%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW101+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 0.12s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW101+1 : TPTP v9.0.0. Released v5.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 11:18:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(false2_type, type, (
% 0.12/0.38 false2: $i)).
% 0.12/0.38 tff(false1_type, type, (
% 0.12/0.38 false1: $i)).
% 0.12/0.38 tff(phi_type, type, (
% 0.12/0.38 phi: $i > $i)).
% 0.12/0.38 tff(f7_type, type, (
% 0.12/0.38 f7: $i > $i)).
% 0.12/0.38 tff(tptp_fun_P_6_type, type, (
% 0.12/0.38 tptp_fun_P_6: $i)).
% 0.12/0.38 tff(forallprefers_type, type, (
% 0.12/0.38 forallprefers: ( $i * $i ) > $o)).
% 0.12/0.38 tff(false_type, type, (
% 0.12/0.38 false: $i)).
% 0.12/0.38 tff(d_type, type, (
% 0.12/0.38 d: $i > $o)).
% 0.12/0.38 tff(err_type, type, (
% 0.12/0.38 err: $i)).
% 0.12/0.38 tff(true_type, type, (
% 0.12/0.38 true: $i)).
% 0.12/0.38 tff(lazy_impl_type, type, (
% 0.12/0.38 lazy_impl: ( $i * $i ) > $i)).
% 0.12/0.38 tff(prop_type, type, (
% 0.12/0.38 prop: $i > $i)).
% 0.12/0.38 tff(bool_type, type, (
% 0.12/0.38 bool: $i > $o)).
% 0.12/0.38 tff(not1_type, type, (
% 0.12/0.38 not1: $i > $i)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (((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))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (?[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))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(3,axiom,(?[P: $i] : ((false2 = phi(f7(P))) & (~?[P1: $i] : forallprefers(f7(P1), f7(P))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','def_false2')).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (?[P: $i] : ((false2 = phi(f7(P))) & (~?[P1: $i] : forallprefers(f7(P1), f7(P))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 ((false2 = phi(f7(P!6))) & ![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (false2 = phi(f7(P!6))),
% 0.12/0.38 inference(and_elim,[status(thm)],[5])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (phi(f7(P!6)) = false2),
% 0.12/0.38 inference(symmetry,[status(thm)],[6])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (d(false) <=> d(false)),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(9,axiom,((d(true) & d(false)) & d(err)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','false_true_err_in_d')).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (d(true) & d(false)),
% 0.12/0.38 inference(and_elim,[status(thm)],[9])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (d(false)),
% 0.12/0.38 inference(and_elim,[status(thm)],[10])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (d(false)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[11, 8])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 ((d(false) | (~(phi(false) = err))) | (~d(false))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (d(false) | (~(phi(false) = err))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (^[X: $i] : refl(((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err))))) <=> ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err))))) <=> ![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (^[X: $i] : trans(monotonicity(rewrite((d(X) & (phi(X) = X)) <=> (~((~d(X)) | (~(phi(X) = X))))), rewrite(((~d(X)) & (phi(X) = err)) <=> (~(d(X) | (~(phi(X) = err))))), (((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err))) <=> ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err))))))), rewrite(((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err))))) <=> ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))), (((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err))) <=> ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err))) <=> ![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[17])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err))) <=> ![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(20,axiom,(![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','def_phi')).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.12/0.39 tff(22,plain,(
% 0.12/0.39 ![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[21])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 (![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (((~![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)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(false)) | (~(phi(false) = false)))) | (~(d(false) | (~(phi(false) = err)))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(false)) | (~(phi(false) = false)))) | (~(d(false) | (~(phi(false) = err))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 (~((~d(false)) | (~(phi(false) = false)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[27, 24, 14])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (((~d(false)) | (~(phi(false) = false))) | (phi(false) = false)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 (phi(false) = false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 (^[B: $i] : refl((lazy_impl(true, B) = phi(B)) <=> (lazy_impl(true, B) = phi(B)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 (![B: $i] : (lazy_impl(true, B) = phi(B)) <=> ![B: $i] : (lazy_impl(true, B) = phi(B))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[31])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 (![B: $i] : (lazy_impl(true, B) = phi(B)) <=> ![B: $i] : (lazy_impl(true, B) = phi(B))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(34,axiom,(![B: $i] : (lazy_impl(true, B) = phi(B))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','lazy_impl_axiom3')).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 (![B: $i] : (lazy_impl(true, B) = phi(B))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.12/0.39 tff(36,plain,(
% 0.12/0.39 ![B: $i] : (lazy_impl(true, B) = phi(B))),
% 0.12/0.39 inference(skolemize,[status(sab)],[35])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 (![B: $i] : (lazy_impl(true, B) = phi(B))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 ((~![B: $i] : (lazy_impl(true, B) = phi(B))) | (lazy_impl(true, false) = phi(false))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 (lazy_impl(true, false) = phi(false)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.12/0.39 tff(40,plain,
% 0.12/0.39 (^[X: $i] : refl(((prop(X) = true) <=> bool(X)) <=> ((prop(X) = true) <=> bool(X)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 (![X: $i] : ((prop(X) = true) <=> bool(X)) <=> ![X: $i] : ((prop(X) = true) <=> bool(X))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[40])).
% 0.12/0.39 tff(42,plain,
% 0.12/0.39 (![X: $i] : ((prop(X) = true) <=> bool(X)) <=> ![X: $i] : ((prop(X) = true) <=> bool(X))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(43,axiom,(![X: $i] : ((prop(X) = true) <=> bool(X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','prop_true')).
% 0.12/0.39 tff(44,plain,
% 0.12/0.39 (![X: $i] : ((prop(X) = true) <=> bool(X))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.12/0.39 tff(45,plain,(
% 0.12/0.39 ![X: $i] : ((prop(X) = true) <=> bool(X))),
% 0.12/0.39 inference(skolemize,[status(sab)],[44])).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 (![X: $i] : ((prop(X) = true) <=> bool(X))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 ((~![X: $i] : ((prop(X) = true) <=> bool(X))) | ((prop(false) = true) <=> bool(false))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(48,plain,
% 0.12/0.39 ((prop(false) = true) <=> bool(false)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.12/0.39 tff(49,plain,
% 0.12/0.39 ((not1(false) = true) <=> (not1(false) = true)),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(50,axiom,(not1(false) = true), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','not1_axiom2')).
% 0.12/0.39 tff(51,plain,
% 0.12/0.39 (not1(false) = true),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.12/0.39 tff(52,plain,
% 0.12/0.39 ((not1(false) = phi(false)) <=> (true = false)),
% 0.12/0.39 inference(monotonicity,[status(thm)],[51, 30])).
% 0.12/0.39 tff(53,plain,
% 0.12/0.39 ((true = false) <=> (not1(false) = phi(false))),
% 0.12/0.39 inference(symmetry,[status(thm)],[52])).
% 0.12/0.39 tff(54,plain,
% 0.12/0.39 ((~(true = false)) <=> (~(not1(false) = phi(false)))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[53])).
% 0.12/0.39 tff(55,plain,
% 0.12/0.39 ((~(true = false)) <=> (~(true = false))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(56,axiom,(((~(true = false)) & (~(true = err))) & (~(false = err))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','distinct_false_true_err')).
% 0.12/0.39 tff(57,plain,
% 0.12/0.39 ((~(true = false)) & (~(true = err))),
% 0.12/0.39 inference(and_elim,[status(thm)],[56])).
% 0.12/0.39 tff(58,plain,
% 0.12/0.39 (~(true = false)),
% 0.12/0.39 inference(and_elim,[status(thm)],[57])).
% 0.12/0.39 tff(59,plain,
% 0.12/0.39 (~(true = false)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[58, 55])).
% 0.12/0.39 tff(60,plain,
% 0.12/0.39 (~(not1(false) = phi(false))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[59, 54])).
% 0.12/0.39 tff(61,plain,
% 0.12/0.39 (^[A: $i] : refl((bool(A) | (not1(A) = phi(A))) <=> (bool(A) | (not1(A) = phi(A))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(62,plain,
% 0.12/0.39 (![A: $i] : (bool(A) | (not1(A) = phi(A))) <=> ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[61])).
% 0.12/0.39 tff(63,plain,
% 0.12/0.39 (![A: $i] : (bool(A) | (not1(A) = phi(A))) <=> ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(64,plain,
% 0.12/0.39 (^[A: $i] : rewrite(((~bool(A)) => (not1(A) = phi(A))) <=> (bool(A) | (not1(A) = phi(A))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(65,plain,
% 0.12/0.39 (![A: $i] : ((~bool(A)) => (not1(A) = phi(A))) <=> ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[64])).
% 0.12/0.39 tff(66,axiom,(![A: $i] : ((~bool(A)) => (not1(A) = phi(A)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','not1_axiom1')).
% 0.12/0.39 tff(67,plain,
% 0.12/0.39 (![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.12/0.39 tff(68,plain,
% 0.12/0.39 (![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.12/0.39 tff(69,plain,(
% 0.12/0.39 ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[68])).
% 0.12/0.39 tff(70,plain,
% 0.12/0.39 (![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.12/0.39 tff(71,plain,
% 0.12/0.39 (((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | (bool(false) | (not1(false) = phi(false)))) <=> ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | bool(false) | (not1(false) = phi(false)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(72,plain,
% 0.12/0.39 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | (bool(false) | (not1(false) = phi(false)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(73,plain,
% 0.12/0.39 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | bool(false) | (not1(false) = phi(false))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.12/0.39 tff(74,plain,
% 0.12/0.39 (bool(false) | (not1(false) = phi(false))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[73, 70])).
% 0.12/0.39 tff(75,plain,
% 0.12/0.39 (bool(false)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[74, 60])).
% 0.12/0.39 tff(76,plain,
% 0.12/0.39 ((~((prop(false) = true) <=> bool(false))) | (prop(false) = true) | (~bool(false))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(77,plain,
% 0.12/0.39 ((~((prop(false) = true) <=> bool(false))) | (prop(false) = true)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.12/0.39 tff(78,plain,
% 0.12/0.39 (prop(false) = true),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[77, 48])).
% 0.12/0.39 tff(79,plain,
% 0.12/0.39 (lazy_impl(prop(false), false) = lazy_impl(true, false)),
% 0.12/0.39 inference(monotonicity,[status(thm)],[78])).
% 0.12/0.39 tff(80,plain,
% 0.12/0.39 (^[P: $i] : refl((f7(P) = lazy_impl(prop(P), P)) <=> (f7(P) = lazy_impl(prop(P), P)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(81,plain,
% 0.12/0.39 (![P: $i] : (f7(P) = lazy_impl(prop(P), P)) <=> ![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[80])).
% 0.12/0.39 tff(82,plain,
% 0.12/0.39 (![P: $i] : (f7(P) = lazy_impl(prop(P), P)) <=> ![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(83,axiom,(![P: $i] : (f7(P) = lazy_impl(prop(P), P))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','def_f7')).
% 0.12/0.39 tff(84,plain,
% 0.12/0.39 (![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.12/0.39 tff(85,plain,(
% 0.12/0.39 ![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 0.12/0.39 inference(skolemize,[status(sab)],[84])).
% 0.12/0.39 tff(86,plain,
% 0.12/0.39 (![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.12/0.39 tff(87,plain,
% 0.12/0.39 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(false) = lazy_impl(prop(false), false))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(88,plain,
% 0.12/0.39 (f7(false) = lazy_impl(prop(false), false)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.12/0.39 tff(89,plain,
% 0.12/0.39 (^[B: $i] : refl((lazy_impl(false, B) = true) <=> (lazy_impl(false, B) = true))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(90,plain,
% 0.12/0.39 (![B: $i] : (lazy_impl(false, B) = true) <=> ![B: $i] : (lazy_impl(false, B) = true)),
% 0.12/0.39 inference(quant_intro,[status(thm)],[89])).
% 0.12/0.39 tff(91,plain,
% 0.12/0.39 (![B: $i] : (lazy_impl(false, B) = true) <=> ![B: $i] : (lazy_impl(false, B) = true)),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(92,axiom,(![B: $i] : (lazy_impl(false, B) = true)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','lazy_impl_axiom2')).
% 0.12/0.39 tff(93,plain,
% 0.12/0.39 (![B: $i] : (lazy_impl(false, B) = true)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.12/0.39 tff(94,plain,(
% 0.12/0.39 ![B: $i] : (lazy_impl(false, B) = true)),
% 0.12/0.39 inference(skolemize,[status(sab)],[93])).
% 0.12/0.39 tff(95,plain,
% 0.12/0.39 (![B: $i] : (lazy_impl(false, B) = true)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.12/0.39 tff(96,plain,
% 0.12/0.39 ((~![B: $i] : (lazy_impl(false, B) = true)) | (lazy_impl(false, P!6) = true)),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(97,plain,
% 0.12/0.39 (lazy_impl(false, P!6) = true),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.12/0.39 tff(98,assumption,(prop(P!6) = false), introduced(assumption)).
% 0.12/0.39 tff(99,plain,
% 0.12/0.39 (lazy_impl(prop(P!6), P!6) = lazy_impl(false, P!6)),
% 0.12/0.39 inference(monotonicity,[status(thm)],[98])).
% 0.12/0.39 tff(100,plain,
% 0.12/0.39 (lazy_impl(prop(P!6), P!6) = true),
% 0.12/0.39 inference(transitivity,[status(thm)],[99, 97])).
% 0.12/0.39 tff(101,plain,
% 0.12/0.39 (^[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)))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(102,plain,
% 0.12/0.39 (![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))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[101])).
% 0.12/0.39 tff(103,plain,
% 0.12/0.39 (^[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)))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(104,plain,
% 0.12/0.39 (![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))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[103])).
% 0.12/0.39 tff(105,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(106,plain,
% 0.12/0.39 (^[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)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(107,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[106])).
% 0.12/0.39 tff(108,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/sandbox2/benchmark/Axioms/SWV012+0.ax','def_forallprefers')).
% 0.12/0.39 tff(109,plain,
% 0.12/0.39 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.12/0.39 tff(110,plain,
% 0.12/0.39 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.12/0.39 tff(111,plain,(
% 0.12/0.39 ![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[110])).
% 0.12/0.39 tff(112,plain,
% 0.12/0.39 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.12/0.39 tff(113,plain,
% 0.12/0.39 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[112, 102])).
% 0.12/0.39 tff(114,plain,
% 0.12/0.39 (((~![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))))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(115,plain,
% 0.12/0.39 ((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)))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(116,plain,
% 0.12/0.39 (((~![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))))))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[115])).
% 0.12/0.40 tff(117,plain,
% 0.12/0.40 (((~![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))))))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[116, 114])).
% 0.12/0.40 tff(118,plain,
% 0.12/0.40 ((~![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))))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(119,plain,
% 0.12/0.40 ((~![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)))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.12/0.40 tff(120,plain,
% 0.12/0.40 (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))))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[119, 113])).
% 0.12/0.40 tff(121,plain,
% 0.12/0.40 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(P!6) = lazy_impl(prop(P!6), P!6))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(122,plain,
% 0.12/0.40 (f7(P!6) = lazy_impl(prop(P!6), P!6)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[121, 86])).
% 0.12/0.40 tff(123,plain,
% 0.12/0.40 (lazy_impl(prop(P!6), P!6) = f7(P!6)),
% 0.12/0.40 inference(symmetry,[status(thm)],[122])).
% 0.12/0.40 tff(124,plain,
% 0.12/0.40 (lazy_impl(prop(false), false) = f7(false)),
% 0.12/0.40 inference(symmetry,[status(thm)],[88])).
% 0.12/0.40 tff(125,plain,
% 0.12/0.40 (lazy_impl(true, false) = lazy_impl(prop(false), false)),
% 0.12/0.40 inference(symmetry,[status(thm)],[79])).
% 0.12/0.40 tff(126,plain,
% 0.12/0.40 (phi(false) = lazy_impl(true, false)),
% 0.12/0.40 inference(symmetry,[status(thm)],[39])).
% 0.12/0.40 tff(127,plain,
% 0.12/0.40 (false = phi(false)),
% 0.12/0.40 inference(symmetry,[status(thm)],[30])).
% 0.12/0.40 tff(128,plain,
% 0.12/0.40 (false = f7(false)),
% 0.12/0.40 inference(transitivity,[status(thm)],[127, 126, 125, 124])).
% 0.12/0.40 tff(129,plain,
% 0.12/0.40 (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> forallprefers(f7(false), f7(P!6))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[128, 123])).
% 0.12/0.40 tff(130,plain,
% 0.12/0.40 (forallprefers(f7(false), f7(P!6)) <=> forallprefers(false, lazy_impl(prop(P!6), P!6))),
% 0.12/0.40 inference(symmetry,[status(thm)],[129])).
% 0.12/0.40 tff(131,plain,
% 0.12/0.40 ((~forallprefers(f7(false), f7(P!6))) <=> (~forallprefers(false, lazy_impl(prop(P!6), P!6)))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[130])).
% 0.12/0.40 tff(132,plain,
% 0.12/0.40 (^[P1: $i] : refl((~forallprefers(f7(P1), f7(P!6))) <=> (~forallprefers(f7(P1), f7(P!6))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(133,plain,
% 0.12/0.40 (![P1: $i] : (~forallprefers(f7(P1), f7(P!6))) <=> ![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[132])).
% 0.12/0.40 tff(134,plain,
% 0.12/0.40 (![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 0.12/0.40 inference(and_elim,[status(thm)],[5])).
% 0.12/0.40 tff(135,plain,
% 0.12/0.40 (![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.12/0.40 tff(136,plain,
% 0.12/0.40 ((~![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))) | (~forallprefers(f7(false), f7(P!6)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(137,plain,
% 0.12/0.40 (~forallprefers(f7(false), f7(P!6))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.12/0.40 tff(138,plain,
% 0.12/0.40 (~forallprefers(false, lazy_impl(prop(P!6), P!6))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[137, 131])).
% 0.12/0.40 tff(139,plain,
% 0.12/0.40 ((~(forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((lazy_impl(prop(P!6), P!6) = true) | (~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6)))))))) | forallprefers(false, lazy_impl(prop(P!6), P!6)) | (~((lazy_impl(prop(P!6), P!6) = true) | (~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6)))))))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(140,plain,
% 0.12/0.40 (~((lazy_impl(prop(P!6), P!6) = true) | (~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[139, 138, 120])).
% 0.12/0.40 tff(141,plain,
% 0.12/0.40 (((lazy_impl(prop(P!6), P!6) = true) | (~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6)))))) | (~(lazy_impl(prop(P!6), P!6) = true))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(142,plain,
% 0.12/0.40 (~(lazy_impl(prop(P!6), P!6) = true)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.12/0.40 tff(143,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[142, 100])).
% 0.12/0.40 tff(144,plain,(~(prop(P!6) = false)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.40 tff(145,plain,
% 0.12/0.40 (^[X: $i] : refl((~(bool(X) <=> (prop(X) = false))) <=> (~(bool(X) <=> (prop(X) = false))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(146,plain,
% 0.12/0.40 (![X: $i] : (~(bool(X) <=> (prop(X) = false))) <=> ![X: $i] : (~(bool(X) <=> (prop(X) = false)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[145])).
% 0.12/0.40 tff(147,plain,
% 0.12/0.40 (![X: $i] : (~(bool(X) <=> (prop(X) = false))) <=> ![X: $i] : (~(bool(X) <=> (prop(X) = false)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(148,plain,
% 0.12/0.40 (^[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)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(149,plain,
% 0.12/0.40 (![X: $i] : ((prop(X) = false) <=> (~bool(X))) <=> ![X: $i] : (~(bool(X) <=> (prop(X) = false)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[148])).
% 0.12/0.40 tff(150,axiom,(![X: $i] : ((prop(X) = false) <=> (~bool(X)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','prop_false')).
% 0.12/0.40 tff(151,plain,
% 0.12/0.40 (![X: $i] : (~(bool(X) <=> (prop(X) = false)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.12/0.40 tff(152,plain,
% 0.12/0.40 (![X: $i] : (~(bool(X) <=> (prop(X) = false)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[151, 147])).
% 0.12/0.40 tff(153,plain,(
% 0.12/0.40 ![X: $i] : (~(bool(X) <=> (prop(X) = false)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[152])).
% 0.12/0.40 tff(154,plain,
% 0.12/0.40 (![X: $i] : (~(bool(X) <=> (prop(X) = false)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[153, 146])).
% 0.12/0.40 tff(155,plain,
% 0.12/0.40 ((~![X: $i] : (~(bool(X) <=> (prop(X) = false)))) | (~(bool(P!6) <=> (prop(P!6) = false)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(156,plain,
% 0.12/0.40 (~(bool(P!6) <=> (prop(P!6) = false))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[155, 154])).
% 0.12/0.40 tff(157,plain,
% 0.12/0.40 ((bool(P!6) <=> (prop(P!6) = false)) | bool(P!6) | (prop(P!6) = false)),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(158,plain,
% 0.12/0.40 (bool(P!6) | (prop(P!6) = false)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[157, 156])).
% 0.12/0.40 tff(159,plain,
% 0.12/0.40 (bool(P!6)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[158, 144])).
% 0.12/0.40 tff(160,plain,
% 0.12/0.40 (^[X: $i] : refl((bool(X) <=> ((X = false) | (X = true))) <=> (bool(X) <=> ((X = false) | (X = true))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(161,plain,
% 0.12/0.40 (![X: $i] : (bool(X) <=> ((X = false) | (X = true))) <=> ![X: $i] : (bool(X) <=> ((X = false) | (X = true)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[160])).
% 0.12/0.40 tff(162,plain,
% 0.12/0.40 (![X: $i] : (bool(X) <=> ((X = false) | (X = true))) <=> ![X: $i] : (bool(X) <=> ((X = false) | (X = true)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(163,axiom,(![X: $i] : (bool(X) <=> ((X = false) | (X = true)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','def_bool')).
% 0.12/0.40 tff(164,plain,
% 0.12/0.40 (![X: $i] : (bool(X) <=> ((X = false) | (X = true)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.12/0.40 tff(165,plain,(
% 0.12/0.40 ![X: $i] : (bool(X) <=> ((X = false) | (X = true)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[164])).
% 0.12/0.40 tff(166,plain,
% 0.12/0.40 (![X: $i] : (bool(X) <=> ((X = false) | (X = true)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[165, 161])).
% 0.12/0.40 tff(167,plain,
% 0.12/0.40 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = true)))) | (bool(P!6) <=> ((P!6 = false) | (P!6 = true)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(168,plain,
% 0.12/0.40 (bool(P!6) <=> ((P!6 = false) | (P!6 = true))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.12/0.40 tff(169,plain,
% 0.12/0.40 ((~(bool(P!6) <=> ((P!6 = false) | (P!6 = true)))) | (~bool(P!6)) | ((P!6 = false) | (P!6 = true))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(170,plain,
% 0.12/0.40 ((~bool(P!6)) | ((P!6 = false) | (P!6 = true))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[169, 168])).
% 0.12/0.40 tff(171,plain,
% 0.12/0.40 ((P!6 = false) | (P!6 = true)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[170, 159])).
% 0.12/0.40 tff(172,plain,
% 0.12/0.40 (d(true) <=> d(true)),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(173,plain,
% 0.12/0.40 (d(true)),
% 0.12/0.40 inference(and_elim,[status(thm)],[10])).
% 0.12/0.40 tff(174,plain,
% 0.12/0.40 (d(true)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.12/0.40 tff(175,plain,
% 0.12/0.40 ((d(true) | (~(phi(true) = err))) | (~d(true))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(176,plain,
% 0.12/0.40 (d(true) | (~(phi(true) = err))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[175, 174])).
% 0.12/0.40 tff(177,plain,
% 0.12/0.40 (((~![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)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(178,plain,
% 0.12/0.40 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(true)) | (~(phi(true) = true)))) | (~(d(true) | (~(phi(true) = err)))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(179,plain,
% 0.12/0.40 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(true)) | (~(phi(true) = true)))) | (~(d(true) | (~(phi(true) = err))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.12/0.40 tff(180,plain,
% 0.12/0.40 (~((~d(true)) | (~(phi(true) = true)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[179, 24, 176])).
% 0.12/0.40 tff(181,plain,
% 0.12/0.40 (((~d(true)) | (~(phi(true) = true))) | (phi(true) = true)),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(182,plain,
% 0.12/0.40 (phi(true) = true),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[181, 180])).
% 0.12/0.40 tff(183,plain,
% 0.12/0.40 ((~![B: $i] : (lazy_impl(true, B) = phi(B))) | (lazy_impl(true, true) = phi(true))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(184,plain,
% 0.12/0.40 (lazy_impl(true, true) = phi(true)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[183, 37])).
% 0.12/0.40 tff(185,plain,
% 0.12/0.40 ((~![X: $i] : ((prop(X) = true) <=> bool(X))) | ((prop(true) = true) <=> bool(true))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(186,plain,
% 0.12/0.40 ((prop(true) = true) <=> bool(true)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[185, 46])).
% 0.12/0.40 tff(187,plain,
% 0.12/0.40 ((false = true) <=> (true = false)),
% 0.12/0.40 inference(commutativity,[status(thm)],[])).
% 0.12/0.40 tff(188,plain,
% 0.12/0.40 ((not1(true) = false) <=> (not1(true) = false)),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(189,axiom,(not1(true) = false), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','not1_axiom3')).
% 0.12/0.40 tff(190,plain,
% 0.12/0.40 (not1(true) = false),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.12/0.40 tff(191,plain,
% 0.12/0.40 ((not1(true) = phi(true)) <=> (false = true)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[190, 182])).
% 0.12/0.40 tff(192,plain,
% 0.12/0.40 ((not1(true) = phi(true)) <=> (true = false)),
% 0.12/0.40 inference(transitivity,[status(thm)],[191, 187])).
% 0.12/0.40 tff(193,plain,
% 0.12/0.40 ((true = false) <=> (not1(true) = phi(true))),
% 0.12/0.40 inference(symmetry,[status(thm)],[192])).
% 0.12/0.40 tff(194,plain,
% 0.12/0.40 ((~(true = false)) <=> (~(not1(true) = phi(true)))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[193])).
% 0.12/0.40 tff(195,plain,
% 0.12/0.40 (~(not1(true) = phi(true))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[59, 194])).
% 0.12/0.40 tff(196,plain,
% 0.12/0.40 (((~![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)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(197,plain,
% 0.12/0.40 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | (bool(true) | (not1(true) = phi(true)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(198,plain,
% 0.12/0.40 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | bool(true) | (not1(true) = phi(true))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.12/0.40 tff(199,plain,
% 0.12/0.40 (bool(true) | (not1(true) = phi(true))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[198, 70])).
% 0.12/0.40 tff(200,plain,
% 0.12/0.40 (bool(true)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[199, 195])).
% 0.12/0.40 tff(201,plain,
% 0.12/0.40 ((~((prop(true) = true) <=> bool(true))) | (prop(true) = true) | (~bool(true))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(202,plain,
% 0.12/0.40 ((~((prop(true) = true) <=> bool(true))) | (prop(true) = true)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[201, 200])).
% 0.12/0.40 tff(203,plain,
% 0.12/0.40 (prop(true) = true),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[202, 186])).
% 0.12/0.40 tff(204,plain,
% 0.12/0.40 (lazy_impl(prop(true), true) = lazy_impl(true, true)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[203])).
% 0.12/0.40 tff(205,plain,
% 0.12/0.40 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(true) = lazy_impl(prop(true), true))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(206,plain,
% 0.12/0.40 (f7(true) = lazy_impl(prop(true), true)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[205, 86])).
% 0.12/0.40 tff(207,assumption,(P!6 = true), introduced(assumption)).
% 0.12/0.40 tff(208,plain,
% 0.12/0.40 (f7(P!6) = f7(true)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[207])).
% 0.12/0.40 tff(209,plain,
% 0.12/0.40 (lazy_impl(prop(P!6), P!6) = true),
% 0.12/0.40 inference(transitivity,[status(thm)],[123, 208, 206, 204, 184, 182])).
% 0.12/0.40 tff(210,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[142, 209])).
% 0.12/0.40 tff(211,plain,(~(P!6 = true)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.40 tff(212,plain,
% 0.12/0.40 ((~((P!6 = false) | (P!6 = true))) | (P!6 = false) | (P!6 = true)),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(213,plain,
% 0.12/0.40 (P!6 = false),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[212, 211, 171])).
% 0.12/0.40 tff(214,plain,
% 0.12/0.40 (f7(P!6) = f7(false)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[213])).
% 0.12/0.40 tff(215,plain,
% 0.12/0.40 (f7(P!6) = false),
% 0.12/0.40 inference(transitivity,[status(thm)],[214, 88, 79, 39, 30])).
% 0.12/0.40 tff(216,plain,
% 0.12/0.40 (phi(f7(P!6)) = phi(false)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[215])).
% 0.12/0.40 tff(217,plain,
% 0.12/0.40 (phi(false) = phi(f7(P!6))),
% 0.12/0.40 inference(symmetry,[status(thm)],[216])).
% 0.12/0.40 tff(218,plain,
% 0.12/0.40 ((false1 = false) <=> (false1 = false)),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(219,axiom,(false1 = false), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','def_false1')).
% 0.12/0.40 tff(220,plain,
% 0.20/0.41 (false1 = false),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.20/0.41 tff(221,plain,
% 0.20/0.41 (false1 = false2),
% 0.20/0.41 inference(transitivity,[status(thm)],[220, 127, 217, 7])).
% 0.20/0.41 tff(222,plain,
% 0.20/0.41 ((~(false1 = false2)) <=> (~(false1 = false2))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(223,axiom,(~(false1 = false2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','false1_false2')).
% 0.20/0.41 tff(224,plain,
% 0.20/0.41 (~(false1 = false2)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.20/0.41 tff(225,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[224, 221])).
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------