TSTP Solution File: SWW102+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW102+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 20:57:47 EDT 2022
% Result : Theorem 0.19s 0.48s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWW102+1 : TPTP v8.1.0. Released v5.2.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.33 % Computer : n019.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sun Sep 4 12:09:35 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 0.19/0.48 % SZS status Theorem
% 0.19/0.48 % SZS output start Proof
% 0.19/0.48 tff(not2_type, type, (
% 0.19/0.48 not2: $i > $i)).
% 0.19/0.48 tff(tptp_fun_P_7_type, type, (
% 0.19/0.48 tptp_fun_P_7: $i)).
% 0.19/0.48 tff(not1_type, type, (
% 0.19/0.48 not1: $i > $i)).
% 0.19/0.48 tff(phi_type, type, (
% 0.19/0.48 phi: $i > $i)).
% 0.19/0.48 tff(f7_type, type, (
% 0.19/0.48 f7: $i > $i)).
% 0.19/0.48 tff(tptp_fun_P_6_type, type, (
% 0.19/0.48 tptp_fun_P_6: $i)).
% 0.19/0.48 tff(impl_type, type, (
% 0.19/0.48 impl: ( $i * $i ) > $i)).
% 0.19/0.48 tff(false2_type, type, (
% 0.19/0.48 false2: $i)).
% 0.19/0.48 tff(forallprefers_type, type, (
% 0.19/0.48 forallprefers: ( $i * $i ) > $o)).
% 0.19/0.48 tff(false_type, type, (
% 0.19/0.48 false: $i)).
% 0.19/0.48 tff(d_type, type, (
% 0.19/0.48 d: $i > $o)).
% 0.19/0.48 tff(err_type, type, (
% 0.19/0.48 err: $i)).
% 0.19/0.48 tff(true_type, type, (
% 0.19/0.48 true: $i)).
% 0.19/0.48 tff(lazy_impl_type, type, (
% 0.19/0.48 lazy_impl: ( $i * $i ) > $i)).
% 0.19/0.48 tff(prop_type, type, (
% 0.19/0.48 prop: $i > $i)).
% 0.19/0.48 tff(bool_type, type, (
% 0.19/0.48 bool: $i > $o)).
% 0.19/0.48 tff(1,plain,
% 0.19/0.48 ((phi(phi(f7(P!6))) = impl(P!7, phi(f7(P!6)))) <=> (impl(P!7, phi(f7(P!6))) = phi(phi(f7(P!6))))),
% 0.19/0.48 inference(commutativity,[status(thm)],[])).
% 0.19/0.48 tff(2,plain,
% 0.19/0.48 (((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))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(3,plain,
% 0.19/0.48 (?[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))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 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')).
% 0.19/0.48 tff(5,plain,
% 0.19/0.48 (?[P: $i] : ((false2 = phi(f7(P))) & (~?[P1: $i] : forallprefers(f7(P1), f7(P))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.48 tff(6,plain,
% 0.19/0.48 ((false2 = phi(f7(P!6))) & ![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.19/0.48 tff(7,plain,
% 0.19/0.48 (false2 = phi(f7(P!6))),
% 0.19/0.48 inference(and_elim,[status(thm)],[6])).
% 0.19/0.48 tff(8,plain,
% 0.19/0.48 (phi(f7(P!6)) = false2),
% 0.19/0.48 inference(symmetry,[status(thm)],[7])).
% 0.19/0.48 tff(9,plain,
% 0.19/0.48 (impl(P!7, phi(f7(P!6))) = impl(P!7, false2)),
% 0.19/0.48 inference(monotonicity,[status(thm)],[8])).
% 0.19/0.48 tff(10,plain,
% 0.19/0.48 (impl(P!7, false2) = impl(P!7, phi(f7(P!6)))),
% 0.19/0.48 inference(symmetry,[status(thm)],[9])).
% 0.19/0.48 tff(11,plain,
% 0.19/0.48 (^[P: $i] : refl((not2(P) = impl(P, false2)) <=> (not2(P) = impl(P, false2)))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(12,plain,
% 0.19/0.48 (![P: $i] : (not2(P) = impl(P, false2)) <=> ![P: $i] : (not2(P) = impl(P, false2))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.48 tff(13,plain,
% 0.19/0.48 (![P: $i] : (not2(P) = impl(P, false2)) <=> ![P: $i] : (not2(P) = impl(P, false2))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(14,axiom,(![P: $i] : (not2(P) = impl(P, false2))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','def_not2')).
% 0.19/0.48 tff(15,plain,
% 0.19/0.48 (![P: $i] : (not2(P) = impl(P, false2))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.19/0.48 tff(16,plain,(
% 0.19/0.48 ![P: $i] : (not2(P) = impl(P, false2))),
% 0.19/0.48 inference(skolemize,[status(sab)],[15])).
% 0.19/0.48 tff(17,plain,
% 0.19/0.48 (![P: $i] : (not2(P) = impl(P, false2))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.19/0.48 tff(18,plain,
% 0.19/0.48 ((~![P: $i] : (not2(P) = impl(P, false2))) | (not2(P!7) = impl(P!7, false2))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(19,plain,
% 0.19/0.48 (not2(P!7) = impl(P!7, false2)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.19/0.48 tff(20,plain,
% 0.19/0.48 (not2(P!7) = impl(P!7, phi(f7(P!6)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[19, 10])).
% 0.19/0.48 tff(21,plain,
% 0.19/0.48 (d(false) <=> d(false)),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(22,axiom,((d(true) & d(false)) & d(err)), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','false_true_err_in_d')).
% 0.19/0.48 tff(23,plain,
% 0.19/0.48 (d(true) & d(false)),
% 0.19/0.48 inference(and_elim,[status(thm)],[22])).
% 0.19/0.48 tff(24,plain,
% 0.19/0.48 (d(false)),
% 0.19/0.48 inference(and_elim,[status(thm)],[23])).
% 0.19/0.48 tff(25,plain,
% 0.19/0.48 (d(false)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.19/0.48 tff(26,plain,
% 0.19/0.48 ((d(false) | (~(phi(false) = err))) | (~d(false))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(27,plain,
% 0.19/0.48 (d(false) | (~(phi(false) = err))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.19/0.48 tff(28,plain,
% 0.19/0.48 (^[X: $i] : refl(((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err))))) <=> ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(29,plain,
% 0.19/0.48 (![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err))))) <=> ![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[28])).
% 0.19/0.48 tff(30,plain,
% 0.19/0.48 (^[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)))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(31,plain,
% 0.19/0.48 (![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err))) <=> ![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[30])).
% 0.19/0.48 tff(32,plain,
% 0.19/0.48 (![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err))) <=> ![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(33,axiom,(![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','def_phi')).
% 0.19/0.48 tff(34,plain,
% 0.19/0.48 (![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.19/0.48 tff(35,plain,(
% 0.19/0.48 ![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err)))),
% 0.19/0.48 inference(skolemize,[status(sab)],[34])).
% 0.19/0.48 tff(36,plain,
% 0.19/0.48 (![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.19/0.48 tff(37,plain,
% 0.19/0.48 (![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.19/0.48 tff(38,plain,
% 0.19/0.48 (((~![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)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(39,plain,
% 0.19/0.48 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(false)) | (~(phi(false) = false)))) | (~(d(false) | (~(phi(false) = err)))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(40,plain,
% 0.19/0.48 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(false)) | (~(phi(false) = false)))) | (~(d(false) | (~(phi(false) = err))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.19/0.48 tff(41,plain,
% 0.19/0.48 (~((~d(false)) | (~(phi(false) = false)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[40, 37, 27])).
% 0.19/0.48 tff(42,plain,
% 0.19/0.48 (((~d(false)) | (~(phi(false) = false))) | (phi(false) = false)),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(43,plain,
% 0.19/0.48 (phi(false) = false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.19/0.48 tff(44,plain,
% 0.19/0.48 (^[B: $i] : refl((lazy_impl(not1(false), B) = phi(B)) <=> (lazy_impl(not1(false), B) = phi(B)))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(45,plain,
% 0.19/0.48 (![B: $i] : (lazy_impl(not1(false), B) = phi(B)) <=> ![B: $i] : (lazy_impl(not1(false), B) = phi(B))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[44])).
% 0.19/0.48 tff(46,plain,
% 0.19/0.48 (^[B: $i] : rewrite((lazy_impl(true, B) = phi(B)) <=> (lazy_impl(not1(false), B) = phi(B)))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(47,plain,
% 0.19/0.48 (![B: $i] : (lazy_impl(true, B) = phi(B)) <=> ![B: $i] : (lazy_impl(not1(false), B) = phi(B))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[46])).
% 0.19/0.48 tff(48,plain,
% 0.19/0.48 (![B: $i] : (lazy_impl(true, B) = phi(B)) <=> ![B: $i] : (lazy_impl(true, B) = phi(B))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(49,axiom,(![B: $i] : (lazy_impl(true, B) = phi(B))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','lazy_impl_axiom3')).
% 0.19/0.48 tff(50,plain,
% 0.19/0.48 (![B: $i] : (lazy_impl(true, B) = phi(B))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.48 tff(51,plain,
% 0.19/0.48 (![B: $i] : (lazy_impl(not1(false), B) = phi(B))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[50, 47])).
% 0.19/0.48 tff(52,plain,(
% 0.19/0.48 ![B: $i] : (lazy_impl(not1(false), B) = phi(B))),
% 0.19/0.48 inference(skolemize,[status(sab)],[51])).
% 0.19/0.48 tff(53,plain,
% 0.19/0.48 (![B: $i] : (lazy_impl(not1(false), B) = phi(B))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.19/0.48 tff(54,plain,
% 0.19/0.48 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), false) = phi(false))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(55,plain,
% 0.19/0.48 (lazy_impl(not1(false), false) = phi(false)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.19/0.48 tff(56,plain,
% 0.19/0.48 (^[X: $i] : refl(((prop(X) = not1(false)) <=> bool(X)) <=> ((prop(X) = not1(false)) <=> bool(X)))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(57,plain,
% 0.19/0.48 (![X: $i] : ((prop(X) = not1(false)) <=> bool(X)) <=> ![X: $i] : ((prop(X) = not1(false)) <=> bool(X))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[56])).
% 0.19/0.48 tff(58,plain,
% 0.19/0.48 (^[X: $i] : rewrite(((prop(X) = true) <=> bool(X)) <=> ((prop(X) = not1(false)) <=> bool(X)))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(59,plain,
% 0.19/0.48 (![X: $i] : ((prop(X) = true) <=> bool(X)) <=> ![X: $i] : ((prop(X) = not1(false)) <=> bool(X))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.48 tff(60,plain,
% 0.19/0.48 (![X: $i] : ((prop(X) = true) <=> bool(X)) <=> ![X: $i] : ((prop(X) = true) <=> bool(X))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(61,axiom,(![X: $i] : ((prop(X) = true) <=> bool(X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','prop_true')).
% 0.19/0.48 tff(62,plain,
% 0.19/0.48 (![X: $i] : ((prop(X) = true) <=> bool(X))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.19/0.48 tff(63,plain,
% 0.19/0.48 (![X: $i] : ((prop(X) = not1(false)) <=> bool(X))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[62, 59])).
% 0.19/0.48 tff(64,plain,(
% 0.19/0.48 ![X: $i] : ((prop(X) = not1(false)) <=> bool(X))),
% 0.19/0.48 inference(skolemize,[status(sab)],[63])).
% 0.19/0.48 tff(65,plain,
% 0.19/0.48 (![X: $i] : ((prop(X) = not1(false)) <=> bool(X))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.19/0.48 tff(66,plain,
% 0.19/0.48 ((~![X: $i] : ((prop(X) = not1(false)) <=> bool(X))) | ((prop(false) = not1(false)) <=> bool(false))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(67,plain,
% 0.19/0.48 ((prop(false) = not1(false)) <=> bool(false)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.19/0.48 tff(68,plain,
% 0.19/0.48 ((not1(false) = phi(false)) <=> (not1(false) = false)),
% 0.19/0.48 inference(monotonicity,[status(thm)],[43])).
% 0.19/0.48 tff(69,plain,
% 0.19/0.48 ((not1(false) = false) <=> (not1(false) = phi(false))),
% 0.19/0.48 inference(symmetry,[status(thm)],[68])).
% 0.19/0.48 tff(70,plain,
% 0.19/0.48 ((~(not1(false) = false)) <=> (~(not1(false) = phi(false)))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[69])).
% 0.19/0.48 tff(71,plain,
% 0.19/0.48 ((~(true = false)) <=> (~(not1(false) = false))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(72,plain,
% 0.19/0.48 ((~(true = false)) <=> (~(true = false))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(73,axiom,(((~(true = false)) & (~(true = err))) & (~(false = err))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','distinct_false_true_err')).
% 0.19/0.48 tff(74,plain,
% 0.19/0.48 ((~(true = false)) & (~(true = err))),
% 0.19/0.48 inference(and_elim,[status(thm)],[73])).
% 0.19/0.48 tff(75,plain,
% 0.19/0.48 (~(true = false)),
% 0.19/0.48 inference(and_elim,[status(thm)],[74])).
% 0.19/0.48 tff(76,plain,
% 0.19/0.48 (~(true = false)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[75, 72])).
% 0.19/0.48 tff(77,plain,
% 0.19/0.48 (~(not1(false) = false)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[76, 71])).
% 0.19/0.48 tff(78,plain,
% 0.19/0.48 (~(not1(false) = phi(false))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.19/0.48 tff(79,plain,
% 0.19/0.48 (^[A: $i] : refl((bool(A) | (not1(A) = phi(A))) <=> (bool(A) | (not1(A) = phi(A))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(80,plain,
% 0.19/0.48 (![A: $i] : (bool(A) | (not1(A) = phi(A))) <=> ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[79])).
% 0.19/0.48 tff(81,plain,
% 0.19/0.48 (![A: $i] : (bool(A) | (not1(A) = phi(A))) <=> ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(82,plain,
% 0.19/0.48 (^[A: $i] : rewrite(((~bool(A)) => (not1(A) = phi(A))) <=> (bool(A) | (not1(A) = phi(A))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(83,plain,
% 0.19/0.48 (![A: $i] : ((~bool(A)) => (not1(A) = phi(A))) <=> ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[82])).
% 0.19/0.48 tff(84,axiom,(![A: $i] : ((~bool(A)) => (not1(A) = phi(A)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','not1_axiom1')).
% 0.19/0.48 tff(85,plain,
% 0.19/0.48 (![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.19/0.48 tff(86,plain,
% 0.19/0.48 (![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.19/0.48 tff(87,plain,(
% 0.19/0.48 ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 0.19/0.48 inference(skolemize,[status(sab)],[86])).
% 0.19/0.48 tff(88,plain,
% 0.19/0.48 (![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[87, 80])).
% 0.19/0.48 tff(89,plain,
% 0.19/0.48 (((~![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)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(90,plain,
% 0.19/0.48 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | (bool(false) | (not1(false) = phi(false)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(91,plain,
% 0.19/0.48 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | bool(false) | (not1(false) = phi(false))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.19/0.48 tff(92,plain,
% 0.19/0.48 (bool(false) | (not1(false) = phi(false))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[91, 88])).
% 0.19/0.48 tff(93,plain,
% 0.19/0.48 (bool(false)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[92, 78])).
% 0.19/0.48 tff(94,plain,
% 0.19/0.48 ((~((prop(false) = not1(false)) <=> bool(false))) | (prop(false) = not1(false)) | (~bool(false))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(95,plain,
% 0.19/0.48 ((~((prop(false) = not1(false)) <=> bool(false))) | (prop(false) = not1(false))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.19/0.48 tff(96,plain,
% 0.19/0.48 (prop(false) = not1(false)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[95, 67])).
% 0.19/0.48 tff(97,plain,
% 0.19/0.48 (lazy_impl(prop(false), false) = lazy_impl(not1(false), false)),
% 0.19/0.48 inference(monotonicity,[status(thm)],[96])).
% 0.19/0.48 tff(98,plain,
% 0.19/0.48 (^[P: $i] : refl((f7(P) = lazy_impl(prop(P), P)) <=> (f7(P) = lazy_impl(prop(P), P)))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(99,plain,
% 0.19/0.48 (![P: $i] : (f7(P) = lazy_impl(prop(P), P)) <=> ![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[98])).
% 0.19/0.48 tff(100,plain,
% 0.19/0.48 (![P: $i] : (f7(P) = lazy_impl(prop(P), P)) <=> ![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(101,axiom,(![P: $i] : (f7(P) = lazy_impl(prop(P), P))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','def_f7')).
% 0.19/0.48 tff(102,plain,
% 0.19/0.48 (![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.19/0.48 tff(103,plain,(
% 0.19/0.48 ![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 0.19/0.48 inference(skolemize,[status(sab)],[102])).
% 0.19/0.48 tff(104,plain,
% 0.19/0.48 (![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.19/0.48 tff(105,plain,
% 0.19/0.48 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(false) = lazy_impl(prop(false), false))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(106,plain,
% 0.19/0.48 (f7(false) = lazy_impl(prop(false), false)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.19/0.48 tff(107,plain,
% 0.19/0.48 (^[B: $i] : refl((lazy_impl(false, B) = not1(false)) <=> (lazy_impl(false, B) = not1(false)))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(108,plain,
% 0.19/0.48 (![B: $i] : (lazy_impl(false, B) = not1(false)) <=> ![B: $i] : (lazy_impl(false, B) = not1(false))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[107])).
% 0.19/0.48 tff(109,plain,
% 0.19/0.48 (^[B: $i] : rewrite((lazy_impl(false, B) = true) <=> (lazy_impl(false, B) = not1(false)))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(110,plain,
% 0.19/0.48 (![B: $i] : (lazy_impl(false, B) = true) <=> ![B: $i] : (lazy_impl(false, B) = not1(false))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[109])).
% 0.19/0.48 tff(111,plain,
% 0.19/0.48 (![B: $i] : (lazy_impl(false, B) = true) <=> ![B: $i] : (lazy_impl(false, B) = true)),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(112,axiom,(![B: $i] : (lazy_impl(false, B) = true)), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','lazy_impl_axiom2')).
% 0.19/0.48 tff(113,plain,
% 0.19/0.48 (![B: $i] : (lazy_impl(false, B) = true)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.19/0.48 tff(114,plain,
% 0.19/0.48 (![B: $i] : (lazy_impl(false, B) = not1(false))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[113, 110])).
% 0.19/0.48 tff(115,plain,(
% 0.19/0.48 ![B: $i] : (lazy_impl(false, B) = not1(false))),
% 0.19/0.48 inference(skolemize,[status(sab)],[114])).
% 0.19/0.48 tff(116,plain,
% 0.19/0.48 (![B: $i] : (lazy_impl(false, B) = not1(false))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[115, 108])).
% 0.19/0.48 tff(117,plain,
% 0.19/0.48 ((~![B: $i] : (lazy_impl(false, B) = not1(false))) | (lazy_impl(false, P!6) = not1(false))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(118,plain,
% 0.19/0.48 (lazy_impl(false, P!6) = not1(false)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.19/0.48 tff(119,assumption,(prop(P!6) = false), introduced(assumption)).
% 0.19/0.48 tff(120,plain,
% 0.19/0.48 (lazy_impl(prop(P!6), P!6) = lazy_impl(false, P!6)),
% 0.19/0.48 inference(monotonicity,[status(thm)],[119])).
% 0.19/0.48 tff(121,plain,
% 0.19/0.48 (lazy_impl(prop(P!6), P!6) = not1(false)),
% 0.19/0.48 inference(transitivity,[status(thm)],[120, 118])).
% 0.19/0.48 tff(122,plain,
% 0.19/0.48 (^[X: $i, Y: $i] : refl((forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false))))))) <=> (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(123,plain,
% 0.19/0.48 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false))))))) <=> ![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[122])).
% 0.19/0.48 tff(124,plain,
% 0.19/0.48 (^[X: $i, Y: $i] : rewrite((forallprefers(X, Y) <=> (((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)) | ((X = false) & (Y = not1(false))))) <=> (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(125,plain,
% 0.19/0.48 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)) | ((X = false) & (Y = not1(false))))) <=> ![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[124])).
% 0.19/0.48 tff(126,plain,
% 0.19/0.48 (^[X: $i, Y: $i] : rewrite((forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)))) <=> (forallprefers(X, Y) <=> (((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)) | ((X = false) & (Y = not1(false))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(127,plain,
% 0.19/0.48 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)))) <=> ![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)) | ((X = false) & (Y = not1(false)))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[126])).
% 0.19/0.48 tff(128,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(129,plain,
% 0.19/0.49 (^[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)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(130,plain,
% 0.19/0.49 (![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))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[129])).
% 0.19/0.49 tff(131,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')).
% 0.19/0.49 tff(132,plain,
% 0.19/0.49 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.19/0.49 tff(133,plain,
% 0.19/0.49 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[132, 128])).
% 0.19/0.49 tff(134,plain,
% 0.19/0.49 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)) | ((X = false) & (Y = not1(false)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[133, 127])).
% 0.19/0.49 tff(135,plain,(
% 0.19/0.49 ![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)) | ((X = false) & (Y = not1(false)))))),
% 0.19/0.49 inference(skolemize,[status(sab)],[134])).
% 0.19/0.49 tff(136,plain,
% 0.19/0.49 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[135, 125])).
% 0.19/0.49 tff(137,plain,
% 0.19/0.49 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[136, 123])).
% 0.19/0.49 tff(138,plain,
% 0.19/0.49 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))) | (lazy_impl(prop(P!6), P!6) = not1(false))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))) | (lazy_impl(prop(P!6), P!6) = not1(false)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(139,plain,
% 0.19/0.49 ((forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(false) | (~d(false)))) | (~((~(false = false)) | (~(lazy_impl(prop(P!6), P!6) = not1(false))))))) <=> (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))) | (lazy_impl(prop(P!6), P!6) = not1(false))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(140,plain,
% 0.19/0.49 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(false) | (~d(false)))) | (~((~(false = false)) | (~(lazy_impl(prop(P!6), P!6) = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))) | (lazy_impl(prop(P!6), P!6) = not1(false)))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[139])).
% 0.19/0.49 tff(141,plain,
% 0.19/0.49 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(false) | (~d(false)))) | (~((~(false = false)) | (~(lazy_impl(prop(P!6), P!6) = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))) | (lazy_impl(prop(P!6), P!6) = not1(false)))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[140, 138])).
% 0.19/0.49 tff(142,plain,
% 0.19/0.49 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(false) | (~d(false)))) | (~((~(false = false)) | (~(lazy_impl(prop(P!6), P!6) = not1(false)))))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(143,plain,
% 0.19/0.49 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))) | (lazy_impl(prop(P!6), P!6) = not1(false))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.19/0.49 tff(144,plain,
% 0.19/0.49 (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))) | (lazy_impl(prop(P!6), P!6) = not1(false)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[143, 137])).
% 0.19/0.49 tff(145,plain,
% 0.19/0.49 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(P!6) = lazy_impl(prop(P!6), P!6))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(146,plain,
% 0.19/0.49 (f7(P!6) = lazy_impl(prop(P!6), P!6)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[145, 104])).
% 0.19/0.49 tff(147,plain,
% 0.19/0.49 (lazy_impl(prop(P!6), P!6) = f7(P!6)),
% 0.19/0.49 inference(symmetry,[status(thm)],[146])).
% 0.19/0.49 tff(148,plain,
% 0.19/0.49 (lazy_impl(prop(false), false) = f7(false)),
% 0.19/0.49 inference(symmetry,[status(thm)],[106])).
% 0.19/0.49 tff(149,plain,
% 0.19/0.49 (lazy_impl(not1(false), false) = lazy_impl(prop(false), false)),
% 0.19/0.49 inference(symmetry,[status(thm)],[97])).
% 0.19/0.49 tff(150,plain,
% 0.19/0.49 (phi(false) = lazy_impl(not1(false), false)),
% 0.19/0.49 inference(symmetry,[status(thm)],[55])).
% 0.19/0.49 tff(151,plain,
% 0.19/0.49 (false = phi(false)),
% 0.19/0.49 inference(symmetry,[status(thm)],[43])).
% 0.19/0.49 tff(152,plain,
% 0.19/0.49 (false = f7(false)),
% 0.19/0.49 inference(transitivity,[status(thm)],[151, 150, 149, 148])).
% 0.19/0.49 tff(153,plain,
% 0.19/0.49 (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> forallprefers(f7(false), f7(P!6))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[152, 147])).
% 0.19/0.49 tff(154,plain,
% 0.19/0.49 (forallprefers(f7(false), f7(P!6)) <=> forallprefers(false, lazy_impl(prop(P!6), P!6))),
% 0.19/0.49 inference(symmetry,[status(thm)],[153])).
% 0.19/0.49 tff(155,plain,
% 0.19/0.49 ((~forallprefers(f7(false), f7(P!6))) <=> (~forallprefers(false, lazy_impl(prop(P!6), P!6)))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[154])).
% 0.19/0.49 tff(156,plain,
% 0.19/0.49 (^[P1: $i] : refl((~forallprefers(f7(P1), f7(P!6))) <=> (~forallprefers(f7(P1), f7(P!6))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(157,plain,
% 0.19/0.49 (![P1: $i] : (~forallprefers(f7(P1), f7(P!6))) <=> ![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[156])).
% 0.19/0.49 tff(158,plain,
% 0.19/0.49 (![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 0.19/0.49 inference(and_elim,[status(thm)],[6])).
% 0.19/0.49 tff(159,plain,
% 0.19/0.49 (![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.19/0.49 tff(160,plain,
% 0.19/0.49 ((~![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))) | (~forallprefers(f7(false), f7(P!6)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(161,plain,
% 0.19/0.49 (~forallprefers(f7(false), f7(P!6))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[160, 159])).
% 0.19/0.49 tff(162,plain,
% 0.19/0.49 (~forallprefers(false, lazy_impl(prop(P!6), P!6))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[161, 155])).
% 0.19/0.49 tff(163,plain,
% 0.19/0.49 ((~(forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))) | (lazy_impl(prop(P!6), P!6) = not1(false))))) | forallprefers(false, lazy_impl(prop(P!6), P!6)) | (~((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))) | (lazy_impl(prop(P!6), P!6) = not1(false))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(164,plain,
% 0.19/0.49 (~((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))) | (lazy_impl(prop(P!6), P!6) = not1(false)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[163, 162, 144])).
% 0.19/0.49 tff(165,plain,
% 0.19/0.49 (((~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))) | (lazy_impl(prop(P!6), P!6) = not1(false))) | (~(lazy_impl(prop(P!6), P!6) = not1(false)))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(166,plain,
% 0.19/0.49 (~(lazy_impl(prop(P!6), P!6) = not1(false))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[165, 164])).
% 0.19/0.49 tff(167,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[166, 121])).
% 0.19/0.49 tff(168,plain,(~(prop(P!6) = false)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(169,plain,
% 0.19/0.49 (^[X: $i] : refl(((prop(X) = false) <=> (~bool(X))) <=> ((prop(X) = false) <=> (~bool(X))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(170,plain,
% 0.19/0.49 (![X: $i] : ((prop(X) = false) <=> (~bool(X))) <=> ![X: $i] : ((prop(X) = false) <=> (~bool(X)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[169])).
% 0.19/0.49 tff(171,plain,
% 0.19/0.49 (![X: $i] : ((prop(X) = false) <=> (~bool(X))) <=> ![X: $i] : ((prop(X) = false) <=> (~bool(X)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(172,axiom,(![X: $i] : ((prop(X) = false) <=> (~bool(X)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','prop_false')).
% 0.19/0.49 tff(173,plain,
% 0.19/0.49 (![X: $i] : ((prop(X) = false) <=> (~bool(X)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.19/0.49 tff(174,plain,(
% 0.19/0.49 ![X: $i] : ((prop(X) = false) <=> (~bool(X)))),
% 0.19/0.49 inference(skolemize,[status(sab)],[173])).
% 0.19/0.49 tff(175,plain,
% 0.19/0.49 (![X: $i] : ((prop(X) = false) <=> (~bool(X)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[174, 170])).
% 0.19/0.49 tff(176,plain,
% 0.19/0.49 ((~![X: $i] : ((prop(X) = false) <=> (~bool(X)))) | ((prop(P!6) = false) <=> (~bool(P!6)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(177,plain,
% 0.19/0.49 ((prop(P!6) = false) <=> (~bool(P!6))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[176, 175])).
% 0.19/0.49 tff(178,plain,
% 0.19/0.49 ((~((prop(P!6) = false) <=> (~bool(P!6)))) | (prop(P!6) = false) | bool(P!6)),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(179,plain,
% 0.19/0.49 ((prop(P!6) = false) | bool(P!6)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[178, 177])).
% 0.19/0.49 tff(180,plain,
% 0.19/0.49 (bool(P!6)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[179, 168])).
% 0.19/0.49 tff(181,plain,
% 0.19/0.49 (^[X: $i] : refl((bool(X) <=> ((X = false) | (X = not1(false)))) <=> (bool(X) <=> ((X = false) | (X = not1(false)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(182,plain,
% 0.19/0.49 (![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false)))) <=> ![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[181])).
% 0.19/0.49 tff(183,plain,
% 0.19/0.49 (^[X: $i] : rewrite((bool(X) <=> ((X = false) | (X = true))) <=> (bool(X) <=> ((X = false) | (X = not1(false)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(184,plain,
% 0.19/0.49 (![X: $i] : (bool(X) <=> ((X = false) | (X = true))) <=> ![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[183])).
% 0.19/0.49 tff(185,plain,
% 0.19/0.49 (![X: $i] : (bool(X) <=> ((X = false) | (X = true))) <=> ![X: $i] : (bool(X) <=> ((X = false) | (X = true)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(186,axiom,(![X: $i] : (bool(X) <=> ((X = false) | (X = true)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','def_bool')).
% 0.19/0.49 tff(187,plain,
% 0.19/0.49 (![X: $i] : (bool(X) <=> ((X = false) | (X = true)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.19/0.49 tff(188,plain,
% 0.19/0.49 (![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[187, 184])).
% 0.19/0.49 tff(189,plain,(
% 0.19/0.49 ![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))),
% 0.19/0.49 inference(skolemize,[status(sab)],[188])).
% 0.19/0.49 tff(190,plain,
% 0.19/0.49 (![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[189, 182])).
% 0.19/0.49 tff(191,plain,
% 0.19/0.49 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(P!6) <=> ((P!6 = false) | (P!6 = not1(false))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(192,plain,
% 0.19/0.49 (bool(P!6) <=> ((P!6 = false) | (P!6 = not1(false)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[191, 190])).
% 0.19/0.49 tff(193,plain,
% 0.19/0.49 ((~(bool(P!6) <=> ((P!6 = false) | (P!6 = not1(false))))) | (~bool(P!6)) | ((P!6 = false) | (P!6 = not1(false)))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(194,plain,
% 0.19/0.49 ((~bool(P!6)) | ((P!6 = false) | (P!6 = not1(false)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[193, 192])).
% 0.19/0.49 tff(195,plain,
% 0.19/0.49 ((P!6 = false) | (P!6 = not1(false))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[194, 180])).
% 0.19/0.49 tff(196,plain,
% 0.19/0.49 (d(true) <=> d(not1(false))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(197,plain,
% 0.19/0.49 (d(true) <=> d(true)),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(198,plain,
% 0.19/0.49 (d(true)),
% 0.19/0.49 inference(and_elim,[status(thm)],[23])).
% 0.19/0.49 tff(199,plain,
% 0.19/0.49 (d(true)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.19/0.49 tff(200,plain,
% 0.19/0.49 (d(not1(false))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[199, 196])).
% 0.19/0.49 tff(201,plain,
% 0.19/0.49 ((d(not1(false)) | (~(phi(not1(false)) = err))) | (~d(not1(false)))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(202,plain,
% 0.19/0.49 (d(not1(false)) | (~(phi(not1(false)) = err))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[201, 200])).
% 0.19/0.49 tff(203,plain,
% 0.19/0.49 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(not1(false))) | (~(phi(not1(false)) = not1(false))))) | (~(d(not1(false)) | (~(phi(not1(false)) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(not1(false))) | (~(phi(not1(false)) = not1(false))))) | (~(d(not1(false)) | (~(phi(not1(false)) = err)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(204,plain,
% 0.19/0.49 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(not1(false))) | (~(phi(not1(false)) = not1(false))))) | (~(d(not1(false)) | (~(phi(not1(false)) = err)))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(205,plain,
% 0.19/0.49 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(not1(false))) | (~(phi(not1(false)) = not1(false))))) | (~(d(not1(false)) | (~(phi(not1(false)) = err))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.19/0.49 tff(206,plain,
% 0.19/0.49 (~((~d(not1(false))) | (~(phi(not1(false)) = not1(false))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[205, 37, 202])).
% 0.19/0.49 tff(207,plain,
% 0.19/0.49 (((~d(not1(false))) | (~(phi(not1(false)) = not1(false)))) | (phi(not1(false)) = not1(false))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(208,plain,
% 0.19/0.49 (phi(not1(false)) = not1(false)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[207, 206])).
% 0.19/0.49 tff(209,plain,
% 0.19/0.49 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), not1(false)) = phi(not1(false)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(210,plain,
% 0.19/0.49 (lazy_impl(not1(false), not1(false)) = phi(not1(false))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[209, 53])).
% 0.19/0.49 tff(211,plain,
% 0.19/0.49 ((~![X: $i] : ((prop(X) = not1(false)) <=> bool(X))) | ((prop(not1(false)) = not1(false)) <=> bool(not1(false)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(212,plain,
% 0.19/0.49 ((prop(not1(false)) = not1(false)) <=> bool(not1(false))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[211, 65])).
% 0.19/0.49 tff(213,plain,
% 0.19/0.49 ((false = not1(false)) <=> (not1(false) = false)),
% 0.19/0.49 inference(commutativity,[status(thm)],[])).
% 0.19/0.49 tff(214,plain,
% 0.19/0.49 ((not1(true) = false) <=> (not1(not1(false)) = false)),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(215,plain,
% 0.19/0.49 ((not1(true) = false) <=> (not1(true) = false)),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(216,axiom,(not1(true) = false), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','not1_axiom3')).
% 0.19/0.49 tff(217,plain,
% 0.19/0.49 (not1(true) = false),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.19/0.49 tff(218,plain,
% 0.19/0.49 (not1(not1(false)) = false),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[217, 214])).
% 0.19/0.49 tff(219,plain,
% 0.19/0.49 ((not1(not1(false)) = phi(not1(false))) <=> (false = not1(false))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[218, 208])).
% 0.19/0.49 tff(220,plain,
% 0.19/0.49 ((not1(not1(false)) = phi(not1(false))) <=> (not1(false) = false)),
% 0.19/0.49 inference(transitivity,[status(thm)],[219, 213])).
% 0.19/0.49 tff(221,plain,
% 0.19/0.49 ((not1(false) = false) <=> (not1(not1(false)) = phi(not1(false)))),
% 0.19/0.49 inference(symmetry,[status(thm)],[220])).
% 0.19/0.49 tff(222,plain,
% 0.19/0.49 ((~(not1(false) = false)) <=> (~(not1(not1(false)) = phi(not1(false))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[221])).
% 0.19/0.49 tff(223,plain,
% 0.19/0.49 (~(not1(not1(false)) = phi(not1(false)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[77, 222])).
% 0.19/0.49 tff(224,plain,
% 0.19/0.49 (((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | (bool(not1(false)) | (not1(not1(false)) = phi(not1(false))))) <=> ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | bool(not1(false)) | (not1(not1(false)) = phi(not1(false))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(225,plain,
% 0.19/0.49 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | (bool(not1(false)) | (not1(not1(false)) = phi(not1(false))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(226,plain,
% 0.19/0.49 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | bool(not1(false)) | (not1(not1(false)) = phi(not1(false)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.19/0.49 tff(227,plain,
% 0.19/0.49 (bool(not1(false)) | (not1(not1(false)) = phi(not1(false)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[226, 88])).
% 0.19/0.49 tff(228,plain,
% 0.19/0.49 (bool(not1(false))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[227, 223])).
% 0.19/0.49 tff(229,plain,
% 0.19/0.49 ((~((prop(not1(false)) = not1(false)) <=> bool(not1(false)))) | (prop(not1(false)) = not1(false)) | (~bool(not1(false)))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(230,plain,
% 0.19/0.49 ((~((prop(not1(false)) = not1(false)) <=> bool(not1(false)))) | (prop(not1(false)) = not1(false))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[229, 228])).
% 0.19/0.49 tff(231,plain,
% 0.19/0.49 (prop(not1(false)) = not1(false)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[230, 212])).
% 0.19/0.49 tff(232,plain,
% 0.19/0.49 (lazy_impl(prop(not1(false)), not1(false)) = lazy_impl(not1(false), not1(false))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[231])).
% 0.19/0.49 tff(233,plain,
% 0.19/0.49 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(not1(false)) = lazy_impl(prop(not1(false)), not1(false)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(234,plain,
% 0.19/0.49 (f7(not1(false)) = lazy_impl(prop(not1(false)), not1(false))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[233, 104])).
% 0.19/0.49 tff(235,assumption,(P!6 = not1(false)), introduced(assumption)).
% 0.19/0.49 tff(236,plain,
% 0.19/0.49 (f7(P!6) = f7(not1(false))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[235])).
% 0.19/0.49 tff(237,plain,
% 0.19/0.49 (lazy_impl(prop(P!6), P!6) = not1(false)),
% 0.19/0.49 inference(transitivity,[status(thm)],[147, 236, 234, 232, 210, 208])).
% 0.19/0.49 tff(238,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[166, 237])).
% 0.19/0.49 tff(239,plain,(~(P!6 = not1(false))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(240,plain,
% 0.19/0.49 ((~((P!6 = false) | (P!6 = not1(false)))) | (P!6 = false) | (P!6 = not1(false))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(241,plain,
% 0.19/0.49 (P!6 = false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[240, 239, 195])).
% 0.19/0.49 tff(242,plain,
% 0.19/0.49 (f7(P!6) = f7(false)),
% 0.19/0.49 inference(monotonicity,[status(thm)],[241])).
% 0.19/0.49 tff(243,plain,
% 0.19/0.49 (f7(P!6) = false),
% 0.19/0.49 inference(transitivity,[status(thm)],[242, 106, 97, 55, 43])).
% 0.19/0.49 tff(244,plain,
% 0.19/0.49 (phi(f7(P!6)) = phi(false)),
% 0.19/0.49 inference(monotonicity,[status(thm)],[243])).
% 0.19/0.49 tff(245,plain,
% 0.19/0.49 (phi(f7(P!6)) = false),
% 0.19/0.49 inference(transitivity,[status(thm)],[244, 43])).
% 0.19/0.49 tff(246,plain,
% 0.19/0.49 (phi(phi(f7(P!6))) = phi(false)),
% 0.19/0.49 inference(monotonicity,[status(thm)],[245])).
% 0.19/0.49 tff(247,plain,
% 0.19/0.49 (phi(false) = phi(phi(f7(P!6)))),
% 0.19/0.49 inference(symmetry,[status(thm)],[246])).
% 0.19/0.49 tff(248,plain,
% 0.19/0.49 (^[B: $i] : refl(((~bool(B)) | (impl(false, B) = not1(false))) <=> ((~bool(B)) | (impl(false, B) = not1(false))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(249,plain,
% 0.19/0.49 (![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false))) <=> ![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[248])).
% 0.19/0.49 tff(250,plain,
% 0.19/0.49 (^[B: $i] : rewrite(((~bool(B)) | (impl(false, B) = true)) <=> ((~bool(B)) | (impl(false, B) = not1(false))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(251,plain,
% 0.19/0.49 (![B: $i] : ((~bool(B)) | (impl(false, B) = true)) <=> ![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[250])).
% 0.19/0.49 tff(252,plain,
% 0.19/0.49 (![B: $i] : ((~bool(B)) | (impl(false, B) = true)) <=> ![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(253,plain,
% 0.19/0.49 (^[B: $i] : rewrite((bool(B) => (impl(false, B) = true)) <=> ((~bool(B)) | (impl(false, B) = true)))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(254,plain,
% 0.19/0.49 (![B: $i] : (bool(B) => (impl(false, B) = true)) <=> ![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[253])).
% 0.19/0.49 tff(255,axiom,(![B: $i] : (bool(B) => (impl(false, B) = true))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','impl_axiom3')).
% 0.19/0.49 tff(256,plain,
% 0.19/0.49 (![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.19/0.49 tff(257,plain,
% 0.19/0.49 (![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[256, 252])).
% 0.19/0.49 tff(258,plain,
% 0.19/0.49 (![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[257, 251])).
% 0.19/0.49 tff(259,plain,(
% 0.19/0.49 ![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))),
% 0.19/0.49 inference(skolemize,[status(sab)],[258])).
% 0.19/0.49 tff(260,plain,
% 0.19/0.49 (![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[259, 249])).
% 0.19/0.49 tff(261,plain,
% 0.19/0.49 (((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | ((~bool(false)) | (impl(false, false) = not1(false)))) <=> ((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | (~bool(false)) | (impl(false, false) = not1(false)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(262,plain,
% 0.19/0.49 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | ((~bool(false)) | (impl(false, false) = not1(false)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(263,plain,
% 0.19/0.49 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = not1(false)))) | (~bool(false)) | (impl(false, false) = not1(false))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.19/0.49 tff(264,plain,
% 0.19/0.49 (impl(false, false) = not1(false)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[263, 260, 93])).
% 0.19/0.49 tff(265,plain,
% 0.19/0.49 (false2 = false),
% 0.19/0.49 inference(transitivity,[status(thm)],[7, 244, 43])).
% 0.19/0.49 tff(266,plain,
% 0.19/0.49 (impl(false, false2) = impl(false, false)),
% 0.19/0.49 inference(monotonicity,[status(thm)],[265])).
% 0.19/0.49 tff(267,plain,
% 0.19/0.49 ((~![P: $i] : (not2(P) = impl(P, false2))) | (not2(false) = impl(false, false2))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(268,plain,
% 0.19/0.49 (not2(false) = impl(false, false2)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[267, 17])).
% 0.19/0.49 tff(269,assumption,(lazy_impl(prop(P!7), P!7) = false), introduced(assumption)).
% 0.19/0.49 tff(270,plain,
% 0.19/0.49 ((~![X: $i] : ((prop(X) = not1(false)) <=> bool(X))) | ((prop(P!7) = not1(false)) <=> bool(P!7))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(271,plain,
% 0.19/0.49 ((prop(P!7) = not1(false)) <=> bool(P!7)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[270, 65])).
% 0.19/0.49 tff(272,plain,
% 0.19/0.49 ((phi(P!7) = impl(P!7, phi(f7(P!6)))) <=> (impl(P!7, phi(f7(P!6))) = phi(P!7))),
% 0.19/0.49 inference(commutativity,[status(thm)],[])).
% 0.19/0.49 tff(273,assumption,(~bool(P!7)), introduced(assumption)).
% 0.19/0.49 tff(274,plain,
% 0.19/0.49 (((~![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)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(275,plain,
% 0.19/0.49 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | (bool(P!7) | (not1(P!7) = phi(P!7)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(276,plain,
% 0.19/0.49 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | bool(P!7) | (not1(P!7) = phi(P!7))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.19/0.49 tff(277,plain,
% 0.19/0.49 (bool(P!7) | (not1(P!7) = phi(P!7))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[276, 88])).
% 0.19/0.49 tff(278,plain,
% 0.19/0.49 (not1(P!7) = phi(P!7)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[277, 273])).
% 0.19/0.49 tff(279,plain,
% 0.19/0.49 ((not1(P!7) = not2(P!7)) <=> (phi(P!7) = impl(P!7, phi(f7(P!6))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[278, 20])).
% 0.19/0.49 tff(280,plain,
% 0.19/0.49 ((not1(P!7) = not2(P!7)) <=> (impl(P!7, phi(f7(P!6))) = phi(P!7))),
% 0.19/0.49 inference(transitivity,[status(thm)],[279, 272])).
% 0.19/0.49 tff(281,plain,
% 0.19/0.49 ((impl(P!7, phi(f7(P!6))) = phi(P!7)) <=> (not1(P!7) = not2(P!7))),
% 0.19/0.49 inference(symmetry,[status(thm)],[280])).
% 0.19/0.49 tff(282,plain,
% 0.19/0.49 (^[A: $i, B: $i] : refl((bool(A) | (impl(A, B) = phi(A))) <=> (bool(A) | (impl(A, B) = phi(A))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(283,plain,
% 0.19/0.49 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A))) <=> ![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[282])).
% 0.19/0.49 tff(284,plain,
% 0.19/0.49 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A))) <=> ![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(285,plain,
% 0.19/0.49 (^[A: $i, B: $i] : rewrite(((~bool(A)) => (impl(A, B) = phi(A))) <=> (bool(A) | (impl(A, B) = phi(A))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(286,plain,
% 0.19/0.49 (![A: $i, B: $i] : ((~bool(A)) => (impl(A, B) = phi(A))) <=> ![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[285])).
% 0.19/0.49 tff(287,axiom,(![A: $i, B: $i] : ((~bool(A)) => (impl(A, B) = phi(A)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','impl_axiom1')).
% 0.19/0.49 tff(288,plain,
% 0.19/0.49 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.19/0.49 tff(289,plain,
% 0.19/0.49 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[288, 284])).
% 0.19/0.49 tff(290,plain,(
% 0.19/0.49 ![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 0.19/0.49 inference(skolemize,[status(sab)],[289])).
% 0.19/0.49 tff(291,plain,
% 0.19/0.49 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[290, 283])).
% 0.19/0.49 tff(292,plain,
% 0.19/0.49 (((~![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)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(293,plain,
% 0.19/0.49 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(P!7) | (impl(P!7, phi(f7(P!6))) = phi(P!7)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(294,plain,
% 0.19/0.49 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(P!7) | (impl(P!7, phi(f7(P!6))) = phi(P!7))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[293, 292])).
% 0.19/0.49 tff(295,plain,
% 0.19/0.49 (bool(P!7) | (impl(P!7, phi(f7(P!6))) = phi(P!7))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[294, 291])).
% 0.19/0.49 tff(296,plain,
% 0.19/0.49 (impl(P!7, phi(f7(P!6))) = phi(P!7)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[295, 273])).
% 0.19/0.49 tff(297,plain,
% 0.19/0.49 (not1(P!7) = not2(P!7)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[296, 281])).
% 0.19/0.49 tff(298,plain,
% 0.19/0.49 ((~![P: $i] : (not1(P) = not2(P))) <=> (~![P: $i] : (not1(P) = not2(P)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(299,axiom,(~![P: $i] : (not1(P) = not2(P))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not1_not2')).
% 0.19/0.49 tff(300,plain,
% 0.19/0.49 (~![P: $i] : (not1(P) = not2(P))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[299, 298])).
% 0.19/0.49 tff(301,plain,
% 0.19/0.49 (~![P: $i] : (not1(P) = not2(P))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[300, 298])).
% 0.19/0.49 tff(302,plain,
% 0.19/0.49 (~![P: $i] : (not1(P) = not2(P))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[301, 298])).
% 0.19/0.49 tff(303,plain,
% 0.19/0.49 (~![P: $i] : (not1(P) = not2(P))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[302, 298])).
% 0.19/0.49 tff(304,plain,
% 0.19/0.49 (~![P: $i] : (not1(P) = not2(P))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[303, 298])).
% 0.19/0.49 tff(305,plain,
% 0.19/0.49 (~![P: $i] : (not1(P) = not2(P))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[304, 298])).
% 0.19/0.49 tff(306,plain,
% 0.19/0.49 (~![P: $i] : (not1(P) = not2(P))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[305, 298])).
% 0.19/0.49 tff(307,plain,
% 0.19/0.49 (~![P: $i] : (not1(P) = not2(P))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[306, 298])).
% 0.19/0.49 tff(308,plain,(
% 0.19/0.49 ~(not1(P!7) = not2(P!7))),
% 0.19/0.49 inference(skolemize,[status(sab)],[307])).
% 0.19/0.49 tff(309,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[308, 297])).
% 0.19/0.49 tff(310,plain,(bool(P!7)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(311,plain,
% 0.19/0.49 ((~((prop(P!7) = not1(false)) <=> bool(P!7))) | (prop(P!7) = not1(false)) | (~bool(P!7))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(312,plain,
% 0.19/0.49 ((~((prop(P!7) = not1(false)) <=> bool(P!7))) | (prop(P!7) = not1(false))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[311, 310])).
% 0.19/0.49 tff(313,plain,
% 0.19/0.49 (prop(P!7) = not1(false)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[312, 271])).
% 0.19/0.49 tff(314,plain,
% 0.19/0.49 (not1(false) = prop(P!7)),
% 0.19/0.49 inference(symmetry,[status(thm)],[313])).
% 0.19/0.49 tff(315,plain,
% 0.19/0.49 (lazy_impl(not1(false), P!7) = lazy_impl(prop(P!7), P!7)),
% 0.19/0.49 inference(monotonicity,[status(thm)],[314])).
% 0.19/0.49 tff(316,plain,
% 0.19/0.49 ((~![B: $i] : (lazy_impl(not1(false), B) = phi(B))) | (lazy_impl(not1(false), P!7) = phi(P!7))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(317,plain,
% 0.19/0.49 (lazy_impl(not1(false), P!7) = phi(P!7)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[316, 53])).
% 0.19/0.49 tff(318,plain,
% 0.19/0.49 (phi(P!7) = lazy_impl(not1(false), P!7)),
% 0.19/0.50 inference(symmetry,[status(thm)],[317])).
% 0.19/0.50 tff(319,plain,
% 0.19/0.50 ((err = not1(false)) <=> (not1(false) = err)),
% 0.19/0.50 inference(commutativity,[status(thm)],[])).
% 0.19/0.50 tff(320,assumption,(phi(P!7) = err), introduced(assumption)).
% 0.19/0.50 tff(321,plain,
% 0.19/0.50 (lazy_impl(prop(P!7), P!7) = lazy_impl(not1(false), P!7)),
% 0.19/0.50 inference(symmetry,[status(thm)],[315])).
% 0.19/0.50 tff(322,plain,
% 0.19/0.50 (lazy_impl(prop(P!7), P!7) = err),
% 0.19/0.50 inference(transitivity,[status(thm)],[321, 317, 320])).
% 0.19/0.50 tff(323,plain,
% 0.19/0.50 ((lazy_impl(prop(P!7), P!7) = not1(false)) <=> (err = not1(false))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[322])).
% 0.19/0.50 tff(324,plain,
% 0.19/0.50 ((lazy_impl(prop(P!7), P!7) = not1(false)) <=> (not1(false) = err)),
% 0.19/0.50 inference(transitivity,[status(thm)],[323, 319])).
% 0.19/0.50 tff(325,plain,
% 0.19/0.50 ((not1(false) = err) <=> (lazy_impl(prop(P!7), P!7) = not1(false))),
% 0.19/0.50 inference(symmetry,[status(thm)],[324])).
% 0.19/0.50 tff(326,plain,
% 0.19/0.50 ((~(not1(false) = err)) <=> (~(lazy_impl(prop(P!7), P!7) = not1(false)))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[325])).
% 0.19/0.50 tff(327,plain,
% 0.19/0.50 ((~(true = err)) <=> (~(not1(false) = err))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(328,plain,
% 0.19/0.50 ((~(true = err)) <=> (~(true = err))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(329,plain,
% 0.19/0.50 (~(true = err)),
% 0.19/0.50 inference(and_elim,[status(thm)],[74])).
% 0.19/0.50 tff(330,plain,
% 0.19/0.50 (~(true = err)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.19/0.50 tff(331,plain,
% 0.19/0.50 (~(not1(false) = err)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[330, 327])).
% 0.19/0.50 tff(332,plain,
% 0.19/0.50 (~(lazy_impl(prop(P!7), P!7) = not1(false))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[331, 326])).
% 0.19/0.50 tff(333,plain,
% 0.19/0.50 ((err = false) <=> (false = err)),
% 0.19/0.50 inference(commutativity,[status(thm)],[])).
% 0.19/0.50 tff(334,plain,
% 0.19/0.50 ((lazy_impl(prop(P!7), P!7) = false) <=> (err = false)),
% 0.19/0.50 inference(monotonicity,[status(thm)],[322])).
% 0.19/0.50 tff(335,plain,
% 0.19/0.50 ((lazy_impl(prop(P!7), P!7) = false) <=> (false = err)),
% 0.19/0.50 inference(transitivity,[status(thm)],[334, 333])).
% 0.19/0.50 tff(336,plain,
% 0.19/0.50 ((false = err) <=> (lazy_impl(prop(P!7), P!7) = false)),
% 0.19/0.50 inference(symmetry,[status(thm)],[335])).
% 0.19/0.50 tff(337,plain,
% 0.19/0.50 ((~(false = err)) <=> (~(lazy_impl(prop(P!7), P!7) = false))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[336])).
% 0.19/0.50 tff(338,plain,
% 0.19/0.50 ((~(false = err)) <=> (~(false = err))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(339,plain,
% 0.19/0.50 (~(false = err)),
% 0.19/0.50 inference(and_elim,[status(thm)],[73])).
% 0.19/0.50 tff(340,plain,
% 0.19/0.50 (~(false = err)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[339, 338])).
% 0.19/0.50 tff(341,plain,
% 0.19/0.50 (~(lazy_impl(prop(P!7), P!7) = false)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[340, 337])).
% 0.19/0.50 tff(342,plain,
% 0.19/0.50 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(lazy_impl(prop(P!7), P!7)) <=> ((lazy_impl(prop(P!7), P!7) = false) | (lazy_impl(prop(P!7), P!7) = not1(false))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(343,plain,
% 0.19/0.50 (bool(lazy_impl(prop(P!7), P!7)) <=> ((lazy_impl(prop(P!7), P!7) = false) | (lazy_impl(prop(P!7), P!7) = not1(false)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[342, 190])).
% 0.19/0.50 tff(344,plain,
% 0.19/0.50 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(P!7), P!7), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7))))) | (~((~(lazy_impl(prop(P!7), P!7) = false)) | (~(false = not1(false))))) | (~((~d(false)) | d(lazy_impl(prop(P!7), P!7))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(P!7), P!7), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7))))) | (~((~(lazy_impl(prop(P!7), P!7) = false)) | (~(false = not1(false))))) | (~((~d(false)) | d(lazy_impl(prop(P!7), P!7)))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(345,plain,
% 0.19/0.50 ((forallprefers(lazy_impl(prop(P!7), P!7), false) <=> ((~(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))))) | (~((~(lazy_impl(prop(P!7), P!7) = false)) | (~(false = not1(false))))))) <=> (forallprefers(lazy_impl(prop(P!7), P!7), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7))))) | (~((~(lazy_impl(prop(P!7), P!7) = false)) | (~(false = not1(false))))) | (~((~d(false)) | d(lazy_impl(prop(P!7), P!7))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(346,plain,
% 0.19/0.50 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(P!7), P!7), false) <=> ((~(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))))) | (~((~(lazy_impl(prop(P!7), P!7) = false)) | (~(false = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(P!7), P!7), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7))))) | (~((~(lazy_impl(prop(P!7), P!7) = false)) | (~(false = not1(false))))) | (~((~d(false)) | d(lazy_impl(prop(P!7), P!7)))))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[345])).
% 0.19/0.50 tff(347,plain,
% 0.19/0.50 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(P!7), P!7), false) <=> ((~(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))))) | (~((~(lazy_impl(prop(P!7), P!7) = false)) | (~(false = not1(false)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(P!7), P!7), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7))))) | (~((~(lazy_impl(prop(P!7), P!7) = false)) | (~(false = not1(false))))) | (~((~d(false)) | d(lazy_impl(prop(P!7), P!7)))))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[346, 344])).
% 0.19/0.50 tff(348,plain,
% 0.19/0.50 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(P!7), P!7), false) <=> ((~(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))))) | (~((~(lazy_impl(prop(P!7), P!7) = false)) | (~(false = not1(false)))))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(349,plain,
% 0.19/0.50 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))) | (~((~(X = false)) | (~(Y = not1(false)))))))) | (forallprefers(lazy_impl(prop(P!7), P!7), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7))))) | (~((~(lazy_impl(prop(P!7), P!7) = false)) | (~(false = not1(false))))) | (~((~d(false)) | d(lazy_impl(prop(P!7), P!7))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[348, 347])).
% 0.19/0.50 tff(350,plain,
% 0.19/0.50 (forallprefers(lazy_impl(prop(P!7), P!7), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7))))) | (~((~(lazy_impl(prop(P!7), P!7) = false)) | (~(false = not1(false))))) | (~((~d(false)) | d(lazy_impl(prop(P!7), P!7)))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[349, 137])).
% 0.19/0.50 tff(351,plain,
% 0.19/0.50 (f7(false) = f7(P!6)),
% 0.19/0.50 inference(symmetry,[status(thm)],[242])).
% 0.19/0.50 tff(352,plain,
% 0.19/0.50 (false = f7(P!6)),
% 0.19/0.50 inference(transitivity,[status(thm)],[151, 150, 149, 148, 351])).
% 0.19/0.50 tff(353,plain,
% 0.19/0.50 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(P!7) = lazy_impl(prop(P!7), P!7))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(354,plain,
% 0.19/0.50 (f7(P!7) = lazy_impl(prop(P!7), P!7)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[353, 104])).
% 0.19/0.50 tff(355,plain,
% 0.19/0.50 (lazy_impl(prop(P!7), P!7) = f7(P!7)),
% 0.19/0.50 inference(symmetry,[status(thm)],[354])).
% 0.19/0.50 tff(356,plain,
% 0.19/0.50 (forallprefers(lazy_impl(prop(P!7), P!7), false) <=> forallprefers(f7(P!7), f7(P!6))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[355, 352])).
% 0.19/0.50 tff(357,plain,
% 0.19/0.50 (forallprefers(f7(P!7), f7(P!6)) <=> forallprefers(lazy_impl(prop(P!7), P!7), false)),
% 0.19/0.50 inference(symmetry,[status(thm)],[356])).
% 0.19/0.50 tff(358,plain,
% 0.19/0.50 ((~forallprefers(f7(P!7), f7(P!6))) <=> (~forallprefers(lazy_impl(prop(P!7), P!7), false))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[357])).
% 0.19/0.50 tff(359,plain,
% 0.19/0.50 ((~![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))) | (~forallprefers(f7(P!7), f7(P!6)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(360,plain,
% 0.19/0.50 (~forallprefers(f7(P!7), f7(P!6))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[359, 159])).
% 0.19/0.50 tff(361,plain,
% 0.19/0.50 (~forallprefers(lazy_impl(prop(P!7), P!7), false)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[360, 358])).
% 0.19/0.50 tff(362,plain,
% 0.19/0.50 ((~(forallprefers(lazy_impl(prop(P!7), P!7), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7))))) | (~((~(lazy_impl(prop(P!7), P!7) = false)) | (~(false = not1(false))))) | (~((~d(false)) | d(lazy_impl(prop(P!7), P!7))))))) | forallprefers(lazy_impl(prop(P!7), P!7), false) | (~((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7))))) | (~((~(lazy_impl(prop(P!7), P!7) = false)) | (~(false = not1(false))))) | (~((~d(false)) | d(lazy_impl(prop(P!7), P!7))))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(363,plain,
% 0.19/0.50 (~((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7))))) | (~((~(lazy_impl(prop(P!7), P!7) = false)) | (~(false = not1(false))))) | (~((~d(false)) | d(lazy_impl(prop(P!7), P!7)))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[362, 361, 350])).
% 0.19/0.50 tff(364,plain,
% 0.19/0.50 (((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7))))) | (~((~(lazy_impl(prop(P!7), P!7) = false)) | (~(false = not1(false))))) | (~((~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))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(365,plain,
% 0.19/0.50 ((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[364, 363])).
% 0.19/0.50 tff(366,plain,
% 0.19/0.50 (((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(P!7), P!7)) | (~d(lazy_impl(prop(P!7), P!7))))) | (~((~(lazy_impl(prop(P!7), P!7) = false)) | (~(false = not1(false))))) | (~((~d(false)) | d(lazy_impl(prop(P!7), P!7))))) | ((~d(false)) | d(lazy_impl(prop(P!7), P!7)))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(367,plain,
% 0.19/0.50 ((~d(false)) | d(lazy_impl(prop(P!7), P!7))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[366, 363])).
% 0.19/0.50 tff(368,plain,
% 0.19/0.50 ((~((~d(false)) | d(lazy_impl(prop(P!7), P!7)))) | (~d(false)) | d(lazy_impl(prop(P!7), P!7))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(369,plain,
% 0.19/0.50 ((~((~d(false)) | d(lazy_impl(prop(P!7), P!7)))) | d(lazy_impl(prop(P!7), P!7))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[368, 25])).
% 0.19/0.50 tff(370,plain,
% 0.19/0.50 (d(lazy_impl(prop(P!7), P!7))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[369, 367])).
% 0.19/0.50 tff(371,plain,
% 0.19/0.50 ((~((~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)))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(372,plain,
% 0.19/0.50 ((~((~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)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[371, 25, 93])).
% 0.19/0.50 tff(373,plain,
% 0.19/0.50 (bool(lazy_impl(prop(P!7), P!7))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[372, 370, 365])).
% 0.19/0.50 tff(374,plain,
% 0.19/0.50 ((~(bool(lazy_impl(prop(P!7), P!7)) <=> ((lazy_impl(prop(P!7), P!7) = false) | (lazy_impl(prop(P!7), P!7) = not1(false))))) | (~bool(lazy_impl(prop(P!7), P!7))) | ((lazy_impl(prop(P!7), P!7) = false) | (lazy_impl(prop(P!7), P!7) = not1(false)))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(375,plain,
% 0.19/0.50 ((~(bool(lazy_impl(prop(P!7), P!7)) <=> ((lazy_impl(prop(P!7), P!7) = false) | (lazy_impl(prop(P!7), P!7) = not1(false))))) | ((lazy_impl(prop(P!7), P!7) = false) | (lazy_impl(prop(P!7), P!7) = not1(false)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[374, 373])).
% 0.19/0.50 tff(376,plain,
% 0.19/0.50 ((lazy_impl(prop(P!7), P!7) = false) | (lazy_impl(prop(P!7), P!7) = not1(false))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[375, 343])).
% 0.19/0.50 tff(377,plain,
% 0.19/0.50 ((~((lazy_impl(prop(P!7), P!7) = false) | (lazy_impl(prop(P!7), P!7) = not1(false)))) | (lazy_impl(prop(P!7), P!7) = false) | (lazy_impl(prop(P!7), P!7) = not1(false))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(378,plain,
% 0.19/0.50 ((lazy_impl(prop(P!7), P!7) = false) | (lazy_impl(prop(P!7), P!7) = not1(false))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[377, 376])).
% 0.19/0.50 tff(379,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[378, 341, 332])).
% 0.19/0.50 tff(380,plain,(~(phi(P!7) = err)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(381,plain,
% 0.19/0.50 ((d(P!7) | (~(phi(P!7) = err))) | (phi(P!7) = err)),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(382,plain,
% 0.19/0.50 (d(P!7) | (~(phi(P!7) = err))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[381, 380])).
% 0.19/0.50 tff(383,plain,
% 0.19/0.50 (((~![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)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(384,plain,
% 0.19/0.50 ((~![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)))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(385,plain,
% 0.19/0.50 ((~![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))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[384, 383])).
% 0.19/0.50 tff(386,plain,
% 0.19/0.50 ((~((~d(P!7)) | (~(phi(P!7) = P!7)))) | (~(d(P!7) | (~(phi(P!7) = err))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[385, 37])).
% 0.19/0.50 tff(387,plain,
% 0.19/0.50 (~((~d(P!7)) | (~(phi(P!7) = P!7)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[386, 382])).
% 0.19/0.50 tff(388,plain,
% 0.19/0.50 (((~d(P!7)) | (~(phi(P!7) = P!7))) | (phi(P!7) = P!7)),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(389,plain,
% 0.19/0.50 (phi(P!7) = P!7),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[388, 387])).
% 0.19/0.50 tff(390,plain,
% 0.19/0.50 (P!7 = phi(P!7)),
% 0.19/0.50 inference(symmetry,[status(thm)],[389])).
% 0.19/0.50 tff(391,plain,
% 0.19/0.50 (P!7 = false),
% 0.19/0.50 inference(transitivity,[status(thm)],[390, 318, 315, 269])).
% 0.19/0.50 tff(392,plain,
% 0.19/0.50 (not2(P!7) = not2(false)),
% 0.19/0.50 inference(monotonicity,[status(thm)],[391])).
% 0.19/0.50 tff(393,plain,
% 0.19/0.50 (impl(P!7, false2) = not2(P!7)),
% 0.19/0.50 inference(symmetry,[status(thm)],[19])).
% 0.19/0.50 tff(394,plain,
% 0.19/0.50 (impl(P!7, false2) = not1(false)),
% 0.19/0.50 inference(transitivity,[status(thm)],[393, 392, 268, 266, 264])).
% 0.19/0.50 tff(395,assumption,(impl(P!7, false2) = not1(false)), introduced(assumption)).
% 0.19/0.50 tff(396,plain,
% 0.19/0.50 (not1(false) = impl(P!7, false2)),
% 0.19/0.50 inference(symmetry,[status(thm)],[395])).
% 0.19/0.50 tff(397,assumption,(P!7 = false), introduced(assumption)).
% 0.19/0.50 tff(398,plain,
% 0.19/0.50 (not1(P!7) = not1(false)),
% 0.19/0.50 inference(monotonicity,[status(thm)],[397])).
% 0.19/0.50 tff(399,plain,
% 0.19/0.50 (not1(P!7) = not2(P!7)),
% 0.19/0.50 inference(transitivity,[status(thm)],[398, 396, 393])).
% 0.19/0.50 tff(400,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[308, 399])).
% 0.19/0.50 tff(401,plain,((~(P!7 = false)) | (~(impl(P!7, false2) = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(402,plain,
% 0.19/0.50 (~(P!7 = false)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[401, 395])).
% 0.19/0.50 tff(403,plain,
% 0.19/0.50 (^[B: $i] : refl(((~bool(B)) | (impl(not1(false), B) = B)) <=> ((~bool(B)) | (impl(not1(false), B) = B)))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(404,plain,
% 0.19/0.50 (![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B)) <=> ![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[403])).
% 0.19/0.50 tff(405,plain,
% 0.19/0.50 (^[B: $i] : rewrite(((~bool(B)) | (impl(true, B) = B)) <=> ((~bool(B)) | (impl(not1(false), B) = B)))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(406,plain,
% 0.19/0.50 (![B: $i] : ((~bool(B)) | (impl(true, B) = B)) <=> ![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[405])).
% 0.19/0.50 tff(407,plain,
% 0.19/0.50 (![B: $i] : ((~bool(B)) | (impl(true, B) = B)) <=> ![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(408,plain,
% 0.19/0.50 (^[B: $i] : rewrite((bool(B) => (impl(true, B) = B)) <=> ((~bool(B)) | (impl(true, B) = B)))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(409,plain,
% 0.19/0.50 (![B: $i] : (bool(B) => (impl(true, B) = B)) <=> ![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[408])).
% 0.19/0.50 tff(410,axiom,(![B: $i] : (bool(B) => (impl(true, B) = B))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','impl_axiom4')).
% 0.19/0.50 tff(411,plain,
% 0.19/0.50 (![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[410, 409])).
% 0.19/0.50 tff(412,plain,
% 0.19/0.50 (![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[411, 407])).
% 0.19/0.50 tff(413,plain,
% 0.19/0.50 (![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[412, 406])).
% 0.19/0.50 tff(414,plain,(
% 0.19/0.50 ![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))),
% 0.19/0.50 inference(skolemize,[status(sab)],[413])).
% 0.19/0.50 tff(415,plain,
% 0.19/0.50 (![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[414, 404])).
% 0.19/0.50 tff(416,plain,
% 0.19/0.50 (((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | ((~bool(false)) | (impl(not1(false), false) = false))) <=> ((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | (~bool(false)) | (impl(not1(false), false) = false))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(417,plain,
% 0.19/0.50 ((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | ((~bool(false)) | (impl(not1(false), false) = false))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(418,plain,
% 0.19/0.50 ((~![B: $i] : ((~bool(B)) | (impl(not1(false), B) = B))) | (~bool(false)) | (impl(not1(false), false) = false)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[417, 416])).
% 0.19/0.50 tff(419,plain,
% 0.19/0.50 (impl(not1(false), false) = false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[418, 415, 93])).
% 0.19/0.50 tff(420,plain,
% 0.19/0.50 (phi(false) = phi(f7(P!6))),
% 0.19/0.50 inference(symmetry,[status(thm)],[244])).
% 0.19/0.50 tff(421,plain,
% 0.19/0.50 (false = false2),
% 0.19/0.50 inference(transitivity,[status(thm)],[151, 420, 8])).
% 0.19/0.50 tff(422,plain,
% 0.19/0.50 (impl(not1(false), false) = impl(not1(false), false2)),
% 0.19/0.50 inference(monotonicity,[status(thm)],[421])).
% 0.19/0.50 tff(423,plain,
% 0.19/0.50 (impl(not1(false), false2) = impl(not1(false), false)),
% 0.19/0.50 inference(symmetry,[status(thm)],[422])).
% 0.19/0.50 tff(424,plain,
% 0.19/0.50 ((~![P: $i] : (not2(P) = impl(P, false2))) | (not2(not1(false)) = impl(not1(false), false2))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(425,plain,
% 0.19/0.50 (not2(not1(false)) = impl(not1(false), false2)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[424, 17])).
% 0.19/0.50 tff(426,assumption,(P!7 = not1(false)), introduced(assumption)).
% 0.19/0.50 tff(427,plain,
% 0.19/0.50 (not1(false) = P!7),
% 0.19/0.50 inference(symmetry,[status(thm)],[426])).
% 0.19/0.50 tff(428,plain,
% 0.19/0.50 (not2(not1(false)) = not2(P!7)),
% 0.19/0.50 inference(monotonicity,[status(thm)],[427])).
% 0.19/0.50 tff(429,plain,
% 0.19/0.50 (not2(P!7) = not2(not1(false))),
% 0.19/0.50 inference(symmetry,[status(thm)],[428])).
% 0.19/0.50 tff(430,plain,
% 0.19/0.50 (not1(false) = false),
% 0.19/0.50 inference(transitivity,[status(thm)],[396, 393, 429, 425, 423, 419])).
% 0.19/0.50 tff(431,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[77, 430])).
% 0.19/0.50 tff(432,plain,((~(P!7 = not1(false))) | (~(impl(P!7, false2) = not1(false)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(433,plain,
% 0.19/0.50 (~(P!7 = not1(false))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[432, 395])).
% 0.19/0.50 tff(434,plain,
% 0.19/0.50 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = not1(false))))) | (bool(P!7) <=> ((P!7 = false) | (P!7 = not1(false))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(435,plain,
% 0.19/0.50 (bool(P!7) <=> ((P!7 = false) | (P!7 = not1(false)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[434, 190])).
% 0.19/0.50 tff(436,plain,
% 0.19/0.50 ((~(bool(P!7) <=> ((P!7 = false) | (P!7 = not1(false))))) | (~bool(P!7)) | ((P!7 = false) | (P!7 = not1(false)))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(437,plain,
% 0.19/0.50 ((~(bool(P!7) <=> ((P!7 = false) | (P!7 = not1(false))))) | ((P!7 = false) | (P!7 = not1(false)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[436, 310])).
% 0.19/0.50 tff(438,plain,
% 0.19/0.50 ((P!7 = false) | (P!7 = not1(false))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[437, 435])).
% 0.19/0.50 tff(439,plain,
% 0.19/0.50 ((~((P!7 = false) | (P!7 = not1(false)))) | (P!7 = false) | (P!7 = not1(false))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(440,plain,
% 0.19/0.50 ((P!7 = false) | (P!7 = not1(false))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[439, 438])).
% 0.19/0.50 tff(441,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[440, 433, 402])).
% 0.19/0.50 tff(442,plain,(~(impl(P!7, false2) = not1(false))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(443,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[442, 394])).
% 0.19/0.50 tff(444,plain,(~(lazy_impl(prop(P!7), P!7) = false)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(445,plain,
% 0.19/0.50 (lazy_impl(prop(P!7), P!7) = not1(false)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[378, 444])).
% 0.19/0.50 tff(446,plain,
% 0.19/0.50 (P!7 = not1(false)),
% 0.19/0.50 inference(transitivity,[status(thm)],[390, 318, 315, 445])).
% 0.19/0.50 tff(447,plain,
% 0.19/0.50 (not1(P!7) = not1(not1(false))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[446])).
% 0.19/0.50 tff(448,plain,
% 0.19/0.50 (not1(P!7) = phi(phi(f7(P!6)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[447, 218, 151, 247])).
% 0.19/0.50 tff(449,plain,
% 0.19/0.50 ((not1(P!7) = not2(P!7)) <=> (phi(phi(f7(P!6))) = impl(P!7, phi(f7(P!6))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[448, 20])).
% 0.19/0.50 tff(450,plain,
% 0.19/0.50 ((not1(P!7) = not2(P!7)) <=> (impl(P!7, phi(f7(P!6))) = phi(phi(f7(P!6))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[449, 1])).
% 0.19/0.50 tff(451,plain,
% 0.19/0.50 ((impl(P!7, phi(f7(P!6))) = phi(phi(f7(P!6)))) <=> (not1(P!7) = not2(P!7))),
% 0.19/0.50 inference(symmetry,[status(thm)],[450])).
% 0.19/0.50 tff(452,plain,
% 0.19/0.50 (impl(not1(false), false2) = impl(not1(false), false)),
% 0.19/0.50 inference(monotonicity,[status(thm)],[265])).
% 0.19/0.50 tff(453,plain,
% 0.19/0.50 (not2(P!7) = not2(not1(false))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[446])).
% 0.19/0.50 tff(454,plain,
% 0.19/0.50 (impl(P!7, phi(f7(P!6))) = phi(phi(f7(P!6)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[9, 393, 453, 425, 452, 419, 151, 247])).
% 0.19/0.50 tff(455,plain,
% 0.19/0.50 (not1(P!7) = not2(P!7)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[454, 451])).
% 0.19/0.50 tff(456,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[308, 455])).
% 0.19/0.50 % SZS output end Proof
%------------------------------------------------------------------------------