%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET885+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 05:26:36 AM UTC 2025
% Result : Theorem 2.94s 3.17s
% Output : Proof 2.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.15 % Problem : SET885+1 : TPTP v9.0.0. Released v3.2.0.
% 0.09/0.15 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n016.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 05:50:17 EDT 2025
% 0.14/0.36 % CPUTime :
% 2.94/3.17 % SZS status Theorem
% 2.94/3.17 % SZS output start Proof
% 2.94/3.17 tff(tptp_fun_C_5_type, type, (
% 2.94/3.17 tptp_fun_C_5: $i)).
% 2.94/3.17 tff(tptp_fun_A_7_type, type, (
% 2.94/3.17 tptp_fun_A_7: $i)).
% 2.94/3.17 tff(in_type, type, (
% 2.94/3.17 in: ( $i * $i ) > $o)).
% 2.94/3.17 tff(singleton_type, type, (
% 2.94/3.17 singleton: $i > $i)).
% 2.94/3.17 tff(unordered_pair_type, type, (
% 2.94/3.17 unordered_pair: ( $i * $i ) > $i)).
% 2.94/3.17 tff(tptp_fun_B_6_type, type, (
% 2.94/3.17 tptp_fun_B_6: $i)).
% 2.94/3.17 tff(tptp_fun_D_1_type, type, (
% 2.94/3.17 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 2.94/3.17 tff(subset_type, type, (
% 2.94/3.17 subset: ( $i * $i ) > $o)).
% 2.94/3.17 tff(tptp_fun_C_2_type, type, (
% 2.94/3.17 tptp_fun_C_2: ( $i * $i ) > $i)).
% 2.94/3.17 tff(tptp_fun_C_0_type, type, (
% 2.94/3.17 tptp_fun_C_0: ( $i * $i ) > $i)).
% 2.94/3.17 tff(1,plain,
% 2.94/3.17 (^[A: $i, B: $i] : refl((unordered_pair(A, B) = unordered_pair(B, A)) <=> (unordered_pair(A, B) = unordered_pair(B, A)))),
% 2.94/3.17 inference(bind,[status(th)],[])).
% 2.94/3.17 tff(2,plain,
% 2.94/3.17 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 2.94/3.17 inference(quant_intro,[status(thm)],[1])).
% 2.94/3.17 tff(3,plain,
% 2.94/3.17 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 2.94/3.17 inference(rewrite,[status(thm)],[])).
% 2.94/3.17 tff(4,axiom,(![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k2_tarski')).
% 2.94/3.17 tff(5,plain,
% 2.94/3.17 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 2.94/3.17 inference(modus_ponens,[status(thm)],[4, 3])).
% 2.94/3.17 tff(6,plain,(
% 2.94/3.17 ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 2.94/3.17 inference(skolemize,[status(sab)],[5])).
% 2.94/3.17 tff(7,plain,
% 2.94/3.17 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 2.94/3.17 inference(modus_ponens,[status(thm)],[6, 2])).
% 2.94/3.17 tff(8,plain,
% 2.94/3.17 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(A!7, B!6) = unordered_pair(B!6, A!7))),
% 2.94/3.17 inference(quant_inst,[status(thm)],[])).
% 2.94/3.17 tff(9,plain,
% 2.94/3.17 (unordered_pair(A!7, B!6) = unordered_pair(B!6, A!7)),
% 2.94/3.17 inference(unit_resolution,[status(thm)],[8, 7])).
% 2.94/3.17 tff(10,plain,
% 2.94/3.17 (unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)),
% 2.94/3.17 inference(symmetry,[status(thm)],[9])).
% 2.94/3.17 tff(11,plain,
% 2.94/3.17 (in(A!7, unordered_pair(B!6, A!7)) <=> in(A!7, unordered_pair(A!7, B!6))),
% 2.94/3.17 inference(monotonicity,[status(thm)],[10])).
% 2.94/3.17 tff(12,plain,
% 2.94/3.17 (in(A!7, unordered_pair(A!7, B!6)) <=> in(A!7, unordered_pair(B!6, A!7))),
% 2.94/3.17 inference(symmetry,[status(thm)],[11])).
% 2.94/3.17 tff(13,plain,
% 2.94/3.17 ((~in(A!7, unordered_pair(A!7, B!6))) <=> (~in(A!7, unordered_pair(B!6, A!7)))),
% 2.94/3.17 inference(monotonicity,[status(thm)],[12])).
% 2.94/3.17 tff(14,assumption,(~in(A!7, unordered_pair(A!7, B!6))), introduced(assumption)).
% 2.94/3.17 tff(15,plain,
% 2.94/3.17 (~in(A!7, unordered_pair(B!6, A!7))),
% 2.94/3.17 inference(modus_ponens,[status(thm)],[14, 13])).
% 2.94/3.17 tff(16,plain,
% 2.94/3.17 (^[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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))))),
% 2.94/3.17 inference(bind,[status(th)],[])).
% 2.94/3.17 tff(17,plain,
% 2.94/3.17 (![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 2.94/3.17 inference(quant_intro,[status(thm)],[16])).
% 2.94/3.17 tff(18,plain,
% 2.94/3.17 (![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 2.94/3.17 inference(pull_quant,[status(thm)],[])).
% 2.94/3.17 tff(19,plain,
% 2.94/3.17 (^[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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))))),
% 2.94/3.17 inference(bind,[status(th)],[])).
% 2.94/3.17 tff(20,plain,
% 2.94/3.17 (![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 2.94/3.17 inference(quant_intro,[status(thm)],[19])).
% 2.94/3.17 tff(21,plain,
% 2.94/3.17 (![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 2.94/3.17 inference(transitivity,[status(thm)],[20, 18])).
% 2.94/3.17 tff(22,plain,
% 2.94/3.17 (![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 2.94/3.17 inference(transitivity,[status(thm)],[21, 17])).
% 2.94/3.17 tff(23,plain,
% 2.94/3.17 (^[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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))))),
% 2.94/3.17 inference(bind,[status(th)],[])).
% 2.94/3.17 tff(24,plain,
% 2.94/3.17 (![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 2.94/3.17 inference(quant_intro,[status(thm)],[23])).
% 2.94/3.17 tff(25,plain,
% 2.94/3.17 (![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 2.94/3.17 inference(transitivity,[status(thm)],[24, 22])).
% 2.94/3.17 tff(26,plain,
% 2.94/3.17 (^[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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))) <=> (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))), (((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))), rewrite(((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))), (((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))))),
% 2.94/3.17 inference(bind,[status(th)],[])).
% 2.94/3.17 tff(27,plain,
% 2.94/3.17 (![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 2.94/3.17 inference(quant_intro,[status(thm)],[26])).
% 2.94/3.17 tff(28,plain,
% 2.94/3.17 (![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))))),
% 2.94/3.17 inference(rewrite,[status(thm)],[])).
% 2.94/3.17 tff(29,plain,
% 2.94/3.17 (^[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)))))),
% 2.94/3.17 inference(bind,[status(th)],[])).
% 2.94/3.17 tff(30,plain,
% 2.94/3.17 (![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))))),
% 2.94/3.17 inference(quant_intro,[status(thm)],[29])).
% 2.94/3.17 tff(31,axiom,(![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_tarski')).
% 2.94/3.17 tff(32,plain,
% 2.94/3.17 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 2.94/3.17 inference(modus_ponens,[status(thm)],[31, 30])).
% 2.94/3.17 tff(33,plain,
% 2.94/3.17 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 2.94/3.17 inference(modus_ponens,[status(thm)],[32, 28])).
% 2.94/3.17 tff(34,plain,(
% 2.94/3.17 ![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))),
% 2.94/3.17 inference(skolemize,[status(sab)],[33])).
% 2.94/3.17 tff(35,plain,
% 2.94/3.17 (![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 2.94/3.17 inference(modus_ponens,[status(thm)],[34, 27])).
% 2.94/3.17 tff(36,plain,
% 2.94/3.17 (![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 2.94/3.17 inference(modus_ponens,[status(thm)],[35, 25])).
% 2.94/3.17 tff(37,plain,
% 2.94/3.17 (((~![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | in(A!7, unordered_pair(B!6, A!7))) <=> ((~![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | in(A!7, unordered_pair(B!6, A!7)))),
% 2.94/3.17 inference(rewrite,[status(thm)],[])).
% 2.94/3.17 tff(38,plain,
% 2.94/3.17 ((~(~in(A!7, unordered_pair(B!6, A!7)))) <=> in(A!7, unordered_pair(B!6, A!7))),
% 2.94/3.17 inference(rewrite,[status(thm)],[])).
% 2.94/3.17 tff(39,plain,
% 2.94/3.17 (((~in(A!7, unordered_pair(B!6, A!7))) | $false) <=> (~in(A!7, unordered_pair(B!6, A!7)))),
% 2.94/3.17 inference(rewrite,[status(thm)],[])).
% 2.94/3.17 tff(40,plain,
% 2.94/3.17 ((~$true) <=> $false),
% 2.94/3.17 inference(rewrite,[status(thm)],[])).
% 2.94/3.17 tff(41,plain,
% 2.94/3.17 (($true | (~(in(tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6) = A!7) | (tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6) = B!6))))) <=> $true),
% 2.94/3.17 inference(rewrite,[status(thm)],[])).
% 2.94/3.17 tff(42,plain,
% 2.94/3.17 ((~(in(tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6) = A!7) | (tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6) = B!6)))) <=> (~(in(tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6) = A!7) | (tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6) = B!6))))),
% 2.94/3.17 inference(rewrite,[status(thm)],[])).
% 2.94/3.17 tff(43,plain,
% 2.94/3.17 ((unordered_pair(B!6, A!7) = unordered_pair(B!6, A!7)) <=> $true),
% 2.94/3.17 inference(rewrite,[status(thm)],[])).
% 2.94/3.17 tff(44,plain,
% 2.94/3.17 (((unordered_pair(B!6, A!7) = unordered_pair(B!6, A!7)) | (~(in(tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6) = A!7) | (tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6) = B!6))))) <=> ($true | (~(in(tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6) = A!7) | (tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6) = B!6)))))),
% 2.94/3.17 inference(monotonicity,[status(thm)],[43, 42])).
% 2.94/3.17 tff(45,plain,
% 2.94/3.17 (((unordered_pair(B!6, A!7) = unordered_pair(B!6, A!7)) | (~(in(tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6) = A!7) | (tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6) = B!6))))) <=> $true),
% 2.94/3.17 inference(transitivity,[status(thm)],[44, 41])).
% 2.94/3.17 tff(46,plain,
% 2.94/3.17 ((~((unordered_pair(B!6, A!7) = unordered_pair(B!6, A!7)) | (~(in(tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6) = A!7) | (tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6) = B!6)))))) <=> (~$true)),
% 2.94/3.17 inference(monotonicity,[status(thm)],[45])).
% 2.94/3.17 tff(47,plain,
% 2.94/3.17 ((~((unordered_pair(B!6, A!7) = unordered_pair(B!6, A!7)) | (~(in(tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6) = A!7) | (tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6) = B!6)))))) <=> $false),
% 2.94/3.17 inference(transitivity,[status(thm)],[46, 40])).
% 2.94/3.17 tff(48,plain,
% 2.94/3.17 ((~((~(unordered_pair(B!6, A!7) = unordered_pair(B!6, A!7))) | (in(A!7, unordered_pair(B!6, A!7)) <=> ((A!7 = A!7) | (A!7 = B!6))))) <=> (~in(A!7, unordered_pair(B!6, A!7)))),
% 2.94/3.17 inference(rewrite,[status(thm)],[])).
% 2.94/3.17 tff(49,plain,
% 2.94/3.17 (((~((~(unordered_pair(B!6, A!7) = unordered_pair(B!6, A!7))) | (in(A!7, unordered_pair(B!6, A!7)) <=> ((A!7 = A!7) | (A!7 = B!6))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(B!6, A!7)) | (~(in(tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6) = A!7) | (tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6) = B!6))))))) <=> ((~in(A!7, unordered_pair(B!6, A!7))) | $false)),
% 2.94/3.17 inference(monotonicity,[status(thm)],[48, 47])).
% 2.94/3.17 tff(50,plain,
% 2.94/3.17 (((~((~(unordered_pair(B!6, A!7) = unordered_pair(B!6, A!7))) | (in(A!7, unordered_pair(B!6, A!7)) <=> ((A!7 = A!7) | (A!7 = B!6))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(B!6, A!7)) | (~(in(tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6) = A!7) | (tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6) = B!6))))))) <=> (~in(A!7, unordered_pair(B!6, A!7)))),
% 2.94/3.17 inference(transitivity,[status(thm)],[49, 39])).
% 2.94/3.17 tff(51,plain,
% 2.94/3.17 ((~((~((~(unordered_pair(B!6, A!7) = unordered_pair(B!6, A!7))) | (in(A!7, unordered_pair(B!6, A!7)) <=> ((A!7 = A!7) | (A!7 = B!6))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(B!6, A!7)) | (~(in(tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6) = A!7) | (tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6) = B!6)))))))) <=> (~(~in(A!7, unordered_pair(B!6, A!7))))),
% 2.94/3.17 inference(monotonicity,[status(thm)],[50])).
% 2.94/3.17 tff(52,plain,
% 2.94/3.17 ((~((~((~(unordered_pair(B!6, A!7) = unordered_pair(B!6, A!7))) | (in(A!7, unordered_pair(B!6, A!7)) <=> ((A!7 = A!7) | (A!7 = B!6))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(B!6, A!7)) | (~(in(tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6) = A!7) | (tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6) = B!6)))))))) <=> in(A!7, unordered_pair(B!6, A!7))),
% 2.94/3.17 inference(transitivity,[status(thm)],[51, 38])).
% 2.94/3.17 tff(53,plain,
% 2.94/3.17 (((~![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(B!6, A!7))) | (in(A!7, unordered_pair(B!6, A!7)) <=> ((A!7 = A!7) | (A!7 = B!6))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(B!6, A!7)) | (~(in(tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6) = A!7) | (tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6) = B!6))))))))) <=> ((~![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | in(A!7, unordered_pair(B!6, A!7)))),
% 2.94/3.17 inference(monotonicity,[status(thm)],[52])).
% 2.94/3.17 tff(54,plain,
% 2.94/3.17 (((~![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(B!6, A!7))) | (in(A!7, unordered_pair(B!6, A!7)) <=> ((A!7 = A!7) | (A!7 = B!6))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(B!6, A!7)) | (~(in(tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6) = A!7) | (tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6) = B!6))))))))) <=> ((~![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | in(A!7, unordered_pair(B!6, A!7)))),
% 2.94/3.17 inference(transitivity,[status(thm)],[53, 37])).
% 2.94/3.17 tff(55,plain,
% 2.94/3.17 ((~![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(B!6, A!7))) | (in(A!7, unordered_pair(B!6, A!7)) <=> ((A!7 = A!7) | (A!7 = B!6))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(B!6, A!7)) | (~(in(tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6) = A!7) | (tptp_fun_D_1(unordered_pair(B!6, A!7), A!7, B!6) = B!6))))))))),
% 2.94/3.17 inference(quant_inst,[status(thm)],[])).
% 2.94/3.17 tff(56,plain,
% 2.94/3.17 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | in(A!7, unordered_pair(B!6, A!7))),
% 2.94/3.17 inference(modus_ponens,[status(thm)],[55, 54])).
% 2.94/3.17 tff(57,plain,
% 2.94/3.17 (in(A!7, unordered_pair(B!6, A!7))),
% 2.94/3.17 inference(unit_resolution,[status(thm)],[56, 36])).
% 2.94/3.17 tff(58,plain,
% 2.94/3.17 ($false),
% 2.94/3.17 inference(unit_resolution,[status(thm)],[57, 15])).
% 2.94/3.17 tff(59,plain,(in(A!7, unordered_pair(A!7, B!6))), inference(lemma,lemma(discharge,[]))).
% 2.94/3.17 tff(60,plain,
% 2.94/3.17 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))))),
% 2.94/3.17 inference(bind,[status(th)],[])).
% 2.94/3.17 tff(61,plain,
% 2.94/3.17 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 2.94/3.17 inference(quant_intro,[status(thm)],[60])).
% 2.94/3.17 tff(62,plain,
% 2.94/3.17 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))))),
% 2.94/3.17 inference(bind,[status(th)],[])).
% 2.94/3.17 tff(63,plain,
% 2.94/3.17 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 2.94/3.17 inference(quant_intro,[status(thm)],[62])).
% 2.94/3.17 tff(64,plain,
% 2.94/3.17 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 2.94/3.17 inference(transitivity,[status(thm)],[63, 61])).
% 2.94/3.17 tff(65,plain,
% 2.94/3.17 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))))),
% 2.94/3.17 inference(bind,[status(th)],[])).
% 2.94/3.17 tff(66,plain,
% 2.94/3.17 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 2.94/3.17 inference(quant_intro,[status(thm)],[65])).
% 2.94/3.17 tff(67,plain,
% 2.94/3.17 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 2.94/3.17 inference(rewrite,[status(thm)],[])).
% 2.94/3.17 tff(68,plain,
% 2.94/3.17 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 2.94/3.17 inference(bind,[status(th)],[])).
% 2.94/3.17 tff(69,plain,
% 2.94/3.17 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 2.94/3.17 inference(quant_intro,[status(thm)],[68])).
% 2.94/3.17 tff(70,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_tarski')).
% 2.94/3.17 tff(71,plain,
% 2.94/3.17 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 2.94/3.17 inference(modus_ponens,[status(thm)],[70, 69])).
% 2.94/3.17 tff(72,plain,
% 2.94/3.17 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 2.94/3.17 inference(modus_ponens,[status(thm)],[71, 67])).
% 2.94/3.17 tff(73,plain,(
% 2.94/3.17 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))),
% 2.94/3.17 inference(skolemize,[status(sab)],[72])).
% 2.94/3.17 tff(74,plain,
% 2.94/3.17 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 2.94/3.17 inference(modus_ponens,[status(thm)],[73, 66])).
% 2.94/3.17 tff(75,plain,
% 2.94/3.17 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 2.94/3.17 inference(modus_ponens,[status(thm)],[74, 64])).
% 2.94/3.17 tff(76,plain,
% 2.94/3.17 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))) | (~((~((~subset(unordered_pair(A!7, B!6), singleton(C!5))) | ![C: $i] : ((~in(C, unordered_pair(A!7, B!6))) | in(C, singleton(C!5))))) | (~(subset(unordered_pair(A!7, B!6), singleton(C!5)) | (~((~in(tptp_fun_C_2(singleton(C!5), unordered_pair(A!7, B!6)), unordered_pair(A!7, B!6))) | in(tptp_fun_C_2(singleton(C!5), unordered_pair(A!7, B!6)), singleton(C!5))))))))),
% 2.94/3.17 inference(quant_inst,[status(thm)],[])).
% 2.94/3.17 tff(77,plain,
% 2.94/3.17 (~((~((~subset(unordered_pair(A!7, B!6), singleton(C!5))) | ![C: $i] : ((~in(C, unordered_pair(A!7, B!6))) | in(C, singleton(C!5))))) | (~(subset(unordered_pair(A!7, B!6), singleton(C!5)) | (~((~in(tptp_fun_C_2(singleton(C!5), unordered_pair(A!7, B!6)), unordered_pair(A!7, B!6))) | in(tptp_fun_C_2(singleton(C!5), unordered_pair(A!7, B!6)), singleton(C!5)))))))),
% 2.94/3.17 inference(unit_resolution,[status(thm)],[76, 75])).
% 2.94/3.17 tff(78,plain,
% 2.94/3.17 (((~((~subset(unordered_pair(A!7, B!6), singleton(C!5))) | ![C: $i] : ((~in(C, unordered_pair(A!7, B!6))) | in(C, singleton(C!5))))) | (~(subset(unordered_pair(A!7, B!6), singleton(C!5)) | (~((~in(tptp_fun_C_2(singleton(C!5), unordered_pair(A!7, B!6)), unordered_pair(A!7, B!6))) | in(tptp_fun_C_2(singleton(C!5), unordered_pair(A!7, B!6)), singleton(C!5))))))) | ((~subset(unordered_pair(A!7, B!6), singleton(C!5))) | ![C: $i] : ((~in(C, unordered_pair(A!7, B!6))) | in(C, singleton(C!5))))),
% 2.94/3.18 inference(tautology,[status(thm)],[])).
% 2.94/3.18 tff(79,plain,
% 2.94/3.18 ((~subset(unordered_pair(A!7, B!6), singleton(C!5))) | ![C: $i] : ((~in(C, unordered_pair(A!7, B!6))) | in(C, singleton(C!5)))),
% 2.94/3.18 inference(unit_resolution,[status(thm)],[78, 77])).
% 2.94/3.18 tff(80,plain,
% 2.94/3.18 ((~![A: $i, B: $i, C: $i] : ((~subset(unordered_pair(A, B), singleton(C))) | (A = C))) <=> (~![A: $i, B: $i, C: $i] : ((~subset(unordered_pair(A, B), singleton(C))) | (A = C)))),
% 2.94/3.18 inference(rewrite,[status(thm)],[])).
% 2.94/3.18 tff(81,plain,
% 2.94/3.18 ((~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), singleton(C)) => (A = C))) <=> (~![A: $i, B: $i, C: $i] : ((~subset(unordered_pair(A, B), singleton(C))) | (A = C)))),
% 2.94/3.18 inference(rewrite,[status(thm)],[])).
% 2.94/3.18 tff(82,axiom,(~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), singleton(C)) => (A = C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t26_zfmisc_1')).
% 2.94/3.18 tff(83,plain,
% 2.94/3.18 (~![A: $i, B: $i, C: $i] : ((~subset(unordered_pair(A, B), singleton(C))) | (A = C))),
% 2.94/3.18 inference(modus_ponens,[status(thm)],[82, 81])).
% 2.94/3.18 tff(84,plain,
% 2.94/3.18 (~![A: $i, B: $i, C: $i] : ((~subset(unordered_pair(A, B), singleton(C))) | (A = C))),
% 2.94/3.18 inference(modus_ponens,[status(thm)],[83, 80])).
% 2.94/3.18 tff(85,plain,
% 2.94/3.18 (~![A: $i, B: $i, C: $i] : ((~subset(unordered_pair(A, B), singleton(C))) | (A = C))),
% 2.94/3.18 inference(modus_ponens,[status(thm)],[84, 80])).
% 2.94/3.18 tff(86,plain,
% 2.94/3.18 (~![A: $i, B: $i, C: $i] : ((~subset(unordered_pair(A, B), singleton(C))) | (A = C))),
% 2.94/3.18 inference(modus_ponens,[status(thm)],[85, 80])).
% 2.94/3.18 tff(87,plain,(
% 2.94/3.18 ~((~subset(unordered_pair(A!7, B!6), singleton(C!5))) | (A!7 = C!5))),
% 2.94/3.18 inference(skolemize,[status(sab)],[86])).
% 2.94/3.18 tff(88,plain,
% 2.94/3.18 (subset(unordered_pair(A!7, B!6), singleton(C!5))),
% 2.94/3.18 inference(or_elim,[status(thm)],[87])).
% 2.94/3.18 tff(89,plain,
% 2.94/3.18 ((~((~subset(unordered_pair(A!7, B!6), singleton(C!5))) | ![C: $i] : ((~in(C, unordered_pair(A!7, B!6))) | in(C, singleton(C!5))))) | (~subset(unordered_pair(A!7, B!6), singleton(C!5))) | ![C: $i] : ((~in(C, unordered_pair(A!7, B!6))) | in(C, singleton(C!5)))),
% 2.94/3.18 inference(tautology,[status(thm)],[])).
% 2.94/3.18 tff(90,plain,
% 2.94/3.18 ((~((~subset(unordered_pair(A!7, B!6), singleton(C!5))) | ![C: $i] : ((~in(C, unordered_pair(A!7, B!6))) | in(C, singleton(C!5))))) | ![C: $i] : ((~in(C, unordered_pair(A!7, B!6))) | in(C, singleton(C!5)))),
% 2.94/3.18 inference(unit_resolution,[status(thm)],[89, 88])).
% 2.94/3.18 tff(91,plain,
% 2.94/3.18 (![C: $i] : ((~in(C, unordered_pair(A!7, B!6))) | in(C, singleton(C!5)))),
% 2.94/3.18 inference(unit_resolution,[status(thm)],[90, 79])).
% 2.94/3.18 tff(92,plain,
% 2.94/3.18 (((~![C: $i] : ((~in(C, unordered_pair(A!7, B!6))) | in(C, singleton(C!5)))) | ((~in(A!7, unordered_pair(A!7, B!6))) | in(A!7, singleton(C!5)))) <=> ((~![C: $i] : ((~in(C, unordered_pair(A!7, B!6))) | in(C, singleton(C!5)))) | (~in(A!7, unordered_pair(A!7, B!6))) | in(A!7, singleton(C!5)))),
% 2.94/3.18 inference(rewrite,[status(thm)],[])).
% 2.94/3.18 tff(93,plain,
% 2.94/3.18 ((~![C: $i] : ((~in(C, unordered_pair(A!7, B!6))) | in(C, singleton(C!5)))) | ((~in(A!7, unordered_pair(A!7, B!6))) | in(A!7, singleton(C!5)))),
% 2.94/3.18 inference(quant_inst,[status(thm)],[])).
% 2.94/3.18 tff(94,plain,
% 2.94/3.18 ((~![C: $i] : ((~in(C, unordered_pair(A!7, B!6))) | in(C, singleton(C!5)))) | (~in(A!7, unordered_pair(A!7, B!6))) | in(A!7, singleton(C!5))),
% 2.94/3.18 inference(modus_ponens,[status(thm)],[93, 92])).
% 2.94/3.18 tff(95,plain,
% 2.94/3.18 (in(A!7, singleton(C!5))),
% 2.94/3.18 inference(unit_resolution,[status(thm)],[94, 91, 59])).
% 2.94/3.18 tff(96,plain,
% 2.94/3.18 (~(A!7 = C!5)),
% 2.94/3.18 inference(or_elim,[status(thm)],[87])).
% 2.94/3.18 tff(97,plain,
% 2.94/3.18 ((~(in(A!7, singleton(C!5)) <=> (A!7 = C!5))) | (~in(A!7, singleton(C!5))) | (A!7 = C!5)),
% 2.94/3.18 inference(tautology,[status(thm)],[])).
% 2.94/3.18 tff(98,plain,
% 2.94/3.18 (~(in(A!7, singleton(C!5)) <=> (A!7 = C!5))),
% 2.94/3.18 inference(unit_resolution,[status(thm)],[97, 96, 95])).
% 2.94/3.18 tff(99,plain,
% 2.94/3.18 (^[A: $i, B: $i, C: $i] : refl((~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 2.94/3.18 inference(bind,[status(th)],[])).
% 2.94/3.18 tff(100,plain,
% 2.94/3.18 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 2.94/3.18 inference(quant_intro,[status(thm)],[99])).
% 2.94/3.18 tff(101,plain,
% 2.94/3.18 (![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 2.94/3.18 inference(pull_quant,[status(thm)],[])).
% 2.94/3.18 tff(102,plain,
% 2.94/3.18 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> (~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), pull_quant((~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A))))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), pull_quant((?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> (~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))))), pull_quant((~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))))),
% 2.94/3.18 inference(bind,[status(th)],[])).
% 2.94/3.18 tff(103,plain,
% 2.94/3.18 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 2.94/3.18 inference(quant_intro,[status(thm)],[102])).
% 2.94/3.18 tff(104,plain,
% 2.94/3.18 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 2.94/3.18 inference(transitivity,[status(thm)],[103, 101])).
% 2.94/3.18 tff(105,plain,
% 2.94/3.18 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 2.94/3.18 inference(transitivity,[status(thm)],[104, 100])).
% 2.94/3.18 tff(106,plain,
% 2.94/3.18 (^[A: $i, B: $i] : rewrite((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 2.94/3.18 inference(bind,[status(th)],[])).
% 2.94/3.18 tff(107,plain,
% 2.94/3.18 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 2.94/3.18 inference(quant_intro,[status(thm)],[106])).
% 2.94/3.18 tff(108,plain,
% 2.94/3.18 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 2.94/3.18 inference(transitivity,[status(thm)],[107, 105])).
% 2.94/3.18 tff(109,plain,
% 2.94/3.18 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))), trans(monotonicity(rewrite((~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))) <=> (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))), (((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))) <=> ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))), rewrite(((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))) <=> ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))), (((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))) <=> ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))), rewrite((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))))),
% 2.94/3.18 inference(bind,[status(th)],[])).
% 2.94/3.18 tff(110,plain,
% 2.94/3.18 (![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 2.94/3.18 inference(quant_intro,[status(thm)],[109])).
% 2.94/3.18 tff(111,plain,
% 2.94/3.18 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A))) <=> ![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 2.94/3.18 inference(rewrite,[status(thm)],[])).
% 2.94/3.18 tff(112,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_tarski')).
% 2.94/3.18 tff(113,plain,
% 2.94/3.18 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 2.94/3.18 inference(modus_ponens,[status(thm)],[112, 111])).
% 2.94/3.18 tff(114,plain,(
% 2.94/3.18 ![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))),
% 2.94/3.18 inference(skolemize,[status(sab)],[113])).
% 2.94/3.18 tff(115,plain,
% 2.94/3.18 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 2.94/3.18 inference(modus_ponens,[status(thm)],[114, 110])).
% 2.94/3.18 tff(116,plain,
% 2.94/3.18 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 2.94/3.18 inference(modus_ponens,[status(thm)],[115, 108])).
% 2.94/3.18 tff(117,plain,
% 2.94/3.18 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(A!7, singleton(C!5)) <=> (A!7 = C!5))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(A!7, singleton(C!5)) <=> (A!7 = C!5)))),
% 2.94/3.18 inference(rewrite,[status(thm)],[])).
% 2.94/3.18 tff(118,plain,
% 2.94/3.18 ((~(~(in(A!7, singleton(C!5)) <=> (A!7 = C!5)))) <=> (in(A!7, singleton(C!5)) <=> (A!7 = C!5))),
% 2.94/3.18 inference(rewrite,[status(thm)],[])).
% 2.94/3.18 tff(119,plain,
% 2.94/3.18 (((~(in(A!7, singleton(C!5)) <=> (A!7 = C!5))) | $false) <=> (~(in(A!7, singleton(C!5)) <=> (A!7 = C!5)))),
% 2.94/3.18 inference(rewrite,[status(thm)],[])).
% 2.94/3.18 tff(120,plain,
% 2.94/3.18 (($true | (~(in(tptp_fun_C_0(singleton(C!5), C!5), singleton(C!5)) <=> (tptp_fun_C_0(singleton(C!5), C!5) = C!5)))) <=> $true),
% 2.94/3.18 inference(rewrite,[status(thm)],[])).
% 2.94/3.18 tff(121,plain,
% 2.94/3.18 ((~(in(tptp_fun_C_0(singleton(C!5), C!5), singleton(C!5)) <=> (tptp_fun_C_0(singleton(C!5), C!5) = C!5))) <=> (~(in(tptp_fun_C_0(singleton(C!5), C!5), singleton(C!5)) <=> (tptp_fun_C_0(singleton(C!5), C!5) = C!5)))),
% 2.94/3.18 inference(rewrite,[status(thm)],[])).
% 2.94/3.18 tff(122,plain,
% 2.94/3.18 ((singleton(C!5) = singleton(C!5)) <=> $true),
% 2.94/3.18 inference(rewrite,[status(thm)],[])).
% 2.94/3.18 tff(123,plain,
% 2.94/3.18 (((singleton(C!5) = singleton(C!5)) | (~(in(tptp_fun_C_0(singleton(C!5), C!5), singleton(C!5)) <=> (tptp_fun_C_0(singleton(C!5), C!5) = C!5)))) <=> ($true | (~(in(tptp_fun_C_0(singleton(C!5), C!5), singleton(C!5)) <=> (tptp_fun_C_0(singleton(C!5), C!5) = C!5))))),
% 2.94/3.18 inference(monotonicity,[status(thm)],[122, 121])).
% 2.94/3.18 tff(124,plain,
% 2.94/3.18 (((singleton(C!5) = singleton(C!5)) | (~(in(tptp_fun_C_0(singleton(C!5), C!5), singleton(C!5)) <=> (tptp_fun_C_0(singleton(C!5), C!5) = C!5)))) <=> $true),
% 2.94/3.18 inference(transitivity,[status(thm)],[123, 120])).
% 2.94/3.18 tff(125,plain,
% 2.94/3.18 ((~((singleton(C!5) = singleton(C!5)) | (~(in(tptp_fun_C_0(singleton(C!5), C!5), singleton(C!5)) <=> (tptp_fun_C_0(singleton(C!5), C!5) = C!5))))) <=> (~$true)),
% 2.94/3.18 inference(monotonicity,[status(thm)],[124])).
% 2.94/3.18 tff(126,plain,
% 2.94/3.18 ((~((singleton(C!5) = singleton(C!5)) | (~(in(tptp_fun_C_0(singleton(C!5), C!5), singleton(C!5)) <=> (tptp_fun_C_0(singleton(C!5), C!5) = C!5))))) <=> $false),
% 2.94/3.18 inference(transitivity,[status(thm)],[125, 40])).
% 2.94/3.18 tff(127,plain,
% 2.94/3.18 ((~(in(A!7, singleton(C!5)) <=> (A!7 = C!5))) <=> (~(in(A!7, singleton(C!5)) <=> (A!7 = C!5)))),
% 2.94/3.18 inference(rewrite,[status(thm)],[])).
% 2.94/3.18 tff(128,plain,
% 2.94/3.18 (($false | (in(A!7, singleton(C!5)) <=> (A!7 = C!5))) <=> (in(A!7, singleton(C!5)) <=> (A!7 = C!5))),
% 2.94/3.18 inference(rewrite,[status(thm)],[])).
% 2.94/3.18 tff(129,plain,
% 2.94/3.18 ((~(singleton(C!5) = singleton(C!5))) <=> (~$true)),
% 2.94/3.18 inference(monotonicity,[status(thm)],[122])).
% 2.94/3.18 tff(130,plain,
% 2.94/3.18 ((~(singleton(C!5) = singleton(C!5))) <=> $false),
% 2.94/3.18 inference(transitivity,[status(thm)],[129, 40])).
% 2.94/3.18 tff(131,plain,
% 2.94/3.18 (((~(singleton(C!5) = singleton(C!5))) | (in(A!7, singleton(C!5)) <=> (A!7 = C!5))) <=> ($false | (in(A!7, singleton(C!5)) <=> (A!7 = C!5)))),
% 2.94/3.18 inference(monotonicity,[status(thm)],[130])).
% 2.94/3.18 tff(132,plain,
% 2.94/3.18 (((~(singleton(C!5) = singleton(C!5))) | (in(A!7, singleton(C!5)) <=> (A!7 = C!5))) <=> (in(A!7, singleton(C!5)) <=> (A!7 = C!5))),
% 2.94/3.18 inference(transitivity,[status(thm)],[131, 128])).
% 2.94/3.18 tff(133,plain,
% 2.94/3.18 ((~((~(singleton(C!5) = singleton(C!5))) | (in(A!7, singleton(C!5)) <=> (A!7 = C!5)))) <=> (~(in(A!7, singleton(C!5)) <=> (A!7 = C!5)))),
% 2.94/3.18 inference(monotonicity,[status(thm)],[132])).
% 2.94/3.18 tff(134,plain,
% 2.94/3.18 ((~((~(singleton(C!5) = singleton(C!5))) | (in(A!7, singleton(C!5)) <=> (A!7 = C!5)))) <=> (~(in(A!7, singleton(C!5)) <=> (A!7 = C!5)))),
% 2.94/3.18 inference(transitivity,[status(thm)],[133, 127])).
% 2.94/3.18 tff(135,plain,
% 2.94/3.18 (((~((~(singleton(C!5) = singleton(C!5))) | (in(A!7, singleton(C!5)) <=> (A!7 = C!5)))) | (~((singleton(C!5) = singleton(C!5)) | (~(in(tptp_fun_C_0(singleton(C!5), C!5), singleton(C!5)) <=> (tptp_fun_C_0(singleton(C!5), C!5) = C!5)))))) <=> ((~(in(A!7, singleton(C!5)) <=> (A!7 = C!5))) | $false)),
% 2.94/3.18 inference(monotonicity,[status(thm)],[134, 126])).
% 2.94/3.18 tff(136,plain,
% 2.94/3.18 (((~((~(singleton(C!5) = singleton(C!5))) | (in(A!7, singleton(C!5)) <=> (A!7 = C!5)))) | (~((singleton(C!5) = singleton(C!5)) | (~(in(tptp_fun_C_0(singleton(C!5), C!5), singleton(C!5)) <=> (tptp_fun_C_0(singleton(C!5), C!5) = C!5)))))) <=> (~(in(A!7, singleton(C!5)) <=> (A!7 = C!5)))),
% 2.94/3.18 inference(transitivity,[status(thm)],[135, 119])).
% 2.94/3.18 tff(137,plain,
% 2.94/3.18 ((~((~((~(singleton(C!5) = singleton(C!5))) | (in(A!7, singleton(C!5)) <=> (A!7 = C!5)))) | (~((singleton(C!5) = singleton(C!5)) | (~(in(tptp_fun_C_0(singleton(C!5), C!5), singleton(C!5)) <=> (tptp_fun_C_0(singleton(C!5), C!5) = C!5))))))) <=> (~(~(in(A!7, singleton(C!5)) <=> (A!7 = C!5))))),
% 2.94/3.18 inference(monotonicity,[status(thm)],[136])).
% 2.94/3.18 tff(138,plain,
% 2.94/3.18 ((~((~((~(singleton(C!5) = singleton(C!5))) | (in(A!7, singleton(C!5)) <=> (A!7 = C!5)))) | (~((singleton(C!5) = singleton(C!5)) | (~(in(tptp_fun_C_0(singleton(C!5), C!5), singleton(C!5)) <=> (tptp_fun_C_0(singleton(C!5), C!5) = C!5))))))) <=> (in(A!7, singleton(C!5)) <=> (A!7 = C!5))),
% 2.94/3.18 inference(transitivity,[status(thm)],[137, 118])).
% 2.94/3.18 tff(139,plain,
% 2.94/3.18 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(C!5) = singleton(C!5))) | (in(A!7, singleton(C!5)) <=> (A!7 = C!5)))) | (~((singleton(C!5) = singleton(C!5)) | (~(in(tptp_fun_C_0(singleton(C!5), C!5), singleton(C!5)) <=> (tptp_fun_C_0(singleton(C!5), C!5) = C!5)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(A!7, singleton(C!5)) <=> (A!7 = C!5)))),
% 2.94/3.18 inference(monotonicity,[status(thm)],[138])).
% 2.94/3.18 tff(140,plain,
% 2.94/3.18 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(C!5) = singleton(C!5))) | (in(A!7, singleton(C!5)) <=> (A!7 = C!5)))) | (~((singleton(C!5) = singleton(C!5)) | (~(in(tptp_fun_C_0(singleton(C!5), C!5), singleton(C!5)) <=> (tptp_fun_C_0(singleton(C!5), C!5) = C!5)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(A!7, singleton(C!5)) <=> (A!7 = C!5)))),
% 2.94/3.18 inference(transitivity,[status(thm)],[139, 117])).
% 2.94/3.18 tff(141,plain,
% 2.94/3.18 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(C!5) = singleton(C!5))) | (in(A!7, singleton(C!5)) <=> (A!7 = C!5)))) | (~((singleton(C!5) = singleton(C!5)) | (~(in(tptp_fun_C_0(singleton(C!5), C!5), singleton(C!5)) <=> (tptp_fun_C_0(singleton(C!5), C!5) = C!5)))))))),
% 2.94/3.18 inference(quant_inst,[status(thm)],[])).
% 2.94/3.18 tff(142,plain,
% 2.94/3.18 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(A!7, singleton(C!5)) <=> (A!7 = C!5))),
% 2.94/3.18 inference(modus_ponens,[status(thm)],[141, 140])).
% 2.94/3.18 tff(143,plain,
% 2.94/3.18 ($false),
% 2.94/3.18 inference(unit_resolution,[status(thm)],[142, 116, 98])).
% 2.94/3.18 % SZS output end Proof
% 2.94/3.19 % E exiting
%------------------------------------------------------------------------------