%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET916+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:26:39 AM UTC 2025
% Result : Theorem 2.08s 2.29s
% Output : Proof 2.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET916+1 : TPTP v9.0.0. Released v3.2.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 05:50:47 EDT 2025
% 0.12/0.33 % CPUTime :
% 2.08/2.29 % SZS status Theorem
% 2.08/2.29 % SZS output start Proof
% 2.08/2.29 tff(in_type, type, (
% 2.08/2.29 in: ( $i * $i ) > $o)).
% 2.08/2.29 tff(tptp_fun_B_6_type, type, (
% 2.08/2.29 tptp_fun_B_6: $i)).
% 2.08/2.29 tff(tptp_fun_C_4_type, type, (
% 2.08/2.29 tptp_fun_C_4: ( $i * $i ) > $i)).
% 2.08/2.29 tff(unordered_pair_type, type, (
% 2.08/2.29 unordered_pair: ( $i * $i ) > $i)).
% 2.08/2.29 tff(tptp_fun_A_7_type, type, (
% 2.08/2.29 tptp_fun_A_7: $i)).
% 2.08/2.29 tff(tptp_fun_C_5_type, type, (
% 2.08/2.29 tptp_fun_C_5: $i)).
% 2.08/2.29 tff(disjoint_type, type, (
% 2.08/2.29 disjoint: ( $i * $i ) > $o)).
% 2.08/2.29 tff(set_intersection2_type, type, (
% 2.08/2.29 set_intersection2: ( $i * $i ) > $i)).
% 2.08/2.29 tff(tptp_fun_D_1_type, type, (
% 2.08/2.29 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 2.08/2.29 tff(tptp_fun_D_0_type, type, (
% 2.08/2.29 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 2.08/2.29 tff(1,assumption,(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5), introduced(assumption)).
% 2.08/2.29 tff(2,plain,
% 2.08/2.29 (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6) <=> in(C!5, B!6)),
% 2.08/2.29 inference(monotonicity,[status(thm)],[1])).
% 2.08/2.29 tff(3,plain,
% 2.08/2.29 (in(C!5, B!6) <=> in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)),
% 2.08/2.29 inference(symmetry,[status(thm)],[2])).
% 2.08/2.29 tff(4,plain,
% 2.08/2.29 ((~in(C!5, B!6)) <=> (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6))),
% 2.08/2.29 inference(monotonicity,[status(thm)],[3])).
% 2.08/2.29 tff(5,plain,
% 2.08/2.29 ((~![A: $i, B: $i, C: $i] : (~((~in(A, B)) & (~in(C, B)) & (~disjoint(unordered_pair(A, C), B))))) <=> (~![A: $i, B: $i, C: $i] : (~((~in(A, B)) & (~in(C, B)) & (~disjoint(unordered_pair(A, C), B)))))),
% 2.08/2.29 inference(rewrite,[status(thm)],[])).
% 2.08/2.29 tff(6,plain,
% 2.08/2.29 ((~![A: $i, B: $i, C: $i] : (~(((~in(A, B)) & (~in(C, B))) & (~disjoint(unordered_pair(A, C), B))))) <=> (~![A: $i, B: $i, C: $i] : (~((~in(A, B)) & (~in(C, B)) & (~disjoint(unordered_pair(A, C), B)))))),
% 2.08/2.29 inference(rewrite,[status(thm)],[])).
% 2.08/2.29 tff(7,axiom,(~![A: $i, B: $i, C: $i] : (~(((~in(A, B)) & (~in(C, B))) & (~disjoint(unordered_pair(A, C), B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t57_zfmisc_1')).
% 2.08/2.29 tff(8,plain,
% 2.08/2.29 (~![A: $i, B: $i, C: $i] : (~((~in(A, B)) & (~in(C, B)) & (~disjoint(unordered_pair(A, C), B))))),
% 2.08/2.29 inference(modus_ponens,[status(thm)],[7, 6])).
% 2.08/2.29 tff(9,plain,
% 2.08/2.29 (~![A: $i, B: $i, C: $i] : (~((~in(A, B)) & (~in(C, B)) & (~disjoint(unordered_pair(A, C), B))))),
% 2.08/2.29 inference(modus_ponens,[status(thm)],[8, 5])).
% 2.08/2.29 tff(10,plain,
% 2.08/2.29 (~![A: $i, B: $i, C: $i] : (~((~in(A, B)) & (~in(C, B)) & (~disjoint(unordered_pair(A, C), B))))),
% 2.08/2.29 inference(modus_ponens,[status(thm)],[9, 5])).
% 2.08/2.29 tff(11,plain,
% 2.08/2.29 (~![A: $i, B: $i, C: $i] : (~((~in(A, B)) & (~in(C, B)) & (~disjoint(unordered_pair(A, C), B))))),
% 2.08/2.29 inference(modus_ponens,[status(thm)],[10, 5])).
% 2.08/2.29 tff(12,plain,(
% 2.08/2.29 (~in(A!7, B!6)) & (~in(C!5, B!6)) & (~disjoint(unordered_pair(A!7, C!5), B!6))),
% 2.08/2.29 inference(skolemize,[status(sab)],[11])).
% 2.08/2.29 tff(13,plain,
% 2.08/2.29 (~in(C!5, B!6)),
% 2.08/2.29 inference(and_elim,[status(thm)],[12])).
% 2.08/2.29 tff(14,plain,
% 2.08/2.29 (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)),
% 2.08/2.29 inference(modus_ponens,[status(thm)],[13, 4])).
% 2.08/2.29 tff(15,assumption,((~((~(set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (~(((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6))) <=> in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))))))) | (~((set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), B!6, unordered_pair(C!5, A!7)), B!6))) <=> in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), B!6, unordered_pair(C!5, A!7)), set_intersection2(B!6, unordered_pair(C!5, A!7))))))), introduced(assumption)).
% 2.08/2.29 tff(16,plain,
% 2.08/2.29 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))))),
% 2.08/2.29 inference(bind,[status(th)],[])).
% 2.08/2.29 tff(17,plain,
% 2.08/2.29 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 2.08/2.29 inference(quant_intro,[status(thm)],[16])).
% 2.08/2.29 tff(18,plain,
% 2.08/2.29 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 2.08/2.29 inference(pull_quant,[status(thm)],[])).
% 2.08/2.29 tff(19,plain,
% 2.08/2.29 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C)))) <=> ![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) <=> (~![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))))), pull_quant((~![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C)))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))) <=> (?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))), pull_quant((?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> (~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))))), pull_quant((~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))))),
% 2.08/2.29 inference(bind,[status(th)],[])).
% 2.08/2.29 tff(20,plain,
% 2.08/2.29 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 2.08/2.29 inference(quant_intro,[status(thm)],[19])).
% 2.08/2.29 tff(21,plain,
% 2.08/2.29 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 2.08/2.29 inference(transitivity,[status(thm)],[20, 18])).
% 2.08/2.29 tff(22,plain,
% 2.08/2.29 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 2.08/2.29 inference(transitivity,[status(thm)],[21, 17])).
% 2.08/2.29 tff(23,plain,
% 2.08/2.29 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))))),
% 2.08/2.29 inference(bind,[status(th)],[])).
% 2.08/2.29 tff(24,plain,
% 2.08/2.29 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 2.08/2.29 inference(quant_intro,[status(thm)],[23])).
% 2.08/2.29 tff(25,plain,
% 2.08/2.29 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 2.08/2.29 inference(transitivity,[status(thm)],[24, 22])).
% 2.08/2.29 tff(26,plain,
% 2.08/2.29 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) <=> ((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))), rewrite(((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B))))) <=> ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))), ((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B)))))) <=> (((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C)))) & ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))), rewrite((((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C)))) & ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))), ((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B)))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))))),
% 2.08/2.29 inference(bind,[status(th)],[])).
% 2.08/2.29 tff(27,plain,
% 2.08/2.29 (![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 2.08/2.29 inference(quant_intro,[status(thm)],[26])).
% 2.08/2.29 tff(28,plain,
% 2.08/2.29 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 2.08/2.29 inference(rewrite,[status(thm)],[])).
% 2.08/2.29 tff(29,axiom,(![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_xboole_0')).
% 2.08/2.29 tff(30,plain,
% 2.08/2.29 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 2.08/2.29 inference(modus_ponens,[status(thm)],[29, 28])).
% 2.08/2.29 tff(31,plain,(
% 2.08/2.29 ![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B))))))),
% 2.08/2.29 inference(skolemize,[status(sab)],[30])).
% 2.08/2.29 tff(32,plain,
% 2.08/2.29 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 2.08/2.29 inference(modus_ponens,[status(thm)],[31, 27])).
% 2.08/2.29 tff(33,plain,
% 2.08/2.29 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 2.08/2.29 inference(modus_ponens,[status(thm)],[32, 25])).
% 2.08/2.29 tff(34,plain,
% 2.08/2.29 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~((~((~(set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (~(((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6))) <=> in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))))))) | (~((set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), B!6, unordered_pair(C!5, A!7)), B!6))) <=> in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), B!6, unordered_pair(C!5, A!7)), set_intersection2(B!6, unordered_pair(C!5, A!7))))))))),
% 2.08/2.29 inference(quant_inst,[status(thm)],[])).
% 2.08/2.29 tff(35,plain,
% 2.08/2.29 ($false),
% 2.08/2.29 inference(unit_resolution,[status(thm)],[34, 33, 15])).
% 2.08/2.29 tff(36,plain,(~((~((~(set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (~(((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6))) <=> in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))))))) | (~((set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), B!6, unordered_pair(C!5, A!7)), B!6))) <=> in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), B!6, unordered_pair(C!5, A!7)), set_intersection2(B!6, unordered_pair(C!5, A!7)))))))), inference(lemma,lemma(discharge,[]))).
% 2.08/2.29 tff(37,plain,
% 2.08/2.29 (((~((~(set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (~(((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6))) <=> in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))))))) | (~((set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (((~in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), B!6, unordered_pair(C!5, A!7)), B!6))) <=> in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), B!6, unordered_pair(C!5, A!7)), set_intersection2(B!6, unordered_pair(C!5, A!7))))))) | ((~(set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (~(((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6))) <=> in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))))))),
% 2.08/2.29 inference(tautology,[status(thm)],[])).
% 2.08/2.29 tff(38,plain,
% 2.08/2.29 ((~(set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (~(((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6))) <=> in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7)))))),
% 2.08/2.29 inference(unit_resolution,[status(thm)],[37, 36])).
% 2.08/2.29 tff(39,plain,
% 2.08/2.29 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 2.08/2.29 inference(bind,[status(th)],[])).
% 2.08/2.29 tff(40,plain,
% 2.08/2.29 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 2.08/2.29 inference(quant_intro,[status(thm)],[39])).
% 2.08/2.29 tff(41,plain,
% 2.08/2.29 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 2.08/2.29 inference(rewrite,[status(thm)],[])).
% 2.08/2.29 tff(42,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 2.08/2.29 tff(43,plain,
% 2.08/2.29 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 2.08/2.29 inference(modus_ponens,[status(thm)],[42, 41])).
% 2.08/2.29 tff(44,plain,(
% 2.08/2.29 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 2.08/2.29 inference(skolemize,[status(sab)],[43])).
% 2.08/2.29 tff(45,plain,
% 2.08/2.29 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 2.08/2.29 inference(modus_ponens,[status(thm)],[44, 40])).
% 2.08/2.29 tff(46,plain,
% 2.08/2.29 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(unordered_pair(C!5, A!7), B!6))),
% 2.08/2.29 inference(quant_inst,[status(thm)],[])).
% 2.08/2.29 tff(47,plain,
% 2.08/2.29 (set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(unordered_pair(C!5, A!7), B!6)),
% 2.08/2.29 inference(unit_resolution,[status(thm)],[46, 45])).
% 2.08/2.29 tff(48,plain,
% 2.08/2.29 ((~((~(set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (~(((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6))) <=> in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))))))) | (~(set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (~(((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6))) <=> in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7)))))),
% 2.08/2.29 inference(tautology,[status(thm)],[])).
% 2.08/2.29 tff(49,plain,
% 2.08/2.29 ((~((~(set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (~(((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6))) <=> in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))))))) | (~(((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6))) <=> in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7)))))),
% 2.08/2.29 inference(unit_resolution,[status(thm)],[48, 47])).
% 2.08/2.29 tff(50,plain,
% 2.08/2.29 (~(((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6))) <=> in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))))),
% 2.08/2.29 inference(unit_resolution,[status(thm)],[49, 38])).
% 2.08/2.29 tff(51,plain,
% 2.08/2.29 (^[A: $i, B: $i] : rewrite((~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))) <=> (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~((~disjoint(A, B)) | ![C: $i] : (~in(C, set_intersection2(A, B))))))))),
% 2.08/2.29 inference(bind,[status(th)],[])).
% 2.08/2.29 tff(52,plain,
% 2.08/2.29 (![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~((~disjoint(A, B)) | ![C: $i] : (~in(C, set_intersection2(A, B)))))))),
% 2.08/2.29 inference(quant_intro,[status(thm)],[51])).
% 2.08/2.29 tff(53,plain,
% 2.08/2.29 (^[A: $i, B: $i] : refl((~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))) <=> (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))))),
% 2.08/2.29 inference(bind,[status(th)],[])).
% 2.08/2.29 tff(54,plain,
% 2.08/2.29 (![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))))),
% 2.08/2.29 inference(quant_intro,[status(thm)],[53])).
% 2.08/2.29 tff(55,plain,
% 2.08/2.29 (^[A: $i, B: $i] : rewrite((~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))) <=> (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))))),
% 2.08/2.29 inference(bind,[status(th)],[])).
% 2.08/2.29 tff(56,plain,
% 2.08/2.29 (![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))))),
% 2.08/2.29 inference(quant_intro,[status(thm)],[55])).
% 2.08/2.29 tff(57,plain,
% 2.08/2.29 (![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))))),
% 2.08/2.29 inference(transitivity,[status(thm)],[56, 54])).
% 2.08/2.29 tff(58,plain,
% 2.08/2.29 (^[A: $i, B: $i] : trans(monotonicity(rewrite((![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))) <=> (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))), (((disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B))) & (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))) <=> ((disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B))) & (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))), rewrite(((disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B))) & (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))) <=> (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))))), (((disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B))) & (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))) <=> (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))))))),
% 2.08/2.29 inference(bind,[status(th)],[])).
% 2.08/2.29 tff(59,plain,
% 2.08/2.29 (![A: $i, B: $i] : ((disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B))) & (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))))),
% 2.08/2.29 inference(quant_intro,[status(thm)],[58])).
% 2.08/2.29 tff(60,plain,
% 2.08/2.29 (![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~in(C, set_intersection2(A, B))))) & (~(?[C: $i] : in(C, set_intersection2(A, B)) & disjoint(A, B)))) <=> ![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~in(C, set_intersection2(A, B))))) & (~(?[C: $i] : in(C, set_intersection2(A, B)) & disjoint(A, B))))),
% 2.08/2.29 inference(rewrite,[status(thm)],[])).
% 2.08/2.29 tff(61,axiom,(![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~in(C, set_intersection2(A, B))))) & (~(?[C: $i] : in(C, set_intersection2(A, B)) & disjoint(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t4_xboole_0')).
% 2.08/2.29 tff(62,plain,
% 2.08/2.29 (![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~in(C, set_intersection2(A, B))))) & (~(?[C: $i] : in(C, set_intersection2(A, B)) & disjoint(A, B))))),
% 2.08/2.29 inference(modus_ponens,[status(thm)],[61, 60])).
% 2.08/2.29 tff(63,plain,(
% 2.08/2.29 ![A: $i, B: $i] : ((disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B))) & (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))),
% 2.08/2.29 inference(skolemize,[status(sab)],[62])).
% 2.08/2.29 tff(64,plain,
% 2.08/2.29 (![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))))),
% 2.08/2.29 inference(modus_ponens,[status(thm)],[63, 59])).
% 2.08/2.29 tff(65,plain,
% 2.08/2.29 (![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))))),
% 2.08/2.29 inference(modus_ponens,[status(thm)],[64, 57])).
% 2.08/2.29 tff(66,plain,
% 2.08/2.29 (![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~((~disjoint(A, B)) | ![C: $i] : (~in(C, set_intersection2(A, B)))))))),
% 2.08/2.29 inference(modus_ponens,[status(thm)],[65, 52])).
% 2.08/2.29 tff(67,plain,
% 2.08/2.29 ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~((~disjoint(A, B)) | ![C: $i] : (~in(C, set_intersection2(A, B)))))))) | (~((~(disjoint(B!6, unordered_pair(C!5, A!7)) | in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))))) | (~((~disjoint(B!6, unordered_pair(C!5, A!7))) | ![C: $i] : (~in(C, set_intersection2(B!6, unordered_pair(C!5, A!7))))))))),
% 2.08/2.29 inference(quant_inst,[status(thm)],[])).
% 2.08/2.29 tff(68,plain,
% 2.08/2.29 (~((~(disjoint(B!6, unordered_pair(C!5, A!7)) | in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))))) | (~((~disjoint(B!6, unordered_pair(C!5, A!7))) | ![C: $i] : (~in(C, set_intersection2(B!6, unordered_pair(C!5, A!7)))))))),
% 2.08/2.29 inference(unit_resolution,[status(thm)],[67, 66])).
% 2.08/2.29 tff(69,plain,
% 2.08/2.29 (((~(disjoint(B!6, unordered_pair(C!5, A!7)) | in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))))) | (~((~disjoint(B!6, unordered_pair(C!5, A!7))) | ![C: $i] : (~in(C, set_intersection2(B!6, unordered_pair(C!5, A!7))))))) | (disjoint(B!6, unordered_pair(C!5, A!7)) | in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))))),
% 2.08/2.29 inference(tautology,[status(thm)],[])).
% 2.08/2.29 tff(70,plain,
% 2.08/2.29 (disjoint(B!6, unordered_pair(C!5, A!7)) | in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7)))),
% 2.08/2.29 inference(unit_resolution,[status(thm)],[69, 68])).
% 2.08/2.29 tff(71,plain,
% 2.08/2.29 (^[A: $i, B: $i] : refl((unordered_pair(A, B) = unordered_pair(B, A)) <=> (unordered_pair(A, B) = unordered_pair(B, A)))),
% 2.08/2.29 inference(bind,[status(th)],[])).
% 2.08/2.29 tff(72,plain,
% 2.08/2.29 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 2.08/2.29 inference(quant_intro,[status(thm)],[71])).
% 2.08/2.29 tff(73,plain,
% 2.08/2.29 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 2.08/2.29 inference(rewrite,[status(thm)],[])).
% 2.08/2.29 tff(74,axiom,(![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k2_tarski')).
% 2.08/2.29 tff(75,plain,
% 2.08/2.29 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 2.08/2.29 inference(modus_ponens,[status(thm)],[74, 73])).
% 2.08/2.29 tff(76,plain,(
% 2.08/2.29 ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 2.08/2.29 inference(skolemize,[status(sab)],[75])).
% 2.08/2.29 tff(77,plain,
% 2.08/2.29 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 2.08/2.29 inference(modus_ponens,[status(thm)],[76, 72])).
% 2.08/2.29 tff(78,plain,
% 2.08/2.29 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(A!7, C!5) = unordered_pair(C!5, A!7))),
% 2.08/2.29 inference(quant_inst,[status(thm)],[])).
% 2.08/2.29 tff(79,plain,
% 2.08/2.29 (unordered_pair(A!7, C!5) = unordered_pair(C!5, A!7)),
% 2.08/2.29 inference(unit_resolution,[status(thm)],[78, 77])).
% 2.08/2.29 tff(80,plain,
% 2.08/2.29 (unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5)),
% 2.08/2.29 inference(symmetry,[status(thm)],[79])).
% 2.08/2.29 tff(81,plain,
% 2.08/2.29 (disjoint(B!6, unordered_pair(C!5, A!7)) <=> disjoint(B!6, unordered_pair(A!7, C!5))),
% 2.08/2.29 inference(monotonicity,[status(thm)],[80])).
% 2.08/2.29 tff(82,plain,
% 2.08/2.29 (disjoint(B!6, unordered_pair(A!7, C!5)) <=> disjoint(B!6, unordered_pair(C!5, A!7))),
% 2.08/2.29 inference(symmetry,[status(thm)],[81])).
% 2.08/2.29 tff(83,plain,
% 2.08/2.29 ((~disjoint(B!6, unordered_pair(A!7, C!5))) <=> (~disjoint(B!6, unordered_pair(C!5, A!7)))),
% 2.08/2.29 inference(monotonicity,[status(thm)],[82])).
% 2.08/2.29 tff(84,plain,
% 2.08/2.29 (~disjoint(unordered_pair(A!7, C!5), B!6)),
% 2.08/2.29 inference(and_elim,[status(thm)],[12])).
% 2.08/2.29 tff(85,plain,
% 2.08/2.29 (^[A: $i, B: $i] : refl(((~disjoint(A, B)) | disjoint(B, A)) <=> ((~disjoint(A, B)) | disjoint(B, A)))),
% 2.08/2.29 inference(bind,[status(th)],[])).
% 2.08/2.29 tff(86,plain,
% 2.08/2.29 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 2.08/2.29 inference(quant_intro,[status(thm)],[85])).
% 2.08/2.29 tff(87,plain,
% 2.08/2.29 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 2.08/2.29 inference(rewrite,[status(thm)],[])).
% 2.08/2.29 tff(88,plain,
% 2.08/2.29 (^[A: $i, B: $i] : rewrite((disjoint(A, B) => disjoint(B, A)) <=> ((~disjoint(A, B)) | disjoint(B, A)))),
% 2.08/2.29 inference(bind,[status(th)],[])).
% 2.08/2.29 tff(89,plain,
% 2.08/2.29 (![A: $i, B: $i] : (disjoint(A, B) => disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 2.08/2.29 inference(quant_intro,[status(thm)],[88])).
% 2.08/2.29 tff(90,axiom,(![A: $i, B: $i] : (disjoint(A, B) => disjoint(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','symmetry_r1_xboole_0')).
% 2.08/2.29 tff(91,plain,
% 2.08/2.29 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 2.08/2.29 inference(modus_ponens,[status(thm)],[90, 89])).
% 2.08/2.29 tff(92,plain,
% 2.08/2.29 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 2.08/2.29 inference(modus_ponens,[status(thm)],[91, 87])).
% 2.08/2.29 tff(93,plain,(
% 2.08/2.29 ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 2.08/2.29 inference(skolemize,[status(sab)],[92])).
% 2.08/2.29 tff(94,plain,
% 2.08/2.29 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 2.08/2.29 inference(modus_ponens,[status(thm)],[93, 86])).
% 2.08/2.29 tff(95,plain,
% 2.08/2.29 (((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(B!6, unordered_pair(A!7, C!5))) | disjoint(unordered_pair(A!7, C!5), B!6))) <=> ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(B!6, unordered_pair(A!7, C!5))) | disjoint(unordered_pair(A!7, C!5), B!6))),
% 2.08/2.29 inference(rewrite,[status(thm)],[])).
% 2.08/2.29 tff(96,plain,
% 2.08/2.29 ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(B!6, unordered_pair(A!7, C!5))) | disjoint(unordered_pair(A!7, C!5), B!6))),
% 2.08/2.29 inference(quant_inst,[status(thm)],[])).
% 2.08/2.29 tff(97,plain,
% 2.08/2.29 ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(B!6, unordered_pair(A!7, C!5))) | disjoint(unordered_pair(A!7, C!5), B!6)),
% 2.08/2.29 inference(modus_ponens,[status(thm)],[96, 95])).
% 2.08/2.29 tff(98,plain,
% 2.08/2.29 (~disjoint(B!6, unordered_pair(A!7, C!5))),
% 2.08/2.29 inference(unit_resolution,[status(thm)],[97, 94, 84])).
% 2.08/2.29 tff(99,plain,
% 2.08/2.29 (~disjoint(B!6, unordered_pair(C!5, A!7))),
% 2.08/2.29 inference(modus_ponens,[status(thm)],[98, 83])).
% 2.08/2.29 tff(100,plain,
% 2.08/2.29 ((~(disjoint(B!6, unordered_pair(C!5, A!7)) | in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))))) | disjoint(B!6, unordered_pair(C!5, A!7)) | in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7)))),
% 2.08/2.29 inference(tautology,[status(thm)],[])).
% 2.08/2.29 tff(101,plain,
% 2.08/2.29 (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7)))),
% 2.08/2.29 inference(unit_resolution,[status(thm)],[100, 99, 70])).
% 2.08/2.29 tff(102,plain,
% 2.08/2.29 ((((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6))) <=> in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7)))) | (~((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)))) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))))),
% 2.08/2.29 inference(tautology,[status(thm)],[])).
% 2.08/2.29 tff(103,plain,
% 2.08/2.29 ((((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6))) <=> in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7)))) | (~((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6))))),
% 2.08/2.29 inference(unit_resolution,[status(thm)],[102, 101])).
% 2.08/2.29 tff(104,plain,
% 2.08/2.29 (~((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)))),
% 2.08/2.29 inference(unit_resolution,[status(thm)],[103, 50])).
% 2.08/2.29 tff(105,plain,
% 2.08/2.29 (((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6))) | in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)),
% 2.08/2.29 inference(tautology,[status(thm)],[])).
% 2.08/2.29 tff(106,plain,
% 2.08/2.29 (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)),
% 2.08/2.29 inference(unit_resolution,[status(thm)],[105, 104])).
% 2.08/2.29 tff(107,plain,
% 2.08/2.29 ($false),
% 2.08/2.29 inference(unit_resolution,[status(thm)],[106, 14])).
% 2.08/2.29 tff(108,plain,(~(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5)), inference(lemma,lemma(discharge,[]))).
% 2.08/2.29 tff(109,plain,
% 2.08/2.29 (((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6))) | in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))),
% 2.08/2.29 inference(tautology,[status(thm)],[])).
% 2.08/2.29 tff(110,plain,
% 2.08/2.29 (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))),
% 2.08/2.29 inference(unit_resolution,[status(thm)],[109, 104])).
% 2.08/2.29 tff(111,assumption,((~((~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5)) | (~(in(tptp_fun_D_0(unordered_pair(C!5, A!7), C!5, A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_0(unordered_pair(C!5, A!7), C!5, A!7) = C!5) | (tptp_fun_D_0(unordered_pair(C!5, A!7), C!5, A!7) = A!7))))))), introduced(assumption)).
% 2.08/2.29 tff(112,plain,
% 2.08/2.29 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) <=> (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))))),
% 2.08/2.29 inference(bind,[status(th)],[])).
% 2.08/2.29 tff(113,plain,
% 2.08/2.29 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 2.08/2.29 inference(quant_intro,[status(thm)],[112])).
% 2.08/2.29 tff(114,plain,
% 2.08/2.29 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 2.08/2.29 inference(pull_quant,[status(thm)],[])).
% 2.08/2.29 tff(115,plain,
% 2.08/2.29 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))), ((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) <=> (~![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))))), pull_quant((~![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) <=> ?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A)))))), ((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) <=> ?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))))), (((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))) <=> (?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))), pull_quant((?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))) <=> ?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))), (((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))) <=> ?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))), ((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) <=> (~?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))))), pull_quant((~?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) <=> ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))), ((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) <=> ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))))),
% 2.08/2.30 inference(bind,[status(th)],[])).
% 2.08/2.30 tff(116,plain,
% 2.08/2.30 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 2.08/2.30 inference(quant_intro,[status(thm)],[115])).
% 2.08/2.30 tff(117,plain,
% 2.08/2.30 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 2.08/2.30 inference(transitivity,[status(thm)],[116, 114])).
% 2.08/2.30 tff(118,plain,
% 2.08/2.30 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 2.08/2.30 inference(transitivity,[status(thm)],[117, 113])).
% 2.08/2.30 tff(119,plain,
% 2.08/2.30 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))))),
% 2.08/2.30 inference(bind,[status(th)],[])).
% 2.08/2.30 tff(120,plain,
% 2.08/2.30 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 2.08/2.30 inference(quant_intro,[status(thm)],[119])).
% 2.08/2.30 tff(121,plain,
% 2.08/2.30 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 2.08/2.30 inference(transitivity,[status(thm)],[120, 118])).
% 2.08/2.30 tff(122,plain,
% 2.08/2.30 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))), trans(monotonicity(rewrite((~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))) <=> (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))), (((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))), rewrite(((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))), (((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))), ((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))) <=> (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))), rewrite((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))), ((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))))),
% 2.08/2.30 inference(bind,[status(th)],[])).
% 2.08/2.30 tff(123,plain,
% 2.08/2.30 (![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 2.08/2.30 inference(quant_intro,[status(thm)],[122])).
% 2.08/2.30 tff(124,plain,
% 2.08/2.30 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 2.08/2.30 inference(rewrite,[status(thm)],[])).
% 2.08/2.30 tff(125,plain,
% 2.08/2.30 (^[A: $i, B: $i, C: $i] : rewrite(((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) <=> ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))))),
% 2.08/2.30 inference(bind,[status(th)],[])).
% 2.08/2.30 tff(126,plain,
% 2.08/2.30 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) <=> ![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 2.08/2.30 inference(quant_intro,[status(thm)],[125])).
% 2.08/2.30 tff(127,axiom,(![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_tarski')).
% 2.13/2.30 tff(128,plain,
% 2.13/2.30 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[127, 126])).
% 2.13/2.30 tff(129,plain,
% 2.13/2.30 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[128, 124])).
% 2.13/2.30 tff(130,plain,(
% 2.13/2.30 ![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))),
% 2.13/2.30 inference(skolemize,[status(sab)],[129])).
% 2.13/2.30 tff(131,plain,
% 2.13/2.30 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[130, 123])).
% 2.13/2.30 tff(132,plain,
% 2.13/2.30 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[131, 121])).
% 2.13/2.30 tff(133,plain,
% 2.13/2.30 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))) | (~((~((~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5)) | (~(in(tptp_fun_D_0(unordered_pair(C!5, A!7), C!5, A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_0(unordered_pair(C!5, A!7), C!5, A!7) = C!5) | (tptp_fun_D_0(unordered_pair(C!5, A!7), C!5, A!7) = A!7))))))))),
% 2.13/2.30 inference(quant_inst,[status(thm)],[])).
% 2.13/2.30 tff(134,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[133, 132, 111])).
% 2.13/2.30 tff(135,plain,(~((~((~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5)) | (~(in(tptp_fun_D_0(unordered_pair(C!5, A!7), C!5, A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_0(unordered_pair(C!5, A!7), C!5, A!7) = C!5) | (tptp_fun_D_0(unordered_pair(C!5, A!7), C!5, A!7) = A!7)))))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(136,plain,
% 2.13/2.30 (((~((~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5)) | (~(in(tptp_fun_D_0(unordered_pair(C!5, A!7), C!5, A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_0(unordered_pair(C!5, A!7), C!5, A!7) = C!5) | (tptp_fun_D_0(unordered_pair(C!5, A!7), C!5, A!7) = A!7))))))) | ((~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7))))),
% 2.13/2.30 inference(tautology,[status(thm)],[])).
% 2.13/2.30 tff(137,plain,
% 2.13/2.30 ((~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7)))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[136, 135])).
% 2.13/2.30 tff(138,plain,
% 2.13/2.30 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))),
% 2.13/2.30 inference(quant_inst,[status(thm)],[])).
% 2.13/2.30 tff(139,plain,
% 2.13/2.30 (unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[138, 77])).
% 2.13/2.30 tff(140,plain,
% 2.13/2.30 ((~((~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7))))) | (~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7)))),
% 2.13/2.30 inference(tautology,[status(thm)],[])).
% 2.13/2.30 tff(141,plain,
% 2.13/2.30 ((~((~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7))))) | (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7)))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[140, 139])).
% 2.13/2.30 tff(142,plain,
% 2.13/2.30 (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[141, 137])).
% 2.13/2.30 tff(143,plain,
% 2.13/2.30 ((~(in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7)))) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))) | ((tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7))),
% 2.13/2.30 inference(tautology,[status(thm)],[])).
% 2.13/2.30 tff(144,plain,
% 2.13/2.30 ((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))) | ((tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[143, 142])).
% 2.13/2.30 tff(145,plain,
% 2.13/2.30 ((tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[144, 110])).
% 2.13/2.30 tff(146,plain,
% 2.13/2.30 ((~((tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7))) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7)),
% 2.13/2.30 inference(tautology,[status(thm)],[])).
% 2.13/2.30 tff(147,plain,
% 2.13/2.30 ((tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[146, 145])).
% 2.13/2.30 tff(148,plain,
% 2.13/2.30 (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[147, 108])).
% 2.13/2.30 tff(149,plain,
% 2.13/2.30 (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6) <=> in(A!7, B!6)),
% 2.13/2.30 inference(monotonicity,[status(thm)],[148])).
% 2.13/2.30 tff(150,plain,
% 2.13/2.30 (in(A!7, B!6) <=> in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)),
% 2.13/2.30 inference(symmetry,[status(thm)],[149])).
% 2.13/2.30 tff(151,plain,
% 2.13/2.30 ((~in(A!7, B!6)) <=> (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[150])).
% 2.13/2.30 tff(152,plain,
% 2.13/2.30 (~in(A!7, B!6)),
% 2.13/2.30 inference(and_elim,[status(thm)],[12])).
% 2.13/2.30 tff(153,plain,
% 2.13/2.30 (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[152, 151])).
% 2.13/2.30 tff(154,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[106, 153])).
% 2.13/2.30 % SZS output end Proof
% 2.13/2.30 % E exiting
%------------------------------------------------------------------------------