%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU140+1 : TPTP v9.0.0. Released v3.3.0.
% 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 05:27:00 AM UTC 2025
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SEU140+1 : TPTP v9.0.0. Released v3.3.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.13/0.36 % Computer : n015.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Fri Jun 20 06:07:26 EDT 2025
% 0.13/0.36 % CPUTime :
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(subset_type, type, (
% 0.13/0.40 subset: ( $i * $i ) > $o)).
% 0.13/0.40 tff(empty_set_type, type, (
% 0.13/0.40 empty_set: $i)).
% 0.13/0.40 tff(set_intersection2_type, type, (
% 0.13/0.40 set_intersection2: ( $i * $i ) > $i)).
% 0.13/0.40 tff(tptp_fun_A_4_type, type, (
% 0.13/0.40 tptp_fun_A_4: $i)).
% 0.13/0.40 tff(tptp_fun_C_2_type, type, (
% 0.13/0.40 tptp_fun_C_2: $i)).
% 0.13/0.40 tff(tptp_fun_B_3_type, type, (
% 0.13/0.40 tptp_fun_B_3: $i)).
% 0.13/0.40 tff(disjoint_type, type, (
% 0.13/0.40 disjoint: ( $i * $i ) > $o)).
% 0.13/0.40 tff(1,plain,
% 0.13/0.40 (^[A: $i, B: $i] : refl((disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)) <=> (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(4,axiom,(![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d7_xboole_0')).
% 0.13/0.40 tff(5,plain,
% 0.13/0.40 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.40 tff(6,plain,(
% 0.13/0.40 ![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.13/0.40 inference(skolemize,[status(sab)],[5])).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 ((~![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))) | (disjoint(B!3, C!2) <=> (set_intersection2(B!3, C!2) = empty_set))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (disjoint(B!3, C!2) <=> (set_intersection2(B!3, C!2) = empty_set)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 ((~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & disjoint(B, C))) | disjoint(A, C))) <=> (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & disjoint(B, C))) | disjoint(A, C)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 ((~![A: $i, B: $i, C: $i] : ((subset(A, B) & disjoint(B, C)) => disjoint(A, C))) <=> (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & disjoint(B, C))) | disjoint(A, C)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(12,axiom,(~![A: $i, B: $i, C: $i] : ((subset(A, B) & disjoint(B, C)) => disjoint(A, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t63_xboole_1')).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & disjoint(B, C))) | disjoint(A, C))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & disjoint(B, C))) | disjoint(A, C))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & disjoint(B, C))) | disjoint(A, C))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & disjoint(B, C))) | disjoint(A, C))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.13/0.40 tff(17,plain,(
% 0.13/0.40 ~((~(subset(A!4, B!3) & disjoint(B!3, C!2))) | disjoint(A!4, C!2))),
% 0.13/0.40 inference(skolemize,[status(sab)],[16])).
% 0.13/0.40 tff(18,plain,
% 0.13/0.40 (subset(A!4, B!3) & disjoint(B!3, C!2)),
% 0.13/0.40 inference(or_elim,[status(thm)],[17])).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 (disjoint(B!3, C!2)),
% 0.13/0.40 inference(and_elim,[status(thm)],[18])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 ((~(disjoint(B!3, C!2) <=> (set_intersection2(B!3, C!2) = empty_set))) | (~disjoint(B!3, C!2)) | (set_intersection2(B!3, C!2) = empty_set)),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 ((~(disjoint(B!3, C!2) <=> (set_intersection2(B!3, C!2) = empty_set))) | (set_intersection2(B!3, C!2) = empty_set)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 (set_intersection2(B!3, C!2) = empty_set),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[21, 9])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 (empty_set = set_intersection2(B!3, C!2)),
% 0.13/0.40 inference(symmetry,[status(thm)],[22])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[24])).
% 0.13/0.40 tff(26,plain,
% 0.13/0.40 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(27,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 0.13/0.40 tff(28,plain,
% 0.13/0.40 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.13/0.40 tff(29,plain,(
% 0.13/0.40 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.13/0.40 inference(skolemize,[status(sab)],[28])).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.13/0.40 tff(31,plain,
% 0.13/0.40 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(A!4, C!2) = set_intersection2(C!2, A!4))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 (set_intersection2(A!4, C!2) = set_intersection2(C!2, A!4)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.13/0.40 tff(33,plain,
% 0.13/0.40 (set_intersection2(C!2, A!4) = set_intersection2(A!4, C!2)),
% 0.13/0.40 inference(symmetry,[status(thm)],[32])).
% 0.13/0.40 tff(34,plain,
% 0.13/0.40 (subset(set_intersection2(C!2, A!4), empty_set) <=> subset(set_intersection2(A!4, C!2), set_intersection2(B!3, C!2))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[33, 23])).
% 0.13/0.40 tff(35,plain,
% 0.13/0.40 (subset(set_intersection2(A!4, C!2), set_intersection2(B!3, C!2)) <=> subset(set_intersection2(C!2, A!4), empty_set)),
% 0.13/0.40 inference(symmetry,[status(thm)],[34])).
% 0.13/0.40 tff(36,plain,
% 0.13/0.40 (subset(A!4, B!3)),
% 0.13/0.40 inference(and_elim,[status(thm)],[18])).
% 0.13/0.40 tff(37,plain,
% 0.13/0.40 (^[A: $i, B: $i, C: $i] : refl(((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C))) <=> ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(38,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[37])).
% 0.13/0.40 tff(39,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(40,plain,
% 0.13/0.40 (^[A: $i, B: $i, C: $i] : rewrite((subset(A, B) => subset(set_intersection2(A, C), set_intersection2(B, C))) <=> ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(41,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : (subset(A, B) => subset(set_intersection2(A, C), set_intersection2(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[40])).
% 0.13/0.40 tff(42,axiom,(![A: $i, B: $i, C: $i] : (subset(A, B) => subset(set_intersection2(A, C), set_intersection2(B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t26_xboole_1')).
% 0.13/0.40 tff(43,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.13/0.40 tff(44,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.13/0.40 tff(45,plain,(
% 0.13/0.40 ![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[44])).
% 0.13/0.40 tff(46,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.13/0.40 tff(47,plain,
% 0.13/0.40 (((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C)))) | ((~subset(A!4, B!3)) | subset(set_intersection2(A!4, C!2), set_intersection2(B!3, C!2)))) <=> ((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C)))) | (~subset(A!4, B!3)) | subset(set_intersection2(A!4, C!2), set_intersection2(B!3, C!2)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(48,plain,
% 0.13/0.40 ((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C)))) | ((~subset(A!4, B!3)) | subset(set_intersection2(A!4, C!2), set_intersection2(B!3, C!2)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(49,plain,
% 0.13/0.40 ((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C)))) | (~subset(A!4, B!3)) | subset(set_intersection2(A!4, C!2), set_intersection2(B!3, C!2))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.13/0.40 tff(50,plain,
% 0.13/0.40 (subset(set_intersection2(A!4, C!2), set_intersection2(B!3, C!2))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[49, 46, 36])).
% 0.13/0.40 tff(51,plain,
% 0.13/0.40 (subset(set_intersection2(C!2, A!4), empty_set)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[50, 35])).
% 0.13/0.40 tff(52,plain,
% 0.13/0.40 ((~![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))) | (disjoint(C!2, A!4) <=> (set_intersection2(C!2, A!4) = empty_set))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(53,plain,
% 0.13/0.40 (disjoint(C!2, A!4) <=> (set_intersection2(C!2, A!4) = empty_set)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[52, 7])).
% 0.13/0.40 tff(54,plain,
% 0.13/0.40 (~disjoint(A!4, C!2)),
% 0.13/0.40 inference(or_elim,[status(thm)],[17])).
% 0.13/0.40 tff(55,plain,
% 0.13/0.40 (^[A: $i, B: $i] : refl(((~disjoint(A, B)) | disjoint(B, A)) <=> ((~disjoint(A, B)) | disjoint(B, A)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(56,plain,
% 0.13/0.40 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[55])).
% 0.13/0.40 tff(57,plain,
% 0.13/0.40 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(58,plain,
% 0.13/0.40 (^[A: $i, B: $i] : rewrite((disjoint(A, B) => disjoint(B, A)) <=> ((~disjoint(A, B)) | disjoint(B, A)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(59,plain,
% 0.13/0.40 (![A: $i, B: $i] : (disjoint(A, B) => disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[58])).
% 0.13/0.40 tff(60,axiom,(![A: $i, B: $i] : (disjoint(A, B) => disjoint(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','symmetry_r1_xboole_0')).
% 0.13/0.40 tff(61,plain,
% 0.13/0.40 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.13/0.40 tff(62,plain,
% 0.13/0.40 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.13/0.40 tff(63,plain,(
% 0.13/0.40 ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.13/0.40 inference(skolemize,[status(sab)],[62])).
% 0.13/0.40 tff(64,plain,
% 0.13/0.40 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.13/0.40 tff(65,plain,
% 0.13/0.40 (((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(C!2, A!4)) | disjoint(A!4, C!2))) <=> ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(C!2, A!4)) | disjoint(A!4, C!2))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(66,plain,
% 0.13/0.40 ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(C!2, A!4)) | disjoint(A!4, C!2))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(67,plain,
% 0.13/0.40 ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(C!2, A!4)) | disjoint(A!4, C!2)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.13/0.40 tff(68,plain,
% 0.13/0.40 (~disjoint(C!2, A!4)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[67, 64, 54])).
% 0.13/0.40 tff(69,plain,
% 0.13/0.40 ((~(disjoint(C!2, A!4) <=> (set_intersection2(C!2, A!4) = empty_set))) | disjoint(C!2, A!4) | (~(set_intersection2(C!2, A!4) = empty_set))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(70,plain,
% 0.13/0.40 ((~(disjoint(C!2, A!4) <=> (set_intersection2(C!2, A!4) = empty_set))) | (~(set_intersection2(C!2, A!4) = empty_set))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.13/0.40 tff(71,plain,
% 0.13/0.40 (~(set_intersection2(C!2, A!4) = empty_set)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[70, 53])).
% 0.13/0.40 tff(72,plain,
% 0.13/0.40 (^[A: $i] : refl(((~subset(A, empty_set)) | (A = empty_set)) <=> ((~subset(A, empty_set)) | (A = empty_set)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(73,plain,
% 0.13/0.40 (![A: $i] : ((~subset(A, empty_set)) | (A = empty_set)) <=> ![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[72])).
% 0.13/0.40 tff(74,plain,
% 0.13/0.40 (![A: $i] : ((~subset(A, empty_set)) | (A = empty_set)) <=> ![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(75,plain,
% 0.13/0.40 (^[A: $i] : rewrite((subset(A, empty_set) => (A = empty_set)) <=> ((~subset(A, empty_set)) | (A = empty_set)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(76,plain,
% 0.13/0.40 (![A: $i] : (subset(A, empty_set) => (A = empty_set)) <=> ![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[75])).
% 0.13/0.40 tff(77,axiom,(![A: $i] : (subset(A, empty_set) => (A = empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t3_xboole_1')).
% 0.13/0.40 tff(78,plain,
% 0.13/0.40 (![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.13/0.40 tff(79,plain,
% 0.13/0.40 (![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.13/0.40 tff(80,plain,(
% 0.13/0.40 ![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))),
% 0.13/0.40 inference(skolemize,[status(sab)],[79])).
% 0.13/0.40 tff(81,plain,
% 0.13/0.40 (![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.13/0.40 tff(82,plain,
% 0.13/0.40 (((~![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))) | ((~subset(set_intersection2(C!2, A!4), empty_set)) | (set_intersection2(C!2, A!4) = empty_set))) <=> ((~![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))) | (~subset(set_intersection2(C!2, A!4), empty_set)) | (set_intersection2(C!2, A!4) = empty_set))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(83,plain,
% 0.13/0.40 ((~![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))) | ((~subset(set_intersection2(C!2, A!4), empty_set)) | (set_intersection2(C!2, A!4) = empty_set))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(84,plain,
% 0.13/0.40 ((~![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))) | (~subset(set_intersection2(C!2, A!4), empty_set)) | (set_intersection2(C!2, A!4) = empty_set)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.13/0.40 tff(85,plain,
% 0.13/0.40 (~subset(set_intersection2(C!2, A!4), empty_set)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[84, 81, 71])).
% 0.13/0.40 tff(86,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[85, 51])).
% 0.13/0.40 % SZS output end Proof
% 0.13/0.41 % E exiting
%------------------------------------------------------------------------------