%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU159+3 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:05 AM UTC 2025
% Result : Theorem 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : SEU159+3 : TPTP v9.0.0. Released v3.2.0.
% 0.01/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.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 06:08:33 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % SZS output start Proof
% 0.19/0.37 tff(in_type, type, (
% 0.19/0.37 in: ( $i * $i ) > $o)).
% 0.19/0.37 tff(unordered_pair_type, type, (
% 0.19/0.37 unordered_pair: ( $i * $i ) > $i)).
% 0.19/0.37 tff(tptp_fun_A_6_type, type, (
% 0.19/0.37 tptp_fun_A_6: $i)).
% 0.19/0.37 tff(tptp_fun_B_5_type, type, (
% 0.19/0.37 tptp_fun_B_5: $i)).
% 0.19/0.37 tff(tptp_fun_C_4_type, type, (
% 0.19/0.37 tptp_fun_C_4: $i)).
% 0.19/0.37 tff(subset_type, type, (
% 0.19/0.37 subset: ( $i * $i ) > $o)).
% 0.19/0.37 tff(tptp_fun_C_1_type, type, (
% 0.19/0.37 tptp_fun_C_1: ( $i * $i ) > $i)).
% 0.19/0.37 tff(tptp_fun_D_0_type, type, (
% 0.19/0.37 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 0.19/0.37 tff(1,plain,
% 0.19/0.37 (^[A: $i, B: $i] : refl((unordered_pair(A, B) = unordered_pair(B, A)) <=> (unordered_pair(A, B) = unordered_pair(B, A)))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(2,plain,
% 0.19/0.37 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.37 tff(3,plain,
% 0.19/0.37 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 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')).
% 0.19/0.37 tff(5,plain,
% 0.19/0.37 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.37 tff(6,plain,(
% 0.19/0.37 ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.19/0.37 inference(skolemize,[status(sab)],[5])).
% 0.19/0.37 tff(7,plain,
% 0.19/0.37 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.37 tff(8,plain,
% 0.19/0.37 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(A!6, B!5) = unordered_pair(B!5, A!6))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(9,plain,
% 0.19/0.37 (unordered_pair(A!6, B!5) = unordered_pair(B!5, A!6)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.37 tff(10,plain,
% 0.19/0.37 (unordered_pair(B!5, A!6) = unordered_pair(A!6, B!5)),
% 0.19/0.37 inference(symmetry,[status(thm)],[9])).
% 0.19/0.37 tff(11,plain,
% 0.19/0.37 (in(A!6, unordered_pair(B!5, A!6)) <=> in(A!6, unordered_pair(A!6, B!5))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[10])).
% 0.19/0.37 tff(12,plain,
% 0.19/0.37 (in(A!6, unordered_pair(A!6, B!5)) <=> in(A!6, unordered_pair(B!5, A!6))),
% 0.19/0.37 inference(symmetry,[status(thm)],[11])).
% 0.19/0.37 tff(13,plain,
% 0.19/0.37 ((~in(A!6, unordered_pair(A!6, B!5))) <=> (~in(A!6, unordered_pair(B!5, A!6)))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[12])).
% 0.19/0.37 tff(14,plain,
% 0.19/0.37 (^[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)))))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(15,plain,
% 0.19/0.37 (![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))))))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.37 tff(16,plain,
% 0.19/0.37 (![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))))))))),
% 0.19/0.37 inference(pull_quant,[status(thm)],[])).
% 0.19/0.37 tff(17,plain,
% 0.19/0.37 (^[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))))))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(18,plain,
% 0.19/0.37 (![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))))))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.37 tff(19,plain,
% 0.19/0.37 (![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))))))))),
% 0.19/0.37 inference(transitivity,[status(thm)],[18, 16])).
% 0.19/0.37 tff(20,plain,
% 0.19/0.37 (![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))))))))),
% 0.19/0.37 inference(transitivity,[status(thm)],[19, 15])).
% 0.19/0.37 tff(21,plain,
% 0.19/0.37 (^[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)))))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(22,plain,
% 0.19/0.37 (![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))))))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[21])).
% 0.19/0.37 tff(23,plain,
% 0.19/0.37 (![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))))))))),
% 0.19/0.37 inference(transitivity,[status(thm)],[22, 20])).
% 0.19/0.37 tff(24,plain,
% 0.19/0.37 (^[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))))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(25,plain,
% 0.19/0.38 (![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))))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[24])).
% 0.19/0.38 tff(26,plain,
% 0.19/0.38 (![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))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(27,plain,
% 0.19/0.38 (^[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)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(28,plain,
% 0.19/0.38 (![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))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.38 tff(29,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')).
% 0.19/0.38 tff(30,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.19/0.38 tff(31,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.19/0.38 tff(32,plain,(
% 0.19/0.38 ![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))))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[31])).
% 0.19/0.38 tff(33,plain,
% 0.19/0.38 (![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))))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.19/0.38 tff(34,plain,
% 0.19/0.38 (![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))))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[33, 23])).
% 0.19/0.38 tff(35,plain,
% 0.19/0.38 ((~![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(B!5, A!6) = unordered_pair(A!6, B!5))) | (in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)) = B!5) | (tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)) = A!6))))) | (~((unordered_pair(B!5, A!6) = unordered_pair(A!6, B!5)) | (~(in(tptp_fun_D_0(unordered_pair(B!5, A!6), B!5, A!6), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_0(unordered_pair(B!5, A!6), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(B!5, A!6), B!5, A!6) = A!6))))))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(36,plain,
% 0.19/0.38 (~((~((~(unordered_pair(B!5, A!6) = unordered_pair(A!6, B!5))) | (in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)) = B!5) | (tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)) = A!6))))) | (~((unordered_pair(B!5, A!6) = unordered_pair(A!6, B!5)) | (~(in(tptp_fun_D_0(unordered_pair(B!5, A!6), B!5, A!6), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_0(unordered_pair(B!5, A!6), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(B!5, A!6), B!5, A!6) = A!6)))))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.19/0.38 tff(37,plain,
% 0.19/0.38 (((~((~(unordered_pair(B!5, A!6) = unordered_pair(A!6, B!5))) | (in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)) = B!5) | (tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)) = A!6))))) | (~((unordered_pair(B!5, A!6) = unordered_pair(A!6, B!5)) | (~(in(tptp_fun_D_0(unordered_pair(B!5, A!6), B!5, A!6), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_0(unordered_pair(B!5, A!6), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(B!5, A!6), B!5, A!6) = A!6))))))) | ((~(unordered_pair(B!5, A!6) = unordered_pair(A!6, B!5))) | (in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)) = B!5) | (tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)) = A!6))))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(38,plain,
% 0.19/0.38 ((~(unordered_pair(B!5, A!6) = unordered_pair(A!6, B!5))) | (in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)) = B!5) | (tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)) = A!6)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.19/0.38 tff(39,plain,
% 0.19/0.38 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(B!5, A!6) = unordered_pair(A!6, B!5))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(40,plain,
% 0.19/0.38 (unordered_pair(B!5, A!6) = unordered_pair(A!6, B!5)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[39, 7])).
% 0.19/0.38 tff(41,plain,
% 0.19/0.38 ((~((~(unordered_pair(B!5, A!6) = unordered_pair(A!6, B!5))) | (in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)) = B!5) | (tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)) = A!6))))) | (~(unordered_pair(B!5, A!6) = unordered_pair(A!6, B!5))) | (in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)) = B!5) | (tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)) = A!6)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(42,plain,
% 0.19/0.38 ((~((~(unordered_pair(B!5, A!6) = unordered_pair(A!6, B!5))) | (in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)) = B!5) | (tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)) = A!6))))) | (in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)) = B!5) | (tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)) = A!6)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.19/0.38 tff(43,plain,
% 0.19/0.38 (in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)) = B!5) | (tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)) = A!6))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[42, 38])).
% 0.19/0.38 tff(44,plain,
% 0.19/0.38 (in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), unordered_pair(B!5, A!6)) <=> in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[10])).
% 0.19/0.38 tff(45,plain,
% 0.19/0.38 (in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5)) <=> in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), unordered_pair(B!5, A!6))),
% 0.19/0.38 inference(symmetry,[status(thm)],[44])).
% 0.19/0.38 tff(46,assumption,(~subset(unordered_pair(A!6, B!5), C!4)), introduced(assumption)).
% 0.19/0.38 tff(47,plain,
% 0.19/0.38 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(48,plain,
% 0.19/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(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_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.38 tff(49,plain,
% 0.19/0.38 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(50,plain,
% 0.19/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(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_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[49])).
% 0.19/0.38 tff(51,plain,
% 0.19/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(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_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[50, 48])).
% 0.19/0.38 tff(52,plain,
% 0.19/0.38 (^[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_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(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_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[52])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 (^[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))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[55])).
% 0.19/0.39 tff(57,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')).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.19/0.39 tff(60,plain,(
% 0.19/0.39 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[59])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[61, 51])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))) | (~((~((~subset(unordered_pair(A!6, B!5), C!4)) | ![C: $i] : ((~in(C, unordered_pair(A!6, B!5))) | in(C, C!4)))) | (~(subset(unordered_pair(A!6, B!5), C!4) | (~((~in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5))) | in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), C!4)))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 (~((~((~subset(unordered_pair(A!6, B!5), C!4)) | ![C: $i] : ((~in(C, unordered_pair(A!6, B!5))) | in(C, C!4)))) | (~(subset(unordered_pair(A!6, B!5), C!4) | (~((~in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5))) | in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), C!4))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.19/0.39 tff(65,plain,
% 0.19/0.39 (((~((~subset(unordered_pair(A!6, B!5), C!4)) | ![C: $i] : ((~in(C, unordered_pair(A!6, B!5))) | in(C, C!4)))) | (~(subset(unordered_pair(A!6, B!5), C!4) | (~((~in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5))) | in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), C!4)))))) | (subset(unordered_pair(A!6, B!5), C!4) | (~((~in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5))) | in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), C!4))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(66,plain,
% 0.19/0.39 (subset(unordered_pair(A!6, B!5), C!4) | (~((~in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5))) | in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), C!4)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.19/0.39 tff(67,plain,
% 0.19/0.39 ((~(subset(unordered_pair(A!6, B!5), C!4) | (~((~in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5))) | in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), C!4))))) | subset(unordered_pair(A!6, B!5), C!4) | (~((~in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5))) | in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), C!4)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(68,plain,
% 0.19/0.39 (subset(unordered_pair(A!6, B!5), C!4) | (~((~in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5))) | in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), C!4)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.19/0.39 tff(69,plain,
% 0.19/0.39 (~((~in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5))) | in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), C!4))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[68, 46])).
% 0.19/0.39 tff(70,plain,
% 0.19/0.39 (((~in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5))) | in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), C!4)) | in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(71,plain,
% 0.19/0.39 (in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.19/0.39 tff(72,plain,
% 0.19/0.39 (in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), unordered_pair(B!5, A!6))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[71, 45])).
% 0.19/0.39 tff(73,plain,
% 0.19/0.39 ((~(in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)) = B!5) | (tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)) = A!6)))) | (~in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), unordered_pair(B!5, A!6))) | ((tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)) = B!5) | (tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)) = A!6))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(74,plain,
% 0.19/0.39 ((tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)) = B!5) | (tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)) = A!6)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[73, 72, 43])).
% 0.19/0.39 tff(75,plain,
% 0.19/0.39 ((~(~(((~in(A!6, C!4)) | (~in(B!5, C!4))) <=> subset(unordered_pair(A!6, B!5), C!4)))) <=> (((~in(A!6, C!4)) | (~in(B!5, C!4))) <=> subset(unordered_pair(A!6, B!5), C!4))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(76,plain,
% 0.19/0.39 ((~(((~in(A!6, C!4)) | (~in(B!5, C!4))) <=> subset(unordered_pair(A!6, B!5), C!4))) <=> (~(((~in(A!6, C!4)) | (~in(B!5, C!4))) <=> subset(unordered_pair(A!6, B!5), C!4)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(77,plain,
% 0.19/0.39 ((subset(unordered_pair(A!6, B!5), C!4) <=> (~((~in(A!6, C!4)) | (~in(B!5, C!4))))) <=> (~(((~in(A!6, C!4)) | (~in(B!5, C!4))) <=> subset(unordered_pair(A!6, B!5), C!4)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(78,plain,
% 0.19/0.39 ((in(A!6, C!4) & in(B!5, C!4)) <=> (~((~in(A!6, C!4)) | (~in(B!5, C!4))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(79,plain,
% 0.19/0.39 ((subset(unordered_pair(A!6, B!5), C!4) <=> (in(A!6, C!4) & in(B!5, C!4))) <=> (subset(unordered_pair(A!6, B!5), C!4) <=> (~((~in(A!6, C!4)) | (~in(B!5, C!4)))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[78])).
% 0.19/0.39 tff(80,plain,
% 0.19/0.39 ((subset(unordered_pair(A!6, B!5), C!4) <=> (in(A!6, C!4) & in(B!5, C!4))) <=> (~(((~in(A!6, C!4)) | (~in(B!5, C!4))) <=> subset(unordered_pair(A!6, B!5), C!4)))),
% 0.19/0.39 inference(transitivity,[status(thm)],[79, 77])).
% 0.19/0.39 tff(81,plain,
% 0.19/0.39 ((subset(unordered_pair(A!6, B!5), C!4) <=> (in(A!6, C!4) & in(B!5, C!4))) <=> (~(((~in(A!6, C!4)) | (~in(B!5, C!4))) <=> subset(unordered_pair(A!6, B!5), C!4)))),
% 0.19/0.39 inference(transitivity,[status(thm)],[80, 76])).
% 0.19/0.39 tff(82,plain,
% 0.19/0.39 ((~(subset(unordered_pair(A!6, B!5), C!4) <=> (in(A!6, C!4) & in(B!5, C!4)))) <=> (~(~(((~in(A!6, C!4)) | (~in(B!5, C!4))) <=> subset(unordered_pair(A!6, B!5), C!4))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[81])).
% 0.19/0.39 tff(83,plain,
% 0.19/0.39 ((~(subset(unordered_pair(A!6, B!5), C!4) <=> (in(A!6, C!4) & in(B!5, C!4)))) <=> (((~in(A!6, C!4)) | (~in(B!5, C!4))) <=> subset(unordered_pair(A!6, B!5), C!4))),
% 0.19/0.39 inference(transitivity,[status(thm)],[82, 75])).
% 0.19/0.39 tff(84,plain,
% 0.19/0.39 ((~(subset(unordered_pair(A!6, B!5), C!4) <=> (in(A!6, C!4) & in(B!5, C!4)))) <=> (~(subset(unordered_pair(A!6, B!5), C!4) <=> (in(A!6, C!4) & in(B!5, C!4))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(85,plain,
% 0.19/0.39 ((~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))) <=> (~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(86,axiom,(~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t38_zfmisc_1')).
% 0.19/0.39 tff(87,plain,
% 0.19/0.39 (~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.19/0.39 tff(88,plain,
% 0.19/0.39 (~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[87, 85])).
% 0.19/0.39 tff(89,plain,
% 0.19/0.39 (~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[88, 85])).
% 0.19/0.39 tff(90,plain,
% 0.19/0.39 (~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.19/0.39 tff(91,plain,(
% 0.19/0.39 ~(subset(unordered_pair(A!6, B!5), C!4) <=> (in(A!6, C!4) & in(B!5, C!4)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[90])).
% 0.19/0.39 tff(92,plain,
% 0.19/0.39 (~(subset(unordered_pair(A!6, B!5), C!4) <=> (in(A!6, C!4) & in(B!5, C!4)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.19/0.39 tff(93,plain,
% 0.19/0.39 (((~in(A!6, C!4)) | (~in(B!5, C!4))) <=> subset(unordered_pair(A!6, B!5), C!4)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[92, 83])).
% 0.19/0.39 tff(94,plain,
% 0.19/0.39 ((~((~in(A!6, C!4)) | (~in(B!5, C!4)))) | subset(unordered_pair(A!6, B!5), C!4) | (~(((~in(A!6, C!4)) | (~in(B!5, C!4))) <=> subset(unordered_pair(A!6, B!5), C!4)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(95,plain,
% 0.19/0.39 ((~((~in(A!6, C!4)) | (~in(B!5, C!4)))) | subset(unordered_pair(A!6, B!5), C!4)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.19/0.39 tff(96,plain,
% 0.19/0.39 (~((~in(A!6, C!4)) | (~in(B!5, C!4)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[95, 46])).
% 0.19/0.39 tff(97,plain,
% 0.19/0.39 (((~in(A!6, C!4)) | (~in(B!5, C!4))) | in(B!5, C!4)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(98,plain,
% 0.19/0.39 (in(B!5, C!4)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.19/0.39 tff(99,plain,
% 0.19/0.39 (((~in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5))) | in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), C!4)) | (~in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), C!4))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(100,plain,
% 0.19/0.39 (~in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), C!4)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[99, 69])).
% 0.19/0.39 tff(101,assumption,(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)) = B!5), introduced(assumption)).
% 0.19/0.39 tff(102,plain,
% 0.19/0.39 (in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), C!4) <=> in(B!5, C!4)),
% 0.19/0.39 inference(monotonicity,[status(thm)],[101])).
% 0.19/0.39 tff(103,plain,
% 0.19/0.39 (in(B!5, C!4) <=> in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), C!4)),
% 0.19/0.39 inference(symmetry,[status(thm)],[102])).
% 0.19/0.39 tff(104,assumption,(in(B!5, C!4)), introduced(assumption)).
% 0.19/0.39 tff(105,plain,
% 0.19/0.39 (in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), C!4)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.39 tff(106,assumption,(~in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), C!4)), introduced(assumption)).
% 0.19/0.39 tff(107,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.19/0.39 tff(108,plain,((~(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)) = B!5)) | in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), C!4) | (~in(B!5, C!4))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(109,plain,
% 0.19/0.39 (~(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)) = B!5)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[108, 100, 98])).
% 0.19/0.39 tff(110,plain,
% 0.19/0.39 ((~((tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)) = B!5) | (tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)) = A!6))) | (tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)) = B!5) | (tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)) = A!6)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(111,plain,
% 0.19/0.39 (tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)) = A!6),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[110, 109, 74])).
% 0.19/0.40 tff(112,plain,
% 0.19/0.40 (in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), C!4) <=> in(A!6, C!4)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[111])).
% 0.19/0.40 tff(113,plain,
% 0.19/0.40 (in(A!6, C!4) <=> in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), C!4)),
% 0.19/0.40 inference(symmetry,[status(thm)],[112])).
% 0.19/0.40 tff(114,plain,
% 0.19/0.40 (((~in(A!6, C!4)) | (~in(B!5, C!4))) | in(A!6, C!4)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(115,plain,
% 0.19/0.40 (in(A!6, C!4)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[114, 96])).
% 0.19/0.40 tff(116,plain,
% 0.19/0.40 (in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), C!4)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[115, 113])).
% 0.19/0.40 tff(117,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[100, 116])).
% 0.19/0.40 tff(118,plain,(subset(unordered_pair(A!6, B!5), C!4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(119,plain,
% 0.19/0.40 (((~((~subset(unordered_pair(A!6, B!5), C!4)) | ![C: $i] : ((~in(C, unordered_pair(A!6, B!5))) | in(C, C!4)))) | (~(subset(unordered_pair(A!6, B!5), C!4) | (~((~in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5))) | in(tptp_fun_C_1(C!4, unordered_pair(A!6, B!5)), C!4)))))) | ((~subset(unordered_pair(A!6, B!5), C!4)) | ![C: $i] : ((~in(C, unordered_pair(A!6, B!5))) | in(C, C!4)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(120,plain,
% 0.19/0.40 ((~subset(unordered_pair(A!6, B!5), C!4)) | ![C: $i] : ((~in(C, unordered_pair(A!6, B!5))) | in(C, C!4))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[119, 64])).
% 0.19/0.40 tff(121,plain,
% 0.19/0.40 ((~((~subset(unordered_pair(A!6, B!5), C!4)) | ![C: $i] : ((~in(C, unordered_pair(A!6, B!5))) | in(C, C!4)))) | (~subset(unordered_pair(A!6, B!5), C!4)) | ![C: $i] : ((~in(C, unordered_pair(A!6, B!5))) | in(C, C!4))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(122,plain,
% 0.19/0.40 ((~subset(unordered_pair(A!6, B!5), C!4)) | ![C: $i] : ((~in(C, unordered_pair(A!6, B!5))) | in(C, C!4))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.19/0.40 tff(123,plain,
% 0.19/0.40 (![C: $i] : ((~in(C, unordered_pair(A!6, B!5))) | in(C, C!4))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[122, 118])).
% 0.19/0.40 tff(124,plain,
% 0.19/0.40 (in(B!5, unordered_pair(B!5, A!6)) <=> in(B!5, unordered_pair(A!6, B!5))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[10])).
% 0.19/0.40 tff(125,plain,
% 0.19/0.40 (in(B!5, unordered_pair(A!6, B!5)) <=> in(B!5, unordered_pair(B!5, A!6))),
% 0.19/0.40 inference(symmetry,[status(thm)],[124])).
% 0.19/0.40 tff(126,plain,
% 0.19/0.40 ((~in(B!5, unordered_pair(A!6, B!5))) <=> (~in(B!5, unordered_pair(B!5, A!6)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[125])).
% 0.19/0.40 tff(127,assumption,(~in(B!5, unordered_pair(A!6, B!5))), introduced(assumption)).
% 0.19/0.40 tff(128,plain,
% 0.19/0.40 (~in(B!5, unordered_pair(B!5, A!6))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.19/0.40 tff(129,plain,
% 0.19/0.40 (((~![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))))))))) | in(B!5, unordered_pair(B!5, A!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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))) | in(B!5, unordered_pair(B!5, A!6)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(130,plain,
% 0.19/0.40 ((~(~in(B!5, unordered_pair(B!5, A!6)))) <=> in(B!5, unordered_pair(B!5, A!6))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(131,plain,
% 0.19/0.40 (((~in(B!5, unordered_pair(B!5, A!6))) | $false) <=> (~in(B!5, unordered_pair(B!5, A!6)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(132,plain,
% 0.19/0.40 ((~$true) <=> $false),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(133,plain,
% 0.19/0.40 (($true | (~(in(tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = B!5))))) <=> $true),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(134,plain,
% 0.19/0.40 ((~(in(tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = B!5)))) <=> (~(in(tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = B!5))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(135,plain,
% 0.19/0.40 ((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) <=> $true),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(136,plain,
% 0.19/0.40 (((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | (~(in(tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = B!5))))) <=> ($true | (~(in(tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = B!5)))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[135, 134])).
% 0.19/0.40 tff(137,plain,
% 0.19/0.40 (((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | (~(in(tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = B!5))))) <=> $true),
% 0.19/0.40 inference(transitivity,[status(thm)],[136, 133])).
% 0.19/0.40 tff(138,plain,
% 0.19/0.40 ((~((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | (~(in(tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = B!5)))))) <=> (~$true)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[137])).
% 0.19/0.40 tff(139,plain,
% 0.19/0.40 ((~((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | (~(in(tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = B!5)))))) <=> $false),
% 0.19/0.40 inference(transitivity,[status(thm)],[138, 132])).
% 0.19/0.40 tff(140,plain,
% 0.19/0.40 ((~((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(B!5, unordered_pair(B!5, A!6)) <=> ((B!5 = A!6) | (B!5 = B!5))))) <=> (~in(B!5, unordered_pair(B!5, A!6)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(141,plain,
% 0.19/0.40 (((~((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(B!5, unordered_pair(B!5, A!6)) <=> ((B!5 = A!6) | (B!5 = B!5))))) | (~((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | (~(in(tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = B!5))))))) <=> ((~in(B!5, unordered_pair(B!5, A!6))) | $false)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[140, 139])).
% 0.19/0.40 tff(142,plain,
% 0.19/0.40 (((~((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(B!5, unordered_pair(B!5, A!6)) <=> ((B!5 = A!6) | (B!5 = B!5))))) | (~((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | (~(in(tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = B!5))))))) <=> (~in(B!5, unordered_pair(B!5, A!6)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[141, 131])).
% 0.19/0.40 tff(143,plain,
% 0.19/0.40 ((~((~((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(B!5, unordered_pair(B!5, A!6)) <=> ((B!5 = A!6) | (B!5 = B!5))))) | (~((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | (~(in(tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = B!5)))))))) <=> (~(~in(B!5, unordered_pair(B!5, A!6))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[142])).
% 0.19/0.40 tff(144,plain,
% 0.19/0.40 ((~((~((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(B!5, unordered_pair(B!5, A!6)) <=> ((B!5 = A!6) | (B!5 = B!5))))) | (~((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | (~(in(tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = B!5)))))))) <=> in(B!5, unordered_pair(B!5, A!6))),
% 0.19/0.40 inference(transitivity,[status(thm)],[143, 130])).
% 0.19/0.40 tff(145,plain,
% 0.19/0.40 (((~![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(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(B!5, unordered_pair(B!5, A!6)) <=> ((B!5 = A!6) | (B!5 = B!5))))) | (~((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | (~(in(tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = B!5))))))))) <=> ((~![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))))))))) | in(B!5, unordered_pair(B!5, A!6)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[144])).
% 0.19/0.40 tff(146,plain,
% 0.19/0.40 (((~![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(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(B!5, unordered_pair(B!5, A!6)) <=> ((B!5 = A!6) | (B!5 = B!5))))) | (~((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | (~(in(tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = B!5))))))))) <=> ((~![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))))))))) | in(B!5, unordered_pair(B!5, A!6)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[145, 129])).
% 0.19/0.40 tff(147,plain,
% 0.19/0.40 ((~![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(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(B!5, unordered_pair(B!5, A!6)) <=> ((B!5 = A!6) | (B!5 = B!5))))) | (~((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | (~(in(tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = B!5))))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(148,plain,
% 0.19/0.40 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))) | in(B!5, unordered_pair(B!5, A!6))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.19/0.40 tff(149,plain,
% 0.19/0.40 (in(B!5, unordered_pair(B!5, A!6))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[148, 34])).
% 0.19/0.40 tff(150,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[149, 128])).
% 0.19/0.40 tff(151,plain,(in(B!5, unordered_pair(A!6, B!5))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(152,plain,
% 0.19/0.40 (((~![C: $i] : ((~in(C, unordered_pair(A!6, B!5))) | in(C, C!4))) | ((~in(B!5, unordered_pair(A!6, B!5))) | in(B!5, C!4))) <=> ((~![C: $i] : ((~in(C, unordered_pair(A!6, B!5))) | in(C, C!4))) | (~in(B!5, unordered_pair(A!6, B!5))) | in(B!5, C!4))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(153,plain,
% 0.19/0.41 ((~![C: $i] : ((~in(C, unordered_pair(A!6, B!5))) | in(C, C!4))) | ((~in(B!5, unordered_pair(A!6, B!5))) | in(B!5, C!4))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(154,plain,
% 0.19/0.41 ((~![C: $i] : ((~in(C, unordered_pair(A!6, B!5))) | in(C, C!4))) | (~in(B!5, unordered_pair(A!6, B!5))) | in(B!5, C!4)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.19/0.41 tff(155,plain,
% 0.19/0.41 (in(B!5, C!4)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[154, 123, 151])).
% 0.19/0.41 tff(156,plain,
% 0.19/0.41 (((~in(A!6, C!4)) | (~in(B!5, C!4))) | (~subset(unordered_pair(A!6, B!5), C!4)) | (~(((~in(A!6, C!4)) | (~in(B!5, C!4))) <=> subset(unordered_pair(A!6, B!5), C!4)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(157,plain,
% 0.19/0.41 (((~in(A!6, C!4)) | (~in(B!5, C!4))) | (~subset(unordered_pair(A!6, B!5), C!4))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[156, 93])).
% 0.19/0.41 tff(158,plain,
% 0.19/0.41 ((~in(A!6, C!4)) | (~in(B!5, C!4))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[157, 118])).
% 0.19/0.41 tff(159,plain,
% 0.19/0.41 ((~((~in(A!6, C!4)) | (~in(B!5, C!4)))) | (~in(A!6, C!4)) | (~in(B!5, C!4))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(160,plain,
% 0.19/0.41 ((~in(A!6, C!4)) | (~in(B!5, C!4))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.19/0.41 tff(161,plain,
% 0.19/0.41 (~in(A!6, C!4)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[160, 155])).
% 0.19/0.41 tff(162,plain,
% 0.19/0.41 (((~![C: $i] : ((~in(C, unordered_pair(A!6, B!5))) | in(C, C!4))) | ((~in(A!6, unordered_pair(A!6, B!5))) | in(A!6, C!4))) <=> ((~![C: $i] : ((~in(C, unordered_pair(A!6, B!5))) | in(C, C!4))) | (~in(A!6, unordered_pair(A!6, B!5))) | in(A!6, C!4))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(163,plain,
% 0.19/0.41 ((~![C: $i] : ((~in(C, unordered_pair(A!6, B!5))) | in(C, C!4))) | ((~in(A!6, unordered_pair(A!6, B!5))) | in(A!6, C!4))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(164,plain,
% 0.19/0.41 ((~![C: $i] : ((~in(C, unordered_pair(A!6, B!5))) | in(C, C!4))) | (~in(A!6, unordered_pair(A!6, B!5))) | in(A!6, C!4)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.19/0.41 tff(165,plain,
% 0.19/0.41 (~in(A!6, unordered_pair(A!6, B!5))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[164, 161, 123])).
% 0.19/0.41 tff(166,plain,
% 0.19/0.41 (~in(A!6, unordered_pair(B!5, A!6))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[165, 13])).
% 0.19/0.41 tff(167,plain,
% 0.19/0.41 (((~![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))))))))) | in(A!6, unordered_pair(B!5, A!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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))) | in(A!6, unordered_pair(B!5, A!6)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(168,plain,
% 0.19/0.41 ((~(~in(A!6, unordered_pair(B!5, A!6)))) <=> in(A!6, unordered_pair(B!5, A!6))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(169,plain,
% 0.19/0.41 (((~in(A!6, unordered_pair(B!5, A!6))) | $false) <=> (~in(A!6, unordered_pair(B!5, A!6)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(170,plain,
% 0.19/0.41 ((~((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(A!6, unordered_pair(B!5, A!6)) <=> ((A!6 = A!6) | (A!6 = B!5))))) <=> (~in(A!6, unordered_pair(B!5, A!6)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(171,plain,
% 0.19/0.41 (((~((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(A!6, unordered_pair(B!5, A!6)) <=> ((A!6 = A!6) | (A!6 = B!5))))) | (~((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | (~(in(tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = B!5))))))) <=> ((~in(A!6, unordered_pair(B!5, A!6))) | $false)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[170, 139])).
% 0.19/0.41 tff(172,plain,
% 0.19/0.41 (((~((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(A!6, unordered_pair(B!5, A!6)) <=> ((A!6 = A!6) | (A!6 = B!5))))) | (~((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | (~(in(tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = B!5))))))) <=> (~in(A!6, unordered_pair(B!5, A!6)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[171, 169])).
% 0.19/0.41 tff(173,plain,
% 0.19/0.41 ((~((~((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(A!6, unordered_pair(B!5, A!6)) <=> ((A!6 = A!6) | (A!6 = B!5))))) | (~((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | (~(in(tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = B!5)))))))) <=> (~(~in(A!6, unordered_pair(B!5, A!6))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[172])).
% 0.19/0.41 tff(174,plain,
% 0.19/0.41 ((~((~((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(A!6, unordered_pair(B!5, A!6)) <=> ((A!6 = A!6) | (A!6 = B!5))))) | (~((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | (~(in(tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = B!5)))))))) <=> in(A!6, unordered_pair(B!5, A!6))),
% 0.19/0.41 inference(transitivity,[status(thm)],[173, 168])).
% 0.19/0.41 tff(175,plain,
% 0.19/0.41 (((~![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(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(A!6, unordered_pair(B!5, A!6)) <=> ((A!6 = A!6) | (A!6 = B!5))))) | (~((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | (~(in(tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = B!5))))))))) <=> ((~![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))))))))) | in(A!6, unordered_pair(B!5, A!6)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[174])).
% 0.19/0.41 tff(176,plain,
% 0.19/0.41 (((~![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(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(A!6, unordered_pair(B!5, A!6)) <=> ((A!6 = A!6) | (A!6 = B!5))))) | (~((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | (~(in(tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = B!5))))))))) <=> ((~![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))))))))) | in(A!6, unordered_pair(B!5, A!6)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[175, 167])).
% 0.19/0.41 tff(177,plain,
% 0.19/0.41 ((~![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(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(A!6, unordered_pair(B!5, A!6)) <=> ((A!6 = A!6) | (A!6 = B!5))))) | (~((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | (~(in(tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6)) <=> ((tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_0(unordered_pair(B!5, A!6), A!6, B!5) = B!5))))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(178,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))) | in(A!6, unordered_pair(B!5, A!6))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.19/0.41 tff(179,plain,
% 0.19/0.41 (in(A!6, unordered_pair(B!5, A!6))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[178, 34])).
% 0.19/0.41 tff(180,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[179, 166])).
% 0.19/0.41 % SZS output end Proof
% 0.19/0.41 % E exiting
%------------------------------------------------------------------------------