).
% 262.46/166.84 tff(1873,plain,
% 262.46/166.84 ((~(forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), not1(false)) <=> ((~((~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)))) | forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), not1(false)) | (~((~((~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)))),
% 262.46/166.85 inference(tautology,[status(thm)],[])).
% 262.46/166.85 tff(1874,plain,
% 262.46/166.85 (~((~((~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false))),
% 262.46/166.85 inference(unit_resolution,[status(thm)],[1873, 1872, 1868])).
% 262.46/166.85 tff(1875,plain,
% 262.46/166.85 (((~((~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | ((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))),
% 262.46/166.85 inference(tautology,[status(thm)],[])).
% 262.46/166.85 tff(1876,plain,
% 262.46/166.85 ((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))),
% 262.46/166.85 inference(unit_resolution,[status(thm)],[1875, 1874])).
% 262.46/166.85 tff(1877,plain,
% 262.46/166.85 (((~((~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | ((~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))),
% 262.52/166.85 inference(tautology,[status(thm)],[])).
% 262.52/166.85 tff(1878,plain,
% 262.52/166.85 ((~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))),
% 262.52/166.85 inference(unit_resolution,[status(thm)],[1877, 1874])).
% 262.52/166.85 tff(1879,plain,
% 262.52/166.85 ((~((~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))) | (~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))),
% 262.52/166.85 inference(tautology,[status(thm)],[])).
% 262.52/166.85 tff(1880,plain,
% 262.52/166.85 ((~((~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))),
% 262.52/166.85 inference(unit_resolution,[status(thm)],[1879, 41])).
% 262.52/166.85 tff(1881,plain,
% 262.52/166.85 (d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))),
% 262.52/166.85 inference(unit_resolution,[status(thm)],[1880, 1878])).
% 262.52/166.85 tff(1882,plain,
% 262.52/166.85 ((~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))),
% 262.52/166.85 inference(tautology,[status(thm)],[])).
% 262.52/166.85 tff(1883,plain,
% 262.52/166.85 ((~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))),
% 262.52/166.85 inference(unit_resolution,[status(thm)],[1882, 41, 81])).
% 262.52/166.85 tff(1884,plain,
% 262.52/166.85 (bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))),
% 262.52/166.85 inference(unit_resolution,[status(thm)],[1883, 1881, 1876])).
% 262.52/166.85 tff(1885,plain,
% 262.52/166.85 ((~(bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) <=> ((lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = not1(false))))) | (~bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))) | ((lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = not1(false)))),
% 262.52/166.86 inference(tautology,[status(thm)],[])).
% 262.52/166.86 tff(1886,plain,
% 262.52/166.86 ((~(bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) <=> ((lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = not1(false))))) | ((lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = not1(false)))),
% 262.52/166.86 inference(unit_resolution,[status(thm)],[1885, 1884])).
% 262.52/166.86 tff(1887,plain,
% 262.52/166.86 ((lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = not1(false))),
% 262.52/166.86 inference(unit_resolution,[status(thm)],[1886, 1861])).
% 262.52/166.86 tff(1888,plain,
% 262.52/166.86 (((~((~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false))),
% 262.52/166.86 inference(tautology,[status(thm)],[])).
% 262.52/166.86 tff(1889,plain,
% 262.52/166.86 (~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)),
% 262.52/166.86 inference(unit_resolution,[status(thm)],[1888, 1874])).
% 262.52/166.86 tff(1890,plain,
% 262.52/166.86 ((~((lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = not1(false)))) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = not1(false))),
% 262.52/166.86 inference(tautology,[status(thm)],[])).
% 262.52/166.86 tff(1891,plain,
% 262.52/166.86 ((~((lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = not1(false)))) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = not1(false))),
% 262.52/166.86 inference(unit_resolution,[status(thm)],[1890, 1889])).
% 262.52/166.86 tff(1892,plain,
% 262.52/166.86 (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = not1(false)),
% 262.52/166.86 inference(unit_resolution,[status(thm)],[1891, 1887])).
% 262.52/166.86 tff(1893,plain,
% 262.52/166.86 (not1(false) = lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(lazy_impl(prop(P!8), P!8), impl(not1(false), lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))),
% 262.52/166.86 inference(symmetry,[status(thm)],[1892])).
% 262.52/166.86 tff(1894,plain,
% 262.52/166.86 (not1(false) = false),
% 262.52/166.86 inference(transitivity,[status(thm)],[1893, 1488, 1859, 1377, 1846, 35, 23])).
% 262.52/166.86 tff(1895,plain,
% 262.52/166.86 ($false),
% 262.52/166.86 inference(unit_resolution,[status(thm)],[65, 1894])).
% 262.52/166.86 tff(1896,plain,(~(Q!7 = not1(false))), inference(lemma,lemma(discharge,[]))).
% 262.52/166.86 tff(1897,plain,
% 262.52/166.86 (Q!7 = false),
% 262.52/166.86 inference(unit_resolution,[status(thm)],[1194, 1896])).
% 262.52/166.86 tff(1898,plain,
% 262.52/166.86 (f1(P!8, Q!7, lazy_impl(prop(P!8), P!8)) = f1(P!8, false, lazy_impl(prop(P!8), P!8))),
% 262.52/166.86 inference(monotonicity,[status(thm)],[1897])).
% 262.52/166.86 tff(1899,plain,
% 262.52/166.86 (f1(P!8, false, lazy_impl(prop(P!8), P!8)) = f1(P!8, Q!7, lazy_impl(prop(P!8), P!8))),
% 262.52/166.86 inference(symmetry,[status(thm)],[1898])).
% 262.52/166.86 tff(1900,plain,
% 262.52/166.86 (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = f1(P!8, Q!7, lazy_impl(prop(P!8), P!8))),
% 262.52/166.86 inference(transitivity,[status(thm)],[1278, 1899])).
% 262.52/166.86 tff(1901,plain,
% 262.52/166.86 (forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), not1(false)) <=> forallprefers(f1(P!8, Q!7, lazy_impl(prop(P!8), P!8)), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.52/166.86 inference(monotonicity,[status(thm)],[1900, 1842])).
% 262.52/166.86 tff(1902,plain,
% 262.52/166.86 (forallprefers(f1(P!8, Q!7, lazy_impl(prop(P!8), P!8)), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))) <=> forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), not1(false))),
% 262.52/166.86 inference(symmetry,[status(thm)],[1901])).
% 262.52/166.86 tff(1903,plain,
% 262.52/166.86 ((~forallprefers(f1(P!8, Q!7, lazy_impl(prop(P!8), P!8)), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))) <=> (~forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), not1(false)))),
% 262.52/166.86 inference(monotonicity,[status(thm)],[1902])).
% 262.52/166.86 tff(1904,plain,
% 262.52/166.86 (~forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), not1(false))),
% 262.52/166.86 inference(modus_ponens,[status(thm)],[1494, 1903])).
% 262.52/166.86 tff(1905,plain,
% 262.52/166.86 ((~(forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), not1(false)) <=> ((~((~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)))) | forallprefers(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))), not1(false)) | (~((~((~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)))),
% 262.52/166.87 inference(tautology,[status(thm)],[])).
% 262.52/166.87 tff(1906,plain,
% 262.52/166.87 (~((~((~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false))),
% 262.52/166.87 inference(unit_resolution,[status(thm)],[1905, 1904, 1287])).
% 262.52/166.87 tff(1907,plain,
% 262.52/166.87 (((~((~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | ((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))),
% 262.52/166.87 inference(tautology,[status(thm)],[])).
% 262.52/166.87 tff(1908,plain,
% 262.52/166.87 ((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))),
% 262.52/166.87 inference(unit_resolution,[status(thm)],[1907, 1906])).
% 262.52/166.87 tff(1909,plain,
% 262.52/166.87 (((~((~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | ((~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))),
% 262.52/166.87 inference(tautology,[status(thm)],[])).
% 262.52/166.87 tff(1910,plain,
% 262.52/166.87 ((~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))),
% 262.52/166.87 inference(unit_resolution,[status(thm)],[1909, 1906])).
% 262.52/166.87 tff(1911,plain,
% 262.52/166.87 ((~((~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))) | (~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))),
% 262.52/166.87 inference(tautology,[status(thm)],[])).
% 262.52/166.87 tff(1912,plain,
% 262.52/166.87 ((~((~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))),
% 262.52/166.87 inference(unit_resolution,[status(thm)],[1911, 41])).
% 262.52/166.87 tff(1913,plain,
% 262.52/166.87 (d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))),
% 262.52/166.87 inference(unit_resolution,[status(thm)],[1912, 1910])).
% 262.52/166.87 tff(1914,plain,
% 262.52/166.87 ((~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))),
% 262.52/166.87 inference(tautology,[status(thm)],[])).
% 262.52/166.87 tff(1915,plain,
% 262.52/166.87 ((~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))),
% 262.52/166.87 inference(unit_resolution,[status(thm)],[1914, 41, 81])).
% 262.52/166.87 tff(1916,plain,
% 262.52/166.87 (bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))),
% 262.52/166.87 inference(unit_resolution,[status(thm)],[1915, 1913, 1908])).
% 262.52/166.87 tff(1917,plain,
% 262.52/166.87 ((~(bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) <=> ((lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = not1(false))))) | (~bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))) | ((lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = not1(false)))),
% 262.52/166.87 inference(tautology,[status(thm)],[])).
% 262.52/166.87 tff(1918,plain,
% 262.52/166.87 ((~(bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) <=> ((lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = not1(false))))) | ((lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = not1(false)))),
% 262.52/166.87 inference(unit_resolution,[status(thm)],[1917, 1916])).
% 262.52/166.87 tff(1919,plain,
% 262.52/166.87 ((lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = not1(false))),
% 262.52/166.87 inference(unit_resolution,[status(thm)],[1918, 1280])).
% 262.52/166.87 tff(1920,plain,
% 262.52/166.87 (((~((~d(not1(false))) | d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))) | (~d(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))))))) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)) | (~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false))),
% 262.52/166.87 inference(tautology,[status(thm)],[])).
% 262.52/166.87 tff(1921,plain,
% 262.52/166.87 (~(lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false)),
% 262.52/166.87 inference(unit_resolution,[status(thm)],[1920, 1906])).
% 262.52/166.87 tff(1922,plain,
% 262.52/166.87 ((~((lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = not1(false)))) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = not1(false))),
% 262.52/166.87 inference(tautology,[status(thm)],[])).
% 262.52/166.87 tff(1923,plain,
% 262.52/166.87 ((~((lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = false) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = not1(false)))) | (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = not1(false))),
% 262.52/166.87 inference(unit_resolution,[status(thm)],[1922, 1921])).
% 262.52/166.87 tff(1924,plain,
% 262.52/166.87 (lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8))) = not1(false)),
% 262.52/166.87 inference(unit_resolution,[status(thm)],[1923, 1919])).
% 262.52/166.87 tff(1925,plain,
% 262.52/166.87 (not1(false) = lazy_impl(prop(lazy_impl(prop(P!8), P!8)), impl(impl(P!8, impl(false, lazy_impl(prop(P!8), P!8))), lazy_impl(prop(P!8), P!8)))),
% 262.52/166.87 inference(symmetry,[status(thm)],[1924])).
% 262.52/166.87 tff(1926,plain,
% 262.52/166.87 (not1(false) = false),
% 262.52/166.87 inference(transitivity,[status(thm)],[1925, 1278, 1275, 174, 172, 35, 23])).
% 262.52/166.87 tff(1927,plain,
% 262.52/166.87 ($false),
% 262.52/166.87 inference(unit_resolution,[status(thm)],[65, 1926])).
% 262.52/166.87 tff(1928,plain,(~(P!8 = false)), inference(lemma,lemma(discharge,[]))).
% 262.52/166.87 tff(1929,plain,
% 262.52/166.87 (P!8 = not1(false)),
% 262.52/166.87 inference(unit_resolution,[status(thm)],[1854, 1928])).
% 262.52/166.87 tff(1930,plain,
% 262.52/166.87 (not1(false) = P!8),
% 262.52/166.87 inference(symmetry,[status(thm)],[1929])).
% 262.52/166.87 tff(1931,plain,
% 262.52/166.87 (f1(not1(false), false, false) = f1(P!8, false, false)),
% 262.52/166.87 inference(monotonicity,[status(thm)],[1930])).
% 262.52/166.87 tff(1932,plain,
% 262.52/166.87 (f1(P!8, false, false) = f1(not1(false), false, false)),
% 262.52/166.87 inference(symmetry,[status(thm)],[1931])).
% 262.52/166.87 tff(1933,plain,
% 262.52/166.87 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) <=> ((lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false) | (lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = not1(false))))),
% 262.52/166.87 inference(quant_inst,[status(thm)],[])).
% 262.52/166.87 tff(1934,plain,
% 262.52/166.87 (bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) <=> ((lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false) | (lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = not1(false)))),
% 262.52/166.88 inference(unit_resolution,[status(thm)],[1933, 229])).
% 262.52/166.88 tff(1935,plain,
% 262.52/166.88 (((~![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(impl(P!8, impl(false, false)), false)), not1(false)) <=> ((~((~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))))) | (lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), 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(impl(P!8, impl(false, false)), false)), not1(false)) <=> ((~((~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))))) | (lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false))))),
% 262.52/166.88 inference(rewrite,[status(thm)],[])).
% 262.52/166.88 tff(1936,plain,
% 262.52/166.88 ((forallprefers(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)), not1(false)) <=> ((~(d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(not1(false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false)) | (~(not1(false) = not1(false))))))) <=> (forallprefers(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)), not1(false)) <=> ((~((~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))))) | (lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false)))),
% 262.52/166.88 inference(rewrite,[status(thm)],[])).
% 262.52/166.88 tff(1937,plain,
% 262.52/166.88 (((~![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(impl(P!8, impl(false, false)), false)), not1(false)) <=> ((~(d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(not1(false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false)) | (~(not1(false) = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)), not1(false)) <=> ((~((~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))))) | (lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false))))),
% 262.52/166.88 inference(monotonicity,[status(thm)],[1936])).
% 262.52/166.88 tff(1938,plain,
% 262.52/166.88 (((~![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(impl(P!8, impl(false, false)), false)), not1(false)) <=> ((~(d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(not1(false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false)) | (~(not1(false) = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)), not1(false)) <=> ((~((~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))))) | (lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false))))),
% 262.52/166.88 inference(transitivity,[status(thm)],[1937, 1935])).
% 262.52/166.88 tff(1939,plain,
% 262.52/166.88 ((~![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(impl(P!8, impl(false, false)), false)), not1(false)) <=> ((~(d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(not1(false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))))) | (~((~(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false)) | (~(not1(false) = not1(false)))))))),
% 262.52/166.88 inference(quant_inst,[status(thm)],[])).
% 262.52/166.88 tff(1940,plain,
% 262.52/166.88 ((~![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(impl(P!8, impl(false, false)), false)), not1(false)) <=> ((~((~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))))) | (lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false)))),
% 262.52/166.88 inference(modus_ponens,[status(thm)],[1939, 1938])).
% 262.52/166.88 tff(1941,plain,
% 262.52/166.88 (forallprefers(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)), not1(false)) <=> ((~((~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))))) | (lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false))),
% 262.52/166.88 inference(unit_resolution,[status(thm)],[1940, 493])).
% 262.52/166.88 tff(1942,plain,
% 262.52/166.88 (f1(P!8, Q!7, false) = f1(P!8, false, false)),
% 262.52/166.88 inference(monotonicity,[status(thm)],[1897])).
% 262.52/166.88 tff(1943,plain,
% 262.52/166.88 (f1(P!8, false, false) = f1(P!8, Q!7, false)),
% 262.52/166.88 inference(symmetry,[status(thm)],[1942])).
% 262.52/166.88 tff(1944,plain,
% 262.52/166.88 (lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = f1(P!8, Q!7, false)),
% 262.52/166.88 inference(transitivity,[status(thm)],[1545, 1943])).
% 262.52/166.88 tff(1945,plain,
% 262.52/166.88 (forallprefers(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)), not1(false)) <=> forallprefers(f1(P!8, Q!7, false), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))),
% 262.52/166.88 inference(monotonicity,[status(thm)],[1944, 1842])).
% 262.52/166.88 tff(1946,plain,
% 262.52/166.88 (forallprefers(f1(P!8, Q!7, false), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8))) <=> forallprefers(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)), not1(false))),
% 262.52/166.89 inference(symmetry,[status(thm)],[1945])).
% 262.52/166.89 tff(1947,plain,
% 262.52/166.89 ((~forallprefers(f1(P!8, Q!7, false), f1(P!8, Q!7, tptp_fun_R_0(Q!7, P!8)))) <=> (~forallprefers(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)), not1(false)))),
% 262.52/166.89 inference(monotonicity,[status(thm)],[1946])).
% 262.52/166.89 tff(1948,plain,
% 262.52/166.89 (~forallprefers(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)), not1(false))),
% 262.52/166.89 inference(modus_ponens,[status(thm)],[802, 1947])).
% 262.52/166.89 tff(1949,plain,
% 262.52/166.89 ((~(forallprefers(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)), not1(false)) <=> ((~((~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))))) | (lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false)))) | forallprefers(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)), not1(false)) | (~((~((~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))))) | (lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false)))),
% 262.52/166.89 inference(tautology,[status(thm)],[])).
% 262.52/166.89 tff(1950,plain,
% 262.52/166.89 (~((~((~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))))) | (lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false))),
% 262.52/166.89 inference(unit_resolution,[status(thm)],[1949, 1948, 1941])).
% 262.52/166.89 tff(1951,plain,
% 262.52/166.89 (((~((~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))))) | (lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false)) | ((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))))),
% 262.52/166.89 inference(tautology,[status(thm)],[])).
% 262.52/166.89 tff(1952,plain,
% 262.52/166.89 ((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))))),
% 262.52/166.89 inference(unit_resolution,[status(thm)],[1951, 1950])).
% 262.52/166.89 tff(1953,plain,
% 262.52/166.89 (((~((~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))))) | (lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false)) | ((~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))))),
% 262.52/166.89 inference(tautology,[status(thm)],[])).
% 262.52/166.89 tff(1954,plain,
% 262.52/166.89 ((~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))),
% 262.52/166.89 inference(unit_resolution,[status(thm)],[1953, 1950])).
% 262.52/166.89 tff(1955,plain,
% 262.52/166.89 ((~((~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))))) | (~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))),
% 262.52/166.89 inference(tautology,[status(thm)],[])).
% 262.52/166.89 tff(1956,plain,
% 262.52/166.89 ((~((~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))))) | d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))),
% 262.52/166.89 inference(unit_resolution,[status(thm)],[1955, 41])).
% 262.52/166.89 tff(1957,plain,
% 262.52/166.89 (d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))),
% 262.52/166.89 inference(unit_resolution,[status(thm)],[1956, 1954])).
% 262.52/166.89 tff(1958,plain,
% 262.52/166.89 ((~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))))) | (~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))))),
% 262.52/166.89 inference(tautology,[status(thm)],[])).
% 262.52/166.89 tff(1959,plain,
% 262.52/166.89 ((~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))))),
% 262.52/166.89 inference(unit_resolution,[status(thm)],[1958, 41, 81])).
% 262.52/166.89 tff(1960,plain,
% 262.52/166.89 (bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))),
% 262.52/166.89 inference(unit_resolution,[status(thm)],[1959, 1957, 1952])).
% 262.52/166.89 tff(1961,plain,
% 262.52/166.89 ((~(bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) <=> ((lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false) | (lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = not1(false))))) | (~bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))) | ((lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false) | (lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = not1(false)))),
% 262.52/166.89 inference(tautology,[status(thm)],[])).
% 262.52/166.89 tff(1962,plain,
% 262.52/166.89 ((~(bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) <=> ((lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false) | (lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = not1(false))))) | ((lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false) | (lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = not1(false)))),
% 262.52/166.89 inference(unit_resolution,[status(thm)],[1961, 1960])).
% 262.52/166.89 tff(1963,plain,
% 262.52/166.89 ((lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false) | (lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = not1(false))),
% 262.52/166.89 inference(unit_resolution,[status(thm)],[1962, 1934])).
% 262.52/166.89 tff(1964,plain,
% 262.52/166.89 (((~((~d(not1(false))) | d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))))) | (~((~d(not1(false))) | (~bool(not1(false))) | bool(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))) | (~d(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)))))) | (lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false)) | (~(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false))),
% 262.52/166.89 inference(tautology,[status(thm)],[])).
% 262.52/166.89 tff(1965,plain,
% 262.52/166.89 (~(lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false)),
% 262.52/166.89 inference(unit_resolution,[status(thm)],[1964, 1950])).
% 262.52/166.89 tff(1966,plain,
% 262.52/166.89 ((~((lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false) | (lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = not1(false)))) | (lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false) | (lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = not1(false))),
% 262.52/166.89 inference(tautology,[status(thm)],[])).
% 262.52/166.89 tff(1967,plain,
% 262.52/166.89 ((~((lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = false) | (lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = not1(false)))) | (lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = not1(false))),
% 262.52/166.89 inference(unit_resolution,[status(thm)],[1966, 1965])).
% 262.52/166.89 tff(1968,plain,
% 262.52/166.89 (lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false)) = not1(false)),
% 262.52/166.89 inference(unit_resolution,[status(thm)],[1967, 1963])).
% 262.52/166.91 tff(1969,plain,
% 262.52/166.91 (not1(false) = lazy_impl(prop(false), impl(impl(P!8, impl(false, false)), false))),
% 262.52/166.91 inference(symmetry,[status(thm)],[1968])).
% 262.52/166.91 tff(1970,plain,
% 262.52/166.91 (not1(false) = false),
% 262.52/166.91 inference(transitivity,[status(thm)],[1969, 1545, 1932, 161, 152, 35, 23])).
% 262.52/166.91 tff(1971,plain,
% 262.52/166.91 ($false),
% 262.52/166.91 inference(unit_resolution,[status(thm)],[65, 1970])).
% 262.52/166.91 % SZS output end Proof
%------------------------------------------------------------------------------