%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW102+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:36:33 AM UTC 2025
% Result : Theorem 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWW102+1 : TPTP v9.0.0. Released v5.2.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 11:14:33 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.21/0.41 % SZS status Theorem
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 tff(not2_type, type, (
% 0.21/0.41 not2: $i > $i)).
% 0.21/0.41 tff(tptp_fun_P_7_type, type, (
% 0.21/0.41 tptp_fun_P_7: $i)).
% 0.21/0.41 tff(not1_type, type, (
% 0.21/0.41 not1: $i > $i)).
% 0.21/0.41 tff(phi_type, type, (
% 0.21/0.41 phi: $i > $i)).
% 0.21/0.41 tff(impl_type, type, (
% 0.21/0.41 impl: ( $i * $i ) > $i)).
% 0.21/0.41 tff(f7_type, type, (
% 0.21/0.41 f7: $i > $i)).
% 0.21/0.41 tff(tptp_fun_P_6_type, type, (
% 0.21/0.41 tptp_fun_P_6: $i)).
% 0.21/0.41 tff(false2_type, type, (
% 0.21/0.41 false2: $i)).
% 0.21/0.41 tff(forallprefers_type, type, (
% 0.21/0.41 forallprefers: ( $i * $i ) > $o)).
% 0.21/0.41 tff(bool_type, type, (
% 0.21/0.41 bool: $i > $o)).
% 0.21/0.41 tff(true_type, type, (
% 0.21/0.41 true: $i)).
% 0.21/0.41 tff(prop_type, type, (
% 0.21/0.41 prop: $i > $i)).
% 0.21/0.41 tff(false_type, type, (
% 0.21/0.41 false: $i)).
% 0.21/0.41 tff(d_type, type, (
% 0.21/0.41 d: $i > $o)).
% 0.21/0.41 tff(err_type, type, (
% 0.21/0.41 err: $i)).
% 0.21/0.41 tff(lazy_impl_type, type, (
% 0.21/0.41 lazy_impl: ( $i * $i ) > $i)).
% 0.21/0.41 tff(1,plain,
% 0.21/0.41 ((phi(P!7) = impl(P!7, phi(f7(P!6)))) <=> (impl(P!7, phi(f7(P!6))) = phi(P!7))),
% 0.21/0.41 inference(commutativity,[status(thm)],[])).
% 0.21/0.41 tff(2,plain,
% 0.21/0.41 (((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))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(3,plain,
% 0.21/0.41 (?[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))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(4,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')).
% 0.21/0.41 tff(5,plain,
% 0.21/0.41 (?[P: $i] : ((false2 = phi(f7(P))) & (~?[P1: $i] : forallprefers(f7(P1), f7(P))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.41 tff(6,plain,
% 0.21/0.41 ((false2 = phi(f7(P!6))) & ![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.21/0.41 tff(7,plain,
% 0.21/0.41 (false2 = phi(f7(P!6))),
% 0.21/0.41 inference(and_elim,[status(thm)],[6])).
% 0.21/0.41 tff(8,plain,
% 0.21/0.41 (phi(f7(P!6)) = false2),
% 0.21/0.41 inference(symmetry,[status(thm)],[7])).
% 0.21/0.41 tff(9,plain,
% 0.21/0.41 (impl(P!7, phi(f7(P!6))) = impl(P!7, false2)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[8])).
% 0.21/0.41 tff(10,plain,
% 0.21/0.41 (impl(P!7, false2) = impl(P!7, phi(f7(P!6)))),
% 0.21/0.41 inference(symmetry,[status(thm)],[9])).
% 0.21/0.41 tff(11,plain,
% 0.21/0.41 (^[P: $i] : refl((not2(P) = impl(P, false2)) <=> (not2(P) = impl(P, false2)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(12,plain,
% 0.21/0.41 (![P: $i] : (not2(P) = impl(P, false2)) <=> ![P: $i] : (not2(P) = impl(P, false2))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[11])).
% 0.21/0.41 tff(13,plain,
% 0.21/0.41 (![P: $i] : (not2(P) = impl(P, false2)) <=> ![P: $i] : (not2(P) = impl(P, false2))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(14,axiom,(![P: $i] : (not2(P) = impl(P, false2))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','def_not2')).
% 0.21/0.41 tff(15,plain,
% 0.21/0.41 (![P: $i] : (not2(P) = impl(P, false2))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.21/0.41 tff(16,plain,(
% 0.21/0.41 ![P: $i] : (not2(P) = impl(P, false2))),
% 0.21/0.41 inference(skolemize,[status(sab)],[15])).
% 0.21/0.41 tff(17,plain,
% 0.21/0.41 (![P: $i] : (not2(P) = impl(P, false2))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.21/0.41 tff(18,plain,
% 0.21/0.41 ((~![P: $i] : (not2(P) = impl(P, false2))) | (not2(P!7) = impl(P!7, false2))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(19,plain,
% 0.21/0.41 (not2(P!7) = impl(P!7, false2)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.21/0.41 tff(20,plain,
% 0.21/0.41 (not2(P!7) = impl(P!7, phi(f7(P!6)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[19, 10])).
% 0.21/0.41 tff(21,plain,
% 0.21/0.41 (^[X: $i] : refl(((prop(X) = true) <=> bool(X)) <=> ((prop(X) = true) <=> bool(X)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(22,plain,
% 0.21/0.41 (![X: $i] : ((prop(X) = true) <=> bool(X)) <=> ![X: $i] : ((prop(X) = true) <=> bool(X))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[21])).
% 0.21/0.41 tff(23,plain,
% 0.21/0.41 (![X: $i] : ((prop(X) = true) <=> bool(X)) <=> ![X: $i] : ((prop(X) = true) <=> bool(X))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(24,axiom,(![X: $i] : ((prop(X) = true) <=> bool(X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','prop_true')).
% 0.21/0.41 tff(25,plain,
% 0.21/0.41 (![X: $i] : ((prop(X) = true) <=> bool(X))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.21/0.41 tff(26,plain,(
% 0.21/0.41 ![X: $i] : ((prop(X) = true) <=> bool(X))),
% 0.21/0.41 inference(skolemize,[status(sab)],[25])).
% 0.21/0.41 tff(27,plain,
% 0.21/0.41 (![X: $i] : ((prop(X) = true) <=> bool(X))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.21/0.41 tff(28,plain,
% 0.21/0.41 ((~![X: $i] : ((prop(X) = true) <=> bool(X))) | ((prop(P!7) = true) <=> bool(P!7))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(29,plain,
% 0.21/0.41 ((prop(P!7) = true) <=> bool(P!7)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.21/0.41 tff(30,plain,
% 0.21/0.41 ((phi(phi(f7(P!6))) = impl(P!7, phi(f7(P!6)))) <=> (impl(P!7, phi(f7(P!6))) = phi(phi(f7(P!6))))),
% 0.21/0.41 inference(commutativity,[status(thm)],[])).
% 0.21/0.41 tff(31,plain,
% 0.21/0.41 (d(false) <=> d(false)),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(32,axiom,((d(true) & d(false)) & d(err)), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','false_true_err_in_d')).
% 0.21/0.41 tff(33,plain,
% 0.21/0.41 (d(true) & d(false)),
% 0.21/0.41 inference(and_elim,[status(thm)],[32])).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 (d(false)),
% 0.21/0.41 inference(and_elim,[status(thm)],[33])).
% 0.21/0.41 tff(35,plain,
% 0.21/0.41 (d(false)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[34, 31])).
% 0.21/0.41 tff(36,plain,
% 0.21/0.41 ((d(false) | (~(phi(false) = err))) | (~d(false))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(37,plain,
% 0.21/0.41 (d(false) | (~(phi(false) = err))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 (^[X: $i] : refl(((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err))))) <=> ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(39,plain,
% 0.21/0.41 (![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err))))) <=> ![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[38])).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 (^[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)))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 (![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err))) <=> ![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[40])).
% 0.21/0.41 tff(42,plain,
% 0.21/0.41 (![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err))) <=> ![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(43,axiom,(![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','def_phi')).
% 0.21/0.41 tff(44,plain,
% 0.21/0.41 (![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.21/0.41 tff(45,plain,(
% 0.21/0.41 ![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[44])).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 (![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.21/0.41 tff(47,plain,
% 0.21/0.41 (![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.21/0.41 tff(48,plain,
% 0.21/0.41 (((~![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)))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(49,plain,
% 0.21/0.41 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(false)) | (~(phi(false) = false)))) | (~(d(false) | (~(phi(false) = err)))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(50,plain,
% 0.21/0.41 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(false)) | (~(phi(false) = false)))) | (~(d(false) | (~(phi(false) = err))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.21/0.41 tff(51,plain,
% 0.21/0.41 (~((~d(false)) | (~(phi(false) = false)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[50, 47, 37])).
% 0.21/0.41 tff(52,plain,
% 0.21/0.41 (((~d(false)) | (~(phi(false) = false))) | (phi(false) = false)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(53,plain,
% 0.21/0.41 (phi(false) = false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.21/0.41 tff(54,plain,
% 0.21/0.41 (^[B: $i] : refl((lazy_impl(true, B) = phi(B)) <=> (lazy_impl(true, B) = phi(B)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(55,plain,
% 0.21/0.41 (![B: $i] : (lazy_impl(true, B) = phi(B)) <=> ![B: $i] : (lazy_impl(true, B) = phi(B))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[54])).
% 0.21/0.41 tff(56,plain,
% 0.21/0.41 (![B: $i] : (lazy_impl(true, B) = phi(B)) <=> ![B: $i] : (lazy_impl(true, B) = phi(B))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(57,axiom,(![B: $i] : (lazy_impl(true, B) = phi(B))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','lazy_impl_axiom3')).
% 0.21/0.41 tff(58,plain,
% 0.21/0.41 (![B: $i] : (lazy_impl(true, B) = phi(B))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.21/0.41 tff(59,plain,(
% 0.21/0.41 ![B: $i] : (lazy_impl(true, B) = phi(B))),
% 0.21/0.41 inference(skolemize,[status(sab)],[58])).
% 0.21/0.41 tff(60,plain,
% 0.21/0.41 (![B: $i] : (lazy_impl(true, B) = phi(B))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.21/0.41 tff(61,plain,
% 0.21/0.41 ((~![B: $i] : (lazy_impl(true, B) = phi(B))) | (lazy_impl(true, false) = phi(false))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(62,plain,
% 0.21/0.41 (lazy_impl(true, false) = phi(false)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.21/0.41 tff(63,plain,
% 0.21/0.41 ((~![X: $i] : ((prop(X) = true) <=> bool(X))) | ((prop(false) = true) <=> bool(false))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(64,plain,
% 0.21/0.41 ((prop(false) = true) <=> bool(false)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[63, 27])).
% 0.21/0.41 tff(65,plain,
% 0.21/0.41 ((not1(false) = true) <=> (not1(false) = true)),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(66,axiom,(not1(false) = true), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','not1_axiom2')).
% 0.21/0.41 tff(67,plain,
% 0.21/0.41 (not1(false) = true),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.21/0.41 tff(68,plain,
% 0.21/0.41 ((not1(false) = phi(false)) <=> (true = false)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[67, 53])).
% 0.21/0.41 tff(69,plain,
% 0.21/0.41 ((true = false) <=> (not1(false) = phi(false))),
% 0.21/0.41 inference(symmetry,[status(thm)],[68])).
% 0.21/0.41 tff(70,plain,
% 0.21/0.41 ((~(true = false)) <=> (~(not1(false) = phi(false)))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[69])).
% 0.21/0.41 tff(71,plain,
% 0.21/0.41 ((~(true = false)) <=> (~(true = false))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(72,axiom,(((~(true = false)) & (~(true = err))) & (~(false = err))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','distinct_false_true_err')).
% 0.21/0.41 tff(73,plain,
% 0.21/0.41 ((~(true = false)) & (~(true = err))),
% 0.21/0.41 inference(and_elim,[status(thm)],[72])).
% 0.21/0.41 tff(74,plain,
% 0.21/0.41 (~(true = false)),
% 0.21/0.41 inference(and_elim,[status(thm)],[73])).
% 0.21/0.41 tff(75,plain,
% 0.21/0.41 (~(true = false)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[74, 71])).
% 0.21/0.41 tff(76,plain,
% 0.21/0.41 (~(not1(false) = phi(false))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[75, 70])).
% 0.21/0.41 tff(77,plain,
% 0.21/0.41 (^[A: $i] : refl((bool(A) | (not1(A) = phi(A))) <=> (bool(A) | (not1(A) = phi(A))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(78,plain,
% 0.21/0.41 (![A: $i] : (bool(A) | (not1(A) = phi(A))) <=> ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[77])).
% 0.21/0.41 tff(79,plain,
% 0.21/0.41 (![A: $i] : (bool(A) | (not1(A) = phi(A))) <=> ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(80,plain,
% 0.21/0.41 (^[A: $i] : rewrite(((~bool(A)) => (not1(A) = phi(A))) <=> (bool(A) | (not1(A) = phi(A))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(81,plain,
% 0.21/0.42 (![A: $i] : ((~bool(A)) => (not1(A) = phi(A))) <=> ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[80])).
% 0.21/0.42 tff(82,axiom,(![A: $i] : ((~bool(A)) => (not1(A) = phi(A)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','not1_axiom1')).
% 0.21/0.42 tff(83,plain,
% 0.21/0.42 (![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.21/0.42 tff(84,plain,
% 0.21/0.42 (![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.21/0.42 tff(85,plain,(
% 0.21/0.42 ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[84])).
% 0.21/0.42 tff(86,plain,
% 0.21/0.42 (![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.21/0.42 tff(87,plain,
% 0.21/0.42 (((~![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)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(88,plain,
% 0.21/0.42 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | (bool(false) | (not1(false) = phi(false)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(89,plain,
% 0.21/0.42 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | bool(false) | (not1(false) = phi(false))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.21/0.42 tff(90,plain,
% 0.21/0.42 (bool(false) | (not1(false) = phi(false))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[89, 86])).
% 0.21/0.42 tff(91,plain,
% 0.21/0.42 (bool(false)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[90, 76])).
% 0.21/0.42 tff(92,plain,
% 0.21/0.42 ((~((prop(false) = true) <=> bool(false))) | (prop(false) = true) | (~bool(false))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(93,plain,
% 0.21/0.42 ((~((prop(false) = true) <=> bool(false))) | (prop(false) = true)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.21/0.42 tff(94,plain,
% 0.21/0.42 (prop(false) = true),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[93, 64])).
% 0.21/0.42 tff(95,plain,
% 0.21/0.42 (lazy_impl(prop(false), false) = lazy_impl(true, false)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[94])).
% 0.21/0.42 tff(96,plain,
% 0.21/0.42 (^[P: $i] : refl((f7(P) = lazy_impl(prop(P), P)) <=> (f7(P) = lazy_impl(prop(P), P)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(97,plain,
% 0.21/0.42 (![P: $i] : (f7(P) = lazy_impl(prop(P), P)) <=> ![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[96])).
% 0.21/0.42 tff(98,plain,
% 0.21/0.42 (![P: $i] : (f7(P) = lazy_impl(prop(P), P)) <=> ![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(99,axiom,(![P: $i] : (f7(P) = lazy_impl(prop(P), P))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','def_f7')).
% 0.21/0.42 tff(100,plain,
% 0.21/0.42 (![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.21/0.42 tff(101,plain,(
% 0.21/0.42 ![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 0.21/0.42 inference(skolemize,[status(sab)],[100])).
% 0.21/0.42 tff(102,plain,
% 0.21/0.42 (![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.21/0.42 tff(103,plain,
% 0.21/0.42 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(false) = lazy_impl(prop(false), false))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(104,plain,
% 0.21/0.42 (f7(false) = lazy_impl(prop(false), false)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.21/0.42 tff(105,plain,
% 0.21/0.42 (^[B: $i] : refl((lazy_impl(false, B) = true) <=> (lazy_impl(false, B) = true))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(106,plain,
% 0.21/0.42 (![B: $i] : (lazy_impl(false, B) = true) <=> ![B: $i] : (lazy_impl(false, B) = true)),
% 0.21/0.42 inference(quant_intro,[status(thm)],[105])).
% 0.21/0.42 tff(107,plain,
% 0.21/0.42 (![B: $i] : (lazy_impl(false, B) = true) <=> ![B: $i] : (lazy_impl(false, B) = true)),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(108,axiom,(![B: $i] : (lazy_impl(false, B) = true)), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','lazy_impl_axiom2')).
% 0.21/0.42 tff(109,plain,
% 0.21/0.42 (![B: $i] : (lazy_impl(false, B) = true)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.21/0.42 tff(110,plain,(
% 0.21/0.42 ![B: $i] : (lazy_impl(false, B) = true)),
% 0.21/0.42 inference(skolemize,[status(sab)],[109])).
% 0.21/0.42 tff(111,plain,
% 0.21/0.42 (![B: $i] : (lazy_impl(false, B) = true)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.21/0.42 tff(112,plain,
% 0.21/0.42 ((~![B: $i] : (lazy_impl(false, B) = true)) | (lazy_impl(false, P!6) = true)),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(113,plain,
% 0.21/0.42 (lazy_impl(false, P!6) = true),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.21/0.42 tff(114,assumption,(prop(P!6) = false), introduced(assumption)).
% 0.21/0.42 tff(115,plain,
% 0.21/0.42 (lazy_impl(prop(P!6), P!6) = lazy_impl(false, P!6)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[114])).
% 0.21/0.42 tff(116,plain,
% 0.21/0.42 (lazy_impl(prop(P!6), P!6) = true),
% 0.21/0.42 inference(transitivity,[status(thm)],[115, 113])).
% 0.21/0.42 tff(117,plain,
% 0.21/0.42 (^[X: $i, Y: $i] : refl((forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))))) <=> (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(118,plain,
% 0.21/0.42 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))))) <=> ![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[117])).
% 0.21/0.42 tff(119,plain,
% 0.21/0.42 (^[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) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(120,plain,
% 0.21/0.42 (![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(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[119])).
% 0.21/0.42 tff(121,plain,
% 0.21/0.42 (![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))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(122,plain,
% 0.21/0.42 (^[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)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(123,plain,
% 0.21/0.42 (![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))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[122])).
% 0.21/0.42 tff(124,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')).
% 0.21/0.42 tff(125,plain,
% 0.21/0.42 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.21/0.42 tff(126,plain,
% 0.21/0.42 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[125, 121])).
% 0.21/0.42 tff(127,plain,(
% 0.21/0.42 ![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[126])).
% 0.21/0.42 tff(128,plain,
% 0.21/0.42 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[127, 120])).
% 0.21/0.42 tff(129,plain,
% 0.21/0.42 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[128, 118])).
% 0.21/0.42 tff(130,plain,
% 0.21/0.42 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((lazy_impl(prop(P!6), P!6) = true) | (~(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)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((lazy_impl(prop(P!6), P!6) = true) | (~(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))))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(131,plain,
% 0.21/0.42 ((forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~((~(false = false)) | (~(lazy_impl(prop(P!6), P!6) = true)))) | (~(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)))))) <=> (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((lazy_impl(prop(P!6), P!6) = true) | (~(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)))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(132,plain,
% 0.21/0.42 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~((~(false = false)) | (~(lazy_impl(prop(P!6), P!6) = true)))) | (~(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))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((lazy_impl(prop(P!6), P!6) = true) | (~(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))))))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[131])).
% 0.21/0.42 tff(133,plain,
% 0.21/0.42 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~((~(false = false)) | (~(lazy_impl(prop(P!6), P!6) = true)))) | (~(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))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((lazy_impl(prop(P!6), P!6) = true) | (~(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))))))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[132, 130])).
% 0.21/0.42 tff(134,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~((~(false = false)) | (~(lazy_impl(prop(P!6), P!6) = true)))) | (~(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))))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(135,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((lazy_impl(prop(P!6), P!6) = true) | (~(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)))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.21/0.43 tff(136,plain,
% 0.21/0.43 (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((lazy_impl(prop(P!6), P!6) = true) | (~(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))))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[135, 129])).
% 0.21/0.43 tff(137,plain,
% 0.21/0.43 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(P!6) = lazy_impl(prop(P!6), P!6))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(138,plain,
% 0.21/0.43 (f7(P!6) = lazy_impl(prop(P!6), P!6)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[137, 102])).
% 0.21/0.43 tff(139,plain,
% 0.21/0.43 (lazy_impl(prop(P!6), P!6) = f7(P!6)),
% 0.21/0.43 inference(symmetry,[status(thm)],[138])).
% 0.21/0.43 tff(140,plain,
% 0.21/0.43 (lazy_impl(prop(false), false) = f7(false)),
% 0.21/0.43 inference(symmetry,[status(thm)],[104])).
% 0.21/0.43 tff(141,plain,
% 0.21/0.43 (lazy_impl(true, false) = lazy_impl(prop(false), false)),
% 0.21/0.43 inference(symmetry,[status(thm)],[95])).
% 0.21/0.43 tff(142,plain,
% 0.21/0.43 (phi(false) = lazy_impl(true, false)),
% 0.21/0.43 inference(symmetry,[status(thm)],[62])).
% 0.21/0.43 tff(143,plain,
% 0.21/0.43 (false = phi(false)),
% 0.21/0.43 inference(symmetry,[status(thm)],[53])).
% 0.21/0.43 tff(144,plain,
% 0.21/0.43 (false = f7(false)),
% 0.21/0.43 inference(transitivity,[status(thm)],[143, 142, 141, 140])).
% 0.21/0.43 tff(145,plain,
% 0.21/0.43 (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> forallprefers(f7(false), f7(P!6))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[144, 139])).
% 0.21/0.43 tff(146,plain,
% 0.21/0.43 (forallprefers(f7(false), f7(P!6)) <=> forallprefers(false, lazy_impl(prop(P!6), P!6))),
% 0.21/0.43 inference(symmetry,[status(thm)],[145])).
% 0.21/0.43 tff(147,plain,
% 0.21/0.43 ((~forallprefers(f7(false), f7(P!6))) <=> (~forallprefers(false, lazy_impl(prop(P!6), P!6)))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[146])).
% 0.21/0.43 tff(148,plain,
% 0.21/0.43 (^[P1: $i] : refl((~forallprefers(f7(P1), f7(P!6))) <=> (~forallprefers(f7(P1), f7(P!6))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(149,plain,
% 0.21/0.43 (![P1: $i] : (~forallprefers(f7(P1), f7(P!6))) <=> ![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[148])).
% 0.21/0.43 tff(150,plain,
% 0.21/0.43 (![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 0.21/0.43 inference(and_elim,[status(thm)],[6])).
% 0.21/0.43 tff(151,plain,
% 0.21/0.43 (![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.21/0.43 tff(152,plain,
% 0.21/0.43 ((~![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))) | (~forallprefers(f7(false), f7(P!6)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(153,plain,
% 0.21/0.43 (~forallprefers(f7(false), f7(P!6))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.21/0.43 tff(154,plain,
% 0.21/0.43 (~forallprefers(false, lazy_impl(prop(P!6), P!6))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[153, 147])).
% 0.21/0.43 tff(155,plain,
% 0.21/0.43 ((~(forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((lazy_impl(prop(P!6), P!6) = true) | (~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6)))))))) | forallprefers(false, lazy_impl(prop(P!6), P!6)) | (~((lazy_impl(prop(P!6), P!6) = true) | (~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6)))))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(156,plain,
% 0.21/0.43 (~((lazy_impl(prop(P!6), P!6) = true) | (~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[155, 154, 136])).
% 0.21/0.43 tff(157,plain,
% 0.21/0.43 (((lazy_impl(prop(P!6), P!6) = true) | (~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6)))))) | (~(lazy_impl(prop(P!6), P!6) = true))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(158,plain,
% 0.21/0.43 (~(lazy_impl(prop(P!6), P!6) = true)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[157, 156])).
% 0.21/0.43 tff(159,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[158, 116])).
% 0.21/0.43 tff(160,plain,(~(prop(P!6) = false)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(161,plain,
% 0.21/0.43 (^[X: $i] : refl((~(bool(X) <=> (prop(X) = false))) <=> (~(bool(X) <=> (prop(X) = false))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(162,plain,
% 0.21/0.43 (![X: $i] : (~(bool(X) <=> (prop(X) = false))) <=> ![X: $i] : (~(bool(X) <=> (prop(X) = false)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[161])).
% 0.21/0.43 tff(163,plain,
% 0.21/0.43 (![X: $i] : (~(bool(X) <=> (prop(X) = false))) <=> ![X: $i] : (~(bool(X) <=> (prop(X) = false)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(164,plain,
% 0.21/0.43 (^[X: $i] : trans(rewrite(((prop(X) = false) <=> (~bool(X))) <=> (~(bool(X) <=> (prop(X) = false)))), rewrite((~(bool(X) <=> (prop(X) = false))) <=> (~(bool(X) <=> (prop(X) = false)))), (((prop(X) = false) <=> (~bool(X))) <=> (~(bool(X) <=> (prop(X) = false)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(165,plain,
% 0.21/0.43 (![X: $i] : ((prop(X) = false) <=> (~bool(X))) <=> ![X: $i] : (~(bool(X) <=> (prop(X) = false)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[164])).
% 0.21/0.43 tff(166,axiom,(![X: $i] : ((prop(X) = false) <=> (~bool(X)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','prop_false')).
% 0.21/0.43 tff(167,plain,
% 0.21/0.43 (![X: $i] : (~(bool(X) <=> (prop(X) = false)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.21/0.43 tff(168,plain,
% 0.21/0.43 (![X: $i] : (~(bool(X) <=> (prop(X) = false)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[167, 163])).
% 0.21/0.43 tff(169,plain,(
% 0.21/0.43 ![X: $i] : (~(bool(X) <=> (prop(X) = false)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[168])).
% 0.21/0.43 tff(170,plain,
% 0.21/0.43 (![X: $i] : (~(bool(X) <=> (prop(X) = false)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[169, 162])).
% 0.21/0.43 tff(171,plain,
% 0.21/0.43 ((~![X: $i] : (~(bool(X) <=> (prop(X) = false)))) | (~(bool(P!6) <=> (prop(P!6) = false)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(172,plain,
% 0.21/0.43 (~(bool(P!6) <=> (prop(P!6) = false))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[171, 170])).
% 0.21/0.43 tff(173,plain,
% 0.21/0.43 ((bool(P!6) <=> (prop(P!6) = false)) | bool(P!6) | (prop(P!6) = false)),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(174,plain,
% 0.21/0.43 (bool(P!6) | (prop(P!6) = false)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[173, 172])).
% 0.21/0.43 tff(175,plain,
% 0.21/0.43 (bool(P!6)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[174, 160])).
% 0.21/0.43 tff(176,plain,
% 0.21/0.43 (^[X: $i] : refl((bool(X) <=> ((X = false) | (X = true))) <=> (bool(X) <=> ((X = false) | (X = true))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(177,plain,
% 0.21/0.43 (![X: $i] : (bool(X) <=> ((X = false) | (X = true))) <=> ![X: $i] : (bool(X) <=> ((X = false) | (X = true)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[176])).
% 0.21/0.43 tff(178,plain,
% 0.21/0.43 (![X: $i] : (bool(X) <=> ((X = false) | (X = true))) <=> ![X: $i] : (bool(X) <=> ((X = false) | (X = true)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(179,axiom,(![X: $i] : (bool(X) <=> ((X = false) | (X = true)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','def_bool')).
% 0.21/0.43 tff(180,plain,
% 0.21/0.43 (![X: $i] : (bool(X) <=> ((X = false) | (X = true)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.21/0.43 tff(181,plain,(
% 0.21/0.43 ![X: $i] : (bool(X) <=> ((X = false) | (X = true)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[180])).
% 0.21/0.43 tff(182,plain,
% 0.21/0.43 (![X: $i] : (bool(X) <=> ((X = false) | (X = true)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[181, 177])).
% 0.21/0.43 tff(183,plain,
% 0.21/0.43 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = true)))) | (bool(P!6) <=> ((P!6 = false) | (P!6 = true)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(184,plain,
% 0.21/0.43 (bool(P!6) <=> ((P!6 = false) | (P!6 = true))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[183, 182])).
% 0.21/0.43 tff(185,plain,
% 0.21/0.43 ((~(bool(P!6) <=> ((P!6 = false) | (P!6 = true)))) | (~bool(P!6)) | ((P!6 = false) | (P!6 = true))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(186,plain,
% 0.21/0.43 ((~bool(P!6)) | ((P!6 = false) | (P!6 = true))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[185, 184])).
% 0.21/0.43 tff(187,plain,
% 0.21/0.43 ((P!6 = false) | (P!6 = true)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[186, 175])).
% 0.21/0.43 tff(188,plain,
% 0.21/0.43 (d(true) <=> d(true)),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(189,plain,
% 0.21/0.43 (d(true)),
% 0.21/0.43 inference(and_elim,[status(thm)],[33])).
% 0.21/0.43 tff(190,plain,
% 0.21/0.43 (d(true)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.21/0.43 tff(191,plain,
% 0.21/0.43 ((d(true) | (~(phi(true) = err))) | (~d(true))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(192,plain,
% 0.21/0.43 (d(true) | (~(phi(true) = err))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[191, 190])).
% 0.21/0.43 tff(193,plain,
% 0.21/0.43 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(true)) | (~(phi(true) = true)))) | (~(d(true) | (~(phi(true) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(true)) | (~(phi(true) = true)))) | (~(d(true) | (~(phi(true) = err)))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(194,plain,
% 0.21/0.43 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(true)) | (~(phi(true) = true)))) | (~(d(true) | (~(phi(true) = err)))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(195,plain,
% 0.21/0.43 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(true)) | (~(phi(true) = true)))) | (~(d(true) | (~(phi(true) = err))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.21/0.43 tff(196,plain,
% 0.21/0.43 (~((~d(true)) | (~(phi(true) = true)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[195, 47, 192])).
% 0.21/0.43 tff(197,plain,
% 0.21/0.43 (((~d(true)) | (~(phi(true) = true))) | (phi(true) = true)),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(198,plain,
% 0.21/0.43 (phi(true) = true),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[197, 196])).
% 0.21/0.43 tff(199,plain,
% 0.21/0.43 ((~![B: $i] : (lazy_impl(true, B) = phi(B))) | (lazy_impl(true, true) = phi(true))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(200,plain,
% 0.21/0.43 (lazy_impl(true, true) = phi(true)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[199, 60])).
% 0.21/0.43 tff(201,plain,
% 0.21/0.43 ((~![X: $i] : ((prop(X) = true) <=> bool(X))) | ((prop(true) = true) <=> bool(true))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(202,plain,
% 0.21/0.43 ((prop(true) = true) <=> bool(true)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[201, 27])).
% 0.21/0.43 tff(203,plain,
% 0.21/0.43 ((false = true) <=> (true = false)),
% 0.21/0.43 inference(commutativity,[status(thm)],[])).
% 0.21/0.43 tff(204,plain,
% 0.21/0.43 ((not1(true) = false) <=> (not1(true) = false)),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(205,axiom,(not1(true) = false), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','not1_axiom3')).
% 0.21/0.43 tff(206,plain,
% 0.21/0.43 (not1(true) = false),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.21/0.43 tff(207,plain,
% 0.21/0.43 ((not1(true) = phi(true)) <=> (false = true)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[206, 198])).
% 0.21/0.43 tff(208,plain,
% 0.21/0.43 ((not1(true) = phi(true)) <=> (true = false)),
% 0.21/0.43 inference(transitivity,[status(thm)],[207, 203])).
% 0.21/0.43 tff(209,plain,
% 0.21/0.43 ((true = false) <=> (not1(true) = phi(true))),
% 0.21/0.43 inference(symmetry,[status(thm)],[208])).
% 0.21/0.43 tff(210,plain,
% 0.21/0.43 ((~(true = false)) <=> (~(not1(true) = phi(true)))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[209])).
% 0.21/0.43 tff(211,plain,
% 0.21/0.43 (~(not1(true) = phi(true))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[75, 210])).
% 0.21/0.43 tff(212,plain,
% 0.21/0.43 (((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | (bool(true) | (not1(true) = phi(true)))) <=> ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | bool(true) | (not1(true) = phi(true)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(213,plain,
% 0.21/0.43 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | (bool(true) | (not1(true) = phi(true)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(214,plain,
% 0.21/0.43 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | bool(true) | (not1(true) = phi(true))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.21/0.43 tff(215,plain,
% 0.21/0.43 (bool(true) | (not1(true) = phi(true))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[214, 86])).
% 0.21/0.43 tff(216,plain,
% 0.21/0.43 (bool(true)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[215, 211])).
% 0.21/0.43 tff(217,plain,
% 0.21/0.43 ((~((prop(true) = true) <=> bool(true))) | (prop(true) = true) | (~bool(true))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(218,plain,
% 0.21/0.43 ((~((prop(true) = true) <=> bool(true))) | (prop(true) = true)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[217, 216])).
% 0.21/0.43 tff(219,plain,
% 0.21/0.43 (prop(true) = true),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[218, 202])).
% 0.21/0.43 tff(220,plain,
% 0.21/0.43 (lazy_impl(prop(true), true) = lazy_impl(true, true)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[219])).
% 0.21/0.43 tff(221,plain,
% 0.21/0.43 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(true) = lazy_impl(prop(true), true))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(222,plain,
% 0.21/0.43 (f7(true) = lazy_impl(prop(true), true)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[221, 102])).
% 0.21/0.43 tff(223,assumption,(P!6 = true), introduced(assumption)).
% 0.21/0.43 tff(224,plain,
% 0.21/0.43 (f7(P!6) = f7(true)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[223])).
% 0.21/0.43 tff(225,plain,
% 0.21/0.43 (lazy_impl(prop(P!6), P!6) = true),
% 0.21/0.43 inference(transitivity,[status(thm)],[139, 224, 222, 220, 200, 198])).
% 0.21/0.43 tff(226,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[158, 225])).
% 0.21/0.43 tff(227,plain,(~(P!6 = true)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(228,plain,
% 0.21/0.43 ((~((P!6 = false) | (P!6 = true))) | (P!6 = false) | (P!6 = true)),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(229,plain,
% 0.21/0.43 (P!6 = false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[228, 227, 187])).
% 0.21/0.43 tff(230,plain,
% 0.21/0.43 (f7(P!6) = f7(false)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[229])).
% 0.21/0.43 tff(231,plain,
% 0.21/0.43 (f7(P!6) = false),
% 0.21/0.43 inference(transitivity,[status(thm)],[230, 104, 95, 62, 53])).
% 0.21/0.43 tff(232,plain,
% 0.21/0.43 (phi(f7(P!6)) = phi(false)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[231])).
% 0.21/0.43 tff(233,plain,
% 0.21/0.43 (phi(f7(P!6)) = false),
% 0.21/0.43 inference(transitivity,[status(thm)],[232, 53])).
% 0.21/0.43 tff(234,plain,
% 0.21/0.43 (phi(phi(f7(P!6))) = phi(false)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[233])).
% 0.21/0.43 tff(235,plain,
% 0.21/0.43 (phi(false) = phi(phi(f7(P!6)))),
% 0.21/0.43 inference(symmetry,[status(thm)],[234])).
% 0.21/0.43 tff(236,plain,
% 0.21/0.43 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = true)))) | (bool(lazy_impl(prop(P!7), P!7)) <=> ((lazy_impl(prop(P!7), P!7) = false) | (lazy_impl(prop(P!7), P!7) = true)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(237,plain,
% 0.21/0.43 (bool(lazy_impl(prop(P!7), P!7)) <=> ((lazy_impl(prop(P!7), P!7) = false) | (lazy_impl(prop(P!7), P!7) = true))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[236, 182])).
% 0.21/0.43 tff(238,plain,
% 0.21/0.43 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(P!7), P!7), false) <=> ((~((~(lazy_impl(prop(P!7), P!7) = false)) | (~(false = true)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7))))) | (~((~d(false)) | d(lazy_impl(prop(P!7), P!7))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(P!7), P!7), false) <=> ((~((~(lazy_impl(prop(P!7), P!7) = false)) | (~(false = true)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7))))) | (~((~d(false)) | d(lazy_impl(prop(P!7), P!7)))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(239,plain,
% 0.21/0.43 ((forallprefers(lazy_impl(prop(P!7), P!7), false) <=> ((~((~(lazy_impl(prop(P!7), P!7) = false)) | (~(false = true)))) | (~(d(lazy_impl(prop(P!7), P!7)) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7))))))) <=> (forallprefers(lazy_impl(prop(P!7), P!7), false) <=> ((~((~(lazy_impl(prop(P!7), P!7) = false)) | (~(false = true)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7))))) | (~((~d(false)) | d(lazy_impl(prop(P!7), P!7))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(240,plain,
% 0.21/0.44 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(P!7), P!7), false) <=> ((~((~(lazy_impl(prop(P!7), P!7) = false)) | (~(false = true)))) | (~(d(lazy_impl(prop(P!7), P!7)) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(P!7), P!7), false) <=> ((~((~(lazy_impl(prop(P!7), P!7) = false)) | (~(false = true)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7))))) | (~((~d(false)) | d(lazy_impl(prop(P!7), P!7)))))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[239])).
% 0.21/0.44 tff(241,plain,
% 0.21/0.44 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(P!7), P!7), false) <=> ((~((~(lazy_impl(prop(P!7), P!7) = false)) | (~(false = true)))) | (~(d(lazy_impl(prop(P!7), P!7)) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(P!7), P!7), false) <=> ((~((~(lazy_impl(prop(P!7), P!7) = false)) | (~(false = true)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7))))) | (~((~d(false)) | d(lazy_impl(prop(P!7), P!7)))))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[240, 238])).
% 0.21/0.44 tff(242,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(P!7), P!7), false) <=> ((~((~(lazy_impl(prop(P!7), P!7) = false)) | (~(false = true)))) | (~(d(lazy_impl(prop(P!7), P!7)) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7)))))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(243,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(P!7), P!7), false) <=> ((~((~(lazy_impl(prop(P!7), P!7) = false)) | (~(false = true)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7))))) | (~((~d(false)) | d(lazy_impl(prop(P!7), P!7))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.21/0.44 tff(244,plain,
% 0.21/0.44 (forallprefers(lazy_impl(prop(P!7), P!7), false) <=> ((~((~(lazy_impl(prop(P!7), P!7) = false)) | (~(false = true)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7))))) | (~((~d(false)) | d(lazy_impl(prop(P!7), P!7)))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[243, 129])).
% 0.21/0.44 tff(245,plain,
% 0.21/0.44 (f7(false) = f7(P!6)),
% 0.21/0.44 inference(symmetry,[status(thm)],[230])).
% 0.21/0.44 tff(246,plain,
% 0.21/0.44 (false = f7(P!6)),
% 0.21/0.44 inference(transitivity,[status(thm)],[143, 142, 141, 140, 245])).
% 0.21/0.44 tff(247,plain,
% 0.21/0.44 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(P!7) = lazy_impl(prop(P!7), P!7))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(248,plain,
% 0.21/0.44 (f7(P!7) = lazy_impl(prop(P!7), P!7)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[247, 102])).
% 0.21/0.44 tff(249,plain,
% 0.21/0.44 (lazy_impl(prop(P!7), P!7) = f7(P!7)),
% 0.21/0.44 inference(symmetry,[status(thm)],[248])).
% 0.21/0.44 tff(250,plain,
% 0.21/0.44 (forallprefers(lazy_impl(prop(P!7), P!7), false) <=> forallprefers(f7(P!7), f7(P!6))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[249, 246])).
% 0.21/0.44 tff(251,plain,
% 0.21/0.44 (forallprefers(f7(P!7), f7(P!6)) <=> forallprefers(lazy_impl(prop(P!7), P!7), false)),
% 0.21/0.44 inference(symmetry,[status(thm)],[250])).
% 0.21/0.44 tff(252,plain,
% 0.21/0.44 ((~forallprefers(f7(P!7), f7(P!6))) <=> (~forallprefers(lazy_impl(prop(P!7), P!7), false))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[251])).
% 0.21/0.44 tff(253,plain,
% 0.21/0.44 ((~![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))) | (~forallprefers(f7(P!7), f7(P!6)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(254,plain,
% 0.21/0.44 (~forallprefers(f7(P!7), f7(P!6))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[253, 151])).
% 0.21/0.44 tff(255,plain,
% 0.21/0.44 (~forallprefers(lazy_impl(prop(P!7), P!7), false)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[254, 252])).
% 0.21/0.44 tff(256,plain,
% 0.21/0.44 ((~(forallprefers(lazy_impl(prop(P!7), P!7), false) <=> ((~((~(lazy_impl(prop(P!7), P!7) = false)) | (~(false = true)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7))))) | (~((~d(false)) | d(lazy_impl(prop(P!7), P!7))))))) | forallprefers(lazy_impl(prop(P!7), P!7), false) | (~((~((~(lazy_impl(prop(P!7), P!7) = false)) | (~(false = true)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7))))) | (~((~d(false)) | d(lazy_impl(prop(P!7), P!7))))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(257,plain,
% 0.21/0.44 (~((~((~(lazy_impl(prop(P!7), P!7) = false)) | (~(false = true)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7))))) | (~((~d(false)) | d(lazy_impl(prop(P!7), P!7)))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[256, 255, 244])).
% 0.21/0.44 tff(258,plain,
% 0.21/0.44 (((~((~(lazy_impl(prop(P!7), P!7) = false)) | (~(false = true)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7))))) | (~((~d(false)) | d(lazy_impl(prop(P!7), P!7))))) | ((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(259,plain,
% 0.21/0.44 ((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[258, 257])).
% 0.21/0.44 tff(260,plain,
% 0.21/0.44 (((~((~(lazy_impl(prop(P!7), P!7) = false)) | (~(false = true)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7))))) | (~((~d(false)) | d(lazy_impl(prop(P!7), P!7))))) | ((~d(false)) | d(lazy_impl(prop(P!7), P!7)))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(261,plain,
% 0.21/0.44 ((~d(false)) | d(lazy_impl(prop(P!7), P!7))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[260, 257])).
% 0.21/0.44 tff(262,plain,
% 0.21/0.44 ((~((~d(false)) | d(lazy_impl(prop(P!7), P!7)))) | (~d(false)) | d(lazy_impl(prop(P!7), P!7))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(263,plain,
% 0.21/0.44 ((~((~d(false)) | d(lazy_impl(prop(P!7), P!7)))) | d(lazy_impl(prop(P!7), P!7))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[262, 35])).
% 0.21/0.44 tff(264,plain,
% 0.21/0.44 (d(lazy_impl(prop(P!7), P!7))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[263, 261])).
% 0.21/0.44 tff(265,plain,
% 0.21/0.44 ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7))))) | (~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7)))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(266,plain,
% 0.21/0.44 ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7))))) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[265, 35, 91])).
% 0.21/0.44 tff(267,plain,
% 0.21/0.44 (bool(lazy_impl(prop(P!7), P!7))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[266, 264, 259])).
% 0.21/0.44 tff(268,plain,
% 0.21/0.44 ((~(bool(lazy_impl(prop(P!7), P!7)) <=> ((lazy_impl(prop(P!7), P!7) = false) | (lazy_impl(prop(P!7), P!7) = true)))) | (~bool(lazy_impl(prop(P!7), P!7))) | ((lazy_impl(prop(P!7), P!7) = false) | (lazy_impl(prop(P!7), P!7) = true))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(269,plain,
% 0.21/0.44 ((~(bool(lazy_impl(prop(P!7), P!7)) <=> ((lazy_impl(prop(P!7), P!7) = false) | (lazy_impl(prop(P!7), P!7) = true)))) | ((lazy_impl(prop(P!7), P!7) = false) | (lazy_impl(prop(P!7), P!7) = true))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[268, 267])).
% 0.21/0.44 tff(270,plain,
% 0.21/0.44 ((lazy_impl(prop(P!7), P!7) = false) | (lazy_impl(prop(P!7), P!7) = true)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[269, 237])).
% 0.21/0.44 tff(271,assumption,(prop(P!7) = true), introduced(assumption)).
% 0.21/0.44 tff(272,assumption,(lazy_impl(prop(P!7), P!7) = false), introduced(assumption)).
% 0.21/0.44 tff(273,plain,
% 0.21/0.44 (true = prop(P!7)),
% 0.21/0.44 inference(symmetry,[status(thm)],[271])).
% 0.21/0.44 tff(274,plain,
% 0.21/0.44 (lazy_impl(true, P!7) = lazy_impl(prop(P!7), P!7)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[273])).
% 0.21/0.44 tff(275,plain,
% 0.21/0.44 ((~![B: $i] : (lazy_impl(true, B) = phi(B))) | (lazy_impl(true, P!7) = phi(P!7))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(276,plain,
% 0.21/0.44 (lazy_impl(true, P!7) = phi(P!7)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[275, 60])).
% 0.21/0.44 tff(277,plain,
% 0.21/0.44 (phi(P!7) = lazy_impl(true, P!7)),
% 0.21/0.44 inference(symmetry,[status(thm)],[276])).
% 0.21/0.44 tff(278,plain,
% 0.21/0.44 (phi(P!7) = false),
% 0.21/0.44 inference(transitivity,[status(thm)],[277, 274, 272])).
% 0.21/0.44 tff(279,plain,
% 0.21/0.44 ((phi(P!7) = err) <=> (false = err)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[278])).
% 0.21/0.44 tff(280,plain,
% 0.21/0.44 ((false = err) <=> (phi(P!7) = err)),
% 0.21/0.44 inference(symmetry,[status(thm)],[279])).
% 0.21/0.44 tff(281,plain,
% 0.21/0.44 ((~(false = err)) <=> (~(phi(P!7) = err))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[280])).
% 0.21/0.44 tff(282,plain,
% 0.21/0.44 ((~(false = err)) <=> (~(false = err))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(283,plain,
% 0.21/0.44 (~(false = err)),
% 0.21/0.44 inference(and_elim,[status(thm)],[72])).
% 0.21/0.44 tff(284,plain,
% 0.21/0.44 (~(false = err)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[283, 282])).
% 0.21/0.44 tff(285,plain,
% 0.21/0.44 (~(phi(P!7) = err)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[284, 281])).
% 0.21/0.44 tff(286,plain,
% 0.21/0.44 ((d(P!7) | (~(phi(P!7) = err))) | (phi(P!7) = err)),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(287,plain,
% 0.21/0.44 (d(P!7) | (~(phi(P!7) = err))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[286, 285])).
% 0.21/0.44 tff(288,plain,
% 0.21/0.44 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(P!7)) | (~(phi(P!7) = P!7)))) | (~(d(P!7) | (~(phi(P!7) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(P!7)) | (~(phi(P!7) = P!7)))) | (~(d(P!7) | (~(phi(P!7) = err)))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(289,plain,
% 0.21/0.44 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(P!7)) | (~(phi(P!7) = P!7)))) | (~(d(P!7) | (~(phi(P!7) = err)))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(290,plain,
% 0.21/0.44 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(P!7)) | (~(phi(P!7) = P!7)))) | (~(d(P!7) | (~(phi(P!7) = err))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.21/0.44 tff(291,plain,
% 0.21/0.44 ((~((~d(P!7)) | (~(phi(P!7) = P!7)))) | (~(d(P!7) | (~(phi(P!7) = err))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[290, 47])).
% 0.21/0.44 tff(292,plain,
% 0.21/0.44 (~((~d(P!7)) | (~(phi(P!7) = P!7)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[291, 287])).
% 0.21/0.44 tff(293,plain,
% 0.21/0.44 (((~d(P!7)) | (~(phi(P!7) = P!7))) | (phi(P!7) = P!7)),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(294,plain,
% 0.21/0.44 (phi(P!7) = P!7),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[293, 292])).
% 0.21/0.44 tff(295,plain,
% 0.21/0.44 (P!7 = phi(P!7)),
% 0.21/0.44 inference(symmetry,[status(thm)],[294])).
% 0.21/0.44 tff(296,plain,
% 0.21/0.44 (P!7 = false),
% 0.21/0.44 inference(transitivity,[status(thm)],[295, 277, 274, 272])).
% 0.21/0.44 tff(297,plain,
% 0.21/0.44 (not2(P!7) = not2(false)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[296])).
% 0.21/0.44 tff(298,plain,
% 0.21/0.44 (not2(false) = not2(P!7)),
% 0.21/0.44 inference(symmetry,[status(thm)],[297])).
% 0.21/0.44 tff(299,plain,
% 0.21/0.44 ((~![P: $i] : (not2(P) = impl(P, false2))) | (not2(false) = impl(false, false2))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(300,plain,
% 0.21/0.44 (not2(false) = impl(false, false2)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[299, 17])).
% 0.21/0.44 tff(301,plain,
% 0.21/0.44 (impl(false, false2) = not2(false)),
% 0.21/0.44 inference(symmetry,[status(thm)],[300])).
% 0.21/0.44 tff(302,plain,
% 0.21/0.44 (false2 = false),
% 0.21/0.44 inference(transitivity,[status(thm)],[7, 232, 53])).
% 0.21/0.45 tff(303,plain,
% 0.21/0.45 (impl(false, false2) = impl(false, false)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[302])).
% 0.21/0.45 tff(304,plain,
% 0.21/0.45 (impl(false, false) = impl(false, false2)),
% 0.21/0.45 inference(symmetry,[status(thm)],[303])).
% 0.21/0.45 tff(305,plain,
% 0.21/0.45 (^[B: $i] : refl(((~bool(B)) | (impl(false, B) = true)) <=> ((~bool(B)) | (impl(false, B) = true)))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(306,plain,
% 0.21/0.45 (![B: $i] : ((~bool(B)) | (impl(false, B) = true)) <=> ![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[305])).
% 0.21/0.45 tff(307,plain,
% 0.21/0.45 (![B: $i] : ((~bool(B)) | (impl(false, B) = true)) <=> ![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(308,plain,
% 0.21/0.45 (^[B: $i] : rewrite((bool(B) => (impl(false, B) = true)) <=> ((~bool(B)) | (impl(false, B) = true)))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(309,plain,
% 0.21/0.45 (![B: $i] : (bool(B) => (impl(false, B) = true)) <=> ![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[308])).
% 0.21/0.45 tff(310,axiom,(![B: $i] : (bool(B) => (impl(false, B) = true))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','impl_axiom3')).
% 0.21/0.45 tff(311,plain,
% 0.21/0.45 (![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.21/0.45 tff(312,plain,
% 0.21/0.45 (![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[311, 307])).
% 0.21/0.45 tff(313,plain,(
% 0.21/0.45 ![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 0.21/0.45 inference(skolemize,[status(sab)],[312])).
% 0.21/0.45 tff(314,plain,
% 0.21/0.45 (![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[313, 306])).
% 0.21/0.45 tff(315,plain,
% 0.21/0.45 (((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | ((~bool(false)) | (impl(false, false) = true))) <=> ((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | (~bool(false)) | (impl(false, false) = true))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(316,plain,
% 0.21/0.45 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | ((~bool(false)) | (impl(false, false) = true))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(317,plain,
% 0.21/0.45 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | (~bool(false)) | (impl(false, false) = true)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.21/0.45 tff(318,plain,
% 0.21/0.45 (impl(false, false) = true),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[317, 314, 91])).
% 0.21/0.45 tff(319,plain,
% 0.21/0.45 (true = impl(false, false)),
% 0.21/0.45 inference(symmetry,[status(thm)],[318])).
% 0.21/0.45 tff(320,plain,
% 0.21/0.45 (not1(P!7) = not1(false)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[296])).
% 0.21/0.45 tff(321,plain,
% 0.21/0.45 (not1(P!7) = not2(P!7)),
% 0.21/0.45 inference(transitivity,[status(thm)],[320, 67, 319, 304, 301, 298])).
% 0.21/0.45 tff(322,plain,
% 0.21/0.45 ((~![P: $i] : (not1(P) = not2(P))) <=> (~![P: $i] : (not1(P) = not2(P)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(323,axiom,(~![P: $i] : (not1(P) = not2(P))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not1_not2')).
% 0.21/0.45 tff(324,plain,
% 0.21/0.45 (~![P: $i] : (not1(P) = not2(P))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[323, 322])).
% 0.21/0.45 tff(325,plain,
% 0.21/0.45 (~![P: $i] : (not1(P) = not2(P))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[324, 322])).
% 0.21/0.45 tff(326,plain,
% 0.21/0.45 (~![P: $i] : (not1(P) = not2(P))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[325, 322])).
% 0.21/0.45 tff(327,plain,
% 0.21/0.45 (~![P: $i] : (not1(P) = not2(P))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[326, 322])).
% 0.21/0.45 tff(328,plain,(
% 0.21/0.45 ~(not1(P!7) = not2(P!7))),
% 0.21/0.45 inference(skolemize,[status(sab)],[327])).
% 0.21/0.45 tff(329,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[328, 321])).
% 0.21/0.45 tff(330,plain,((~(lazy_impl(prop(P!7), P!7) = false)) | (~(prop(P!7) = true))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(331,plain,
% 0.21/0.45 (~(lazy_impl(prop(P!7), P!7) = false)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[330, 271])).
% 0.21/0.45 tff(332,plain,
% 0.21/0.45 ((~((lazy_impl(prop(P!7), P!7) = false) | (lazy_impl(prop(P!7), P!7) = true))) | (lazy_impl(prop(P!7), P!7) = false) | (lazy_impl(prop(P!7), P!7) = true)),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(333,plain,
% 0.21/0.45 (lazy_impl(prop(P!7), P!7) = true),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[332, 331, 270])).
% 0.21/0.45 tff(334,plain,
% 0.21/0.45 (phi(P!7) = true),
% 0.21/0.45 inference(transitivity,[status(thm)],[277, 274, 333])).
% 0.21/0.45 tff(335,plain,
% 0.21/0.45 ((phi(P!7) = err) <=> (true = err)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[334])).
% 0.21/0.45 tff(336,plain,
% 0.21/0.45 ((true = err) <=> (phi(P!7) = err)),
% 0.21/0.45 inference(symmetry,[status(thm)],[335])).
% 0.21/0.45 tff(337,plain,
% 0.21/0.45 ((~(true = err)) <=> (~(phi(P!7) = err))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[336])).
% 0.21/0.45 tff(338,plain,
% 0.21/0.45 ((~(true = err)) <=> (~(true = err))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(339,plain,
% 0.21/0.45 (~(true = err)),
% 0.21/0.45 inference(and_elim,[status(thm)],[73])).
% 0.21/0.45 tff(340,plain,
% 0.21/0.45 (~(true = err)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[339, 338])).
% 0.21/0.45 tff(341,plain,
% 0.21/0.45 (~(phi(P!7) = err)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[340, 337])).
% 0.21/0.45 tff(342,plain,
% 0.21/0.45 (d(P!7) | (~(phi(P!7) = err))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[286, 341])).
% 0.21/0.45 tff(343,plain,
% 0.21/0.45 (~((~d(P!7)) | (~(phi(P!7) = P!7)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[291, 342])).
% 0.21/0.45 tff(344,plain,
% 0.21/0.45 (phi(P!7) = P!7),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[293, 343])).
% 0.21/0.45 tff(345,plain,
% 0.21/0.45 (P!7 = phi(P!7)),
% 0.21/0.45 inference(symmetry,[status(thm)],[344])).
% 0.21/0.45 tff(346,plain,
% 0.21/0.45 (P!7 = true),
% 0.21/0.45 inference(transitivity,[status(thm)],[345, 277, 274, 333])).
% 0.21/0.45 tff(347,plain,
% 0.21/0.45 (not1(P!7) = not1(true)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[346])).
% 0.21/0.45 tff(348,plain,
% 0.21/0.45 (not1(P!7) = phi(phi(f7(P!6)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[347, 206, 143, 235])).
% 0.21/0.45 tff(349,plain,
% 0.21/0.45 ((not1(P!7) = not2(P!7)) <=> (phi(phi(f7(P!6))) = impl(P!7, phi(f7(P!6))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[348, 20])).
% 0.21/0.45 tff(350,plain,
% 0.21/0.45 ((not1(P!7) = not2(P!7)) <=> (impl(P!7, phi(f7(P!6))) = phi(phi(f7(P!6))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[349, 30])).
% 0.21/0.45 tff(351,plain,
% 0.21/0.45 ((impl(P!7, phi(f7(P!6))) = phi(phi(f7(P!6)))) <=> (not1(P!7) = not2(P!7))),
% 0.21/0.45 inference(symmetry,[status(thm)],[350])).
% 0.21/0.45 tff(352,plain,
% 0.21/0.45 (^[B: $i] : refl(((~bool(B)) | (impl(true, B) = B)) <=> ((~bool(B)) | (impl(true, B) = B)))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(353,plain,
% 0.21/0.45 (![B: $i] : ((~bool(B)) | (impl(true, B) = B)) <=> ![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[352])).
% 0.21/0.45 tff(354,plain,
% 0.21/0.45 (![B: $i] : ((~bool(B)) | (impl(true, B) = B)) <=> ![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(355,plain,
% 0.21/0.45 (^[B: $i] : rewrite((bool(B) => (impl(true, B) = B)) <=> ((~bool(B)) | (impl(true, B) = B)))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(356,plain,
% 0.21/0.45 (![B: $i] : (bool(B) => (impl(true, B) = B)) <=> ![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[355])).
% 0.21/0.45 tff(357,axiom,(![B: $i] : (bool(B) => (impl(true, B) = B))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','impl_axiom4')).
% 0.21/0.45 tff(358,plain,
% 0.21/0.45 (![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[357, 356])).
% 0.21/0.45 tff(359,plain,
% 0.21/0.45 (![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[358, 354])).
% 0.21/0.45 tff(360,plain,(
% 0.21/0.45 ![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 0.21/0.45 inference(skolemize,[status(sab)],[359])).
% 0.21/0.45 tff(361,plain,
% 0.21/0.45 (![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[360, 353])).
% 0.21/0.45 tff(362,plain,
% 0.21/0.45 (((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | ((~bool(false)) | (impl(true, false) = false))) <=> ((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | (~bool(false)) | (impl(true, false) = false))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(363,plain,
% 0.21/0.45 ((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | ((~bool(false)) | (impl(true, false) = false))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(364,plain,
% 0.21/0.45 ((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | (~bool(false)) | (impl(true, false) = false)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[363, 362])).
% 0.21/0.45 tff(365,plain,
% 0.21/0.45 (impl(true, false) = false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[364, 361, 91])).
% 0.21/0.45 tff(366,plain,
% 0.21/0.45 (impl(true, false2) = impl(true, false)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[302])).
% 0.21/0.45 tff(367,plain,
% 0.21/0.45 ((~![P: $i] : (not2(P) = impl(P, false2))) | (not2(true) = impl(true, false2))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(368,plain,
% 0.21/0.45 (not2(true) = impl(true, false2)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[367, 17])).
% 0.21/0.45 tff(369,assumption,(lazy_impl(prop(P!7), P!7) = true), introduced(assumption)).
% 0.21/0.45 tff(370,plain,
% 0.21/0.45 (phi(P!7) = true),
% 0.21/0.45 inference(transitivity,[status(thm)],[277, 274, 369])).
% 0.21/0.45 tff(371,plain,
% 0.21/0.45 ((phi(P!7) = err) <=> (true = err)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[370])).
% 0.21/0.45 tff(372,plain,
% 0.21/0.45 ((true = err) <=> (phi(P!7) = err)),
% 0.21/0.45 inference(symmetry,[status(thm)],[371])).
% 0.21/0.45 tff(373,plain,
% 0.21/0.45 ((~(true = err)) <=> (~(phi(P!7) = err))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[372])).
% 0.21/0.45 tff(374,plain,
% 0.21/0.45 (~(phi(P!7) = err)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[340, 373])).
% 0.21/0.45 tff(375,plain,
% 0.21/0.45 (d(P!7) | (~(phi(P!7) = err))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[286, 374])).
% 0.21/0.45 tff(376,plain,
% 0.21/0.45 (~((~d(P!7)) | (~(phi(P!7) = P!7)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[291, 375])).
% 0.21/0.45 tff(377,plain,
% 0.21/0.45 (phi(P!7) = P!7),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[293, 376])).
% 0.21/0.45 tff(378,plain,
% 0.21/0.45 (P!7 = phi(P!7)),
% 0.21/0.45 inference(symmetry,[status(thm)],[377])).
% 0.21/0.45 tff(379,plain,
% 0.21/0.45 (P!7 = true),
% 0.21/0.45 inference(transitivity,[status(thm)],[378, 277, 274, 369])).
% 0.21/0.45 tff(380,plain,
% 0.21/0.45 (not2(P!7) = not2(true)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[379])).
% 0.21/0.45 tff(381,plain,
% 0.21/0.45 (impl(P!7, false2) = not2(P!7)),
% 0.21/0.45 inference(symmetry,[status(thm)],[19])).
% 0.21/0.45 tff(382,plain,
% 0.21/0.45 (impl(P!7, phi(f7(P!6))) = phi(phi(f7(P!6)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[9, 381, 380, 368, 366, 365, 143, 235])).
% 0.21/0.45 tff(383,assumption,(~(impl(P!7, phi(f7(P!6))) = phi(phi(f7(P!6))))), introduced(assumption)).
% 0.21/0.45 tff(384,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[383, 382])).
% 0.21/0.45 tff(385,plain,((~(lazy_impl(prop(P!7), P!7) = true)) | (impl(P!7, phi(f7(P!6))) = phi(phi(f7(P!6)))) | (~(prop(P!7) = true))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(386,plain,
% 0.21/0.45 (impl(P!7, phi(f7(P!6))) = phi(phi(f7(P!6)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[385, 333, 271])).
% 0.21/0.45 tff(387,plain,
% 0.21/0.45 (not1(P!7) = not2(P!7)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[386, 351])).
% 0.21/0.45 tff(388,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[328, 387])).
% 0.21/0.45 tff(389,plain,(~(prop(P!7) = true)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(390,plain,
% 0.21/0.45 ((~((prop(P!7) = true) <=> bool(P!7))) | (prop(P!7) = true) | (~bool(P!7))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(391,plain,
% 0.21/0.45 ((~((prop(P!7) = true) <=> bool(P!7))) | (~bool(P!7))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[390, 389])).
% 0.21/0.45 tff(392,plain,
% 0.21/0.45 (~bool(P!7)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[391, 29])).
% 0.21/0.45 tff(393,plain,
% 0.21/0.45 (((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | (bool(P!7) | (not1(P!7) = phi(P!7)))) <=> ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | bool(P!7) | (not1(P!7) = phi(P!7)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(394,plain,
% 0.21/0.45 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | (bool(P!7) | (not1(P!7) = phi(P!7)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(395,plain,
% 0.21/0.45 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | bool(P!7) | (not1(P!7) = phi(P!7))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[394, 393])).
% 0.21/0.45 tff(396,plain,
% 0.21/0.45 (bool(P!7) | (not1(P!7) = phi(P!7))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[395, 86])).
% 0.21/0.45 tff(397,plain,
% 0.21/0.45 (not1(P!7) = phi(P!7)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[396, 392])).
% 0.21/0.45 tff(398,plain,
% 0.21/0.45 ((not1(P!7) = not2(P!7)) <=> (phi(P!7) = impl(P!7, phi(f7(P!6))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[397, 20])).
% 0.21/0.45 tff(399,plain,
% 0.21/0.45 ((not1(P!7) = not2(P!7)) <=> (impl(P!7, phi(f7(P!6))) = phi(P!7))),
% 0.21/0.45 inference(transitivity,[status(thm)],[398, 1])).
% 0.21/0.45 tff(400,plain,
% 0.21/0.45 ((impl(P!7, phi(f7(P!6))) = phi(P!7)) <=> (not1(P!7) = not2(P!7))),
% 0.21/0.46 inference(symmetry,[status(thm)],[399])).
% 0.21/0.46 tff(401,plain,
% 0.21/0.46 (^[A: $i, B: $i] : refl((bool(A) | (impl(A, B) = phi(A))) <=> (bool(A) | (impl(A, B) = phi(A))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(402,plain,
% 0.21/0.46 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A))) <=> ![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[401])).
% 0.21/0.46 tff(403,plain,
% 0.21/0.46 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A))) <=> ![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(404,plain,
% 0.21/0.46 (^[A: $i, B: $i] : rewrite(((~bool(A)) => (impl(A, B) = phi(A))) <=> (bool(A) | (impl(A, B) = phi(A))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(405,plain,
% 0.21/0.46 (![A: $i, B: $i] : ((~bool(A)) => (impl(A, B) = phi(A))) <=> ![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[404])).
% 0.21/0.46 tff(406,axiom,(![A: $i, B: $i] : ((~bool(A)) => (impl(A, B) = phi(A)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','impl_axiom1')).
% 0.21/0.46 tff(407,plain,
% 0.21/0.46 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[406, 405])).
% 0.21/0.46 tff(408,plain,
% 0.21/0.46 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[407, 403])).
% 0.21/0.46 tff(409,plain,(
% 0.21/0.46 ![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[408])).
% 0.21/0.46 tff(410,plain,
% 0.21/0.46 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[409, 402])).
% 0.21/0.46 tff(411,plain,
% 0.21/0.46 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(P!7) | (impl(P!7, phi(f7(P!6))) = phi(P!7)))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(P!7) | (impl(P!7, phi(f7(P!6))) = phi(P!7)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(412,plain,
% 0.21/0.46 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(P!7) | (impl(P!7, phi(f7(P!6))) = phi(P!7)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(413,plain,
% 0.21/0.46 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(P!7) | (impl(P!7, phi(f7(P!6))) = phi(P!7))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[412, 411])).
% 0.21/0.46 tff(414,plain,
% 0.21/0.46 (bool(P!7) | (impl(P!7, phi(f7(P!6))) = phi(P!7))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[413, 410])).
% 0.21/0.46 tff(415,plain,
% 0.21/0.46 (impl(P!7, phi(f7(P!6))) = phi(P!7)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[414, 392])).
% 0.21/0.46 tff(416,plain,
% 0.21/0.46 (not1(P!7) = not2(P!7)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[415, 400])).
% 0.21/0.46 tff(417,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[328, 416])).
% 0.21/0.46 % SZS output end Proof
% 0.21/0.46 % E exiting
%------------------------------------------------------------------------------