%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET929+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:26:41 AM UTC 2025
% Result : Theorem 0.23s 0.41s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.15 % Problem : SET929+1 : TPTP v9.0.0. Released v3.2.0.
% 0.10/0.15 % Command : run_E %s %d THM
% 0.15/0.37 % Computer : n015.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri Jun 20 05:51:11 EDT 2025
% 0.15/0.37 % CPUTime :
% 0.23/0.41 % SZS status Theorem
% 0.23/0.41 % SZS output start Proof
% 0.23/0.41 tff(in_type, type, (
% 0.23/0.41 in: ( $i * $i ) > $o)).
% 0.23/0.41 tff(tptp_fun_C_2_type, type, (
% 0.23/0.41 tptp_fun_C_2: $i)).
% 0.23/0.41 tff(tptp_fun_B_3_type, type, (
% 0.23/0.41 tptp_fun_B_3: $i)).
% 0.23/0.41 tff(tptp_fun_A_4_type, type, (
% 0.23/0.41 tptp_fun_A_4: $i)).
% 0.23/0.41 tff(empty_set_type, type, (
% 0.23/0.41 empty_set: $i)).
% 0.23/0.41 tff(set_difference_type, type, (
% 0.23/0.41 set_difference: ( $i * $i ) > $i)).
% 0.23/0.41 tff(unordered_pair_type, type, (
% 0.23/0.41 unordered_pair: ( $i * $i ) > $i)).
% 0.23/0.41 tff(subset_type, type, (
% 0.23/0.41 subset: ( $i * $i ) > $o)).
% 0.23/0.41 tff(1,assumption,(~(set_difference(unordered_pair(A!4, B!3), C!2) = empty_set)), introduced(assumption)).
% 0.23/0.41 tff(2,plain,
% 0.23/0.41 ((~(~(((~in(A!4, C!2)) | (~in(B!3, C!2))) <=> (set_difference(unordered_pair(A!4, B!3), C!2) = empty_set)))) <=> (((~in(A!4, C!2)) | (~in(B!3, C!2))) <=> (set_difference(unordered_pair(A!4, B!3), C!2) = empty_set))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(3,plain,
% 0.23/0.41 ((~(((~in(A!4, C!2)) | (~in(B!3, C!2))) <=> (set_difference(unordered_pair(A!4, B!3), C!2) = empty_set))) <=> (~(((~in(A!4, C!2)) | (~in(B!3, C!2))) <=> (set_difference(unordered_pair(A!4, B!3), C!2) = empty_set)))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(4,plain,
% 0.23/0.41 (((set_difference(unordered_pair(A!4, B!3), C!2) = empty_set) <=> (~((~in(A!4, C!2)) | (~in(B!3, C!2))))) <=> (~(((~in(A!4, C!2)) | (~in(B!3, C!2))) <=> (set_difference(unordered_pair(A!4, B!3), C!2) = empty_set)))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(5,plain,
% 0.23/0.41 ((in(A!4, C!2) & in(B!3, C!2)) <=> (~((~in(A!4, C!2)) | (~in(B!3, C!2))))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(6,plain,
% 0.23/0.41 (((set_difference(unordered_pair(A!4, B!3), C!2) = empty_set) <=> (in(A!4, C!2) & in(B!3, C!2))) <=> ((set_difference(unordered_pair(A!4, B!3), C!2) = empty_set) <=> (~((~in(A!4, C!2)) | (~in(B!3, C!2)))))),
% 0.23/0.41 inference(monotonicity,[status(thm)],[5])).
% 0.23/0.41 tff(7,plain,
% 0.23/0.41 (((set_difference(unordered_pair(A!4, B!3), C!2) = empty_set) <=> (in(A!4, C!2) & in(B!3, C!2))) <=> (~(((~in(A!4, C!2)) | (~in(B!3, C!2))) <=> (set_difference(unordered_pair(A!4, B!3), C!2) = empty_set)))),
% 0.23/0.41 inference(transitivity,[status(thm)],[6, 4])).
% 0.23/0.41 tff(8,plain,
% 0.23/0.41 (((set_difference(unordered_pair(A!4, B!3), C!2) = empty_set) <=> (in(A!4, C!2) & in(B!3, C!2))) <=> (~(((~in(A!4, C!2)) | (~in(B!3, C!2))) <=> (set_difference(unordered_pair(A!4, B!3), C!2) = empty_set)))),
% 0.23/0.41 inference(transitivity,[status(thm)],[7, 3])).
% 0.23/0.41 tff(9,plain,
% 0.23/0.41 ((~((set_difference(unordered_pair(A!4, B!3), C!2) = empty_set) <=> (in(A!4, C!2) & in(B!3, C!2)))) <=> (~(~(((~in(A!4, C!2)) | (~in(B!3, C!2))) <=> (set_difference(unordered_pair(A!4, B!3), C!2) = empty_set))))),
% 0.23/0.41 inference(monotonicity,[status(thm)],[8])).
% 0.23/0.41 tff(10,plain,
% 0.23/0.41 ((~((set_difference(unordered_pair(A!4, B!3), C!2) = empty_set) <=> (in(A!4, C!2) & in(B!3, C!2)))) <=> (((~in(A!4, C!2)) | (~in(B!3, C!2))) <=> (set_difference(unordered_pair(A!4, B!3), C!2) = empty_set))),
% 0.23/0.41 inference(transitivity,[status(thm)],[9, 2])).
% 0.23/0.41 tff(11,plain,
% 0.23/0.41 ((~((set_difference(unordered_pair(A!4, B!3), C!2) = empty_set) <=> (in(A!4, C!2) & in(B!3, C!2)))) <=> (~((set_difference(unordered_pair(A!4, B!3), C!2) = empty_set) <=> (in(A!4, C!2) & in(B!3, C!2))))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(12,plain,
% 0.23/0.41 ((~![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = empty_set) <=> (in(A, C) & in(B, C)))) <=> (~![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = empty_set) <=> (in(A, C) & in(B, C))))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(13,axiom,(~![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = empty_set) <=> (in(A, C) & in(B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t73_zfmisc_1')).
% 0.23/0.41 tff(14,plain,
% 0.23/0.41 (~![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = empty_set) <=> (in(A, C) & in(B, C)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.23/0.41 tff(15,plain,
% 0.23/0.41 (~![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = empty_set) <=> (in(A, C) & in(B, C)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[14, 12])).
% 0.23/0.41 tff(16,plain,
% 0.23/0.41 (~![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = empty_set) <=> (in(A, C) & in(B, C)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.23/0.41 tff(17,plain,
% 0.23/0.41 (~![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = empty_set) <=> (in(A, C) & in(B, C)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.23/0.41 tff(18,plain,(
% 0.23/0.41 ~((set_difference(unordered_pair(A!4, B!3), C!2) = empty_set) <=> (in(A!4, C!2) & in(B!3, C!2)))),
% 0.23/0.41 inference(skolemize,[status(sab)],[17])).
% 0.23/0.41 tff(19,plain,
% 0.23/0.41 (~((set_difference(unordered_pair(A!4, B!3), C!2) = empty_set) <=> (in(A!4, C!2) & in(B!3, C!2)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.23/0.41 tff(20,plain,
% 0.23/0.41 (((~in(A!4, C!2)) | (~in(B!3, C!2))) <=> (set_difference(unordered_pair(A!4, B!3), C!2) = empty_set)),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[19, 10])).
% 0.23/0.41 tff(21,plain,
% 0.23/0.41 ((~((~in(A!4, C!2)) | (~in(B!3, C!2)))) | (set_difference(unordered_pair(A!4, B!3), C!2) = empty_set) | (~(((~in(A!4, C!2)) | (~in(B!3, C!2))) <=> (set_difference(unordered_pair(A!4, B!3), C!2) = empty_set)))),
% 0.23/0.41 inference(tautology,[status(thm)],[])).
% 0.23/0.41 tff(22,plain,
% 0.23/0.41 ((~((~in(A!4, C!2)) | (~in(B!3, C!2)))) | (set_difference(unordered_pair(A!4, B!3), C!2) = empty_set)),
% 0.23/0.41 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.23/0.41 tff(23,plain,
% 0.23/0.41 (~((~in(A!4, C!2)) | (~in(B!3, C!2)))),
% 0.23/0.41 inference(unit_resolution,[status(thm)],[22, 1])).
% 0.23/0.41 tff(24,plain,
% 0.23/0.41 (^[A: $i, B: $i] : refl(((set_difference(A, B) = empty_set) <=> subset(A, B)) <=> ((set_difference(A, B) = empty_set) <=> subset(A, B)))),
% 0.23/0.41 inference(bind,[status(th)],[])).
% 0.23/0.41 tff(25,plain,
% 0.23/0.41 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B)) <=> ![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.23/0.41 inference(quant_intro,[status(thm)],[24])).
% 0.23/0.41 tff(26,plain,
% 0.23/0.41 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B)) <=> ![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(27,axiom,(![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t37_xboole_1')).
% 0.23/0.41 tff(28,plain,
% 0.23/0.41 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.23/0.41 tff(29,plain,(
% 0.23/0.41 ![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.23/0.41 inference(skolemize,[status(sab)],[28])).
% 0.23/0.41 tff(30,plain,
% 0.23/0.41 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.23/0.41 tff(31,plain,
% 0.23/0.41 ((~![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))) | ((set_difference(unordered_pair(A!4, B!3), C!2) = empty_set) <=> subset(unordered_pair(A!4, B!3), C!2))),
% 0.23/0.41 inference(quant_inst,[status(thm)],[])).
% 0.23/0.41 tff(32,plain,
% 0.23/0.41 ((set_difference(unordered_pair(A!4, B!3), C!2) = empty_set) <=> subset(unordered_pair(A!4, B!3), C!2)),
% 0.23/0.41 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.23/0.41 tff(33,plain,
% 0.23/0.41 ((~((set_difference(unordered_pair(A!4, B!3), C!2) = empty_set) <=> subset(unordered_pair(A!4, B!3), C!2))) | (set_difference(unordered_pair(A!4, B!3), C!2) = empty_set) | (~subset(unordered_pair(A!4, B!3), C!2))),
% 0.23/0.41 inference(tautology,[status(thm)],[])).
% 0.23/0.41 tff(34,plain,
% 0.23/0.41 ((set_difference(unordered_pair(A!4, B!3), C!2) = empty_set) | (~subset(unordered_pair(A!4, B!3), C!2))),
% 0.23/0.41 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.23/0.41 tff(35,plain,
% 0.23/0.41 (~subset(unordered_pair(A!4, B!3), C!2)),
% 0.23/0.41 inference(unit_resolution,[status(thm)],[34, 1])).
% 0.23/0.41 tff(36,plain,
% 0.23/0.41 (^[A: $i, B: $i, C: $i] : refl((~(((~in(B, C)) | (~in(A, C))) <=> subset(unordered_pair(A, B), C))) <=> (~(((~in(B, C)) | (~in(A, C))) <=> subset(unordered_pair(A, B), C))))),
% 0.23/0.41 inference(bind,[status(th)],[])).
% 0.23/0.41 tff(37,plain,
% 0.23/0.41 (![A: $i, B: $i, C: $i] : (~(((~in(B, C)) | (~in(A, C))) <=> subset(unordered_pair(A, B), C))) <=> ![A: $i, B: $i, C: $i] : (~(((~in(B, C)) | (~in(A, C))) <=> subset(unordered_pair(A, B), C)))),
% 0.23/0.41 inference(quant_intro,[status(thm)],[36])).
% 0.23/0.41 tff(38,plain,
% 0.23/0.41 (^[A: $i, B: $i, C: $i] : trans(trans(monotonicity(rewrite((in(A, C) & in(B, C)) <=> (~((~in(B, C)) | (~in(A, C))))), ((subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C))) <=> (subset(unordered_pair(A, B), C) <=> (~((~in(B, C)) | (~in(A, C))))))), rewrite((subset(unordered_pair(A, B), C) <=> (~((~in(B, C)) | (~in(A, C))))) <=> (~(((~in(B, C)) | (~in(A, C))) <=> subset(unordered_pair(A, B), C)))), ((subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C))) <=> (~(((~in(B, C)) | (~in(A, C))) <=> subset(unordered_pair(A, B), C))))), rewrite((~(((~in(B, C)) | (~in(A, C))) <=> subset(unordered_pair(A, B), C))) <=> (~(((~in(B, C)) | (~in(A, C))) <=> subset(unordered_pair(A, B), C)))), ((subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C))) <=> (~(((~in(B, C)) | (~in(A, C))) <=> subset(unordered_pair(A, B), C)))))),
% 0.23/0.41 inference(bind,[status(th)],[])).
% 0.23/0.41 tff(39,plain,
% 0.23/0.41 (![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C))) <=> ![A: $i, B: $i, C: $i] : (~(((~in(B, C)) | (~in(A, C))) <=> subset(unordered_pair(A, B), C)))),
% 0.23/0.41 inference(quant_intro,[status(thm)],[38])).
% 0.23/0.41 tff(40,plain,
% 0.23/0.41 (![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C))) <=> ![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(41,axiom,(![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t38_zfmisc_1')).
% 0.23/0.41 tff(42,plain,
% 0.23/0.41 (![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.23/0.41 tff(43,plain,(
% 0.23/0.41 ![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))),
% 0.23/0.41 inference(skolemize,[status(sab)],[42])).
% 0.23/0.41 tff(44,plain,
% 0.23/0.41 (![A: $i, B: $i, C: $i] : (~(((~in(B, C)) | (~in(A, C))) <=> subset(unordered_pair(A, B), C)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.23/0.41 tff(45,plain,
% 0.23/0.41 (![A: $i, B: $i, C: $i] : (~(((~in(B, C)) | (~in(A, C))) <=> subset(unordered_pair(A, B), C)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.23/0.41 tff(46,plain,
% 0.23/0.41 (((~![A: $i, B: $i, C: $i] : (~(((~in(B, C)) | (~in(A, C))) <=> subset(unordered_pair(A, B), C)))) | (~(((~in(A!4, C!2)) | (~in(B!3, C!2))) <=> subset(unordered_pair(A!4, B!3), C!2)))) <=> ((~![A: $i, B: $i, C: $i] : (~(((~in(B, C)) | (~in(A, C))) <=> subset(unordered_pair(A, B), C)))) | (~(((~in(A!4, C!2)) | (~in(B!3, C!2))) <=> subset(unordered_pair(A!4, B!3), C!2))))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(47,plain,
% 0.23/0.41 ((~(((~in(A!4, C!2)) | (~in(B!3, C!2))) <=> subset(unordered_pair(A!4, B!3), C!2))) <=> (~(((~in(A!4, C!2)) | (~in(B!3, C!2))) <=> subset(unordered_pair(A!4, B!3), C!2)))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(48,plain,
% 0.23/0.41 ((((~in(B!3, C!2)) | (~in(A!4, C!2))) <=> subset(unordered_pair(A!4, B!3), C!2)) <=> (((~in(A!4, C!2)) | (~in(B!3, C!2))) <=> subset(unordered_pair(A!4, B!3), C!2))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(49,plain,
% 0.23/0.41 ((~(((~in(B!3, C!2)) | (~in(A!4, C!2))) <=> subset(unordered_pair(A!4, B!3), C!2))) <=> (~(((~in(A!4, C!2)) | (~in(B!3, C!2))) <=> subset(unordered_pair(A!4, B!3), C!2)))),
% 0.23/0.41 inference(monotonicity,[status(thm)],[48])).
% 0.23/0.41 tff(50,plain,
% 0.23/0.41 ((~(((~in(B!3, C!2)) | (~in(A!4, C!2))) <=> subset(unordered_pair(A!4, B!3), C!2))) <=> (~(((~in(A!4, C!2)) | (~in(B!3, C!2))) <=> subset(unordered_pair(A!4, B!3), C!2)))),
% 0.23/0.41 inference(transitivity,[status(thm)],[49, 47])).
% 0.23/0.41 tff(51,plain,
% 0.23/0.41 (((~![A: $i, B: $i, C: $i] : (~(((~in(B, C)) | (~in(A, C))) <=> subset(unordered_pair(A, B), C)))) | (~(((~in(B!3, C!2)) | (~in(A!4, C!2))) <=> subset(unordered_pair(A!4, B!3), C!2)))) <=> ((~![A: $i, B: $i, C: $i] : (~(((~in(B, C)) | (~in(A, C))) <=> subset(unordered_pair(A, B), C)))) | (~(((~in(A!4, C!2)) | (~in(B!3, C!2))) <=> subset(unordered_pair(A!4, B!3), C!2))))),
% 0.23/0.41 inference(monotonicity,[status(thm)],[50])).
% 0.23/0.41 tff(52,plain,
% 0.23/0.41 (((~![A: $i, B: $i, C: $i] : (~(((~in(B, C)) | (~in(A, C))) <=> subset(unordered_pair(A, B), C)))) | (~(((~in(B!3, C!2)) | (~in(A!4, C!2))) <=> subset(unordered_pair(A!4, B!3), C!2)))) <=> ((~![A: $i, B: $i, C: $i] : (~(((~in(B, C)) | (~in(A, C))) <=> subset(unordered_pair(A, B), C)))) | (~(((~in(A!4, C!2)) | (~in(B!3, C!2))) <=> subset(unordered_pair(A!4, B!3), C!2))))),
% 0.23/0.42 inference(transitivity,[status(thm)],[51, 46])).
% 0.23/0.42 tff(53,plain,
% 0.23/0.42 ((~![A: $i, B: $i, C: $i] : (~(((~in(B, C)) | (~in(A, C))) <=> subset(unordered_pair(A, B), C)))) | (~(((~in(B!3, C!2)) | (~in(A!4, C!2))) <=> subset(unordered_pair(A!4, B!3), C!2)))),
% 0.23/0.42 inference(quant_inst,[status(thm)],[])).
% 0.23/0.42 tff(54,plain,
% 0.23/0.42 ((~![A: $i, B: $i, C: $i] : (~(((~in(B, C)) | (~in(A, C))) <=> subset(unordered_pair(A, B), C)))) | (~(((~in(A!4, C!2)) | (~in(B!3, C!2))) <=> subset(unordered_pair(A!4, B!3), C!2)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.23/0.42 tff(55,plain,
% 0.23/0.42 (~(((~in(A!4, C!2)) | (~in(B!3, C!2))) <=> subset(unordered_pair(A!4, B!3), C!2))),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[54, 45])).
% 0.23/0.42 tff(56,plain,
% 0.23/0.42 ((((~in(A!4, C!2)) | (~in(B!3, C!2))) <=> subset(unordered_pair(A!4, B!3), C!2)) | ((~in(A!4, C!2)) | (~in(B!3, C!2))) | subset(unordered_pair(A!4, B!3), C!2)),
% 0.23/0.42 inference(tautology,[status(thm)],[])).
% 0.23/0.42 tff(57,plain,
% 0.23/0.42 (((~in(A!4, C!2)) | (~in(B!3, C!2))) | subset(unordered_pair(A!4, B!3), C!2)),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.23/0.42 tff(58,plain,
% 0.23/0.42 ($false),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[57, 35, 23])).
% 0.23/0.42 tff(59,plain,(set_difference(unordered_pair(A!4, B!3), C!2) = empty_set), inference(lemma,lemma(discharge,[]))).
% 0.23/0.42 tff(60,plain,
% 0.23/0.42 (((~in(A!4, C!2)) | (~in(B!3, C!2))) | (~(set_difference(unordered_pair(A!4, B!3), C!2) = empty_set)) | (~(((~in(A!4, C!2)) | (~in(B!3, C!2))) <=> (set_difference(unordered_pair(A!4, B!3), C!2) = empty_set)))),
% 0.23/0.42 inference(tautology,[status(thm)],[])).
% 0.23/0.42 tff(61,plain,
% 0.23/0.42 (((~in(A!4, C!2)) | (~in(B!3, C!2))) | (~(set_difference(unordered_pair(A!4, B!3), C!2) = empty_set))),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[60, 20])).
% 0.23/0.42 tff(62,plain,
% 0.23/0.42 ((~in(A!4, C!2)) | (~in(B!3, C!2))),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[61, 59])).
% 0.23/0.42 tff(63,plain,
% 0.23/0.42 ((~((set_difference(unordered_pair(A!4, B!3), C!2) = empty_set) <=> subset(unordered_pair(A!4, B!3), C!2))) | (~(set_difference(unordered_pair(A!4, B!3), C!2) = empty_set)) | subset(unordered_pair(A!4, B!3), C!2)),
% 0.23/0.42 inference(tautology,[status(thm)],[])).
% 0.23/0.42 tff(64,plain,
% 0.23/0.42 ((~(set_difference(unordered_pair(A!4, B!3), C!2) = empty_set)) | subset(unordered_pair(A!4, B!3), C!2)),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[63, 32])).
% 0.23/0.42 tff(65,plain,
% 0.23/0.42 (subset(unordered_pair(A!4, B!3), C!2)),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[64, 59])).
% 0.23/0.42 tff(66,plain,
% 0.23/0.42 ((((~in(A!4, C!2)) | (~in(B!3, C!2))) <=> subset(unordered_pair(A!4, B!3), C!2)) | (~((~in(A!4, C!2)) | (~in(B!3, C!2)))) | (~subset(unordered_pair(A!4, B!3), C!2))),
% 0.23/0.42 inference(tautology,[status(thm)],[])).
% 0.23/0.42 tff(67,plain,
% 0.23/0.42 ((~((~in(A!4, C!2)) | (~in(B!3, C!2)))) | (~subset(unordered_pair(A!4, B!3), C!2))),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[66, 55])).
% 0.23/0.42 tff(68,plain,
% 0.23/0.42 ($false),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[67, 65, 62])).
% 0.23/0.42 % SZS output end Proof
% 0.23/0.42 % E exiting
%------------------------------------------------------------------------------