%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM383+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:20:52 AM UTC 2025
% Result : Theorem 1.83s 2.05s
% Output : Proof 1.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM383+1 : TPTP v9.0.0. Released v3.2.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n014.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 01:01:39 EDT 2025
% 0.12/0.33 % CPUTime :
% 1.83/2.05 % SZS status Theorem
% 1.83/2.05 % SZS output start Proof
% 1.83/2.05 tff(in_type, type, (
% 1.83/2.05 in: ( $i * $i ) > $o)).
% 1.83/2.05 tff(tptp_fun_A_12_type, type, (
% 1.83/2.05 tptp_fun_A_12: $i)).
% 1.83/2.05 tff(element_type, type, (
% 1.83/2.05 element: ( $i * $i ) > $o)).
% 1.83/2.05 tff(powerset_type, type, (
% 1.83/2.05 powerset: $i > $i)).
% 1.83/2.05 tff(tptp_fun_B_11_type, type, (
% 1.83/2.05 tptp_fun_B_11: $i)).
% 1.83/2.05 tff(subset_type, type, (
% 1.83/2.05 subset: ( $i * $i ) > $o)).
% 1.83/2.05 tff(empty_type, type, (
% 1.83/2.05 empty: $i > $o)).
% 1.83/2.05 tff(1,plain,
% 1.83/2.05 (^[A: $i, B: $i] : refl((element(A, powerset(B)) <=> subset(A, B)) <=> (element(A, powerset(B)) <=> subset(A, B)))),
% 1.83/2.05 inference(bind,[status(th)],[])).
% 1.83/2.05 tff(2,plain,
% 1.83/2.05 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 1.83/2.05 inference(quant_intro,[status(thm)],[1])).
% 1.83/2.05 tff(3,plain,
% 1.83/2.05 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 1.83/2.05 inference(rewrite,[status(thm)],[])).
% 1.83/2.05 tff(4,axiom,(![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3_subset')).
% 1.83/2.05 tff(5,plain,
% 1.83/2.05 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.83/2.05 tff(6,plain,(
% 1.83/2.05 ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 1.83/2.05 inference(skolemize,[status(sab)],[5])).
% 1.83/2.05 tff(7,plain,
% 1.83/2.05 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.83/2.05 tff(8,plain,
% 1.83/2.05 ((~![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))) | (element(B!11, powerset(A!12)) <=> subset(B!11, A!12))),
% 1.83/2.05 inference(quant_inst,[status(thm)],[])).
% 1.83/2.05 tff(9,plain,
% 1.83/2.05 (element(B!11, powerset(A!12)) <=> subset(B!11, A!12)),
% 1.83/2.05 inference(unit_resolution,[status(thm)],[8, 7])).
% 1.83/2.05 tff(10,plain,
% 1.83/2.05 ((~![A: $i, B: $i] : (~(in(A, B) & subset(B, A)))) <=> (~![A: $i, B: $i] : (~(in(A, B) & subset(B, A))))),
% 1.83/2.05 inference(rewrite,[status(thm)],[])).
% 1.83/2.05 tff(11,axiom,(~![A: $i, B: $i] : (~(in(A, B) & subset(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t7_ordinal1')).
% 1.83/2.05 tff(12,plain,
% 1.83/2.05 (~![A: $i, B: $i] : (~(in(A, B) & subset(B, A)))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[11, 10])).
% 1.83/2.05 tff(13,plain,
% 1.83/2.05 (~![A: $i, B: $i] : (~(in(A, B) & subset(B, A)))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[12, 10])).
% 1.83/2.05 tff(14,plain,
% 1.83/2.05 (~![A: $i, B: $i] : (~(in(A, B) & subset(B, A)))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[13, 10])).
% 1.83/2.05 tff(15,plain,
% 1.83/2.05 (~![A: $i, B: $i] : (~(in(A, B) & subset(B, A)))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[14, 10])).
% 1.83/2.05 tff(16,plain,(
% 1.83/2.05 in(A!12, B!11) & subset(B!11, A!12)),
% 1.83/2.05 inference(skolemize,[status(sab)],[15])).
% 1.83/2.05 tff(17,plain,
% 1.83/2.05 (subset(B!11, A!12)),
% 1.83/2.05 inference(and_elim,[status(thm)],[16])).
% 1.83/2.05 tff(18,plain,
% 1.83/2.05 ((~(element(B!11, powerset(A!12)) <=> subset(B!11, A!12))) | element(B!11, powerset(A!12)) | (~subset(B!11, A!12))),
% 1.83/2.05 inference(tautology,[status(thm)],[])).
% 1.83/2.05 tff(19,plain,
% 1.83/2.05 ((~(element(B!11, powerset(A!12)) <=> subset(B!11, A!12))) | element(B!11, powerset(A!12))),
% 1.83/2.05 inference(unit_resolution,[status(thm)],[18, 17])).
% 1.83/2.05 tff(20,plain,
% 1.83/2.05 (element(B!11, powerset(A!12))),
% 1.83/2.05 inference(unit_resolution,[status(thm)],[19, 9])).
% 1.83/2.05 tff(21,plain,
% 1.83/2.05 (in(A!12, B!11)),
% 1.83/2.05 inference(and_elim,[status(thm)],[16])).
% 1.83/2.05 tff(22,plain,
% 1.83/2.05 (^[A: $i, B: $i, C: $i] : refl((element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))))),
% 1.83/2.05 inference(bind,[status(th)],[])).
% 1.83/2.05 tff(23,plain,
% 1.83/2.05 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 1.83/2.05 inference(quant_intro,[status(thm)],[22])).
% 1.83/2.05 tff(24,plain,
% 1.83/2.05 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((in(A, B) & element(B, powerset(C))) <=> (~((~in(A, B)) | (~element(B, powerset(C)))))), ((~(in(A, B) & element(B, powerset(C)))) <=> (~(~((~in(A, B)) | (~element(B, powerset(C)))))))), rewrite((~(~((~in(A, B)) | (~element(B, powerset(C)))))) <=> ((~in(A, B)) | (~element(B, powerset(C))))), ((~(in(A, B) & element(B, powerset(C)))) <=> ((~in(A, B)) | (~element(B, powerset(C)))))), (((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> (((~in(A, B)) | (~element(B, powerset(C)))) | element(A, C)))), rewrite((((~in(A, B)) | (~element(B, powerset(C)))) | element(A, C)) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))), (((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))))),
% 1.83/2.05 inference(bind,[status(th)],[])).
% 1.83/2.05 tff(25,plain,
% 1.83/2.05 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> ![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 1.83/2.05 inference(quant_intro,[status(thm)],[24])).
% 1.83/2.05 tff(26,plain,
% 1.83/2.05 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 1.83/2.05 inference(rewrite,[status(thm)],[])).
% 1.83/2.05 tff(27,plain,
% 1.83/2.05 (^[A: $i, B: $i, C: $i] : rewrite(((in(A, B) & element(B, powerset(C))) => element(A, C)) <=> ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)))),
% 1.83/2.05 inference(bind,[status(th)],[])).
% 1.83/2.05 tff(28,plain,
% 1.83/2.05 (![A: $i, B: $i, C: $i] : ((in(A, B) & element(B, powerset(C))) => element(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 1.83/2.05 inference(quant_intro,[status(thm)],[27])).
% 1.83/2.05 tff(29,axiom,(![A: $i, B: $i, C: $i] : ((in(A, B) & element(B, powerset(C))) => element(A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t4_subset')).
% 1.83/2.05 tff(30,plain,
% 1.83/2.05 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[29, 28])).
% 1.83/2.05 tff(31,plain,
% 1.83/2.05 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[30, 26])).
% 1.83/2.05 tff(32,plain,(
% 1.83/2.05 ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 1.83/2.05 inference(skolemize,[status(sab)],[31])).
% 1.83/2.05 tff(33,plain,
% 1.83/2.05 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[32, 25])).
% 1.83/2.05 tff(34,plain,
% 1.83/2.05 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[33, 23])).
% 1.83/2.05 tff(35,plain,
% 1.83/2.05 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~in(A!12, B!11)) | (~element(B!11, powerset(A!12))) | element(A!12, A!12))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~in(A!12, B!11)) | (~element(B!11, powerset(A!12))) | element(A!12, A!12))),
% 1.83/2.05 inference(rewrite,[status(thm)],[])).
% 1.83/2.05 tff(36,plain,
% 1.83/2.05 ((element(A!12, A!12) | (~in(A!12, B!11)) | (~element(B!11, powerset(A!12)))) <=> ((~in(A!12, B!11)) | (~element(B!11, powerset(A!12))) | element(A!12, A!12))),
% 1.83/2.05 inference(rewrite,[status(thm)],[])).
% 1.83/2.05 tff(37,plain,
% 1.83/2.05 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(A!12, A!12) | (~in(A!12, B!11)) | (~element(B!11, powerset(A!12))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~in(A!12, B!11)) | (~element(B!11, powerset(A!12))) | element(A!12, A!12)))),
% 1.83/2.05 inference(monotonicity,[status(thm)],[36])).
% 1.83/2.05 tff(38,plain,
% 1.83/2.05 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(A!12, A!12) | (~in(A!12, B!11)) | (~element(B!11, powerset(A!12))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~in(A!12, B!11)) | (~element(B!11, powerset(A!12))) | element(A!12, A!12))),
% 1.83/2.05 inference(transitivity,[status(thm)],[37, 35])).
% 1.83/2.05 tff(39,plain,
% 1.83/2.05 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(A!12, A!12) | (~in(A!12, B!11)) | (~element(B!11, powerset(A!12))))),
% 1.83/2.05 inference(quant_inst,[status(thm)],[])).
% 1.83/2.05 tff(40,plain,
% 1.83/2.05 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~in(A!12, B!11)) | (~element(B!11, powerset(A!12))) | element(A!12, A!12)),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[39, 38])).
% 1.83/2.05 tff(41,plain,
% 1.83/2.05 (element(A!12, A!12)),
% 1.83/2.05 inference(unit_resolution,[status(thm)],[40, 34, 21, 20])).
% 1.83/2.05 tff(42,plain,
% 1.83/2.05 (^[A: $i, B: $i, C: $i] : refl(((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))),
% 1.83/2.05 inference(bind,[status(th)],[])).
% 1.83/2.05 tff(43,plain,
% 1.83/2.05 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 1.83/2.05 inference(quant_intro,[status(thm)],[42])).
% 1.83/2.05 tff(44,plain,
% 1.83/2.05 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(A, B) & element(B, powerset(C)) & empty(C)) <=> (~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))), ((~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> (~(~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))))), rewrite((~(~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))), ((~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))))),
% 1.83/2.05 inference(bind,[status(th)],[])).
% 1.83/2.05 tff(45,plain,
% 1.83/2.05 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 1.83/2.05 inference(quant_intro,[status(thm)],[44])).
% 1.83/2.05 tff(46,plain,
% 1.83/2.05 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 1.83/2.05 inference(rewrite,[status(thm)],[])).
% 1.83/2.05 tff(47,plain,
% 1.83/2.05 (^[A: $i, B: $i, C: $i] : rewrite((~((in(A, B) & element(B, powerset(C))) & empty(C))) <=> (~(in(A, B) & element(B, powerset(C)) & empty(C))))),
% 1.83/2.05 inference(bind,[status(th)],[])).
% 1.83/2.05 tff(48,plain,
% 1.83/2.05 (![A: $i, B: $i, C: $i] : (~((in(A, B) & element(B, powerset(C))) & empty(C))) <=> ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 1.83/2.05 inference(quant_intro,[status(thm)],[47])).
% 1.83/2.05 tff(49,axiom,(![A: $i, B: $i, C: $i] : (~((in(A, B) & element(B, powerset(C))) & empty(C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t5_subset')).
% 1.83/2.05 tff(50,plain,
% 1.83/2.05 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[49, 48])).
% 1.83/2.05 tff(51,plain,
% 1.83/2.05 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[50, 46])).
% 1.83/2.05 tff(52,plain,(
% 1.83/2.05 ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 1.83/2.05 inference(skolemize,[status(sab)],[51])).
% 1.83/2.05 tff(53,plain,
% 1.83/2.05 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[52, 45])).
% 1.83/2.05 tff(54,plain,
% 1.83/2.05 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[53, 43])).
% 1.83/2.05 tff(55,plain,
% 1.83/2.05 (((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(A!12)) | (~in(A!12, B!11)) | (~element(B!11, powerset(A!12))))) <=> ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~empty(A!12)) | (~in(A!12, B!11)) | (~element(B!11, powerset(A!12))))),
% 1.83/2.05 inference(rewrite,[status(thm)],[])).
% 1.83/2.05 tff(56,plain,
% 1.83/2.05 ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(A!12)) | (~in(A!12, B!11)) | (~element(B!11, powerset(A!12))))),
% 1.83/2.05 inference(quant_inst,[status(thm)],[])).
% 1.83/2.05 tff(57,plain,
% 1.83/2.05 ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~empty(A!12)) | (~in(A!12, B!11)) | (~element(B!11, powerset(A!12)))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[56, 55])).
% 1.83/2.05 tff(58,plain,
% 1.83/2.05 (~empty(A!12)),
% 1.83/2.05 inference(unit_resolution,[status(thm)],[57, 54, 21, 20])).
% 1.83/2.05 tff(59,plain,
% 1.83/2.05 (^[A: $i, B: $i] : refl((empty(B) | in(A, B) | (~element(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 1.83/2.05 inference(bind,[status(th)],[])).
% 1.83/2.05 tff(60,plain,
% 1.83/2.05 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 1.83/2.05 inference(quant_intro,[status(thm)],[59])).
% 1.83/2.05 tff(61,plain,
% 1.83/2.05 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 1.83/2.05 inference(rewrite,[status(thm)],[])).
% 1.83/2.05 tff(62,plain,
% 1.83/2.05 (^[A: $i, B: $i] : rewrite((element(A, B) => (empty(B) | in(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 1.83/2.05 inference(bind,[status(th)],[])).
% 1.83/2.05 tff(63,plain,
% 1.83/2.05 (![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 1.83/2.05 inference(quant_intro,[status(thm)],[62])).
% 1.83/2.05 tff(64,axiom,(![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2_subset')).
% 1.83/2.05 tff(65,plain,
% 1.83/2.05 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[64, 63])).
% 1.83/2.05 tff(66,plain,
% 1.83/2.05 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[65, 61])).
% 1.83/2.05 tff(67,plain,(
% 1.83/2.05 ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 1.83/2.05 inference(skolemize,[status(sab)],[66])).
% 1.83/2.05 tff(68,plain,
% 1.83/2.05 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[67, 60])).
% 1.83/2.05 tff(69,plain,
% 1.83/2.05 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(A!12) | in(A!12, A!12) | (~element(A!12, A!12)))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(A!12) | in(A!12, A!12) | (~element(A!12, A!12)))),
% 1.83/2.05 inference(rewrite,[status(thm)],[])).
% 1.83/2.05 tff(70,plain,
% 1.83/2.05 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(A!12) | in(A!12, A!12) | (~element(A!12, A!12)))),
% 1.83/2.05 inference(quant_inst,[status(thm)],[])).
% 1.83/2.05 tff(71,plain,
% 1.83/2.05 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(A!12) | in(A!12, A!12) | (~element(A!12, A!12))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[70, 69])).
% 1.83/2.05 tff(72,plain,
% 1.83/2.05 (in(A!12, A!12)),
% 1.83/2.05 inference(unit_resolution,[status(thm)],[71, 68, 58, 41])).
% 1.83/2.05 tff(73,plain,
% 1.83/2.05 (^[A: $i, B: $i] : refl(((~in(B, A)) | (~in(A, B))) <=> ((~in(B, A)) | (~in(A, B))))),
% 1.83/2.05 inference(bind,[status(th)],[])).
% 1.83/2.05 tff(74,plain,
% 1.83/2.05 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B))) <=> ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 1.83/2.05 inference(quant_intro,[status(thm)],[73])).
% 1.83/2.05 tff(75,plain,
% 1.83/2.05 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B))) <=> ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 1.83/2.05 inference(rewrite,[status(thm)],[])).
% 1.83/2.05 tff(76,plain,
% 1.83/2.05 (^[A: $i, B: $i] : rewrite((in(A, B) => (~in(B, A))) <=> ((~in(B, A)) | (~in(A, B))))),
% 1.83/2.05 inference(bind,[status(th)],[])).
% 1.83/2.05 tff(77,plain,
% 1.83/2.05 (![A: $i, B: $i] : (in(A, B) => (~in(B, A))) <=> ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 1.83/2.05 inference(quant_intro,[status(thm)],[76])).
% 1.83/2.05 tff(78,axiom,(![A: $i, B: $i] : (in(A, B) => (~in(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','antisymmetry_r2_hidden')).
% 1.83/2.05 tff(79,plain,
% 1.83/2.05 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[78, 77])).
% 1.83/2.05 tff(80,plain,
% 1.83/2.05 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[79, 75])).
% 1.83/2.05 tff(81,plain,(
% 1.83/2.05 ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 1.83/2.05 inference(skolemize,[status(sab)],[80])).
% 1.83/2.05 tff(82,plain,
% 1.83/2.05 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[81, 74])).
% 1.83/2.05 tff(83,plain,
% 1.83/2.05 (((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(A!12, A!12))) <=> ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(A!12, A!12)))),
% 1.83/2.05 inference(rewrite,[status(thm)],[])).
% 1.83/2.05 tff(84,plain,
% 1.83/2.05 (((~in(A!12, A!12)) | (~in(A!12, A!12))) <=> (~in(A!12, A!12))),
% 1.83/2.05 inference(rewrite,[status(thm)],[])).
% 1.83/2.05 tff(85,plain,
% 1.83/2.05 (((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | ((~in(A!12, A!12)) | (~in(A!12, A!12)))) <=> ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(A!12, A!12)))),
% 1.83/2.05 inference(monotonicity,[status(thm)],[84])).
% 1.83/2.05 tff(86,plain,
% 1.83/2.05 (((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | ((~in(A!12, A!12)) | (~in(A!12, A!12)))) <=> ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(A!12, A!12)))),
% 1.83/2.05 inference(transitivity,[status(thm)],[85, 83])).
% 1.83/2.05 tff(87,plain,
% 1.83/2.05 ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | ((~in(A!12, A!12)) | (~in(A!12, A!12)))),
% 1.83/2.05 inference(quant_inst,[status(thm)],[])).
% 1.83/2.05 tff(88,plain,
% 1.83/2.05 ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(A!12, A!12))),
% 1.83/2.05 inference(modus_ponens,[status(thm)],[87, 86])).
% 1.83/2.05 tff(89,plain,
% 1.83/2.05 ($false),
% 1.83/2.05 inference(unit_resolution,[status(thm)],[88, 82, 72])).
% 1.83/2.05 % SZS output end Proof
% 1.83/2.06 % E exiting
%------------------------------------------------------------------------------