%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU130+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:26:58 AM UTC 2025
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU130+2 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 06:06:38 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(subset_type, type, (
% 0.12/0.39 subset: ( $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_A_7_type, type, (
% 0.12/0.39 tptp_fun_A_7: $i)).
% 0.12/0.39 tff(set_intersection2_type, type, (
% 0.12/0.39 set_intersection2: ( $i * $i ) > $i)).
% 0.12/0.39 tff(tptp_fun_B_6_type, type, (
% 0.12/0.39 tptp_fun_B_6: $i)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(4,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.39 tff(6,plain,(
% 0.12/0.39 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.12/0.39 inference(skolemize,[status(sab)],[5])).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(A!7, B!6) = set_intersection2(B!6, A!7))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (set_intersection2(A!7, B!6) = set_intersection2(B!6, A!7)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (set_intersection2(B!6, A!7) = set_intersection2(A!7, B!6)),
% 0.12/0.39 inference(symmetry,[status(thm)],[9])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 (subset(set_intersection2(B!6, A!7), A!7) <=> subset(set_intersection2(A!7, B!6), A!7)),
% 0.12/0.39 inference(monotonicity,[status(thm)],[10])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (subset(set_intersection2(A!7, B!6), A!7) <=> subset(set_intersection2(B!6, A!7), A!7)),
% 0.12/0.39 inference(symmetry,[status(thm)],[11])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (^[A: $i, B: $i] : refl(subset(set_intersection2(A, B), A) <=> subset(set_intersection2(A, B), A))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (![A: $i, B: $i] : subset(set_intersection2(A, B), A) <=> ![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 0.12/0.39 inference(quant_intro,[status(thm)],[13])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (![A: $i, B: $i] : subset(set_intersection2(A, B), A) <=> ![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(16,axiom,(![A: $i, B: $i] : subset(set_intersection2(A, B), A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t17_xboole_1')).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 (![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.12/0.39 tff(18,plain,(
% 0.12/0.39 ![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 0.12/0.39 inference(skolemize,[status(sab)],[17])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 ((~![A: $i, B: $i] : subset(set_intersection2(A, B), A)) | subset(set_intersection2(A!7, B!6), A!7)),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 (subset(set_intersection2(A!7, B!6), A!7)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (subset(set_intersection2(B!6, A!7), A!7)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[21, 12])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 (^[A: $i, B: $i] : refl((~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[23])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (^[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)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[25])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(28,axiom,(![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d10_xboole_0')).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.12/0.39 tff(30,plain,(
% 0.12/0.39 ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[29])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))) | (~(((~subset(set_intersection2(B!6, A!7), A!7)) | (~subset(A!7, set_intersection2(B!6, A!7)))) <=> (set_intersection2(B!6, A!7) = A!7)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 (~(((~subset(set_intersection2(B!6, A!7), A!7)) | (~subset(A!7, set_intersection2(B!6, A!7)))) <=> (set_intersection2(B!6, A!7) = A!7))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 ((set_intersection2(B!6, A!7) = A!7) <=> (set_intersection2(A!7, B!6) = A!7)),
% 0.12/0.39 inference(monotonicity,[status(thm)],[10])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 ((set_intersection2(A!7, B!6) = A!7) <=> (set_intersection2(B!6, A!7) = A!7)),
% 0.12/0.39 inference(symmetry,[status(thm)],[35])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 ((~(set_intersection2(A!7, B!6) = A!7)) <=> (~(set_intersection2(B!6, A!7) = A!7))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[36])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) <=> (~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 ((~![A: $i, B: $i] : (subset(A, B) => (set_intersection2(A, B) = A))) <=> (~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(40,axiom,(~![A: $i, B: $i] : (subset(A, B) => (set_intersection2(A, B) = A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t28_xboole_1')).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 (~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.12/0.39 tff(42,plain,
% 0.12/0.39 (~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[41, 38])).
% 0.12/0.39 tff(43,plain,
% 0.12/0.39 (~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.12/0.39 tff(44,plain,
% 0.12/0.39 (~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[43, 38])).
% 0.12/0.39 tff(45,plain,(
% 0.12/0.39 ~((~subset(A!7, B!6)) | (set_intersection2(A!7, B!6) = A!7))),
% 0.12/0.39 inference(skolemize,[status(sab)],[44])).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 (~(set_intersection2(A!7, B!6) = A!7)),
% 0.12/0.39 inference(or_elim,[status(thm)],[45])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 (~(set_intersection2(B!6, A!7) = A!7)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[46, 37])).
% 0.12/0.39 tff(48,plain,
% 0.12/0.39 ((((~subset(set_intersection2(B!6, A!7), A!7)) | (~subset(A!7, set_intersection2(B!6, A!7)))) <=> (set_intersection2(B!6, A!7) = A!7)) | ((~subset(set_intersection2(B!6, A!7), A!7)) | (~subset(A!7, set_intersection2(B!6, A!7)))) | (set_intersection2(B!6, A!7) = A!7)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(49,plain,
% 0.12/0.39 ((~subset(set_intersection2(B!6, A!7), A!7)) | (~subset(A!7, set_intersection2(B!6, A!7)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[48, 47, 34])).
% 0.12/0.39 tff(50,plain,
% 0.12/0.39 ((~((~subset(set_intersection2(B!6, A!7), A!7)) | (~subset(A!7, set_intersection2(B!6, A!7))))) | (~subset(set_intersection2(B!6, A!7), A!7)) | (~subset(A!7, set_intersection2(B!6, A!7)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(51,plain,
% 0.12/0.39 (~subset(A!7, set_intersection2(B!6, A!7))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[50, 49, 22])).
% 0.12/0.39 tff(52,plain,
% 0.12/0.39 (subset(A!7, B!6)),
% 0.12/0.39 inference(or_elim,[status(thm)],[45])).
% 0.12/0.39 tff(53,plain,
% 0.12/0.39 (^[A: $i, B: $i, C: $i] : refl((subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C))) <=> (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(54,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i] : (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C))) <=> ![A: $i, B: $i, C: $i] : (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[53])).
% 0.12/0.39 tff(55,plain,
% 0.12/0.39 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((subset(A, B) & subset(A, C)) <=> (~((~subset(A, B)) | (~subset(A, C))))), ((~(subset(A, B) & subset(A, C))) <=> (~(~((~subset(A, B)) | (~subset(A, C))))))), rewrite((~(~((~subset(A, B)) | (~subset(A, C))))) <=> ((~subset(A, B)) | (~subset(A, C)))), ((~(subset(A, B) & subset(A, C))) <=> ((~subset(A, B)) | (~subset(A, C))))), (((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C))) <=> (((~subset(A, B)) | (~subset(A, C))) | subset(A, set_intersection2(B, C))))), rewrite((((~subset(A, B)) | (~subset(A, C))) | subset(A, set_intersection2(B, C))) <=> (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C)))), (((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C))) <=> (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(56,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C))) <=> ![A: $i, B: $i, C: $i] : (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[55])).
% 0.12/0.39 tff(57,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(58,plain,
% 0.12/0.39 (^[A: $i, B: $i, C: $i] : rewrite(((subset(A, B) & subset(A, C)) => subset(A, set_intersection2(B, C))) <=> ((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(59,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(A, C)) => subset(A, set_intersection2(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[58])).
% 0.12/0.39 tff(60,axiom,(![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(A, C)) => subset(A, set_intersection2(B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t19_xboole_1')).
% 0.12/0.39 tff(61,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.12/0.39 tff(62,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.20/0.40 tff(63,plain,(
% 0.20/0.40 ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[62])).
% 0.20/0.40 tff(64,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i] : (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.20/0.40 tff(65,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i] : (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[64, 54])).
% 0.20/0.40 tff(66,plain,
% 0.20/0.40 (((~![A: $i, B: $i, C: $i] : (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C)))) | ((~subset(A!7, B!6)) | (~subset(A!7, A!7)) | subset(A!7, set_intersection2(B!6, A!7)))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C)))) | (~subset(A!7, B!6)) | (~subset(A!7, A!7)) | subset(A!7, set_intersection2(B!6, A!7)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 ((subset(A!7, set_intersection2(B!6, A!7)) | (~subset(A!7, B!6)) | (~subset(A!7, A!7))) <=> ((~subset(A!7, B!6)) | (~subset(A!7, A!7)) | subset(A!7, set_intersection2(B!6, A!7)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(68,plain,
% 0.20/0.40 (((~![A: $i, B: $i, C: $i] : (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C)))) | (subset(A!7, set_intersection2(B!6, A!7)) | (~subset(A!7, B!6)) | (~subset(A!7, A!7)))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C)))) | ((~subset(A!7, B!6)) | (~subset(A!7, A!7)) | subset(A!7, set_intersection2(B!6, A!7))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[67])).
% 0.20/0.40 tff(69,plain,
% 0.20/0.40 (((~![A: $i, B: $i, C: $i] : (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C)))) | (subset(A!7, set_intersection2(B!6, A!7)) | (~subset(A!7, B!6)) | (~subset(A!7, A!7)))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C)))) | (~subset(A!7, B!6)) | (~subset(A!7, A!7)) | subset(A!7, set_intersection2(B!6, A!7)))),
% 0.20/0.40 inference(transitivity,[status(thm)],[68, 66])).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 ((~![A: $i, B: $i, C: $i] : (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C)))) | (subset(A!7, set_intersection2(B!6, A!7)) | (~subset(A!7, B!6)) | (~subset(A!7, A!7)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 ((~![A: $i, B: $i, C: $i] : (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C)))) | (~subset(A!7, B!6)) | (~subset(A!7, A!7)) | subset(A!7, set_intersection2(B!6, A!7))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.40 tff(72,plain,
% 0.20/0.40 (~subset(A!7, A!7)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[71, 65, 52, 51])).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 (^[A: $i] : refl(subset(A, A) <=> subset(A, A))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(74,plain,
% 0.20/0.40 (![A: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 0.20/0.40 inference(quant_intro,[status(thm)],[73])).
% 0.20/0.40 tff(75,plain,
% 0.20/0.40 (![A: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(76,plain,
% 0.20/0.40 (![A: $i, B: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 0.20/0.40 inference(elim_unused_vars,[status(thm)],[])).
% 0.20/0.40 tff(77,axiom,(![A: $i, B: $i] : subset(A, A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reflexivity_r1_tarski')).
% 0.20/0.40 tff(78,plain,
% 0.20/0.40 (![A: $i] : subset(A, A)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.20/0.40 tff(79,plain,
% 0.20/0.40 (![A: $i] : subset(A, A)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[78, 75])).
% 0.20/0.40 tff(80,plain,(
% 0.20/0.40 ![A: $i] : subset(A, A)),
% 0.20/0.40 inference(skolemize,[status(sab)],[79])).
% 0.20/0.40 tff(81,plain,
% 0.20/0.40 (![A: $i] : subset(A, A)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[80, 74])).
% 0.20/0.40 tff(82,plain,
% 0.20/0.40 ((~![A: $i] : subset(A, A)) | subset(A!7, A!7)),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(83,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[82, 81, 72])).
% 0.20/0.40 % SZS output end Proof
% 0.20/0.40 % E exiting
%------------------------------------------------------------------------------