%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU126+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:26:57 AM UTC 2025
% Result : Theorem 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU126+2 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n010.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 : Fri Jun 20 06:08:11 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % SZS output start Proof
% 0.19/0.37 tff(subset_type, type, (
% 0.19/0.37 subset: ( $i * $i ) > $o)).
% 0.19/0.37 tff(tptp_fun_B_6_type, type, (
% 0.19/0.37 tptp_fun_B_6: $i)).
% 0.19/0.37 tff(set_union2_type, type, (
% 0.19/0.37 set_union2: ( $i * $i ) > $i)).
% 0.19/0.37 tff(tptp_fun_A_7_type, type, (
% 0.19/0.37 tptp_fun_A_7: $i)).
% 0.19/0.37 tff(1,plain,
% 0.19/0.37 (^[A: $i, B: $i] : refl((~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(2,plain,
% 0.19/0.37 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.37 tff(3,plain,
% 0.19/0.37 (^[A: $i, B: $i] : trans(trans(monotonicity(rewrite((subset(A, B) & subset(B, A)) <=> (~((~subset(A, B)) | (~subset(B, A))))), (((A = B) <=> (subset(A, B) & subset(B, A))) <=> ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))))), rewrite(((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))), (((A = B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))))), rewrite((~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))), (((A = B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(4,plain,
% 0.19/0.37 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.37 tff(5,plain,
% 0.19/0.37 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(6,axiom,(![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d10_xboole_0')).
% 0.19/0.37 tff(7,plain,
% 0.19/0.37 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.37 tff(8,plain,(
% 0.19/0.37 ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.19/0.37 inference(skolemize,[status(sab)],[7])).
% 0.19/0.37 tff(9,plain,
% 0.19/0.37 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.19/0.37 tff(10,plain,
% 0.19/0.37 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.37 tff(11,plain,
% 0.19/0.37 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))) | (~(((~subset(B!6, set_union2(B!6, A!7))) | (~subset(set_union2(B!6, A!7), B!6))) <=> (B!6 = set_union2(B!6, A!7))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(12,plain,
% 0.19/0.37 (~(((~subset(B!6, set_union2(B!6, A!7))) | (~subset(set_union2(B!6, A!7), B!6))) <=> (B!6 = set_union2(B!6, A!7)))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.19/0.37 tff(13,plain,
% 0.19/0.37 ((B!6 = set_union2(A!7, B!6)) <=> (set_union2(A!7, B!6) = B!6)),
% 0.19/0.37 inference(commutativity,[status(thm)],[])).
% 0.19/0.37 tff(14,plain,
% 0.19/0.37 (^[A: $i, B: $i] : refl((set_union2(A, B) = set_union2(B, A)) <=> (set_union2(A, B) = set_union2(B, A)))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(15,plain,
% 0.19/0.37 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.37 tff(16,plain,
% 0.19/0.37 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(17,axiom,(![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k2_xboole_0')).
% 0.19/0.37 tff(18,plain,
% 0.19/0.37 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.19/0.37 tff(19,plain,(
% 0.19/0.37 ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.19/0.37 inference(skolemize,[status(sab)],[18])).
% 0.19/0.37 tff(20,plain,
% 0.19/0.37 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.19/0.37 tff(21,plain,
% 0.19/0.37 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(A!7, B!6) = set_union2(B!6, A!7))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(22,plain,
% 0.19/0.37 (set_union2(A!7, B!6) = set_union2(B!6, A!7)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.19/0.37 tff(23,plain,
% 0.19/0.37 (set_union2(B!6, A!7) = set_union2(A!7, B!6)),
% 0.19/0.37 inference(symmetry,[status(thm)],[22])).
% 0.19/0.37 tff(24,plain,
% 0.19/0.37 ((B!6 = set_union2(B!6, A!7)) <=> (B!6 = set_union2(A!7, B!6))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[23])).
% 0.19/0.37 tff(25,plain,
% 0.19/0.37 ((B!6 = set_union2(B!6, A!7)) <=> (set_union2(A!7, B!6) = B!6)),
% 0.19/0.37 inference(transitivity,[status(thm)],[24, 13])).
% 0.19/0.37 tff(26,plain,
% 0.19/0.37 ((set_union2(A!7, B!6) = B!6) <=> (B!6 = set_union2(B!6, A!7))),
% 0.19/0.37 inference(symmetry,[status(thm)],[25])).
% 0.19/0.37 tff(27,plain,
% 0.19/0.37 ((~(set_union2(A!7, B!6) = B!6)) <=> (~(B!6 = set_union2(B!6, A!7)))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[26])).
% 0.19/0.37 tff(28,plain,
% 0.19/0.37 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) <=> (~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(29,plain,
% 0.19/0.37 ((~![A: $i, B: $i] : (subset(A, B) => (set_union2(A, B) = B))) <=> (~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(30,axiom,(~![A: $i, B: $i] : (subset(A, B) => (set_union2(A, B) = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t12_xboole_1')).
% 0.19/0.37 tff(31,plain,
% 0.19/0.37 (~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.19/0.37 tff(32,plain,
% 0.19/0.37 (~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[31, 28])).
% 0.19/0.37 tff(33,plain,
% 0.19/0.37 (~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.19/0.37 tff(34,plain,
% 0.19/0.37 (~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[33, 28])).
% 0.19/0.37 tff(35,plain,(
% 0.19/0.37 ~((~subset(A!7, B!6)) | (set_union2(A!7, B!6) = B!6))),
% 0.19/0.37 inference(skolemize,[status(sab)],[34])).
% 0.19/0.37 tff(36,plain,
% 0.19/0.37 (~(set_union2(A!7, B!6) = B!6)),
% 0.19/0.37 inference(or_elim,[status(thm)],[35])).
% 0.19/0.37 tff(37,plain,
% 0.19/0.37 (~(B!6 = set_union2(B!6, A!7))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[36, 27])).
% 0.19/0.37 tff(38,plain,
% 0.19/0.37 ((((~subset(B!6, set_union2(B!6, A!7))) | (~subset(set_union2(B!6, A!7), B!6))) <=> (B!6 = set_union2(B!6, A!7))) | ((~subset(B!6, set_union2(B!6, A!7))) | (~subset(set_union2(B!6, A!7), B!6))) | (B!6 = set_union2(B!6, A!7))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(39,plain,
% 0.19/0.37 ((~subset(B!6, set_union2(B!6, A!7))) | (~subset(set_union2(B!6, A!7), B!6))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[38, 37, 12])).
% 0.19/0.37 tff(40,plain,
% 0.19/0.37 (^[A: $i, B: $i] : refl(subset(A, set_union2(A, B)) <=> subset(A, set_union2(A, B)))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(41,plain,
% 0.19/0.37 (![A: $i, B: $i] : subset(A, set_union2(A, B)) <=> ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[40])).
% 0.19/0.37 tff(42,plain,
% 0.19/0.37 (![A: $i, B: $i] : subset(A, set_union2(A, B)) <=> ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(43,axiom,(![A: $i, B: $i] : subset(A, set_union2(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t7_xboole_1')).
% 0.19/0.37 tff(44,plain,
% 0.19/0.37 (![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.19/0.37 tff(45,plain,(
% 0.19/0.37 ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.19/0.37 inference(skolemize,[status(sab)],[44])).
% 0.19/0.37 tff(46,plain,
% 0.19/0.37 (![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.19/0.37 tff(47,plain,
% 0.19/0.37 ((~![A: $i, B: $i] : subset(A, set_union2(A, B))) | subset(B!6, set_union2(B!6, A!7))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(48,plain,
% 0.19/0.37 (subset(B!6, set_union2(B!6, A!7))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.19/0.37 tff(49,plain,
% 0.19/0.37 ((~((~subset(B!6, set_union2(B!6, A!7))) | (~subset(set_union2(B!6, A!7), B!6)))) | (~subset(B!6, set_union2(B!6, A!7))) | (~subset(set_union2(B!6, A!7), B!6))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(50,plain,
% 0.19/0.38 ((~((~subset(B!6, set_union2(B!6, A!7))) | (~subset(set_union2(B!6, A!7), B!6)))) | (~subset(set_union2(B!6, A!7), B!6))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.19/0.38 tff(51,plain,
% 0.19/0.38 (~subset(set_union2(B!6, A!7), B!6)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[50, 39])).
% 0.19/0.38 tff(52,plain,
% 0.19/0.38 (^[A: $i, B: $i, C: $i] : refl((subset(set_union2(A, C), B) | (~subset(C, B)) | (~subset(A, B))) <=> (subset(set_union2(A, C), B) | (~subset(C, B)) | (~subset(A, B))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(53,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(C, B)) | (~subset(A, B))) <=> ![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(C, B)) | (~subset(A, B)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[52])).
% 0.19/0.38 tff(54,plain,
% 0.19/0.38 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((subset(A, B) & subset(C, B)) <=> (~((~subset(C, B)) | (~subset(A, B))))), ((~(subset(A, B) & subset(C, B))) <=> (~(~((~subset(C, B)) | (~subset(A, B))))))), rewrite((~(~((~subset(C, B)) | (~subset(A, B))))) <=> ((~subset(C, B)) | (~subset(A, B)))), ((~(subset(A, B) & subset(C, B))) <=> ((~subset(C, B)) | (~subset(A, B))))), (((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B)) <=> (((~subset(C, B)) | (~subset(A, B))) | subset(set_union2(A, C), B)))), rewrite((((~subset(C, B)) | (~subset(A, B))) | subset(set_union2(A, C), B)) <=> (subset(set_union2(A, C), B) | (~subset(C, B)) | (~subset(A, B)))), (((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B)) <=> (subset(set_union2(A, C), B) | (~subset(C, B)) | (~subset(A, B)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(55,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B)) <=> ![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(C, B)) | (~subset(A, B)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[54])).
% 0.19/0.38 tff(56,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B)) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(57,plain,
% 0.19/0.38 (^[A: $i, B: $i, C: $i] : rewrite(((subset(A, B) & subset(C, B)) => subset(set_union2(A, C), B)) <=> ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B)))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(58,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(C, B)) => subset(set_union2(A, C), B)) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[57])).
% 0.19/0.38 tff(59,axiom,(![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(C, B)) => subset(set_union2(A, C), B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t8_xboole_1')).
% 0.19/0.38 tff(60,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.19/0.38 tff(61,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.19/0.38 tff(62,plain,(
% 0.19/0.38 ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B))),
% 0.19/0.38 inference(skolemize,[status(sab)],[61])).
% 0.19/0.38 tff(63,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(C, B)) | (~subset(A, B)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.19/0.38 tff(64,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(C, B)) | (~subset(A, B)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[63, 53])).
% 0.19/0.38 tff(65,plain,
% 0.19/0.38 (subset(A!7, B!6)),
% 0.19/0.38 inference(or_elim,[status(thm)],[35])).
% 0.19/0.38 tff(66,plain,
% 0.19/0.38 (((~![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(C, B)) | (~subset(A, B)))) | ((~subset(A!7, B!6)) | subset(set_union2(B!6, A!7), B!6) | (~subset(B!6, B!6)))) <=> ((~![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(C, B)) | (~subset(A, B)))) | (~subset(A!7, B!6)) | subset(set_union2(B!6, A!7), B!6) | (~subset(B!6, B!6)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(67,plain,
% 0.19/0.38 ((subset(set_union2(B!6, A!7), B!6) | (~subset(A!7, B!6)) | (~subset(B!6, B!6))) <=> ((~subset(A!7, B!6)) | subset(set_union2(B!6, A!7), B!6) | (~subset(B!6, B!6)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(68,plain,
% 0.19/0.38 (((~![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(C, B)) | (~subset(A, B)))) | (subset(set_union2(B!6, A!7), B!6) | (~subset(A!7, B!6)) | (~subset(B!6, B!6)))) <=> ((~![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(C, B)) | (~subset(A, B)))) | ((~subset(A!7, B!6)) | subset(set_union2(B!6, A!7), B!6) | (~subset(B!6, B!6))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[67])).
% 0.19/0.38 tff(69,plain,
% 0.19/0.38 (((~![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(C, B)) | (~subset(A, B)))) | (subset(set_union2(B!6, A!7), B!6) | (~subset(A!7, B!6)) | (~subset(B!6, B!6)))) <=> ((~![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(C, B)) | (~subset(A, B)))) | (~subset(A!7, B!6)) | subset(set_union2(B!6, A!7), B!6) | (~subset(B!6, B!6)))),
% 0.19/0.38 inference(transitivity,[status(thm)],[68, 66])).
% 0.19/0.38 tff(70,plain,
% 0.19/0.38 ((~![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(C, B)) | (~subset(A, B)))) | (subset(set_union2(B!6, A!7), B!6) | (~subset(A!7, B!6)) | (~subset(B!6, B!6)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(71,plain,
% 0.19/0.38 ((~![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(C, B)) | (~subset(A, B)))) | (~subset(A!7, B!6)) | subset(set_union2(B!6, A!7), B!6) | (~subset(B!6, B!6))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.19/0.38 tff(72,plain,
% 0.19/0.38 (~subset(B!6, B!6)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[71, 65, 64, 51])).
% 0.19/0.38 tff(73,plain,
% 0.19/0.38 (^[A: $i] : refl(subset(A, A) <=> subset(A, A))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(74,plain,
% 0.19/0.38 (![A: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 0.19/0.38 inference(quant_intro,[status(thm)],[73])).
% 0.19/0.38 tff(75,plain,
% 0.19/0.38 (![A: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(76,plain,
% 0.19/0.38 (![A: $i, B: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 0.19/0.38 inference(elim_unused_vars,[status(thm)],[])).
% 0.19/0.38 tff(77,axiom,(![A: $i, B: $i] : subset(A, A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reflexivity_r1_tarski')).
% 0.19/0.38 tff(78,plain,
% 0.19/0.38 (![A: $i] : subset(A, A)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.19/0.38 tff(79,plain,
% 0.19/0.38 (![A: $i] : subset(A, A)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[78, 75])).
% 0.19/0.38 tff(80,plain,(
% 0.19/0.38 ![A: $i] : subset(A, A)),
% 0.19/0.38 inference(skolemize,[status(sab)],[79])).
% 0.19/0.38 tff(81,plain,
% 0.19/0.38 (![A: $i] : subset(A, A)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[80, 74])).
% 0.19/0.38 tff(82,plain,
% 0.19/0.38 ((~![A: $i] : subset(A, A)) | subset(B!6, B!6)),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(83,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[82, 81, 72])).
% 0.19/0.38 % SZS output end Proof
% 0.19/0.38 % E exiting
%------------------------------------------------------------------------------