%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU149+3 : TPTP v9.0.0. Released v3.2.0.
% 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 05:27:02 AM UTC 2025
% Result : Theorem 1.21s 1.38s
% Output : Proof 1.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU149+3 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n008.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 06:07:48 EDT 2025
% 0.11/0.33 % CPUTime :
% 1.21/1.38 % SZS status Theorem
% 1.21/1.38 % SZS output start Proof
% 1.21/1.38 tff(tptp_fun_B_5_type, type, (
% 1.21/1.38 tptp_fun_B_5: $i)).
% 1.21/1.38 tff(tptp_fun_A_6_type, type, (
% 1.21/1.38 tptp_fun_A_6: $i)).
% 1.21/1.38 tff(in_type, type, (
% 1.21/1.38 in: ( $i * $i ) > $o)).
% 1.21/1.38 tff(unordered_pair_type, type, (
% 1.21/1.38 unordered_pair: ( $i * $i ) > $i)).
% 1.21/1.38 tff(tptp_fun_C_4_type, type, (
% 1.21/1.38 tptp_fun_C_4: $i)).
% 1.21/1.38 tff(singleton_type, type, (
% 1.21/1.38 singleton: $i > $i)).
% 1.21/1.38 tff(tptp_fun_C_0_type, type, (
% 1.21/1.38 tptp_fun_C_0: ( $i * $i ) > $i)).
% 1.21/1.38 tff(tptp_fun_D_1_type, type, (
% 1.21/1.38 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 1.21/1.38 tff(1,plain,
% 1.21/1.38 (^[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))))))))),
% 1.21/1.38 inference(bind,[status(th)],[])).
% 1.21/1.38 tff(2,plain,
% 1.21/1.38 (![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)))))))),
% 1.21/1.38 inference(quant_intro,[status(thm)],[1])).
% 1.21/1.38 tff(3,plain,
% 1.21/1.38 (![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)))))))),
% 1.21/1.38 inference(pull_quant,[status(thm)],[])).
% 1.21/1.38 tff(4,plain,
% 1.21/1.38 (^[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)))))))))),
% 1.21/1.38 inference(bind,[status(th)],[])).
% 1.21/1.38 tff(5,plain,
% 1.21/1.38 (![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)))))))),
% 1.21/1.38 inference(quant_intro,[status(thm)],[4])).
% 1.21/1.38 tff(6,plain,
% 1.21/1.38 (![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)))))))),
% 1.21/1.38 inference(transitivity,[status(thm)],[5, 3])).
% 1.21/1.38 tff(7,plain,
% 1.21/1.38 (![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)))))))),
% 1.21/1.38 inference(transitivity,[status(thm)],[6, 2])).
% 1.21/1.38 tff(8,plain,
% 1.21/1.38 (^[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))))))))),
% 1.21/1.38 inference(bind,[status(th)],[])).
% 1.21/1.38 tff(9,plain,
% 1.21/1.38 (![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)))))))),
% 1.21/1.38 inference(quant_intro,[status(thm)],[8])).
% 1.21/1.38 tff(10,plain,
% 1.21/1.38 (![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)))))))),
% 1.21/1.38 inference(transitivity,[status(thm)],[9, 7])).
% 1.21/1.38 tff(11,plain,
% 1.21/1.38 (^[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)))))))))),
% 1.21/1.38 inference(bind,[status(th)],[])).
% 1.21/1.38 tff(12,plain,
% 1.21/1.38 (![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)))))))),
% 1.21/1.38 inference(quant_intro,[status(thm)],[11])).
% 1.21/1.38 tff(13,plain,
% 1.21/1.38 (![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)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(14,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_tarski')).
% 1.21/1.38 tff(15,plain,
% 1.21/1.38 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[14, 13])).
% 1.21/1.38 tff(16,plain,(
% 1.21/1.38 ![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)))))),
% 1.21/1.38 inference(skolemize,[status(sab)],[15])).
% 1.21/1.38 tff(17,plain,
% 1.21/1.38 (![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)))))))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[16, 12])).
% 1.21/1.38 tff(18,plain,
% 1.21/1.38 (![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)))))))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[17, 10])).
% 1.21/1.38 tff(19,plain,
% 1.21/1.38 ((~![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)))))))) | (~((~((~(unordered_pair(B!5, C!4) = singleton(A!6))) | (in(B!5, unordered_pair(B!5, C!4)) <=> (B!5 = A!6)))) | (~((unordered_pair(B!5, C!4) = singleton(A!6)) | (~(in(tptp_fun_C_0(unordered_pair(B!5, C!4), A!6), unordered_pair(B!5, C!4)) <=> (tptp_fun_C_0(unordered_pair(B!5, C!4), A!6) = A!6)))))))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(20,plain,
% 1.21/1.38 (~((~((~(unordered_pair(B!5, C!4) = singleton(A!6))) | (in(B!5, unordered_pair(B!5, C!4)) <=> (B!5 = A!6)))) | (~((unordered_pair(B!5, C!4) = singleton(A!6)) | (~(in(tptp_fun_C_0(unordered_pair(B!5, C!4), A!6), unordered_pair(B!5, C!4)) <=> (tptp_fun_C_0(unordered_pair(B!5, C!4), A!6) = A!6))))))),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[19, 18])).
% 1.21/1.38 tff(21,plain,
% 1.21/1.38 (((~((~(unordered_pair(B!5, C!4) = singleton(A!6))) | (in(B!5, unordered_pair(B!5, C!4)) <=> (B!5 = A!6)))) | (~((unordered_pair(B!5, C!4) = singleton(A!6)) | (~(in(tptp_fun_C_0(unordered_pair(B!5, C!4), A!6), unordered_pair(B!5, C!4)) <=> (tptp_fun_C_0(unordered_pair(B!5, C!4), A!6) = A!6)))))) | ((~(unordered_pair(B!5, C!4) = singleton(A!6))) | (in(B!5, unordered_pair(B!5, C!4)) <=> (B!5 = A!6)))),
% 1.21/1.38 inference(tautology,[status(thm)],[])).
% 1.21/1.38 tff(22,plain,
% 1.21/1.38 ((~(unordered_pair(B!5, C!4) = singleton(A!6))) | (in(B!5, unordered_pair(B!5, C!4)) <=> (B!5 = A!6))),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[21, 20])).
% 1.21/1.38 tff(23,plain,
% 1.21/1.38 ((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))) <=> (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(24,plain,
% 1.21/1.38 ((~![A: $i, B: $i, C: $i] : ((singleton(A) = unordered_pair(B, C)) => (A = B))) <=> (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(25,axiom,(~![A: $i, B: $i, C: $i] : ((singleton(A) = unordered_pair(B, C)) => (A = B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t8_zfmisc_1')).
% 1.21/1.38 tff(26,plain,
% 1.21/1.38 (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[25, 24])).
% 1.21/1.38 tff(27,plain,
% 1.21/1.38 (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[26, 23])).
% 1.21/1.38 tff(28,plain,
% 1.21/1.38 (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[27, 23])).
% 1.21/1.38 tff(29,plain,
% 1.21/1.38 (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[28, 23])).
% 1.21/1.38 tff(30,plain,(
% 1.21/1.38 ~((~(singleton(A!6) = unordered_pair(B!5, C!4))) | (A!6 = B!5))),
% 1.21/1.38 inference(skolemize,[status(sab)],[29])).
% 1.21/1.38 tff(31,plain,
% 1.21/1.38 (singleton(A!6) = unordered_pair(B!5, C!4)),
% 1.21/1.38 inference(or_elim,[status(thm)],[30])).
% 1.21/1.38 tff(32,plain,
% 1.21/1.38 (unordered_pair(B!5, C!4) = singleton(A!6)),
% 1.21/1.38 inference(symmetry,[status(thm)],[31])).
% 1.21/1.38 tff(33,plain,
% 1.21/1.38 ((~((~(unordered_pair(B!5, C!4) = singleton(A!6))) | (in(B!5, unordered_pair(B!5, C!4)) <=> (B!5 = A!6)))) | (~(unordered_pair(B!5, C!4) = singleton(A!6))) | (in(B!5, unordered_pair(B!5, C!4)) <=> (B!5 = A!6))),
% 1.21/1.38 inference(tautology,[status(thm)],[])).
% 1.21/1.38 tff(34,plain,
% 1.21/1.38 ((~((~(unordered_pair(B!5, C!4) = singleton(A!6))) | (in(B!5, unordered_pair(B!5, C!4)) <=> (B!5 = A!6)))) | (in(B!5, unordered_pair(B!5, C!4)) <=> (B!5 = A!6))),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[33, 32])).
% 1.21/1.38 tff(35,plain,
% 1.21/1.38 (in(B!5, unordered_pair(B!5, C!4)) <=> (B!5 = A!6)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[34, 22])).
% 1.21/1.38 tff(36,assumption,(~in(B!5, unordered_pair(B!5, C!4))), introduced(assumption)).
% 1.21/1.38 tff(37,plain,
% 1.21/1.38 (^[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)))))))))),
% 1.21/1.38 inference(bind,[status(th)],[])).
% 1.21/1.38 tff(38,plain,
% 1.21/1.38 (![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_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))))))))),
% 1.21/1.38 inference(quant_intro,[status(thm)],[37])).
% 1.21/1.38 tff(39,plain,
% 1.21/1.38 (![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_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))))))))),
% 1.21/1.38 inference(pull_quant,[status(thm)],[])).
% 1.21/1.38 tff(40,plain,
% 1.21/1.38 (^[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))))))))))),
% 1.21/1.38 inference(bind,[status(th)],[])).
% 1.21/1.38 tff(41,plain,
% 1.21/1.38 (![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_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))))))))),
% 1.21/1.38 inference(quant_intro,[status(thm)],[40])).
% 1.21/1.38 tff(42,plain,
% 1.21/1.38 (![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_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))))))))),
% 1.21/1.38 inference(transitivity,[status(thm)],[41, 39])).
% 1.21/1.38 tff(43,plain,
% 1.21/1.38 (![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_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))))))))),
% 1.21/1.38 inference(transitivity,[status(thm)],[42, 38])).
% 1.21/1.38 tff(44,plain,
% 1.21/1.38 (^[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)))))))))),
% 1.21/1.38 inference(bind,[status(th)],[])).
% 1.21/1.38 tff(45,plain,
% 1.21/1.38 (![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_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))))))))),
% 1.21/1.38 inference(quant_intro,[status(thm)],[44])).
% 1.21/1.38 tff(46,plain,
% 1.21/1.38 (![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_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))))))))),
% 1.21/1.38 inference(transitivity,[status(thm)],[45, 43])).
% 1.21/1.38 tff(47,plain,
% 1.21/1.38 (^[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))))))))))),
% 1.21/1.38 inference(bind,[status(th)],[])).
% 1.21/1.38 tff(48,plain,
% 1.21/1.38 (![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_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))))))))),
% 1.21/1.38 inference(quant_intro,[status(thm)],[47])).
% 1.21/1.38 tff(49,plain,
% 1.21/1.38 (![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))))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(50,plain,
% 1.21/1.38 (^[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)))))),
% 1.21/1.38 inference(bind,[status(th)],[])).
% 1.21/1.38 tff(51,plain,
% 1.21/1.38 (![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))))),
% 1.21/1.38 inference(quant_intro,[status(thm)],[50])).
% 1.21/1.38 tff(52,axiom,(![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_tarski')).
% 1.21/1.38 tff(53,plain,
% 1.21/1.38 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[52, 51])).
% 1.21/1.38 tff(54,plain,
% 1.21/1.38 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[53, 49])).
% 1.21/1.38 tff(55,plain,(
% 1.21/1.38 ![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))),
% 1.21/1.38 inference(skolemize,[status(sab)],[54])).
% 1.21/1.38 tff(56,plain,
% 1.21/1.38 (![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[55, 48])).
% 1.21/1.38 tff(57,plain,
% 1.21/1.38 (![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[56, 46])).
% 1.21/1.38 tff(58,plain,
% 1.21/1.38 (((~![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | in(B!5, unordered_pair(B!5, C!4))) <=> ((~![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(B!5, unordered_pair(B!5, C!4)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(59,plain,
% 1.21/1.38 ((~(~in(B!5, unordered_pair(B!5, C!4)))) <=> in(B!5, unordered_pair(B!5, C!4))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(60,plain,
% 1.21/1.38 (((~in(B!5, unordered_pair(B!5, C!4))) | $false) <=> (~in(B!5, unordered_pair(B!5, C!4)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(61,plain,
% 1.21/1.38 ((~$true) <=> $false),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(62,plain,
% 1.21/1.38 (($true | (~(in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4)) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = B!5))))) <=> $true),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(63,plain,
% 1.21/1.38 ((~(in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4)) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = B!5)))) <=> (~(in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4)) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = B!5))))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(64,plain,
% 1.21/1.38 ((in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4)) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = B!5))) <=> (in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4)) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = B!5)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(65,plain,
% 1.21/1.38 ((~(in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4)) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = B!5)))) <=> (~(in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4)) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = B!5))))),
% 1.21/1.38 inference(monotonicity,[status(thm)],[64])).
% 1.21/1.38 tff(66,plain,
% 1.21/1.38 ((~(in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4)) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = B!5)))) <=> (~(in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4)) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = B!5))))),
% 1.21/1.38 inference(transitivity,[status(thm)],[65, 63])).
% 1.21/1.38 tff(67,plain,
% 1.21/1.38 ((unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4)) <=> $true),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(68,plain,
% 1.21/1.38 (((unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4)) | (~(in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4)) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = B!5))))) <=> ($true | (~(in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4)) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = B!5)))))),
% 1.21/1.38 inference(monotonicity,[status(thm)],[67, 66])).
% 1.21/1.38 tff(69,plain,
% 1.21/1.38 (((unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4)) | (~(in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4)) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = B!5))))) <=> $true),
% 1.21/1.38 inference(transitivity,[status(thm)],[68, 62])).
% 1.21/1.38 tff(70,plain,
% 1.21/1.38 ((~((unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4)) | (~(in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4)) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = B!5)))))) <=> (~$true)),
% 1.21/1.38 inference(monotonicity,[status(thm)],[69])).
% 1.21/1.38 tff(71,plain,
% 1.21/1.38 ((~((unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4)) | (~(in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4)) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = B!5)))))) <=> $false),
% 1.21/1.38 inference(transitivity,[status(thm)],[70, 61])).
% 1.21/1.38 tff(72,plain,
% 1.21/1.38 ((~((~(unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4))) | (in(B!5, unordered_pair(B!5, C!4)) <=> ((B!5 = C!4) | (B!5 = B!5))))) <=> (~in(B!5, unordered_pair(B!5, C!4)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(73,plain,
% 1.21/1.38 (((~((~(unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4))) | (in(B!5, unordered_pair(B!5, C!4)) <=> ((B!5 = C!4) | (B!5 = B!5))))) | (~((unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4)) | (~(in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4)) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = B!5))))))) <=> ((~in(B!5, unordered_pair(B!5, C!4))) | $false)),
% 1.21/1.38 inference(monotonicity,[status(thm)],[72, 71])).
% 1.21/1.38 tff(74,plain,
% 1.21/1.38 (((~((~(unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4))) | (in(B!5, unordered_pair(B!5, C!4)) <=> ((B!5 = C!4) | (B!5 = B!5))))) | (~((unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4)) | (~(in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4)) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = B!5))))))) <=> (~in(B!5, unordered_pair(B!5, C!4)))),
% 1.21/1.38 inference(transitivity,[status(thm)],[73, 60])).
% 1.21/1.38 tff(75,plain,
% 1.21/1.38 ((~((~((~(unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4))) | (in(B!5, unordered_pair(B!5, C!4)) <=> ((B!5 = C!4) | (B!5 = B!5))))) | (~((unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4)) | (~(in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4)) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = B!5)))))))) <=> (~(~in(B!5, unordered_pair(B!5, C!4))))),
% 1.21/1.38 inference(monotonicity,[status(thm)],[74])).
% 1.21/1.38 tff(76,plain,
% 1.21/1.38 ((~((~((~(unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4))) | (in(B!5, unordered_pair(B!5, C!4)) <=> ((B!5 = C!4) | (B!5 = B!5))))) | (~((unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4)) | (~(in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4)) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = B!5)))))))) <=> in(B!5, unordered_pair(B!5, C!4))),
% 1.21/1.38 inference(transitivity,[status(thm)],[75, 59])).
% 1.21/1.38 tff(77,plain,
% 1.21/1.38 (((~![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4))) | (in(B!5, unordered_pair(B!5, C!4)) <=> ((B!5 = C!4) | (B!5 = B!5))))) | (~((unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4)) | (~(in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4)) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, 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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | in(B!5, unordered_pair(B!5, C!4)))),
% 1.21/1.38 inference(monotonicity,[status(thm)],[76])).
% 1.21/1.38 tff(78,plain,
% 1.21/1.38 (((~![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4))) | (in(B!5, unordered_pair(B!5, C!4)) <=> ((B!5 = C!4) | (B!5 = B!5))))) | (~((unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4)) | (~(in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4)) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, 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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | in(B!5, unordered_pair(B!5, C!4)))),
% 1.21/1.39 inference(transitivity,[status(thm)],[77, 58])).
% 1.21/1.39 tff(79,plain,
% 1.21/1.39 ((~![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))))))))) | (~((~((~(unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4))) | (in(B!5, unordered_pair(B!5, C!4)) <=> ((B!5 = C!4) | (B!5 = B!5))))) | (~((unordered_pair(B!5, C!4) = unordered_pair(B!5, C!4)) | (~(in(tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5), unordered_pair(B!5, C!4)) <=> ((tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = C!4) | (tptp_fun_D_1(unordered_pair(B!5, C!4), C!4, B!5) = B!5))))))))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(80,plain,
% 1.21/1.39 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | in(B!5, unordered_pair(B!5, C!4))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[79, 78])).
% 1.21/1.39 tff(81,plain,
% 1.21/1.39 ($false),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[80, 57, 36])).
% 1.21/1.39 tff(82,plain,(in(B!5, unordered_pair(B!5, C!4))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.39 tff(83,plain,
% 1.21/1.39 ((~(in(B!5, unordered_pair(B!5, C!4)) <=> (B!5 = A!6))) | (~in(B!5, unordered_pair(B!5, C!4))) | (B!5 = A!6)),
% 1.21/1.39 inference(tautology,[status(thm)],[])).
% 1.21/1.39 tff(84,plain,
% 1.21/1.39 ((~(in(B!5, unordered_pair(B!5, C!4)) <=> (B!5 = A!6))) | (B!5 = A!6)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[83, 82])).
% 1.21/1.39 tff(85,plain,
% 1.21/1.39 (B!5 = A!6),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[84, 35])).
% 1.21/1.39 tff(86,plain,
% 1.21/1.39 (A!6 = B!5),
% 1.21/1.39 inference(symmetry,[status(thm)],[85])).
% 1.21/1.39 tff(87,plain,
% 1.21/1.39 (~(A!6 = B!5)),
% 1.21/1.39 inference(or_elim,[status(thm)],[30])).
% 1.21/1.39 tff(88,plain,
% 1.21/1.39 ($false),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[87, 86])).
% 1.21/1.39 % SZS output end Proof
% 1.21/1.39 % E exiting
%------------------------------------------------------------------------------