%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET902+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:26:37 AM UTC 2025
% Result : Theorem 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.11 % Problem : SET902+1 : TPTP v9.0.0. Released v3.2.0.
% 0.08/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n009.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 05:50:03 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.36 % SZS status Theorem
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(empty_set_type, type, (
% 0.11/0.36 empty_set: $i)).
% 0.11/0.36 tff(singleton_type, type, (
% 0.11/0.36 singleton: $i > $i)).
% 0.11/0.36 tff(tptp_fun_A_4_type, type, (
% 0.11/0.36 tptp_fun_A_4: $i)).
% 0.11/0.36 tff(set_union2_type, type, (
% 0.11/0.36 set_union2: ( $i * $i ) > $i)).
% 0.11/0.36 tff(tptp_fun_C_2_type, type, (
% 0.11/0.36 tptp_fun_C_2: $i)).
% 0.11/0.36 tff(tptp_fun_B_3_type, type, (
% 0.11/0.36 tptp_fun_B_3: $i)).
% 0.11/0.36 tff(subset_type, type, (
% 0.11/0.36 subset: ( $i * $i ) > $o)).
% 0.11/0.36 tff(1,plain,
% 0.11/0.36 (^[A: $i] : refl((set_union2(A, A) = A) <=> (set_union2(A, A) = A))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(2,plain,
% 0.11/0.36 (![A: $i] : (set_union2(A, A) = A) <=> ![A: $i] : (set_union2(A, A) = A)),
% 0.11/0.36 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.36 tff(3,plain,
% 0.11/0.36 (![A: $i] : (set_union2(A, A) = A) <=> ![A: $i] : (set_union2(A, A) = A)),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(4,plain,
% 0.11/0.36 (![A: $i, B: $i] : (set_union2(A, A) = A) <=> ![A: $i] : (set_union2(A, A) = A)),
% 0.11/0.36 inference(elim_unused_vars,[status(thm)],[])).
% 0.11/0.36 tff(5,axiom,(![A: $i, B: $i] : (set_union2(A, A) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','idempotence_k2_xboole_0')).
% 0.11/0.36 tff(6,plain,
% 0.11/0.36 (![A: $i] : (set_union2(A, A) = A)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.11/0.36 tff(7,plain,
% 0.11/0.36 (![A: $i] : (set_union2(A, A) = A)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[6, 3])).
% 0.11/0.36 tff(8,plain,(
% 0.11/0.36 ![A: $i] : (set_union2(A, A) = A)),
% 0.11/0.36 inference(skolemize,[status(sab)],[7])).
% 0.11/0.36 tff(9,plain,
% 0.11/0.36 (![A: $i] : (set_union2(A, A) = A)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.11/0.36 tff(10,plain,
% 0.11/0.36 ((~![A: $i] : (set_union2(A, A) = A)) | (set_union2(empty_set, empty_set) = empty_set)),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(11,plain,
% 0.11/0.36 (set_union2(empty_set, empty_set) = empty_set),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[10, 9])).
% 0.11/0.36 tff(12,assumption,(C!2 = singleton(A!4)), introduced(assumption)).
% 0.11/0.36 tff(13,plain,
% 0.11/0.36 ((~(~((~(B!3 = singleton(A!4))) | (~(C!2 = singleton(A!4)))))) <=> ((~(B!3 = singleton(A!4))) | (~(C!2 = singleton(A!4))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(14,plain,
% 0.11/0.36 (((B!3 = singleton(A!4)) & (C!2 = singleton(A!4))) <=> (~((~(B!3 = singleton(A!4))) | (~(C!2 = singleton(A!4)))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(15,plain,
% 0.11/0.36 ((~((B!3 = singleton(A!4)) & (C!2 = singleton(A!4)))) <=> (~(~((~(B!3 = singleton(A!4))) | (~(C!2 = singleton(A!4))))))),
% 0.11/0.36 inference(monotonicity,[status(thm)],[14])).
% 0.11/0.36 tff(16,plain,
% 0.11/0.36 ((~((B!3 = singleton(A!4)) & (C!2 = singleton(A!4)))) <=> ((~(B!3 = singleton(A!4))) | (~(C!2 = singleton(A!4))))),
% 0.11/0.36 inference(transitivity,[status(thm)],[15, 13])).
% 0.11/0.36 tff(17,plain,
% 0.11/0.36 ((~![A: $i, B: $i, C: $i] : (~((singleton(A) = set_union2(B, C)) & (~((B = singleton(A)) & (C = singleton(A)))) & (~((B = empty_set) & (C = singleton(A)))) & (~((B = singleton(A)) & (C = empty_set)))))) <=> (~![A: $i, B: $i, C: $i] : (~((singleton(A) = set_union2(B, C)) & (~((B = singleton(A)) & (C = singleton(A)))) & (~((B = empty_set) & (C = singleton(A)))) & (~((B = singleton(A)) & (C = empty_set))))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(18,plain,
% 0.11/0.36 ((~![A: $i, B: $i, C: $i] : (~((((singleton(A) = set_union2(B, C)) & (~((B = singleton(A)) & (C = singleton(A))))) & (~((B = empty_set) & (C = singleton(A))))) & (~((B = singleton(A)) & (C = empty_set)))))) <=> (~![A: $i, B: $i, C: $i] : (~((singleton(A) = set_union2(B, C)) & (~((B = singleton(A)) & (C = singleton(A)))) & (~((B = empty_set) & (C = singleton(A)))) & (~((B = singleton(A)) & (C = empty_set))))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(19,axiom,(~![A: $i, B: $i, C: $i] : (~((((singleton(A) = set_union2(B, C)) & (~((B = singleton(A)) & (C = singleton(A))))) & (~((B = empty_set) & (C = singleton(A))))) & (~((B = singleton(A)) & (C = empty_set)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t43_zfmisc_1')).
% 0.11/0.36 tff(20,plain,
% 0.11/0.36 (~![A: $i, B: $i, C: $i] : (~((singleton(A) = set_union2(B, C)) & (~((B = singleton(A)) & (C = singleton(A)))) & (~((B = empty_set) & (C = singleton(A)))) & (~((B = singleton(A)) & (C = empty_set)))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.11/0.36 tff(21,plain,
% 0.11/0.36 (~![A: $i, B: $i, C: $i] : (~((singleton(A) = set_union2(B, C)) & (~((B = singleton(A)) & (C = singleton(A)))) & (~((B = empty_set) & (C = singleton(A)))) & (~((B = singleton(A)) & (C = empty_set)))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[20, 17])).
% 0.11/0.36 tff(22,plain,
% 0.11/0.36 (~![A: $i, B: $i, C: $i] : (~((singleton(A) = set_union2(B, C)) & (~((B = singleton(A)) & (C = singleton(A)))) & (~((B = empty_set) & (C = singleton(A)))) & (~((B = singleton(A)) & (C = empty_set)))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.11/0.36 tff(23,plain,
% 0.11/0.36 (~![A: $i, B: $i, C: $i] : (~((singleton(A) = set_union2(B, C)) & (~((B = singleton(A)) & (C = singleton(A)))) & (~((B = empty_set) & (C = singleton(A)))) & (~((B = singleton(A)) & (C = empty_set)))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[22, 17])).
% 0.11/0.36 tff(24,plain,(
% 0.11/0.36 (singleton(A!4) = set_union2(B!3, C!2)) & (~((B!3 = singleton(A!4)) & (C!2 = singleton(A!4)))) & (~((B!3 = empty_set) & (C!2 = singleton(A!4)))) & (~((B!3 = singleton(A!4)) & (C!2 = empty_set)))),
% 0.11/0.36 inference(skolemize,[status(sab)],[23])).
% 0.11/0.36 tff(25,plain,
% 0.11/0.36 (~((B!3 = singleton(A!4)) & (C!2 = singleton(A!4)))),
% 0.11/0.36 inference(and_elim,[status(thm)],[24])).
% 0.11/0.36 tff(26,plain,
% 0.11/0.36 ((~(B!3 = singleton(A!4))) | (~(C!2 = singleton(A!4)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[25, 16])).
% 0.11/0.36 tff(27,plain,
% 0.11/0.36 (~(B!3 = singleton(A!4))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[26, 12])).
% 0.11/0.36 tff(28,plain,
% 0.11/0.36 ((~(~((~(B!3 = empty_set)) | (~(C!2 = singleton(A!4)))))) <=> ((~(B!3 = empty_set)) | (~(C!2 = singleton(A!4))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(29,plain,
% 0.11/0.36 (((B!3 = empty_set) & (C!2 = singleton(A!4))) <=> (~((~(B!3 = empty_set)) | (~(C!2 = singleton(A!4)))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(30,plain,
% 0.11/0.36 ((~((B!3 = empty_set) & (C!2 = singleton(A!4)))) <=> (~(~((~(B!3 = empty_set)) | (~(C!2 = singleton(A!4))))))),
% 0.11/0.36 inference(monotonicity,[status(thm)],[29])).
% 0.11/0.36 tff(31,plain,
% 0.11/0.36 ((~((B!3 = empty_set) & (C!2 = singleton(A!4)))) <=> ((~(B!3 = empty_set)) | (~(C!2 = singleton(A!4))))),
% 0.11/0.36 inference(transitivity,[status(thm)],[30, 28])).
% 0.11/0.36 tff(32,plain,
% 0.11/0.36 (~((B!3 = empty_set) & (C!2 = singleton(A!4)))),
% 0.11/0.36 inference(and_elim,[status(thm)],[24])).
% 0.11/0.36 tff(33,plain,
% 0.11/0.36 ((~(B!3 = empty_set)) | (~(C!2 = singleton(A!4)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.11/0.36 tff(34,plain,
% 0.11/0.36 (~(B!3 = empty_set)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[33, 12])).
% 0.11/0.36 tff(35,plain,
% 0.11/0.36 (^[A: $i, B: $i] : refl((subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B)))) <=> (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B)))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(36,plain,
% 0.11/0.36 (![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B)))) <=> ![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[35])).
% 0.11/0.36 tff(37,plain,
% 0.11/0.36 (![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B)))) <=> ![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(38,axiom,(![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l4_zfmisc_1')).
% 0.11/0.36 tff(39,plain,
% 0.11/0.36 (![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.11/0.36 tff(40,plain,(
% 0.11/0.36 ![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 0.11/0.36 inference(skolemize,[status(sab)],[39])).
% 0.11/0.36 tff(41,plain,
% 0.11/0.36 (![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.11/0.36 tff(42,plain,
% 0.11/0.36 ((~![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))) | (subset(B!3, singleton(A!4)) <=> ((B!3 = empty_set) | (B!3 = singleton(A!4))))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(43,plain,
% 0.11/0.36 (subset(B!3, singleton(A!4)) <=> ((B!3 = empty_set) | (B!3 = singleton(A!4)))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.11/0.36 tff(44,plain,
% 0.11/0.36 (singleton(A!4) = set_union2(B!3, C!2)),
% 0.11/0.36 inference(and_elim,[status(thm)],[24])).
% 0.11/0.36 tff(45,plain,
% 0.11/0.36 (subset(B!3, singleton(A!4)) <=> subset(B!3, set_union2(B!3, C!2))),
% 0.11/0.36 inference(monotonicity,[status(thm)],[44])).
% 0.11/0.36 tff(46,plain,
% 0.11/0.36 (subset(B!3, set_union2(B!3, C!2)) <=> subset(B!3, singleton(A!4))),
% 0.11/0.36 inference(symmetry,[status(thm)],[45])).
% 0.11/0.36 tff(47,plain,
% 0.11/0.36 (^[A: $i, B: $i] : refl(subset(A, set_union2(A, B)) <=> subset(A, set_union2(A, B)))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(48,plain,
% 0.11/0.36 (![A: $i, B: $i] : subset(A, set_union2(A, B)) <=> ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[47])).
% 0.11/0.36 tff(49,plain,
% 0.11/0.36 (![A: $i, B: $i] : subset(A, set_union2(A, B)) <=> ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(50,axiom,(![A: $i, B: $i] : subset(A, set_union2(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t7_xboole_1')).
% 0.11/0.36 tff(51,plain,
% 0.11/0.36 (![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.11/0.36 tff(52,plain,(
% 0.11/0.36 ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.11/0.36 inference(skolemize,[status(sab)],[51])).
% 0.11/0.36 tff(53,plain,
% 0.11/0.36 (![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.11/0.36 tff(54,plain,
% 0.11/0.36 ((~![A: $i, B: $i] : subset(A, set_union2(A, B))) | subset(B!3, set_union2(B!3, C!2))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(55,plain,
% 0.11/0.36 (subset(B!3, set_union2(B!3, C!2))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.11/0.36 tff(56,plain,
% 0.11/0.36 (subset(B!3, singleton(A!4))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[55, 46])).
% 0.11/0.36 tff(57,plain,
% 0.11/0.36 ((~(subset(B!3, singleton(A!4)) <=> ((B!3 = empty_set) | (B!3 = singleton(A!4))))) | (~subset(B!3, singleton(A!4))) | ((B!3 = empty_set) | (B!3 = singleton(A!4)))),
% 0.11/0.36 inference(tautology,[status(thm)],[])).
% 0.11/0.36 tff(58,plain,
% 0.11/0.36 ((B!3 = empty_set) | (B!3 = singleton(A!4))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[57, 56, 43])).
% 0.11/0.36 tff(59,plain,
% 0.11/0.36 ((~((B!3 = empty_set) | (B!3 = singleton(A!4)))) | (B!3 = empty_set) | (B!3 = singleton(A!4))),
% 0.11/0.36 inference(tautology,[status(thm)],[])).
% 0.11/0.36 tff(60,plain,
% 0.11/0.36 ((B!3 = empty_set) | (B!3 = singleton(A!4))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.11/0.36 tff(61,plain,
% 0.11/0.36 ($false),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[60, 34, 27])).
% 0.11/0.36 tff(62,plain,(~(C!2 = singleton(A!4))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.36 tff(63,plain,
% 0.11/0.36 ((~![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))) | (subset(C!2, singleton(A!4)) <=> ((C!2 = empty_set) | (C!2 = singleton(A!4))))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(64,plain,
% 0.11/0.36 (subset(C!2, singleton(A!4)) <=> ((C!2 = empty_set) | (C!2 = singleton(A!4)))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[63, 41])).
% 0.11/0.36 tff(65,plain,
% 0.11/0.36 (^[A: $i, B: $i] : refl((set_union2(A, B) = set_union2(B, A)) <=> (set_union2(A, B) = set_union2(B, A)))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(66,plain,
% 0.11/0.36 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[65])).
% 0.11/0.36 tff(67,plain,
% 0.11/0.36 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(68,axiom,(![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k2_xboole_0')).
% 0.11/0.36 tff(69,plain,
% 0.11/0.36 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.11/0.36 tff(70,plain,(
% 0.11/0.36 ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.11/0.36 inference(skolemize,[status(sab)],[69])).
% 0.11/0.36 tff(71,plain,
% 0.11/0.36 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.11/0.37 tff(72,plain,
% 0.11/0.37 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(B!3, C!2) = set_union2(C!2, B!3))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(73,plain,
% 0.11/0.37 (set_union2(B!3, C!2) = set_union2(C!2, B!3)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.11/0.37 tff(74,plain,
% 0.11/0.37 (singleton(A!4) = set_union2(C!2, B!3)),
% 0.11/0.37 inference(transitivity,[status(thm)],[44, 73])).
% 0.11/0.37 tff(75,plain,
% 0.11/0.37 (subset(C!2, singleton(A!4)) <=> subset(C!2, set_union2(C!2, B!3))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[74])).
% 0.11/0.37 tff(76,plain,
% 0.11/0.37 (subset(C!2, set_union2(C!2, B!3)) <=> subset(C!2, singleton(A!4))),
% 0.11/0.37 inference(symmetry,[status(thm)],[75])).
% 0.11/0.37 tff(77,plain,
% 0.11/0.37 ((~![A: $i, B: $i] : subset(A, set_union2(A, B))) | subset(C!2, set_union2(C!2, B!3))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(78,plain,
% 0.11/0.37 (subset(C!2, set_union2(C!2, B!3))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[77, 53])).
% 0.11/0.37 tff(79,plain,
% 0.11/0.37 (subset(C!2, singleton(A!4))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[78, 76])).
% 0.11/0.37 tff(80,plain,
% 0.11/0.37 ((~(subset(C!2, singleton(A!4)) <=> ((C!2 = empty_set) | (C!2 = singleton(A!4))))) | (~subset(C!2, singleton(A!4))) | ((C!2 = empty_set) | (C!2 = singleton(A!4)))),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(81,plain,
% 0.11/0.37 ((C!2 = empty_set) | (C!2 = singleton(A!4))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[80, 79, 64])).
% 0.11/0.37 tff(82,plain,
% 0.11/0.37 ((~((C!2 = empty_set) | (C!2 = singleton(A!4)))) | (C!2 = empty_set) | (C!2 = singleton(A!4))),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(83,plain,
% 0.11/0.37 ((C!2 = empty_set) | (C!2 = singleton(A!4))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.11/0.37 tff(84,plain,
% 0.11/0.37 (C!2 = empty_set),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[83, 62])).
% 0.11/0.37 tff(85,plain,
% 0.11/0.37 ((~(~((~(B!3 = singleton(A!4))) | (~(C!2 = empty_set))))) <=> ((~(B!3 = singleton(A!4))) | (~(C!2 = empty_set)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(86,plain,
% 0.11/0.37 (((B!3 = singleton(A!4)) & (C!2 = empty_set)) <=> (~((~(B!3 = singleton(A!4))) | (~(C!2 = empty_set))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(87,plain,
% 0.11/0.37 ((~((B!3 = singleton(A!4)) & (C!2 = empty_set))) <=> (~(~((~(B!3 = singleton(A!4))) | (~(C!2 = empty_set)))))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[86])).
% 0.11/0.37 tff(88,plain,
% 0.11/0.37 ((~((B!3 = singleton(A!4)) & (C!2 = empty_set))) <=> ((~(B!3 = singleton(A!4))) | (~(C!2 = empty_set)))),
% 0.11/0.37 inference(transitivity,[status(thm)],[87, 85])).
% 0.11/0.37 tff(89,plain,
% 0.11/0.37 (~((B!3 = singleton(A!4)) & (C!2 = empty_set))),
% 0.11/0.37 inference(and_elim,[status(thm)],[24])).
% 0.11/0.37 tff(90,plain,
% 0.11/0.37 ((~(B!3 = singleton(A!4))) | (~(C!2 = empty_set))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.11/0.37 tff(91,plain,
% 0.11/0.37 (~(B!3 = singleton(A!4))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[90, 84])).
% 0.11/0.37 tff(92,plain,
% 0.11/0.37 (B!3 = empty_set),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[60, 91])).
% 0.11/0.37 tff(93,plain,
% 0.11/0.37 (set_union2(B!3, C!2) = set_union2(empty_set, empty_set)),
% 0.11/0.37 inference(monotonicity,[status(thm)],[92, 84])).
% 0.11/0.37 tff(94,plain,
% 0.11/0.37 (singleton(A!4) = empty_set),
% 0.11/0.37 inference(transitivity,[status(thm)],[44, 93, 11])).
% 0.11/0.37 tff(95,plain,
% 0.11/0.37 (^[A: $i] : refl((~(singleton(A) = empty_set)) <=> (~(singleton(A) = empty_set)))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(96,plain,
% 0.11/0.37 (![A: $i] : (~(singleton(A) = empty_set)) <=> ![A: $i] : (~(singleton(A) = empty_set))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[95])).
% 0.11/0.37 tff(97,plain,
% 0.11/0.37 (![A: $i] : (~(singleton(A) = empty_set)) <=> ![A: $i] : (~(singleton(A) = empty_set))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(98,axiom,(![A: $i] : (~(singleton(A) = empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l1_zfmisc_1')).
% 0.11/0.37 tff(99,plain,
% 0.11/0.37 (![A: $i] : (~(singleton(A) = empty_set))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.11/0.37 tff(100,plain,(
% 0.11/0.37 ![A: $i] : (~(singleton(A) = empty_set))),
% 0.11/0.37 inference(skolemize,[status(sab)],[99])).
% 0.11/0.37 tff(101,plain,
% 0.11/0.37 (![A: $i] : (~(singleton(A) = empty_set))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.11/0.37 tff(102,plain,
% 0.11/0.37 ((~![A: $i] : (~(singleton(A) = empty_set))) | (~(singleton(A!4) = empty_set))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(103,plain,
% 0.11/0.37 (~(singleton(A!4) = empty_set)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.11/0.37 tff(104,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[103, 94])).
% 0.11/0.37 % SZS output end Proof
% 0.11/0.37 % E exiting
%------------------------------------------------------------------------------