TSTP Solution File: SWW101+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW101+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 20:57:46 EDT 2022
% Result : Theorem 0.18s 0.40s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW101+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n013.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Sep 4 12:02:16 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.18/0.40 % SZS status Theorem
% 0.18/0.40 % SZS output start Proof
% 0.18/0.40 tff(false2_type, type, (
% 0.18/0.40 false2: $i)).
% 0.18/0.40 tff(false_type, type, (
% 0.18/0.40 false: $i)).
% 0.18/0.40 tff(phi_type, type, (
% 0.18/0.40 phi: $i > $i)).
% 0.18/0.40 tff(f7_type, type, (
% 0.18/0.40 f7: $i > $i)).
% 0.18/0.40 tff(tptp_fun_P_6_type, type, (
% 0.18/0.40 tptp_fun_P_6: $i)).
% 0.18/0.40 tff(forallprefers_type, type, (
% 0.18/0.40 forallprefers: ( $i * $i ) > $o)).
% 0.18/0.40 tff(d_type, type, (
% 0.18/0.40 d: $i > $o)).
% 0.18/0.40 tff(err_type, type, (
% 0.18/0.40 err: $i)).
% 0.18/0.40 tff(true_type, type, (
% 0.18/0.40 true: $i)).
% 0.18/0.40 tff(lazy_impl_type, type, (
% 0.18/0.40 lazy_impl: ( $i * $i ) > $i)).
% 0.18/0.40 tff(not1_type, type, (
% 0.18/0.40 not1: $i > $i)).
% 0.18/0.40 tff(prop_type, type, (
% 0.18/0.40 prop: $i > $i)).
% 0.18/0.40 tff(bool_type, type, (
% 0.18/0.40 bool: $i > $o)).
% 0.18/0.40 tff(false1_type, type, (
% 0.18/0.40 false1: $i)).
% 0.18/0.40 tff(1,plain,
% 0.18/0.40 (((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))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(2,plain,
% 0.18/0.40 (?[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))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(3,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')).
% 0.18/0.40 tff(4,plain,
% 0.18/0.40 (?[P: $i] : ((false2 = phi(f7(P))) & (~?[P1: $i] : forallprefers(f7(P1), f7(P))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.18/0.40 tff(5,plain,
% 0.18/0.40 ((false2 = phi(f7(P!6))) & ![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.18/0.40 tff(6,plain,
% 0.18/0.40 (false2 = phi(f7(P!6))),
% 0.18/0.40 inference(and_elim,[status(thm)],[5])).
% 0.18/0.40 tff(7,plain,
% 0.18/0.40 (phi(f7(P!6)) = false2),
% 0.18/0.40 inference(symmetry,[status(thm)],[6])).
% 0.18/0.40 tff(8,plain,
% 0.18/0.40 (d(false) <=> d(false)),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(9,axiom,((d(true) & d(false)) & d(err)), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','false_true_err_in_d')).
% 0.18/0.40 tff(10,plain,
% 0.18/0.40 (d(true) & d(false)),
% 0.18/0.40 inference(and_elim,[status(thm)],[9])).
% 0.18/0.40 tff(11,plain,
% 0.18/0.40 (d(false)),
% 0.18/0.40 inference(and_elim,[status(thm)],[10])).
% 0.18/0.40 tff(12,plain,
% 0.18/0.40 (d(false)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[11, 8])).
% 0.18/0.40 tff(13,plain,
% 0.18/0.40 ((d(false) | (~(phi(false) = err))) | (~d(false))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(14,plain,
% 0.18/0.40 (d(false) | (~(phi(false) = err))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.18/0.40 tff(15,plain,
% 0.18/0.40 (^[X: $i] : refl(((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err))))) <=> ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(16,plain,
% 0.18/0.40 (![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err))))) <=> ![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[15])).
% 0.18/0.40 tff(17,plain,
% 0.18/0.40 (^[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)))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(18,plain,
% 0.18/0.40 (![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err))) <=> ![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[17])).
% 0.18/0.40 tff(19,plain,
% 0.18/0.40 (![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err))) <=> ![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(20,axiom,(![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','def_phi')).
% 0.18/0.40 tff(21,plain,
% 0.18/0.40 (![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.18/0.41 tff(22,plain,(
% 0.18/0.41 ![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err)))),
% 0.18/0.41 inference(skolemize,[status(sab)],[21])).
% 0.18/0.41 tff(23,plain,
% 0.18/0.41 (![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.18/0.41 tff(24,plain,
% 0.18/0.41 (![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.18/0.41 tff(25,plain,
% 0.18/0.41 (((~![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)))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(26,plain,
% 0.18/0.41 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(false)) | (~(phi(false) = false)))) | (~(d(false) | (~(phi(false) = err)))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(27,plain,
% 0.18/0.41 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(false)) | (~(phi(false) = false)))) | (~(d(false) | (~(phi(false) = err))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.18/0.41 tff(28,plain,
% 0.18/0.41 (~((~d(false)) | (~(phi(false) = false)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[27, 24, 14])).
% 0.18/0.41 tff(29,plain,
% 0.18/0.41 (((~d(false)) | (~(phi(false) = false))) | (phi(false) = false)),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(30,plain,
% 0.18/0.41 (phi(false) = false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.18/0.41 tff(31,plain,
% 0.18/0.41 (^[B: $i] : refl((lazy_impl(not1(false), B) = phi(B)) <=> (lazy_impl(not1(false), B) = phi(B)))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(32,plain,
% 0.18/0.41 (![B: $i] : (lazy_impl(not1(false), B) = phi(B)) <=> ![B: $i] : (lazy_impl(not1(false), B) = phi(B))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[31])).
% 0.18/0.41 tff(33,plain,
% 0.18/0.41 (^[B: $i] : rewrite((lazy_impl(true, B) = phi(B)) <=> (lazy_impl(not1(false), B) = phi(B)))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(34,plain,
% 0.18/0.41 (![B: $i] : (lazy_impl(true, B) = phi(B)) <=> ![B: $i] : (lazy_impl(not1(false), B) = phi(B))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[33])).
% 0.18/0.41 tff(35,plain,
% 0.18/0.41 (![B: $i] : (lazy_impl(true, B) = phi(B)) <=> ![B: $i] : (lazy_impl(true, B) = phi(B))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(36,axiom,(![B: $i] : (lazy_impl(true, B) = phi(B))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','lazy_impl_axiom3')).
% 0.18/0.41 tff(37,plain,
% 0.18/0.41 (![B: $i] : (lazy_impl(true, B) = phi(B))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.18/0.41 tff(38,plain,
% 0.18/0.41 (![B: $i] : (lazy_impl(not1(false), B) = phi(B))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[37, 34])).
% 0.18/0.41 tff(39,plain,(
% 0.18/0.41 ![B: $i] : (lazy_impl(not1(false), B) = phi(B))),
% 0.18/0.41 inference(skolemize,[status(sab)],[38])).
% 0.18/0.41 tff(40,plain,
% 0.18/0.41 (![B: $i] : (lazy_impl(not1(false), B) = phi(B))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.18/0.41 tff(41,plain,
% 0.18/0.41 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), false) = phi(false))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(42,plain,
% 0.18/0.41 (lazy_impl(not1(false), false) = phi(false)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.18/0.41 tff(43,plain,
% 0.18/0.41 (^[X: $i] : refl(((prop(X) = not1(false)) <=> bool(X)) <=> ((prop(X) = not1(false)) <=> bool(X)))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(44,plain,
% 0.18/0.41 (![X: $i] : ((prop(X) = not1(false)) <=> bool(X)) <=> ![X: $i] : ((prop(X) = not1(false)) <=> bool(X))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[43])).
% 0.18/0.41 tff(45,plain,
% 0.18/0.41 (^[X: $i] : rewrite(((prop(X) = true) <=> bool(X)) <=> ((prop(X) = not1(false)) <=> bool(X)))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(46,plain,
% 0.18/0.41 (![X: $i] : ((prop(X) = true) <=> bool(X)) <=> ![X: $i] : ((prop(X) = not1(false)) <=> bool(X))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[45])).
% 0.18/0.41 tff(47,plain,
% 0.18/0.41 (![X: $i] : ((prop(X) = true) <=> bool(X)) <=> ![X: $i] : ((prop(X) = true) <=> bool(X))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(48,axiom,(![X: $i] : ((prop(X) = true) <=> bool(X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','prop_true')).
% 0.18/0.41 tff(49,plain,
% 0.18/0.41 (![X: $i] : ((prop(X) = true) <=> bool(X))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.18/0.41 tff(50,plain,
% 0.18/0.41 (![X: $i] : ((prop(X) = not1(false)) <=> bool(X))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[49, 46])).
% 0.18/0.41 tff(51,plain,(
% 0.18/0.41 ![X: $i] : ((prop(X) = not1(false)) <=> bool(X))),
% 0.18/0.41 inference(skolemize,[status(sab)],[50])).
% 0.18/0.41 tff(52,plain,
% 0.18/0.41 (![X: $i] : ((prop(X) = not1(false)) <=> bool(X))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.18/0.41 tff(53,plain,
% 0.18/0.41 ((~![X: $i] : ((prop(X) = not1(false)) <=> bool(X))) | ((prop(false) = not1(false)) <=> bool(false))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(54,plain,
% 0.18/0.41 ((prop(false) = not1(false)) <=> bool(false)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.18/0.41 tff(55,plain,
% 0.18/0.41 ((not1(false) = phi(false)) <=> (not1(false) = false)),
% 0.18/0.41 inference(monotonicity,[status(thm)],[30])).
% 0.18/0.41 tff(56,plain,
% 0.18/0.41 ((not1(false) = false) <=> (not1(false) = phi(false))),
% 0.18/0.41 inference(symmetry,[status(thm)],[55])).
% 0.18/0.41 tff(57,plain,
% 0.18/0.41 ((~(not1(false) = false)) <=> (~(not1(false) = phi(false)))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[56])).
% 0.18/0.41 tff(58,plain,
% 0.18/0.41 ((~(true = false)) <=> (~(not1(false) = false))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(59,plain,
% 0.18/0.41 ((~(true = false)) <=> (~(true = false))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(60,axiom,(((~(true = false)) & (~(true = err))) & (~(false = err))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','distinct_false_true_err')).
% 0.18/0.41 tff(61,plain,
% 0.18/0.41 ((~(true = false)) & (~(true = err))),
% 0.18/0.41 inference(and_elim,[status(thm)],[60])).
% 0.18/0.41 tff(62,plain,
% 0.18/0.41 (~(true = false)),
% 0.18/0.41 inference(and_elim,[status(thm)],[61])).
% 0.18/0.41 tff(63,plain,
% 0.18/0.41 (~(true = false)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[62, 59])).
% 0.18/0.41 tff(64,plain,
% 0.18/0.41 (~(not1(false) = false)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[63, 58])).
% 0.18/0.41 tff(65,plain,
% 0.18/0.41 (~(not1(false) = phi(false))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.18/0.41 tff(66,plain,
% 0.18/0.41 (^[A: $i] : refl((bool(A) | (not1(A) = phi(A))) <=> (bool(A) | (not1(A) = phi(A))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(67,plain,
% 0.18/0.41 (![A: $i] : (bool(A) | (not1(A) = phi(A))) <=> ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[66])).
% 0.18/0.41 tff(68,plain,
% 0.18/0.41 (![A: $i] : (bool(A) | (not1(A) = phi(A))) <=> ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(69,plain,
% 0.18/0.41 (^[A: $i] : rewrite(((~bool(A)) => (not1(A) = phi(A))) <=> (bool(A) | (not1(A) = phi(A))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(70,plain,
% 0.18/0.41 (![A: $i] : ((~bool(A)) => (not1(A) = phi(A))) <=> ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[69])).
% 0.18/0.41 tff(71,axiom,(![A: $i] : ((~bool(A)) => (not1(A) = phi(A)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','not1_axiom1')).
% 0.18/0.41 tff(72,plain,
% 0.18/0.41 (![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.18/0.41 tff(73,plain,
% 0.18/0.41 (![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.18/0.41 tff(74,plain,(
% 0.18/0.41 ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 0.18/0.41 inference(skolemize,[status(sab)],[73])).
% 0.18/0.41 tff(75,plain,
% 0.18/0.41 (![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.18/0.41 tff(76,plain,
% 0.18/0.41 (((~![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)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(77,plain,
% 0.18/0.41 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | (bool(false) | (not1(false) = phi(false)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(78,plain,
% 0.18/0.41 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | bool(false) | (not1(false) = phi(false))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.18/0.41 tff(79,plain,
% 0.18/0.41 (bool(false) | (not1(false) = phi(false))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[78, 75])).
% 0.18/0.41 tff(80,plain,
% 0.18/0.41 (bool(false)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[79, 65])).
% 0.18/0.41 tff(81,plain,
% 0.18/0.41 ((~((prop(false) = not1(false)) <=> bool(false))) | (prop(false) = not1(false)) | (~bool(false))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(82,plain,
% 0.18/0.41 ((~((prop(false) = not1(false)) <=> bool(false))) | (prop(false) = not1(false))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.18/0.41 tff(83,plain,
% 0.18/0.41 (prop(false) = not1(false)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[82, 54])).
% 0.18/0.41 tff(84,plain,
% 0.18/0.41 (lazy_impl(prop(false), false) = lazy_impl(not1(false), false)),
% 0.18/0.41 inference(monotonicity,[status(thm)],[83])).
% 0.18/0.41 tff(85,plain,
% 0.18/0.41 (^[P: $i] : refl((f7(P) = lazy_impl(prop(P), P)) <=> (f7(P) = lazy_impl(prop(P), P)))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(86,plain,
% 0.18/0.41 (![P: $i] : (f7(P) = lazy_impl(prop(P), P)) <=> ![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[85])).
% 0.18/0.41 tff(87,plain,
% 0.18/0.41 (![P: $i] : (f7(P) = lazy_impl(prop(P), P)) <=> ![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(88,axiom,(![P: $i] : (f7(P) = lazy_impl(prop(P), P))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','def_f7')).
% 0.18/0.41 tff(89,plain,
% 0.18/0.41 (![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.18/0.41 tff(90,plain,(
% 0.18/0.41 ![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 0.18/0.41 inference(skolemize,[status(sab)],[89])).
% 0.18/0.41 tff(91,plain,
% 0.18/0.41 (![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.18/0.41 tff(92,plain,
% 0.18/0.41 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(false) = lazy_impl(prop(false), false))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(93,plain,
% 0.18/0.41 (f7(false) = lazy_impl(prop(false), false)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.18/0.41 tff(94,plain,
% 0.18/0.41 (d(true) <=> d(not1(false))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(95,plain,
% 0.18/0.41 (d(true) <=> d(true)),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(96,plain,
% 0.18/0.41 (d(true)),
% 0.18/0.41 inference(and_elim,[status(thm)],[10])).
% 0.18/0.41 tff(97,plain,
% 0.18/0.41 (d(true)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.18/0.41 tff(98,plain,
% 0.18/0.41 (d(not1(false))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[97, 94])).
% 0.18/0.41 tff(99,plain,
% 0.18/0.41 ((d(not1(false)) | (~(phi(not1(false)) = err))) | (~d(not1(false)))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(100,plain,
% 0.18/0.41 (d(not1(false)) | (~(phi(not1(false)) = err))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.18/0.41 tff(101,plain,
% 0.18/0.41 (((~![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)))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(102,plain,
% 0.18/0.41 ((~![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)))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(103,plain,
% 0.18/0.41 ((~![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))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.18/0.41 tff(104,plain,
% 0.18/0.41 (~((~d(not1(false))) | (~(phi(not1(false)) = not1(false))))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[103, 24, 100])).
% 0.18/0.41 tff(105,plain,
% 0.18/0.41 (((~d(not1(false))) | (~(phi(not1(false)) = not1(false)))) | (phi(not1(false)) = not1(false))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(106,plain,
% 0.18/0.41 (phi(not1(false)) = not1(false)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.18/0.41 tff(107,plain,
% 0.18/0.41 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), not1(false)) = phi(not1(false)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(108,plain,
% 0.18/0.41 (lazy_impl(not1(false), not1(false)) = phi(not1(false))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[107, 40])).
% 0.18/0.41 tff(109,plain,
% 0.18/0.41 ((~![X: $i] : ((prop(X) = not1(false)) <=> bool(X))) | ((prop(not1(false)) = not1(false)) <=> bool(not1(false)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(110,plain,
% 0.18/0.41 ((prop(not1(false)) = not1(false)) <=> bool(not1(false))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[109, 52])).
% 0.18/0.41 tff(111,plain,
% 0.18/0.41 ((false = not1(false)) <=> (not1(false) = false)),
% 0.18/0.41 inference(commutativity,[status(thm)],[])).
% 0.18/0.41 tff(112,plain,
% 0.18/0.41 ((not1(true) = false) <=> (not1(not1(false)) = false)),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(113,plain,
% 0.18/0.41 ((not1(true) = false) <=> (not1(true) = false)),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(114,axiom,(not1(true) = false), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','not1_axiom3')).
% 0.18/0.41 tff(115,plain,
% 0.18/0.41 (not1(true) = false),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.18/0.41 tff(116,plain,
% 0.18/0.41 (not1(not1(false)) = false),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[115, 112])).
% 0.18/0.41 tff(117,plain,
% 0.18/0.41 ((not1(not1(false)) = phi(not1(false))) <=> (false = not1(false))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[116, 106])).
% 0.18/0.41 tff(118,plain,
% 0.18/0.41 ((not1(not1(false)) = phi(not1(false))) <=> (not1(false) = false)),
% 0.18/0.41 inference(transitivity,[status(thm)],[117, 111])).
% 0.18/0.41 tff(119,plain,
% 0.18/0.41 ((not1(false) = false) <=> (not1(not1(false)) = phi(not1(false)))),
% 0.18/0.41 inference(symmetry,[status(thm)],[118])).
% 0.18/0.41 tff(120,plain,
% 0.18/0.41 ((~(not1(false) = false)) <=> (~(not1(not1(false)) = phi(not1(false))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[119])).
% 0.18/0.41 tff(121,plain,
% 0.18/0.41 (~(not1(not1(false)) = phi(not1(false)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[64, 120])).
% 0.18/0.41 tff(122,plain,
% 0.18/0.41 (((~![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))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(123,plain,
% 0.18/0.41 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | (bool(not1(false)) | (not1(not1(false)) = phi(not1(false))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(124,plain,
% 0.18/0.41 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | bool(not1(false)) | (not1(not1(false)) = phi(not1(false)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.18/0.41 tff(125,plain,
% 0.18/0.41 (bool(not1(false)) | (not1(not1(false)) = phi(not1(false)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[124, 75])).
% 0.18/0.41 tff(126,plain,
% 0.18/0.41 (bool(not1(false))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[125, 121])).
% 0.18/0.41 tff(127,plain,
% 0.18/0.41 ((~((prop(not1(false)) = not1(false)) <=> bool(not1(false)))) | (prop(not1(false)) = not1(false)) | (~bool(not1(false)))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(128,plain,
% 0.18/0.41 ((~((prop(not1(false)) = not1(false)) <=> bool(not1(false)))) | (prop(not1(false)) = not1(false))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.18/0.41 tff(129,plain,
% 0.18/0.41 (prop(not1(false)) = not1(false)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[128, 110])).
% 0.18/0.41 tff(130,plain,
% 0.18/0.41 (lazy_impl(prop(not1(false)), not1(false)) = lazy_impl(not1(false), not1(false))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[129])).
% 0.18/0.41 tff(131,plain,
% 0.18/0.41 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(not1(false)) = lazy_impl(prop(not1(false)), not1(false)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(132,plain,
% 0.18/0.41 (f7(not1(false)) = lazy_impl(prop(not1(false)), not1(false))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[131, 91])).
% 0.18/0.41 tff(133,assumption,(P!6 = not1(false)), introduced(assumption)).
% 0.18/0.41 tff(134,plain,
% 0.18/0.41 (f7(P!6) = f7(not1(false))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[133])).
% 0.18/0.41 tff(135,plain,
% 0.18/0.41 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(P!6) = lazy_impl(prop(P!6), P!6))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(136,plain,
% 0.18/0.42 (f7(P!6) = lazy_impl(prop(P!6), P!6)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[135, 91])).
% 0.18/0.42 tff(137,plain,
% 0.18/0.42 (lazy_impl(prop(P!6), P!6) = f7(P!6)),
% 0.18/0.42 inference(symmetry,[status(thm)],[136])).
% 0.18/0.42 tff(138,plain,
% 0.18/0.42 (lazy_impl(prop(P!6), P!6) = not1(false)),
% 0.18/0.42 inference(transitivity,[status(thm)],[137, 134, 132, 130, 108, 106])).
% 0.18/0.42 tff(139,plain,
% 0.18/0.42 (^[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))))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(140,plain,
% 0.18/0.42 (![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)))))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[139])).
% 0.18/0.42 tff(141,plain,
% 0.18/0.42 (^[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))))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(142,plain,
% 0.18/0.42 (![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)))))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[141])).
% 0.18/0.42 tff(143,plain,
% 0.18/0.42 (^[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))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(144,plain,
% 0.18/0.42 (![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)))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[143])).
% 0.18/0.42 tff(145,plain,
% 0.18/0.42 (![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))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(146,plain,
% 0.18/0.42 (^[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)))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(147,plain,
% 0.18/0.42 (![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))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[146])).
% 0.18/0.42 tff(148,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')).
% 0.18/0.42 tff(149,plain,
% 0.18/0.42 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.18/0.42 tff(150,plain,
% 0.18/0.42 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[149, 145])).
% 0.18/0.42 tff(151,plain,
% 0.18/0.42 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)) | ((X = false) & (Y = not1(false)))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[150, 144])).
% 0.18/0.42 tff(152,plain,(
% 0.18/0.42 ![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)) | ((X = false) & (Y = not1(false)))))),
% 0.18/0.42 inference(skolemize,[status(sab)],[151])).
% 0.18/0.42 tff(153,plain,
% 0.18/0.42 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[152, 142])).
% 0.18/0.42 tff(154,plain,
% 0.18/0.42 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[153, 140])).
% 0.18/0.42 tff(155,plain,
% 0.18/0.42 (((~![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)))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(156,plain,
% 0.18/0.42 ((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))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(157,plain,
% 0.18/0.42 (((~![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)))))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[156])).
% 0.18/0.42 tff(158,plain,
% 0.18/0.42 (((~![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)))))),
% 0.18/0.42 inference(transitivity,[status(thm)],[157, 155])).
% 0.18/0.42 tff(159,plain,
% 0.18/0.42 ((~![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)))))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(160,plain,
% 0.18/0.42 ((~![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))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.18/0.42 tff(161,plain,
% 0.18/0.42 (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)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[160, 154])).
% 0.18/0.42 tff(162,plain,
% 0.18/0.42 (lazy_impl(prop(false), false) = f7(false)),
% 0.18/0.42 inference(symmetry,[status(thm)],[93])).
% 0.18/0.42 tff(163,plain,
% 0.18/0.42 (lazy_impl(not1(false), false) = lazy_impl(prop(false), false)),
% 0.18/0.42 inference(symmetry,[status(thm)],[84])).
% 0.18/0.42 tff(164,plain,
% 0.18/0.42 (phi(false) = lazy_impl(not1(false), false)),
% 0.18/0.42 inference(symmetry,[status(thm)],[42])).
% 0.18/0.42 tff(165,plain,
% 0.18/0.42 (false = phi(false)),
% 0.18/0.42 inference(symmetry,[status(thm)],[30])).
% 0.18/0.42 tff(166,plain,
% 0.18/0.42 (false = f7(false)),
% 0.18/0.42 inference(transitivity,[status(thm)],[165, 164, 163, 162])).
% 0.18/0.42 tff(167,plain,
% 0.18/0.42 (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> forallprefers(f7(false), f7(P!6))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[166, 137])).
% 0.18/0.42 tff(168,plain,
% 0.18/0.42 (forallprefers(f7(false), f7(P!6)) <=> forallprefers(false, lazy_impl(prop(P!6), P!6))),
% 0.18/0.42 inference(symmetry,[status(thm)],[167])).
% 0.18/0.42 tff(169,plain,
% 0.18/0.42 ((~forallprefers(f7(false), f7(P!6))) <=> (~forallprefers(false, lazy_impl(prop(P!6), P!6)))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[168])).
% 0.18/0.42 tff(170,plain,
% 0.18/0.42 (^[P1: $i] : refl((~forallprefers(f7(P1), f7(P!6))) <=> (~forallprefers(f7(P1), f7(P!6))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(171,plain,
% 0.18/0.42 (![P1: $i] : (~forallprefers(f7(P1), f7(P!6))) <=> ![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[170])).
% 0.18/0.42 tff(172,plain,
% 0.18/0.42 (![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 0.18/0.42 inference(and_elim,[status(thm)],[5])).
% 0.18/0.42 tff(173,plain,
% 0.18/0.42 (![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.18/0.42 tff(174,plain,
% 0.18/0.42 ((~![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))) | (~forallprefers(f7(false), f7(P!6)))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(175,plain,
% 0.18/0.42 (~forallprefers(f7(false), f7(P!6))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[174, 173])).
% 0.18/0.42 tff(176,plain,
% 0.18/0.42 (~forallprefers(false, lazy_impl(prop(P!6), P!6))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[175, 169])).
% 0.18/0.42 tff(177,plain,
% 0.18/0.42 ((~(forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))) | (lazy_impl(prop(P!6), P!6) = not1(false))))) | forallprefers(false, lazy_impl(prop(P!6), P!6)) | (~((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))) | (lazy_impl(prop(P!6), P!6) = not1(false))))),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(178,plain,
% 0.18/0.43 (~((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))) | (lazy_impl(prop(P!6), P!6) = not1(false)))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[177, 176, 161])).
% 0.18/0.43 tff(179,plain,
% 0.18/0.43 (((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))) | (lazy_impl(prop(P!6), P!6) = not1(false))) | (~(lazy_impl(prop(P!6), P!6) = not1(false)))),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(180,plain,
% 0.18/0.43 (~(lazy_impl(prop(P!6), P!6) = not1(false))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[179, 178])).
% 0.18/0.43 tff(181,plain,
% 0.18/0.43 ($false),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[180, 138])).
% 0.18/0.43 tff(182,plain,(~(P!6 = not1(false))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.43 tff(183,plain,
% 0.18/0.43 (^[B: $i] : refl((lazy_impl(false, B) = not1(false)) <=> (lazy_impl(false, B) = not1(false)))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(184,plain,
% 0.18/0.43 (![B: $i] : (lazy_impl(false, B) = not1(false)) <=> ![B: $i] : (lazy_impl(false, B) = not1(false))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[183])).
% 0.18/0.43 tff(185,plain,
% 0.18/0.43 (^[B: $i] : rewrite((lazy_impl(false, B) = true) <=> (lazy_impl(false, B) = not1(false)))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(186,plain,
% 0.18/0.43 (![B: $i] : (lazy_impl(false, B) = true) <=> ![B: $i] : (lazy_impl(false, B) = not1(false))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[185])).
% 0.18/0.43 tff(187,plain,
% 0.18/0.43 (![B: $i] : (lazy_impl(false, B) = true) <=> ![B: $i] : (lazy_impl(false, B) = true)),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(188,axiom,(![B: $i] : (lazy_impl(false, B) = true)), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','lazy_impl_axiom2')).
% 0.18/0.43 tff(189,plain,
% 0.18/0.43 (![B: $i] : (lazy_impl(false, B) = true)),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.18/0.43 tff(190,plain,
% 0.18/0.43 (![B: $i] : (lazy_impl(false, B) = not1(false))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[189, 186])).
% 0.18/0.43 tff(191,plain,(
% 0.18/0.43 ![B: $i] : (lazy_impl(false, B) = not1(false))),
% 0.18/0.43 inference(skolemize,[status(sab)],[190])).
% 0.18/0.43 tff(192,plain,
% 0.18/0.43 (![B: $i] : (lazy_impl(false, B) = not1(false))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[191, 184])).
% 0.18/0.43 tff(193,plain,
% 0.18/0.43 ((~![B: $i] : (lazy_impl(false, B) = not1(false))) | (lazy_impl(false, P!6) = not1(false))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(194,plain,
% 0.18/0.43 (lazy_impl(false, P!6) = not1(false)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[193, 192])).
% 0.18/0.43 tff(195,assumption,(prop(P!6) = false), introduced(assumption)).
% 0.18/0.43 tff(196,plain,
% 0.18/0.43 (lazy_impl(prop(P!6), P!6) = lazy_impl(false, P!6)),
% 0.18/0.43 inference(monotonicity,[status(thm)],[195])).
% 0.18/0.43 tff(197,plain,
% 0.18/0.43 (lazy_impl(prop(P!6), P!6) = not1(false)),
% 0.18/0.43 inference(transitivity,[status(thm)],[196, 194])).
% 0.18/0.43 tff(198,plain,
% 0.18/0.43 ($false),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[180, 197])).
% 0.18/0.43 tff(199,plain,(~(prop(P!6) = false)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.43 tff(200,plain,
% 0.18/0.43 (^[X: $i] : refl(((prop(X) = false) <=> (~bool(X))) <=> ((prop(X) = false) <=> (~bool(X))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(201,plain,
% 0.18/0.43 (![X: $i] : ((prop(X) = false) <=> (~bool(X))) <=> ![X: $i] : ((prop(X) = false) <=> (~bool(X)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[200])).
% 0.18/0.43 tff(202,plain,
% 0.18/0.43 (![X: $i] : ((prop(X) = false) <=> (~bool(X))) <=> ![X: $i] : ((prop(X) = false) <=> (~bool(X)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(203,axiom,(![X: $i] : ((prop(X) = false) <=> (~bool(X)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','prop_false')).
% 0.18/0.43 tff(204,plain,
% 0.18/0.43 (![X: $i] : ((prop(X) = false) <=> (~bool(X)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.18/0.43 tff(205,plain,(
% 0.18/0.43 ![X: $i] : ((prop(X) = false) <=> (~bool(X)))),
% 0.18/0.43 inference(skolemize,[status(sab)],[204])).
% 0.18/0.43 tff(206,plain,
% 0.18/0.43 (![X: $i] : ((prop(X) = false) <=> (~bool(X)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[205, 201])).
% 0.18/0.43 tff(207,plain,
% 0.18/0.43 ((~![X: $i] : ((prop(X) = false) <=> (~bool(X)))) | ((prop(P!6) = false) <=> (~bool(P!6)))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(208,plain,
% 0.18/0.43 ((prop(P!6) = false) <=> (~bool(P!6))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[207, 206])).
% 0.18/0.43 tff(209,plain,
% 0.18/0.43 ((~((prop(P!6) = false) <=> (~bool(P!6)))) | (prop(P!6) = false) | bool(P!6)),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(210,plain,
% 0.18/0.43 ((prop(P!6) = false) | bool(P!6)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[209, 208])).
% 0.18/0.43 tff(211,plain,
% 0.18/0.43 (bool(P!6)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[210, 199])).
% 0.18/0.43 tff(212,plain,
% 0.18/0.43 (^[X: $i] : refl((bool(X) <=> ((X = false) | (X = not1(false)))) <=> (bool(X) <=> ((X = false) | (X = not1(false)))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(213,plain,
% 0.18/0.43 (![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false)))) <=> ![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[212])).
% 0.18/0.43 tff(214,plain,
% 0.18/0.43 (^[X: $i] : rewrite((bool(X) <=> ((X = false) | (X = true))) <=> (bool(X) <=> ((X = false) | (X = not1(false)))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(215,plain,
% 0.18/0.43 (![X: $i] : (bool(X) <=> ((X = false) | (X = true))) <=> ![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[214])).
% 0.18/0.43 tff(216,plain,
% 0.18/0.43 (![X: $i] : (bool(X) <=> ((X = false) | (X = true))) <=> ![X: $i] : (bool(X) <=> ((X = false) | (X = true)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(217,axiom,(![X: $i] : (bool(X) <=> ((X = false) | (X = true)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','def_bool')).
% 0.18/0.43 tff(218,plain,
% 0.18/0.43 (![X: $i] : (bool(X) <=> ((X = false) | (X = true)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.18/0.43 tff(219,plain,
% 0.18/0.43 (![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[218, 215])).
% 0.18/0.43 tff(220,plain,(
% 0.18/0.43 ![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))),
% 0.18/0.43 inference(skolemize,[status(sab)],[219])).
% 0.18/0.43 tff(221,plain,
% 0.18/0.43 (![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[220, 213])).
% 0.18/0.43 tff(222,plain,
% 0.18/0.43 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(P!6) <=> ((P!6 = false) | (P!6 = not1(false))))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(223,plain,
% 0.18/0.43 (bool(P!6) <=> ((P!6 = false) | (P!6 = not1(false)))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[222, 221])).
% 0.18/0.43 tff(224,plain,
% 0.18/0.43 ((~(bool(P!6) <=> ((P!6 = false) | (P!6 = not1(false))))) | (~bool(P!6)) | ((P!6 = false) | (P!6 = not1(false)))),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(225,plain,
% 0.18/0.43 ((~bool(P!6)) | ((P!6 = false) | (P!6 = not1(false)))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[224, 223])).
% 0.18/0.43 tff(226,plain,
% 0.18/0.43 ((P!6 = false) | (P!6 = not1(false))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[225, 211])).
% 0.18/0.43 tff(227,plain,
% 0.18/0.43 ((~((P!6 = false) | (P!6 = not1(false)))) | (P!6 = false) | (P!6 = not1(false))),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(228,plain,
% 0.18/0.43 ((P!6 = false) | (P!6 = not1(false))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[227, 226])).
% 0.18/0.43 tff(229,plain,
% 0.18/0.43 (P!6 = false),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[228, 182])).
% 0.18/0.43 tff(230,plain,
% 0.18/0.43 (f7(P!6) = f7(false)),
% 0.18/0.43 inference(monotonicity,[status(thm)],[229])).
% 0.18/0.43 tff(231,plain,
% 0.18/0.43 (f7(P!6) = false),
% 0.18/0.43 inference(transitivity,[status(thm)],[230, 93, 84, 42, 30])).
% 0.18/0.43 tff(232,plain,
% 0.18/0.43 (phi(f7(P!6)) = phi(false)),
% 0.18/0.43 inference(monotonicity,[status(thm)],[231])).
% 0.18/0.43 tff(233,plain,
% 0.18/0.43 (phi(false) = phi(f7(P!6))),
% 0.18/0.43 inference(symmetry,[status(thm)],[232])).
% 0.18/0.43 tff(234,plain,
% 0.18/0.43 (false = false2),
% 0.18/0.43 inference(transitivity,[status(thm)],[165, 233, 7])).
% 0.18/0.43 tff(235,plain,
% 0.18/0.43 ((~(false1 = false2)) <=> (~(false = false2))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(236,plain,
% 0.18/0.43 ((~(false1 = false2)) <=> (~(false1 = false2))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(237,axiom,(~(false1 = false2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','false1_false2')).
% 0.18/0.43 tff(238,plain,
% 0.18/0.43 (~(false1 = false2)),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.18/0.43 tff(239,plain,
% 0.18/0.43 (~(false = false2)),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[238, 235])).
% 0.18/0.43 tff(240,plain,
% 0.18/0.43 ($false),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[239, 234])).
% 0.18/0.43 % SZS output end Proof
%------------------------------------------------------------------------------