%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU142+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:00 AM UTC 2025
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU142+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 06:07:33 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(tptp_fun_A_3_type, type, (
% 0.20/0.38 tptp_fun_A_3: $i)).
% 0.20/0.38 tff(tptp_fun_C_0_type, type, (
% 0.20/0.38 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.20/0.38 tff(unordered_pair_type, type, (
% 0.20/0.38 unordered_pair: ( $i * $i ) > $i)).
% 0.20/0.38 tff(in_type, type, (
% 0.20/0.38 in: ( $i * $i ) > $o)).
% 0.20/0.38 tff(singleton_type, type, (
% 0.20/0.38 singleton: $i > $i)).
% 0.20/0.38 tff(tptp_fun_C_2_type, type, (
% 0.20/0.38 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.20/0.38 tff(tptp_fun_D_1_type, type, (
% 0.20/0.38 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.20/0.38 tff(1,plain,
% 0.20/0.38 (^[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))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (![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)))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (![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)))))))),
% 0.20/0.38 inference(pull_quant,[status(thm)],[])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (^[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)))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 (![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)))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 (![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)))))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[5, 3])).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (![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)))))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[6, 2])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 (^[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))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 (![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)))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[8])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 (![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)))))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[9, 7])).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 (^[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)))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(12,plain,
% 0.20/0.39 (![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)))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.39 tff(13,plain,
% 0.20/0.39 (![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)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(14,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_tarski')).
% 0.20/0.39 tff(15,plain,
% 0.20/0.39 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.39 tff(16,plain,(
% 0.20/0.39 ![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)))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[15])).
% 0.20/0.39 tff(17,plain,
% 0.20/0.39 (![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)))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.20/0.39 tff(18,plain,
% 0.20/0.39 (![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)))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 ((~![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)))))))) | (~((~((~(unordered_pair(A!3, A!3) = singleton(A!3))) | (in(tptp_fun_C_2(A!3, unordered_pair(A!3, A!3)), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_2(A!3, unordered_pair(A!3, A!3)) = A!3)))) | (~((unordered_pair(A!3, A!3) = singleton(A!3)) | (~(in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)))))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(20,plain,
% 0.20/0.39 (~((~((~(unordered_pair(A!3, A!3) = singleton(A!3))) | (in(tptp_fun_C_2(A!3, unordered_pair(A!3, A!3)), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_2(A!3, unordered_pair(A!3, A!3)) = A!3)))) | (~((unordered_pair(A!3, A!3) = singleton(A!3)) | (~(in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 (((~((~(unordered_pair(A!3, A!3) = singleton(A!3))) | (in(tptp_fun_C_2(A!3, unordered_pair(A!3, A!3)), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_2(A!3, unordered_pair(A!3, A!3)) = A!3)))) | (~((unordered_pair(A!3, A!3) = singleton(A!3)) | (~(in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)))))) | ((unordered_pair(A!3, A!3) = singleton(A!3)) | (~(in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 ((unordered_pair(A!3, A!3) = singleton(A!3)) | (~(in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.20/0.39 tff(23,plain,
% 0.20/0.39 ((~![A: $i] : (unordered_pair(A, A) = singleton(A))) <=> (~![A: $i] : (unordered_pair(A, A) = singleton(A)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(24,axiom,(~![A: $i] : (unordered_pair(A, A) = singleton(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t69_enumset1')).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 (~![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 (~![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[25, 23])).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 (~![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[26, 23])).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 (~![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.20/0.39 tff(29,plain,(
% 0.20/0.39 ~(unordered_pair(A!3, A!3) = singleton(A!3))),
% 0.20/0.39 inference(skolemize,[status(sab)],[28])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 ((~((unordered_pair(A!3, A!3) = singleton(A!3)) | (~(in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))))) | (unordered_pair(A!3, A!3) = singleton(A!3)) | (~(in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 ((~((unordered_pair(A!3, A!3) = singleton(A!3)) | (~(in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))))) | (~(in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 (~(in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[31, 22])).
% 0.20/0.39 tff(33,plain,
% 0.20/0.39 (^[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)))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(34,plain,
% 0.20/0.39 (![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))))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[33])).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 (![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))))))))),
% 0.20/0.39 inference(pull_quant,[status(thm)],[])).
% 0.20/0.39 tff(36,plain,
% 0.20/0.39 (^[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))))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(37,plain,
% 0.20/0.39 (![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))))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[36])).
% 0.20/0.39 tff(38,plain,
% 0.20/0.39 (![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))))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[37, 35])).
% 0.20/0.39 tff(39,plain,
% 0.20/0.39 (![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))))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[38, 34])).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 (^[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)))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 (![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))))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[40])).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 (![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))))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[41, 39])).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 (^[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))))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 (![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))))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[43])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 (![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))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 (^[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)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 (![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))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[46])).
% 0.20/0.39 tff(48,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')).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.20/0.39 tff(50,plain,
% 0.20/0.39 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.20/0.39 tff(51,plain,(
% 0.20/0.39 ![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))))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[50])).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 (![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))))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 (![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))))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[52, 42])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 (((~![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(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))) <=> ((~![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(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(55,plain,
% 0.20/0.40 ((~(~(in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)))) <=> (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(56,plain,
% 0.20/0.40 (((~(in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))) | $false) <=> (~(in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(57,plain,
% 0.20/0.40 ((~$true) <=> $false),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(58,plain,
% 0.20/0.40 (($true | (~(in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3)))) <=> $true),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(59,plain,
% 0.20/0.40 ((~(in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3))) <=> (~(in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(60,plain,
% 0.20/0.40 ((in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3) | (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3))) <=> (in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(61,plain,
% 0.20/0.40 ((~(in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3) | (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3)))) <=> (~(in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3)))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[60])).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 ((~(in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3) | (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3)))) <=> (~(in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3)))),
% 0.20/0.40 inference(transitivity,[status(thm)],[61, 59])).
% 0.20/0.40 tff(63,plain,
% 0.20/0.40 ((unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3)) <=> $true),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(64,plain,
% 0.20/0.40 (((unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3)) | (~(in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3) | (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3))))) <=> ($true | (~(in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[63, 62])).
% 0.20/0.40 tff(65,plain,
% 0.20/0.40 (((unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3)) | (~(in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3) | (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3))))) <=> $true),
% 0.20/0.40 inference(transitivity,[status(thm)],[64, 58])).
% 0.20/0.40 tff(66,plain,
% 0.20/0.40 ((~((unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3)) | (~(in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3) | (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3)))))) <=> (~$true)),
% 0.20/0.40 inference(monotonicity,[status(thm)],[65])).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 ((~((unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3)) | (~(in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3) | (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3)))))) <=> $false),
% 0.20/0.40 inference(transitivity,[status(thm)],[66, 57])).
% 0.20/0.40 tff(68,plain,
% 0.20/0.40 ((~(in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))) <=> (~(in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(69,plain,
% 0.20/0.40 (($false | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))) <=> (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 ((in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3) | (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))) <=> (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 ((~(unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3))) <=> (~$true)),
% 0.20/0.40 inference(monotonicity,[status(thm)],[63])).
% 0.20/0.40 tff(72,plain,
% 0.20/0.40 ((~(unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3))) <=> $false),
% 0.20/0.40 inference(transitivity,[status(thm)],[71, 57])).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 (((~(unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3))) | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3) | (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)))) <=> ($false | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[72, 70])).
% 0.20/0.40 tff(74,plain,
% 0.20/0.40 (((~(unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3))) | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3) | (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)))) <=> (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))),
% 0.20/0.40 inference(transitivity,[status(thm)],[73, 69])).
% 0.20/0.40 tff(75,plain,
% 0.20/0.40 ((~((~(unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3))) | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3) | (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))))) <=> (~(in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[74])).
% 0.20/0.40 tff(76,plain,
% 0.20/0.40 ((~((~(unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3))) | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3) | (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))))) <=> (~(in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)))),
% 0.20/0.40 inference(transitivity,[status(thm)],[75, 68])).
% 0.20/0.40 tff(77,plain,
% 0.20/0.40 (((~((~(unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3))) | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3) | (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))))) | (~((unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3)) | (~(in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3) | (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3))))))) <=> ((~(in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))) | $false)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[76, 67])).
% 0.20/0.41 tff(78,plain,
% 0.20/0.41 (((~((~(unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3))) | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3) | (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))))) | (~((unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3)) | (~(in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3) | (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3))))))) <=> (~(in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[77, 56])).
% 0.20/0.41 tff(79,plain,
% 0.20/0.41 ((~((~((~(unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3))) | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3) | (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))))) | (~((unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3)) | (~(in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3) | (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3)))))))) <=> (~(~(in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[78])).
% 0.20/0.41 tff(80,plain,
% 0.20/0.41 ((~((~((~(unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3))) | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3) | (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))))) | (~((unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3)) | (~(in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3) | (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3)))))))) <=> (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))),
% 0.20/0.41 inference(transitivity,[status(thm)],[79, 55])).
% 0.20/0.41 tff(81,plain,
% 0.20/0.41 (((~![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3))) | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3) | (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))))) | (~((unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3)) | (~(in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3) | (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3))))))))) <=> ((~![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(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[80])).
% 0.20/0.41 tff(82,plain,
% 0.20/0.41 (((~![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3))) | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3) | (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))))) | (~((unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3)) | (~(in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3) | (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3))))))))) <=> ((~![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(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[81, 54])).
% 0.20/0.41 tff(83,plain,
% 0.20/0.41 ((~![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3))) | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3) | (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))))) | (~((unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3)) | (~(in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3) | (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3))))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(84,plain,
% 0.20/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.41 tff(85,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[84, 53, 32])).
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------