%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU267+1 : TPTP v9.0.0. Released v3.3.0.
% 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 05:27:26 AM UTC 2025
% Result : Theorem 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU267+1 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n009.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 06:32:48 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 % SZS output start Proof
% 0.19/0.43 tff(pair_second_type, type, (
% 0.19/0.43 pair_second: $i > $i)).
% 0.19/0.43 tff(ordered_pair_type, type, (
% 0.19/0.43 ordered_pair: ( $i * $i ) > $i)).
% 0.19/0.43 tff(tptp_fun_B_3_type, type, (
% 0.19/0.43 tptp_fun_B_3: $i)).
% 0.19/0.43 tff(tptp_fun_A_4_type, type, (
% 0.19/0.43 tptp_fun_A_4: $i)).
% 0.19/0.43 tff(tptp_fun_D_7_type, type, (
% 0.19/0.43 tptp_fun_D_7: ( $i * $i ) > $i)).
% 0.19/0.43 tff(tptp_fun_C_8_type, type, (
% 0.19/0.43 tptp_fun_C_8: ( $i * $i ) > $i)).
% 0.19/0.43 tff(pair_first_type, type, (
% 0.19/0.43 pair_first: $i > $i)).
% 0.19/0.43 tff(tptp_fun_C_6_type, type, (
% 0.19/0.43 tptp_fun_C_6: ( $i * $i ) > $i)).
% 0.19/0.43 tff(tptp_fun_D_5_type, type, (
% 0.19/0.43 tptp_fun_D_5: ( $i * $i ) > $i)).
% 0.19/0.43 tff(1,plain,
% 0.19/0.43 (((~![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C)))) | $false) <=> (~![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(2,plain,
% 0.19/0.43 ((~$true) <=> $false),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(3,plain,
% 0.19/0.43 ((ordered_pair(A!4, B!3) = ordered_pair(A!4, B!3)) <=> $true),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(4,plain,
% 0.19/0.43 ((~(ordered_pair(A!4, B!3) = ordered_pair(A!4, B!3))) <=> (~$true)),
% 0.19/0.43 inference(monotonicity,[status(thm)],[3])).
% 0.19/0.43 tff(5,plain,
% 0.19/0.43 ((~(ordered_pair(A!4, B!3) = ordered_pair(A!4, B!3))) <=> $false),
% 0.19/0.43 inference(transitivity,[status(thm)],[4, 2])).
% 0.19/0.43 tff(6,plain,
% 0.19/0.43 (((~![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C)))) | (~(ordered_pair(A!4, B!3) = ordered_pair(A!4, B!3)))) <=> ((~![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C)))) | $false)),
% 0.19/0.43 inference(monotonicity,[status(thm)],[5])).
% 0.19/0.43 tff(7,plain,
% 0.19/0.43 (((~![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C)))) | (~(ordered_pair(A!4, B!3) = ordered_pair(A!4, B!3)))) <=> (~![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[6, 1])).
% 0.19/0.43 tff(8,plain,
% 0.19/0.43 ((~![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C)))) | (~(ordered_pair(A!4, B!3) = ordered_pair(A!4, B!3)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(9,plain,
% 0.19/0.43 (~![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.19/0.43 tff(10,assumption,(![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C)))), introduced(assumption)).
% 0.19/0.43 tff(11,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[10, 9])).
% 0.19/0.43 tff(12,plain,(~![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(13,plain,
% 0.19/0.43 (^[A: $i] : refl((![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A))))))))) <=> (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A))))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(14,plain,
% 0.19/0.43 (![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A))))))))) <=> ![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A)))))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.43 tff(15,plain,
% 0.19/0.43 (^[A: $i] : rewrite((![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A))))))))) <=> (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A))))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(16,plain,
% 0.19/0.44 (![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A))))))))) <=> ![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A)))))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.44 tff(17,plain,
% 0.19/0.44 (![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A))))))))) <=> ![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A)))))))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[16, 14])).
% 0.19/0.44 tff(18,plain,
% 0.19/0.44 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite(((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D))) <=> ((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D)))), rewrite(((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A))))) <=> ((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A)))))), ((((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D))) & ((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A)))))) <=> (((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D))) & ((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A)))))))), rewrite((((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D))) & ((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A)))))) <=> (~((~((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A))))))))), ((((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D))) & ((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A)))))) <=> (~((~((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A))))))))))), (![B: $i] : (((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D))) & ((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A)))))) <=> ![B: $i] : (~((~((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A)))))))))), ((![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D))) & ((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A))))))) <=> (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A))))))))))), rewrite((![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A))))))))) <=> (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A)))))))))), ((![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D))) & ((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A))))))) <=> (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A)))))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(19,plain,
% 0.19/0.44 (![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D))) & ((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A))))))) <=> ![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A)))))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[18])).
% 0.19/0.44 tff(20,plain,
% 0.19/0.44 (![A: $i] : ((~?[B: $i, C: $i] : (A = ordered_pair(B, C))) | ![B: $i] : ((B = pair_second(A)) <=> ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D)))) <=> ![A: $i] : ((~?[B: $i, C: $i] : (A = ordered_pair(B, C))) | ![B: $i] : ((B = pair_second(A)) <=> ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(21,plain,
% 0.19/0.44 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite(((B = pair_second(A)) <=> ![C: $i, D: $i] : ((A = ordered_pair(C, D)) => (B = D))) <=> ((B = pair_second(A)) <=> ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D))))), (![B: $i] : ((B = pair_second(A)) <=> ![C: $i, D: $i] : ((A = ordered_pair(C, D)) => (B = D))) <=> ![B: $i] : ((B = pair_second(A)) <=> ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D))))), ((?[B: $i, C: $i] : (A = ordered_pair(B, C)) => ![B: $i] : ((B = pair_second(A)) <=> ![C: $i, D: $i] : ((A = ordered_pair(C, D)) => (B = D)))) <=> (?[B: $i, C: $i] : (A = ordered_pair(B, C)) => ![B: $i] : ((B = pair_second(A)) <=> ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D)))))), rewrite((?[B: $i, C: $i] : (A = ordered_pair(B, C)) => ![B: $i] : ((B = pair_second(A)) <=> ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D)))) <=> ((~?[B: $i, C: $i] : (A = ordered_pair(B, C))) | ![B: $i] : ((B = pair_second(A)) <=> ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D))))), ((?[B: $i, C: $i] : (A = ordered_pair(B, C)) => ![B: $i] : ((B = pair_second(A)) <=> ![C: $i, D: $i] : ((A = ordered_pair(C, D)) => (B = D)))) <=> ((~?[B: $i, C: $i] : (A = ordered_pair(B, C))) | ![B: $i] : ((B = pair_second(A)) <=> ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(22,plain,
% 0.19/0.44 (![A: $i] : (?[B: $i, C: $i] : (A = ordered_pair(B, C)) => ![B: $i] : ((B = pair_second(A)) <=> ![C: $i, D: $i] : ((A = ordered_pair(C, D)) => (B = D)))) <=> ![A: $i] : ((~?[B: $i, C: $i] : (A = ordered_pair(B, C))) | ![B: $i] : ((B = pair_second(A)) <=> ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[21])).
% 0.19/0.44 tff(23,axiom,(![A: $i] : (?[B: $i, C: $i] : (A = ordered_pair(B, C)) => ![B: $i] : ((B = pair_second(A)) <=> ![C: $i, D: $i] : ((A = ordered_pair(C, D)) => (B = D))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_mcart_1')).
% 0.19/0.44 tff(24,plain,
% 0.19/0.44 (![A: $i] : ((~?[B: $i, C: $i] : (A = ordered_pair(B, C))) | ![B: $i] : ((B = pair_second(A)) <=> ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.19/0.44 tff(25,plain,
% 0.19/0.44 (![A: $i] : ((~?[B: $i, C: $i] : (A = ordered_pair(B, C))) | ![B: $i] : ((B = pair_second(A)) <=> ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.19/0.44 tff(26,plain,(
% 0.19/0.44 ![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D))) & ((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A)))))))),
% 0.19/0.44 inference(skolemize,[status(sab)],[25])).
% 0.19/0.44 tff(27,plain,
% 0.19/0.44 (![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A)))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.19/0.44 tff(28,plain,
% 0.19/0.44 (![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A)))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.19/0.44 tff(29,plain,
% 0.19/0.44 (((~![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A)))))))))) | (![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = D)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(B, ordered_pair(A!4, B!3)), tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = pair_second(ordered_pair(A!4, B!3))))))))) <=> ((~![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A)))))))))) | ![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = D)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(B, ordered_pair(A!4, B!3)), tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = pair_second(ordered_pair(A!4, B!3))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(30,plain,
% 0.19/0.44 ((![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = D)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(B, ordered_pair(A!4, B!3)), tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = pair_second(ordered_pair(A!4, B!3)))))))) <=> (![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = D)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(B, ordered_pair(A!4, B!3)), tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = pair_second(ordered_pair(A!4, B!3))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(31,plain,
% 0.19/0.44 (^[B: $i] : rewrite((~((~((~(B = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(ordered_pair(A!4, B!3))) | (~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(B, ordered_pair(A!4, B!3)), tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_D_7(B, ordered_pair(A!4, B!3))))))))) <=> (~((~((~(B = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = D)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(B, ordered_pair(A!4, B!3)), tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = pair_second(ordered_pair(A!4, B!3))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(32,plain,
% 0.19/0.44 (![B: $i] : (~((~((~(B = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(ordered_pair(A!4, B!3))) | (~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(B, ordered_pair(A!4, B!3)), tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_D_7(B, ordered_pair(A!4, B!3))))))))) <=> ![B: $i] : (~((~((~(B = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = D)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(B, ordered_pair(A!4, B!3)), tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = pair_second(ordered_pair(A!4, B!3)))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[31])).
% 0.19/0.44 tff(33,plain,
% 0.19/0.44 ((![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(ordered_pair(A!4, B!3))) | (~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(B, ordered_pair(A!4, B!3)), tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_D_7(B, ordered_pair(A!4, B!3)))))))))) <=> (![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = D)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(B, ordered_pair(A!4, B!3)), tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = pair_second(ordered_pair(A!4, B!3))))))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[32])).
% 0.19/0.44 tff(34,plain,
% 0.19/0.44 ((![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(ordered_pair(A!4, B!3))) | (~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(B, ordered_pair(A!4, B!3)), tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_D_7(B, ordered_pair(A!4, B!3)))))))))) <=> (![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = D)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(B, ordered_pair(A!4, B!3)), tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = pair_second(ordered_pair(A!4, B!3))))))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[33, 30])).
% 0.19/0.44 tff(35,plain,
% 0.19/0.44 (((~![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A)))))))))) | (![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(ordered_pair(A!4, B!3))) | (~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(B, ordered_pair(A!4, B!3)), tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_D_7(B, ordered_pair(A!4, B!3))))))))))) <=> ((~![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A)))))))))) | (![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = D)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(B, ordered_pair(A!4, B!3)), tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = pair_second(ordered_pair(A!4, B!3)))))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[34])).
% 0.19/0.45 tff(36,plain,
% 0.19/0.45 (((~![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A)))))))))) | (![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(ordered_pair(A!4, B!3))) | (~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(B, ordered_pair(A!4, B!3)), tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_D_7(B, ordered_pair(A!4, B!3))))))))))) <=> ((~![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A)))))))))) | ![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = D)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(B, ordered_pair(A!4, B!3)), tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = pair_second(ordered_pair(A!4, B!3))))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[35, 29])).
% 0.19/0.45 tff(37,plain,
% 0.19/0.45 ((~![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A)))))))))) | (![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(ordered_pair(A!4, B!3))) | (~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(B, ordered_pair(A!4, B!3)), tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_D_7(B, ordered_pair(A!4, B!3))))))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(38,plain,
% 0.19/0.45 ((~![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = D)))) | (~((B = pair_second(A)) | (~((~(A = ordered_pair(tptp_fun_C_8(B, A), tptp_fun_D_7(B, A)))) | (B = tptp_fun_D_7(B, A)))))))))) | ![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = D)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(B, ordered_pair(A!4, B!3)), tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = pair_second(ordered_pair(A!4, B!3)))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.45 tff(39,plain,
% 0.19/0.45 (![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = D)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(B, ordered_pair(A!4, B!3)), tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = pair_second(ordered_pair(A!4, B!3)))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[38, 28])).
% 0.19/0.45 tff(40,plain,
% 0.19/0.45 (![B: $i] : (~((~((~(B = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = D)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(B, ordered_pair(A!4, B!3)), tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = pair_second(ordered_pair(A!4, B!3)))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[39, 12])).
% 0.19/0.45 tff(41,plain,
% 0.19/0.45 (((~![B: $i] : (~((~((~(B = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = D)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(B, ordered_pair(A!4, B!3)), tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = pair_second(ordered_pair(A!4, B!3)))))))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_second(ordered_pair(A!4, B!3)) = D))) <=> ((~![B: $i] : (~((~((~(B = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = D)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(B, ordered_pair(A!4, B!3)), tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = pair_second(ordered_pair(A!4, B!3)))))))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_second(ordered_pair(A!4, B!3)) = D)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(42,plain,
% 0.19/0.45 ((~(~![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_second(ordered_pair(A!4, B!3)) = D)))) <=> ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_second(ordered_pair(A!4, B!3)) = D))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(43,plain,
% 0.19/0.45 (((~![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_second(ordered_pair(A!4, B!3)) = D))) | $false) <=> (~![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_second(ordered_pair(A!4, B!3)) = D)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(44,plain,
% 0.19/0.45 (((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3)), tptp_fun_D_7(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_second(ordered_pair(A!4, B!3)) = tptp_fun_D_7(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | $true) <=> $true),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(45,plain,
% 0.19/0.45 ((pair_second(ordered_pair(A!4, B!3)) = pair_second(ordered_pair(A!4, B!3))) <=> $true),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(46,plain,
% 0.19/0.45 (((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3)), tptp_fun_D_7(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_second(ordered_pair(A!4, B!3)) = tptp_fun_D_7(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_second(ordered_pair(A!4, B!3)) = pair_second(ordered_pair(A!4, B!3)))) <=> ((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3)), tptp_fun_D_7(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_second(ordered_pair(A!4, B!3)) = tptp_fun_D_7(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | $true)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[45])).
% 0.19/0.45 tff(47,plain,
% 0.19/0.45 (((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3)), tptp_fun_D_7(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_second(ordered_pair(A!4, B!3)) = tptp_fun_D_7(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_second(ordered_pair(A!4, B!3)) = pair_second(ordered_pair(A!4, B!3)))) <=> $true),
% 0.19/0.45 inference(transitivity,[status(thm)],[46, 44])).
% 0.19/0.45 tff(48,plain,
% 0.19/0.45 ((~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3)), tptp_fun_D_7(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_second(ordered_pair(A!4, B!3)) = tptp_fun_D_7(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_second(ordered_pair(A!4, B!3)) = pair_second(ordered_pair(A!4, B!3))))) <=> (~$true)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[47])).
% 0.19/0.45 tff(49,plain,
% 0.19/0.45 ((~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3)), tptp_fun_D_7(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_second(ordered_pair(A!4, B!3)) = tptp_fun_D_7(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_second(ordered_pair(A!4, B!3)) = pair_second(ordered_pair(A!4, B!3))))) <=> $false),
% 0.19/0.45 inference(transitivity,[status(thm)],[48, 2])).
% 0.19/0.45 tff(50,plain,
% 0.19/0.45 ((~((~(pair_second(ordered_pair(A!4, B!3)) = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_second(ordered_pair(A!4, B!3)) = D)))) <=> (~![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_second(ordered_pair(A!4, B!3)) = D)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(51,plain,
% 0.19/0.45 (((~((~(pair_second(ordered_pair(A!4, B!3)) = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_second(ordered_pair(A!4, B!3)) = D)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3)), tptp_fun_D_7(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_second(ordered_pair(A!4, B!3)) = tptp_fun_D_7(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_second(ordered_pair(A!4, B!3)) = pair_second(ordered_pair(A!4, B!3)))))) <=> ((~![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_second(ordered_pair(A!4, B!3)) = D))) | $false)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[50, 49])).
% 0.19/0.45 tff(52,plain,
% 0.19/0.45 (((~((~(pair_second(ordered_pair(A!4, B!3)) = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_second(ordered_pair(A!4, B!3)) = D)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3)), tptp_fun_D_7(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_second(ordered_pair(A!4, B!3)) = tptp_fun_D_7(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_second(ordered_pair(A!4, B!3)) = pair_second(ordered_pair(A!4, B!3)))))) <=> (~![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_second(ordered_pair(A!4, B!3)) = D)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[51, 43])).
% 0.19/0.45 tff(53,plain,
% 0.19/0.45 ((~((~((~(pair_second(ordered_pair(A!4, B!3)) = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_second(ordered_pair(A!4, B!3)) = D)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3)), tptp_fun_D_7(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_second(ordered_pair(A!4, B!3)) = tptp_fun_D_7(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_second(ordered_pair(A!4, B!3)) = pair_second(ordered_pair(A!4, B!3))))))) <=> (~(~![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_second(ordered_pair(A!4, B!3)) = D))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[52])).
% 0.19/0.45 tff(54,plain,
% 0.19/0.45 ((~((~((~(pair_second(ordered_pair(A!4, B!3)) = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_second(ordered_pair(A!4, B!3)) = D)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3)), tptp_fun_D_7(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_second(ordered_pair(A!4, B!3)) = tptp_fun_D_7(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_second(ordered_pair(A!4, B!3)) = pair_second(ordered_pair(A!4, B!3))))))) <=> ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_second(ordered_pair(A!4, B!3)) = D))),
% 0.19/0.45 inference(transitivity,[status(thm)],[53, 42])).
% 0.19/0.45 tff(55,plain,
% 0.19/0.45 (((~![B: $i] : (~((~((~(B = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = D)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(B, ordered_pair(A!4, B!3)), tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = pair_second(ordered_pair(A!4, B!3)))))))) | (~((~((~(pair_second(ordered_pair(A!4, B!3)) = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_second(ordered_pair(A!4, B!3)) = D)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3)), tptp_fun_D_7(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_second(ordered_pair(A!4, B!3)) = tptp_fun_D_7(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_second(ordered_pair(A!4, B!3)) = pair_second(ordered_pair(A!4, B!3)))))))) <=> ((~![B: $i] : (~((~((~(B = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = D)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(B, ordered_pair(A!4, B!3)), tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = pair_second(ordered_pair(A!4, B!3)))))))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_second(ordered_pair(A!4, B!3)) = D)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[54])).
% 0.19/0.45 tff(56,plain,
% 0.19/0.45 (((~![B: $i] : (~((~((~(B = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = D)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(B, ordered_pair(A!4, B!3)), tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = pair_second(ordered_pair(A!4, B!3)))))))) | (~((~((~(pair_second(ordered_pair(A!4, B!3)) = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_second(ordered_pair(A!4, B!3)) = D)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3)), tptp_fun_D_7(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_second(ordered_pair(A!4, B!3)) = tptp_fun_D_7(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_second(ordered_pair(A!4, B!3)) = pair_second(ordered_pair(A!4, B!3)))))))) <=> ((~![B: $i] : (~((~((~(B = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = D)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(B, ordered_pair(A!4, B!3)), tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = pair_second(ordered_pair(A!4, B!3)))))))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_second(ordered_pair(A!4, B!3)) = D)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[55, 41])).
% 0.19/0.46 tff(57,plain,
% 0.19/0.46 ((~![B: $i] : (~((~((~(B = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = D)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(B, ordered_pair(A!4, B!3)), tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = pair_second(ordered_pair(A!4, B!3)))))))) | (~((~((~(pair_second(ordered_pair(A!4, B!3)) = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_second(ordered_pair(A!4, B!3)) = D)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3)), tptp_fun_D_7(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_second(ordered_pair(A!4, B!3)) = tptp_fun_D_7(pair_second(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_second(ordered_pair(A!4, B!3)) = pair_second(ordered_pair(A!4, B!3)))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(58,plain,
% 0.19/0.46 ((~![B: $i] : (~((~((~(B = pair_second(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = D)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_8(B, ordered_pair(A!4, B!3)), tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_D_7(B, ordered_pair(A!4, B!3))))) | (B = pair_second(ordered_pair(A!4, B!3)))))))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_second(ordered_pair(A!4, B!3)) = D))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.19/0.46 tff(59,plain,
% 0.19/0.46 (![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_second(ordered_pair(A!4, B!3)) = D))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[58, 40])).
% 0.19/0.46 tff(60,plain,
% 0.19/0.46 (^[A: $i] : refl((![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A))))))))) <=> (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A))))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(61,plain,
% 0.19/0.46 (![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A))))))))) <=> ![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A)))))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[60])).
% 0.19/0.46 tff(62,plain,
% 0.19/0.46 (^[A: $i] : rewrite((![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A))))))))) <=> (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A))))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(63,plain,
% 0.19/0.46 (![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A))))))))) <=> ![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A)))))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[62])).
% 0.19/0.46 tff(64,plain,
% 0.19/0.46 (![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A))))))))) <=> ![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A)))))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[63, 61])).
% 0.19/0.46 tff(65,plain,
% 0.19/0.46 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite(((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C))) <=> ((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C)))), rewrite(((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A))))) <=> ((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A)))))), ((((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C))) & ((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A)))))) <=> (((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C))) & ((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A)))))))), rewrite((((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C))) & ((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A)))))) <=> (~((~((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A))))))))), ((((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C))) & ((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A)))))) <=> (~((~((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A))))))))))), (![B: $i] : (((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C))) & ((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A)))))) <=> ![B: $i] : (~((~((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A)))))))))), ((![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C))) & ((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A))))))) <=> (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A))))))))))), rewrite((![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A))))))))) <=> (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A)))))))))), ((![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C))) & ((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A))))))) <=> (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A)))))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(66,plain,
% 0.19/0.46 (![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C))) & ((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A))))))) <=> ![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A)))))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.46 tff(67,plain,
% 0.19/0.46 (![A: $i] : ((~?[B: $i, C: $i] : (A = ordered_pair(B, C))) | ![B: $i] : ((B = pair_first(A)) <=> ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C)))) <=> ![A: $i] : ((~?[B: $i, C: $i] : (A = ordered_pair(B, C))) | ![B: $i] : ((B = pair_first(A)) <=> ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(68,plain,
% 0.19/0.46 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite(((B = pair_first(A)) <=> ![C: $i, D: $i] : ((A = ordered_pair(C, D)) => (B = C))) <=> ((B = pair_first(A)) <=> ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C))))), (![B: $i] : ((B = pair_first(A)) <=> ![C: $i, D: $i] : ((A = ordered_pair(C, D)) => (B = C))) <=> ![B: $i] : ((B = pair_first(A)) <=> ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C))))), ((?[B: $i, C: $i] : (A = ordered_pair(B, C)) => ![B: $i] : ((B = pair_first(A)) <=> ![C: $i, D: $i] : ((A = ordered_pair(C, D)) => (B = C)))) <=> (?[B: $i, C: $i] : (A = ordered_pair(B, C)) => ![B: $i] : ((B = pair_first(A)) <=> ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C)))))), rewrite((?[B: $i, C: $i] : (A = ordered_pair(B, C)) => ![B: $i] : ((B = pair_first(A)) <=> ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C)))) <=> ((~?[B: $i, C: $i] : (A = ordered_pair(B, C))) | ![B: $i] : ((B = pair_first(A)) <=> ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C))))), ((?[B: $i, C: $i] : (A = ordered_pair(B, C)) => ![B: $i] : ((B = pair_first(A)) <=> ![C: $i, D: $i] : ((A = ordered_pair(C, D)) => (B = C)))) <=> ((~?[B: $i, C: $i] : (A = ordered_pair(B, C))) | ![B: $i] : ((B = pair_first(A)) <=> ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(69,plain,
% 0.19/0.46 (![A: $i] : (?[B: $i, C: $i] : (A = ordered_pair(B, C)) => ![B: $i] : ((B = pair_first(A)) <=> ![C: $i, D: $i] : ((A = ordered_pair(C, D)) => (B = C)))) <=> ![A: $i] : ((~?[B: $i, C: $i] : (A = ordered_pair(B, C))) | ![B: $i] : ((B = pair_first(A)) <=> ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[68])).
% 0.19/0.46 tff(70,axiom,(![A: $i] : (?[B: $i, C: $i] : (A = ordered_pair(B, C)) => ![B: $i] : ((B = pair_first(A)) <=> ![C: $i, D: $i] : ((A = ordered_pair(C, D)) => (B = C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_mcart_1')).
% 0.19/0.46 tff(71,plain,
% 0.19/0.46 (![A: $i] : ((~?[B: $i, C: $i] : (A = ordered_pair(B, C))) | ![B: $i] : ((B = pair_first(A)) <=> ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.19/0.46 tff(72,plain,
% 0.19/0.46 (![A: $i] : ((~?[B: $i, C: $i] : (A = ordered_pair(B, C))) | ![B: $i] : ((B = pair_first(A)) <=> ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.19/0.46 tff(73,plain,(
% 0.19/0.46 ![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C))) & ((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A)))))))),
% 0.19/0.46 inference(skolemize,[status(sab)],[72])).
% 0.19/0.46 tff(74,plain,
% 0.19/0.46 (![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A)))))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.19/0.46 tff(75,plain,
% 0.19/0.46 (![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A)))))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[74, 64])).
% 0.19/0.46 tff(76,plain,
% 0.19/0.46 (((~![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A)))))))))) | (![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = C)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(B, ordered_pair(A!4, B!3)), tptp_fun_D_5(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_C_6(B, ordered_pair(A!4, B!3))))) | (B = pair_first(ordered_pair(A!4, B!3))))))))) <=> ((~![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A)))))))))) | ![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = C)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(B, ordered_pair(A!4, B!3)), tptp_fun_D_5(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_C_6(B, ordered_pair(A!4, B!3))))) | (B = pair_first(ordered_pair(A!4, B!3))))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(77,plain,
% 0.19/0.46 ((![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = C)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(B, ordered_pair(A!4, B!3)), tptp_fun_D_5(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_C_6(B, ordered_pair(A!4, B!3))))) | (B = pair_first(ordered_pair(A!4, B!3)))))))) <=> (![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = C)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(B, ordered_pair(A!4, B!3)), tptp_fun_D_5(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_C_6(B, ordered_pair(A!4, B!3))))) | (B = pair_first(ordered_pair(A!4, B!3))))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(78,plain,
% 0.19/0.46 (^[B: $i] : rewrite((~((~((~(B = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(ordered_pair(A!4, B!3))) | (~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(B, ordered_pair(A!4, B!3)), tptp_fun_D_5(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_C_6(B, ordered_pair(A!4, B!3))))))))) <=> (~((~((~(B = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = C)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(B, ordered_pair(A!4, B!3)), tptp_fun_D_5(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_C_6(B, ordered_pair(A!4, B!3))))) | (B = pair_first(ordered_pair(A!4, B!3))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(79,plain,
% 0.19/0.46 (![B: $i] : (~((~((~(B = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(ordered_pair(A!4, B!3))) | (~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(B, ordered_pair(A!4, B!3)), tptp_fun_D_5(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_C_6(B, ordered_pair(A!4, B!3))))))))) <=> ![B: $i] : (~((~((~(B = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = C)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(B, ordered_pair(A!4, B!3)), tptp_fun_D_5(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_C_6(B, ordered_pair(A!4, B!3))))) | (B = pair_first(ordered_pair(A!4, B!3)))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[78])).
% 0.19/0.46 tff(80,plain,
% 0.19/0.46 ((![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(ordered_pair(A!4, B!3))) | (~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(B, ordered_pair(A!4, B!3)), tptp_fun_D_5(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_C_6(B, ordered_pair(A!4, B!3)))))))))) <=> (![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = C)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(B, ordered_pair(A!4, B!3)), tptp_fun_D_5(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_C_6(B, ordered_pair(A!4, B!3))))) | (B = pair_first(ordered_pair(A!4, B!3))))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[79])).
% 0.19/0.46 tff(81,plain,
% 0.19/0.46 ((![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(ordered_pair(A!4, B!3))) | (~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(B, ordered_pair(A!4, B!3)), tptp_fun_D_5(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_C_6(B, ordered_pair(A!4, B!3)))))))))) <=> (![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = C)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(B, ordered_pair(A!4, B!3)), tptp_fun_D_5(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_C_6(B, ordered_pair(A!4, B!3))))) | (B = pair_first(ordered_pair(A!4, B!3))))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[80, 77])).
% 0.19/0.46 tff(82,plain,
% 0.19/0.46 (((~![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A)))))))))) | (![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(ordered_pair(A!4, B!3))) | (~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(B, ordered_pair(A!4, B!3)), tptp_fun_D_5(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_C_6(B, ordered_pair(A!4, B!3))))))))))) <=> ((~![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A)))))))))) | (![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = C)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(B, ordered_pair(A!4, B!3)), tptp_fun_D_5(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_C_6(B, ordered_pair(A!4, B!3))))) | (B = pair_first(ordered_pair(A!4, B!3)))))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[81])).
% 0.19/0.46 tff(83,plain,
% 0.19/0.46 (((~![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A)))))))))) | (![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(ordered_pair(A!4, B!3))) | (~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(B, ordered_pair(A!4, B!3)), tptp_fun_D_5(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_C_6(B, ordered_pair(A!4, B!3))))))))))) <=> ((~![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A)))))))))) | ![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = C)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(B, ordered_pair(A!4, B!3)), tptp_fun_D_5(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_C_6(B, ordered_pair(A!4, B!3))))) | (B = pair_first(ordered_pair(A!4, B!3))))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[82, 76])).
% 0.19/0.46 tff(84,plain,
% 0.19/0.46 ((~![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A)))))))))) | (![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(ordered_pair(A!4, B!3))) | (~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(B, ordered_pair(A!4, B!3)), tptp_fun_D_5(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_C_6(B, ordered_pair(A!4, B!3))))))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(85,plain,
% 0.19/0.46 ((~![A: $i] : (![B: $i, C: $i] : (~(A = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(A))) | ![C: $i, D: $i] : ((~(A = ordered_pair(C, D))) | (B = C)))) | (~((B = pair_first(A)) | (~((~(A = ordered_pair(tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (B = tptp_fun_C_6(B, A)))))))))) | ![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = C)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(B, ordered_pair(A!4, B!3)), tptp_fun_D_5(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_C_6(B, ordered_pair(A!4, B!3))))) | (B = pair_first(ordered_pair(A!4, B!3)))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.19/0.47 tff(86,plain,
% 0.19/0.47 (![B: $i, C: $i] : (~(ordered_pair(A!4, B!3) = ordered_pair(B, C))) | ![B: $i] : (~((~((~(B = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = C)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(B, ordered_pair(A!4, B!3)), tptp_fun_D_5(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_C_6(B, ordered_pair(A!4, B!3))))) | (B = pair_first(ordered_pair(A!4, B!3)))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[85, 75])).
% 0.19/0.47 tff(87,plain,
% 0.19/0.47 (![B: $i] : (~((~((~(B = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = C)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(B, ordered_pair(A!4, B!3)), tptp_fun_D_5(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_C_6(B, ordered_pair(A!4, B!3))))) | (B = pair_first(ordered_pair(A!4, B!3)))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[86, 12])).
% 0.19/0.47 tff(88,plain,
% 0.19/0.47 (((~![B: $i] : (~((~((~(B = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = C)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(B, ordered_pair(A!4, B!3)), tptp_fun_D_5(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_C_6(B, ordered_pair(A!4, B!3))))) | (B = pair_first(ordered_pair(A!4, B!3)))))))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_first(ordered_pair(A!4, B!3)) = C))) <=> ((~![B: $i] : (~((~((~(B = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = C)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(B, ordered_pair(A!4, B!3)), tptp_fun_D_5(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_C_6(B, ordered_pair(A!4, B!3))))) | (B = pair_first(ordered_pair(A!4, B!3)))))))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_first(ordered_pair(A!4, B!3)) = C)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(89,plain,
% 0.19/0.47 ((~(~![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_first(ordered_pair(A!4, B!3)) = C)))) <=> ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_first(ordered_pair(A!4, B!3)) = C))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(90,plain,
% 0.19/0.47 (((~![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_first(ordered_pair(A!4, B!3)) = C))) | $false) <=> (~![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_first(ordered_pair(A!4, B!3)) = C)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(91,plain,
% 0.19/0.47 (((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3)), tptp_fun_D_5(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_first(ordered_pair(A!4, B!3)) = tptp_fun_C_6(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | $true) <=> $true),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(92,plain,
% 0.19/0.47 ((pair_first(ordered_pair(A!4, B!3)) = pair_first(ordered_pair(A!4, B!3))) <=> $true),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(93,plain,
% 0.19/0.47 (((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3)), tptp_fun_D_5(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_first(ordered_pair(A!4, B!3)) = tptp_fun_C_6(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_first(ordered_pair(A!4, B!3)) = pair_first(ordered_pair(A!4, B!3)))) <=> ((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3)), tptp_fun_D_5(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_first(ordered_pair(A!4, B!3)) = tptp_fun_C_6(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | $true)),
% 0.19/0.47 inference(monotonicity,[status(thm)],[92])).
% 0.19/0.47 tff(94,plain,
% 0.19/0.47 (((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3)), tptp_fun_D_5(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_first(ordered_pair(A!4, B!3)) = tptp_fun_C_6(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_first(ordered_pair(A!4, B!3)) = pair_first(ordered_pair(A!4, B!3)))) <=> $true),
% 0.19/0.47 inference(transitivity,[status(thm)],[93, 91])).
% 0.19/0.47 tff(95,plain,
% 0.19/0.47 ((~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3)), tptp_fun_D_5(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_first(ordered_pair(A!4, B!3)) = tptp_fun_C_6(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_first(ordered_pair(A!4, B!3)) = pair_first(ordered_pair(A!4, B!3))))) <=> (~$true)),
% 0.19/0.47 inference(monotonicity,[status(thm)],[94])).
% 0.19/0.47 tff(96,plain,
% 0.19/0.47 ((~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3)), tptp_fun_D_5(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_first(ordered_pair(A!4, B!3)) = tptp_fun_C_6(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_first(ordered_pair(A!4, B!3)) = pair_first(ordered_pair(A!4, B!3))))) <=> $false),
% 0.19/0.47 inference(transitivity,[status(thm)],[95, 2])).
% 0.19/0.47 tff(97,plain,
% 0.19/0.47 ((~((~(pair_first(ordered_pair(A!4, B!3)) = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_first(ordered_pair(A!4, B!3)) = C)))) <=> (~![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_first(ordered_pair(A!4, B!3)) = C)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(98,plain,
% 0.19/0.47 (((~((~(pair_first(ordered_pair(A!4, B!3)) = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_first(ordered_pair(A!4, B!3)) = C)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3)), tptp_fun_D_5(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_first(ordered_pair(A!4, B!3)) = tptp_fun_C_6(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_first(ordered_pair(A!4, B!3)) = pair_first(ordered_pair(A!4, B!3)))))) <=> ((~![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_first(ordered_pair(A!4, B!3)) = C))) | $false)),
% 0.19/0.47 inference(monotonicity,[status(thm)],[97, 96])).
% 0.19/0.47 tff(99,plain,
% 0.19/0.47 (((~((~(pair_first(ordered_pair(A!4, B!3)) = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_first(ordered_pair(A!4, B!3)) = C)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3)), tptp_fun_D_5(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_first(ordered_pair(A!4, B!3)) = tptp_fun_C_6(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_first(ordered_pair(A!4, B!3)) = pair_first(ordered_pair(A!4, B!3)))))) <=> (~![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_first(ordered_pair(A!4, B!3)) = C)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[98, 90])).
% 0.19/0.47 tff(100,plain,
% 0.19/0.47 ((~((~((~(pair_first(ordered_pair(A!4, B!3)) = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_first(ordered_pair(A!4, B!3)) = C)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3)), tptp_fun_D_5(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_first(ordered_pair(A!4, B!3)) = tptp_fun_C_6(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_first(ordered_pair(A!4, B!3)) = pair_first(ordered_pair(A!4, B!3))))))) <=> (~(~![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_first(ordered_pair(A!4, B!3)) = C))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[99])).
% 0.19/0.47 tff(101,plain,
% 0.19/0.47 ((~((~((~(pair_first(ordered_pair(A!4, B!3)) = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_first(ordered_pair(A!4, B!3)) = C)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3)), tptp_fun_D_5(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_first(ordered_pair(A!4, B!3)) = tptp_fun_C_6(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_first(ordered_pair(A!4, B!3)) = pair_first(ordered_pair(A!4, B!3))))))) <=> ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_first(ordered_pair(A!4, B!3)) = C))),
% 0.19/0.47 inference(transitivity,[status(thm)],[100, 89])).
% 0.19/0.47 tff(102,plain,
% 0.19/0.47 (((~![B: $i] : (~((~((~(B = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = C)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(B, ordered_pair(A!4, B!3)), tptp_fun_D_5(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_C_6(B, ordered_pair(A!4, B!3))))) | (B = pair_first(ordered_pair(A!4, B!3)))))))) | (~((~((~(pair_first(ordered_pair(A!4, B!3)) = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_first(ordered_pair(A!4, B!3)) = C)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3)), tptp_fun_D_5(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_first(ordered_pair(A!4, B!3)) = tptp_fun_C_6(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_first(ordered_pair(A!4, B!3)) = pair_first(ordered_pair(A!4, B!3)))))))) <=> ((~![B: $i] : (~((~((~(B = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = C)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(B, ordered_pair(A!4, B!3)), tptp_fun_D_5(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_C_6(B, ordered_pair(A!4, B!3))))) | (B = pair_first(ordered_pair(A!4, B!3)))))))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_first(ordered_pair(A!4, B!3)) = C)))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[101])).
% 0.19/0.47 tff(103,plain,
% 0.19/0.47 (((~![B: $i] : (~((~((~(B = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = C)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(B, ordered_pair(A!4, B!3)), tptp_fun_D_5(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_C_6(B, ordered_pair(A!4, B!3))))) | (B = pair_first(ordered_pair(A!4, B!3)))))))) | (~((~((~(pair_first(ordered_pair(A!4, B!3)) = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_first(ordered_pair(A!4, B!3)) = C)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3)), tptp_fun_D_5(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_first(ordered_pair(A!4, B!3)) = tptp_fun_C_6(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_first(ordered_pair(A!4, B!3)) = pair_first(ordered_pair(A!4, B!3)))))))) <=> ((~![B: $i] : (~((~((~(B = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = C)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(B, ordered_pair(A!4, B!3)), tptp_fun_D_5(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_C_6(B, ordered_pair(A!4, B!3))))) | (B = pair_first(ordered_pair(A!4, B!3)))))))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_first(ordered_pair(A!4, B!3)) = C)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[102, 88])).
% 0.19/0.47 tff(104,plain,
% 0.19/0.47 ((~![B: $i] : (~((~((~(B = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = C)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(B, ordered_pair(A!4, B!3)), tptp_fun_D_5(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_C_6(B, ordered_pair(A!4, B!3))))) | (B = pair_first(ordered_pair(A!4, B!3)))))))) | (~((~((~(pair_first(ordered_pair(A!4, B!3)) = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_first(ordered_pair(A!4, B!3)) = C)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3)), tptp_fun_D_5(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_first(ordered_pair(A!4, B!3)) = tptp_fun_C_6(pair_first(ordered_pair(A!4, B!3)), ordered_pair(A!4, B!3))))) | (pair_first(ordered_pair(A!4, B!3)) = pair_first(ordered_pair(A!4, B!3)))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(105,plain,
% 0.19/0.47 ((~![B: $i] : (~((~((~(B = pair_first(ordered_pair(A!4, B!3)))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (B = C)))) | (~((~((~(ordered_pair(A!4, B!3) = ordered_pair(tptp_fun_C_6(B, ordered_pair(A!4, B!3)), tptp_fun_D_5(B, ordered_pair(A!4, B!3))))) | (B = tptp_fun_C_6(B, ordered_pair(A!4, B!3))))) | (B = pair_first(ordered_pair(A!4, B!3)))))))) | ![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_first(ordered_pair(A!4, B!3)) = C))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.47 tff(106,plain,
% 0.19/0.47 (![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_first(ordered_pair(A!4, B!3)) = C))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[105, 87])).
% 0.19/0.47 tff(107,assumption,(![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_first(ordered_pair(A!4, B!3)) = C))), introduced(assumption)).
% 0.19/0.47 tff(108,assumption,(~(pair_first(ordered_pair(A!4, B!3)) = A!4)), introduced(assumption)).
% 0.19/0.47 tff(109,plain,
% 0.19/0.47 (((~![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_first(ordered_pair(A!4, B!3)) = C))) | (pair_first(ordered_pair(A!4, B!3)) = A!4)) <=> ((~![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_first(ordered_pair(A!4, B!3)) = C))) | (pair_first(ordered_pair(A!4, B!3)) = A!4))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(110,plain,
% 0.19/0.47 (($false | (pair_first(ordered_pair(A!4, B!3)) = A!4)) <=> (pair_first(ordered_pair(A!4, B!3)) = A!4)),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(111,plain,
% 0.19/0.47 (((~(ordered_pair(A!4, B!3) = ordered_pair(A!4, B!3))) | (pair_first(ordered_pair(A!4, B!3)) = A!4)) <=> ($false | (pair_first(ordered_pair(A!4, B!3)) = A!4))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[5])).
% 0.19/0.47 tff(112,plain,
% 0.19/0.47 (((~(ordered_pair(A!4, B!3) = ordered_pair(A!4, B!3))) | (pair_first(ordered_pair(A!4, B!3)) = A!4)) <=> (pair_first(ordered_pair(A!4, B!3)) = A!4)),
% 0.19/0.47 inference(transitivity,[status(thm)],[111, 110])).
% 0.19/0.47 tff(113,plain,
% 0.19/0.47 (((~![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_first(ordered_pair(A!4, B!3)) = C))) | ((~(ordered_pair(A!4, B!3) = ordered_pair(A!4, B!3))) | (pair_first(ordered_pair(A!4, B!3)) = A!4))) <=> ((~![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_first(ordered_pair(A!4, B!3)) = C))) | (pair_first(ordered_pair(A!4, B!3)) = A!4))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[112])).
% 0.19/0.47 tff(114,plain,
% 0.19/0.47 (((~![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_first(ordered_pair(A!4, B!3)) = C))) | ((~(ordered_pair(A!4, B!3) = ordered_pair(A!4, B!3))) | (pair_first(ordered_pair(A!4, B!3)) = A!4))) <=> ((~![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_first(ordered_pair(A!4, B!3)) = C))) | (pair_first(ordered_pair(A!4, B!3)) = A!4))),
% 0.19/0.47 inference(transitivity,[status(thm)],[113, 109])).
% 0.19/0.47 tff(115,plain,
% 0.19/0.47 ((~![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_first(ordered_pair(A!4, B!3)) = C))) | ((~(ordered_pair(A!4, B!3) = ordered_pair(A!4, B!3))) | (pair_first(ordered_pair(A!4, B!3)) = A!4))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(116,plain,
% 0.19/0.47 ((~![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_first(ordered_pair(A!4, B!3)) = C))) | (pair_first(ordered_pair(A!4, B!3)) = A!4)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.19/0.47 tff(117,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[116, 108, 107])).
% 0.19/0.47 tff(118,plain,((~![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_first(ordered_pair(A!4, B!3)) = C))) | (pair_first(ordered_pair(A!4, B!3)) = A!4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(119,plain,
% 0.19/0.47 (pair_first(ordered_pair(A!4, B!3)) = A!4),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[118, 106])).
% 0.19/0.47 tff(120,plain,
% 0.19/0.47 ((~(~((~(pair_first(ordered_pair(A!4, B!3)) = A!4)) | (~(pair_second(ordered_pair(A!4, B!3)) = B!3))))) <=> ((~(pair_first(ordered_pair(A!4, B!3)) = A!4)) | (~(pair_second(ordered_pair(A!4, B!3)) = B!3)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(121,plain,
% 0.19/0.47 (((pair_first(ordered_pair(A!4, B!3)) = A!4) & (pair_second(ordered_pair(A!4, B!3)) = B!3)) <=> (~((~(pair_first(ordered_pair(A!4, B!3)) = A!4)) | (~(pair_second(ordered_pair(A!4, B!3)) = B!3))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(122,plain,
% 0.19/0.47 ((~((pair_first(ordered_pair(A!4, B!3)) = A!4) & (pair_second(ordered_pair(A!4, B!3)) = B!3))) <=> (~(~((~(pair_first(ordered_pair(A!4, B!3)) = A!4)) | (~(pair_second(ordered_pair(A!4, B!3)) = B!3)))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[121])).
% 0.19/0.47 tff(123,plain,
% 0.19/0.47 ((~((pair_first(ordered_pair(A!4, B!3)) = A!4) & (pair_second(ordered_pair(A!4, B!3)) = B!3))) <=> ((~(pair_first(ordered_pair(A!4, B!3)) = A!4)) | (~(pair_second(ordered_pair(A!4, B!3)) = B!3)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[122, 120])).
% 0.19/0.47 tff(124,plain,
% 0.19/0.47 ((~![A: $i, B: $i] : ((pair_first(ordered_pair(A, B)) = A) & (pair_second(ordered_pair(A, B)) = B))) <=> (~![A: $i, B: $i] : ((pair_first(ordered_pair(A, B)) = A) & (pair_second(ordered_pair(A, B)) = B)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(125,axiom,(~![A: $i, B: $i] : ((pair_first(ordered_pair(A, B)) = A) & (pair_second(ordered_pair(A, B)) = B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t7_mcart_1')).
% 0.19/0.47 tff(126,plain,
% 0.19/0.47 (~![A: $i, B: $i] : ((pair_first(ordered_pair(A, B)) = A) & (pair_second(ordered_pair(A, B)) = B))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.19/0.47 tff(127,plain,
% 0.19/0.47 (~![A: $i, B: $i] : ((pair_first(ordered_pair(A, B)) = A) & (pair_second(ordered_pair(A, B)) = B))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[126, 124])).
% 0.19/0.47 tff(128,plain,
% 0.19/0.47 (~![A: $i, B: $i] : ((pair_first(ordered_pair(A, B)) = A) & (pair_second(ordered_pair(A, B)) = B))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[127, 124])).
% 0.19/0.47 tff(129,plain,
% 0.19/0.47 (~![A: $i, B: $i] : ((pair_first(ordered_pair(A, B)) = A) & (pair_second(ordered_pair(A, B)) = B))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.19/0.47 tff(130,plain,(
% 0.19/0.47 ~((pair_first(ordered_pair(A!4, B!3)) = A!4) & (pair_second(ordered_pair(A!4, B!3)) = B!3))),
% 0.19/0.47 inference(skolemize,[status(sab)],[129])).
% 0.19/0.47 tff(131,plain,
% 0.19/0.47 ((~(pair_first(ordered_pair(A!4, B!3)) = A!4)) | (~(pair_second(ordered_pair(A!4, B!3)) = B!3))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[130, 123])).
% 0.19/0.47 tff(132,plain,
% 0.19/0.47 (~(pair_second(ordered_pair(A!4, B!3)) = B!3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[131, 119])).
% 0.19/0.47 tff(133,plain,
% 0.19/0.47 (((~![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_second(ordered_pair(A!4, B!3)) = D))) | (pair_second(ordered_pair(A!4, B!3)) = B!3)) <=> ((~![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_second(ordered_pair(A!4, B!3)) = D))) | (pair_second(ordered_pair(A!4, B!3)) = B!3))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(134,plain,
% 0.19/0.47 (($false | (pair_second(ordered_pair(A!4, B!3)) = B!3)) <=> (pair_second(ordered_pair(A!4, B!3)) = B!3)),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(135,plain,
% 0.19/0.47 (((~(ordered_pair(A!4, B!3) = ordered_pair(A!4, B!3))) | (pair_second(ordered_pair(A!4, B!3)) = B!3)) <=> ($false | (pair_second(ordered_pair(A!4, B!3)) = B!3))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[5])).
% 0.19/0.47 tff(136,plain,
% 0.19/0.47 (((~(ordered_pair(A!4, B!3) = ordered_pair(A!4, B!3))) | (pair_second(ordered_pair(A!4, B!3)) = B!3)) <=> (pair_second(ordered_pair(A!4, B!3)) = B!3)),
% 0.19/0.47 inference(transitivity,[status(thm)],[135, 134])).
% 0.19/0.47 tff(137,plain,
% 0.19/0.47 (((~![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_second(ordered_pair(A!4, B!3)) = D))) | ((~(ordered_pair(A!4, B!3) = ordered_pair(A!4, B!3))) | (pair_second(ordered_pair(A!4, B!3)) = B!3))) <=> ((~![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_second(ordered_pair(A!4, B!3)) = D))) | (pair_second(ordered_pair(A!4, B!3)) = B!3))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[136])).
% 0.19/0.47 tff(138,plain,
% 0.19/0.47 (((~![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_second(ordered_pair(A!4, B!3)) = D))) | ((~(ordered_pair(A!4, B!3) = ordered_pair(A!4, B!3))) | (pair_second(ordered_pair(A!4, B!3)) = B!3))) <=> ((~![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_second(ordered_pair(A!4, B!3)) = D))) | (pair_second(ordered_pair(A!4, B!3)) = B!3))),
% 0.19/0.47 inference(transitivity,[status(thm)],[137, 133])).
% 0.19/0.47 tff(139,plain,
% 0.19/0.47 ((~![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_second(ordered_pair(A!4, B!3)) = D))) | ((~(ordered_pair(A!4, B!3) = ordered_pair(A!4, B!3))) | (pair_second(ordered_pair(A!4, B!3)) = B!3))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(140,plain,
% 0.19/0.47 ((~![C: $i, D: $i] : ((~(ordered_pair(A!4, B!3) = ordered_pair(C, D))) | (pair_second(ordered_pair(A!4, B!3)) = D))) | (pair_second(ordered_pair(A!4, B!3)) = B!3)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.19/0.47 tff(141,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[140, 132, 59])).
% 0.19/0.47 % SZS output end Proof
% 0.19/0.48 % E exiting
%------------------------------------------------------------------------------