%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET988+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:46 AM UTC 2025
% Result : Theorem 0.65s 0.81s
% Output : Proof 0.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET988+1 : TPTP v9.0.0. Released v3.2.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n016.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 05:56:47 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.65/0.81 % SZS status Theorem
% 0.65/0.81 % SZS output start Proof
% 0.65/0.81 tff(ordered_pair_type, type, (
% 0.65/0.81 ordered_pair: ( $i * $i ) > $i)).
% 0.65/0.81 tff(tptp_fun_D_10_type, type, (
% 0.65/0.81 tptp_fun_D_10: $i > $i)).
% 0.65/0.81 tff(tptp_fun_B_17_type, type, (
% 0.65/0.81 tptp_fun_B_17: $i > $i)).
% 0.65/0.81 tff(tptp_fun_A_9_type, type, (
% 0.65/0.81 tptp_fun_A_9: $i)).
% 0.65/0.81 tff(tptp_fun_C_11_type, type, (
% 0.65/0.81 tptp_fun_C_11: $i > $i)).
% 0.65/0.81 tff(in_type, type, (
% 0.65/0.81 in: ( $i * $i ) > $o)).
% 0.65/0.81 tff(relation_type, type, (
% 0.65/0.81 relation: $i > $o)).
% 0.65/0.81 tff(tptp_fun_D_15_type, type, (
% 0.65/0.81 tptp_fun_D_15: $i > $i)).
% 0.65/0.81 tff(tptp_fun_C_16_type, type, (
% 0.65/0.81 tptp_fun_C_16: $i > $i)).
% 0.65/0.81 tff(function_type, type, (
% 0.65/0.81 function: $i > $o)).
% 0.65/0.81 tff(tptp_fun_D_12_type, type, (
% 0.65/0.81 tptp_fun_D_12: $i > $i)).
% 0.65/0.81 tff(tptp_fun_C_13_type, type, (
% 0.65/0.81 tptp_fun_C_13: $i > $i)).
% 0.65/0.81 tff(tptp_fun_B_14_type, type, (
% 0.65/0.81 tptp_fun_B_14: $i > $i)).
% 0.65/0.81 tff(1,plain,
% 0.65/0.81 (^[A: $i] : refl((~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D)))))))))) <=> (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D)))))))))))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(2,plain,
% 0.65/0.81 (![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D)))))))))) <=> ![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D))))))))))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[1])).
% 0.65/0.81 tff(3,plain,
% 0.65/0.81 (^[A: $i] : rewrite((~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D)))))))))) <=> (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D)))))))))))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(4,plain,
% 0.65/0.81 (![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D)))))))))) <=> ![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D))))))))))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[3])).
% 0.65/0.81 tff(5,plain,
% 0.65/0.81 (![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D)))))))))) <=> ![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D))))))))))),
% 0.65/0.81 inference(transitivity,[status(thm)],[4, 2])).
% 0.65/0.81 tff(6,plain,
% 0.65/0.81 (^[A: $i] : trans(monotonicity(rewrite(((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B))))) <=> ((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))), rewrite((relation(A) | (in(tptp_fun_B_17(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D))))) <=> (relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D)))))))), ((((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B))))) & (relation(A) | (in(tptp_fun_B_17(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D)))))) <=> (((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B))))) & (relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D)))))))))), rewrite((((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B))))) & (relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D)))))))) <=> (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D))))))))))), ((((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B))))) & (relation(A) | (in(tptp_fun_B_17(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D)))))) <=> (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D))))))))))))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(7,plain,
% 0.65/0.81 (![A: $i] : (((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B))))) & (relation(A) | (in(tptp_fun_B_17(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D)))))) <=> ![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D))))))))))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[6])).
% 0.65/0.81 tff(8,plain,
% 0.65/0.81 (![A: $i] : (relation(A) <=> ![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(B = ordered_pair(C, D)))))) <=> ![A: $i] : (relation(A) <=> ![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(B = ordered_pair(C, D))))))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(9,axiom,(![A: $i] : (relation(A) <=> ![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(B = ordered_pair(C, D))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_relat_1')).
% 0.65/0.81 tff(10,plain,
% 0.65/0.81 (![A: $i] : (relation(A) <=> ![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(B = ordered_pair(C, D))))))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.65/0.81 tff(11,plain,(
% 0.65/0.81 ![A: $i] : (((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B))))) & (relation(A) | (in(tptp_fun_B_17(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D))))))),
% 0.65/0.81 inference(skolemize,[status(sab)],[10])).
% 0.65/0.81 tff(12,plain,
% 0.65/0.81 (![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D))))))))))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.65/0.81 tff(13,plain,
% 0.65/0.81 (![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D))))))))))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.65/0.81 tff(14,plain,
% 0.65/0.81 ((~![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_17(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A) = ordered_pair(C, D))))))))))) | (~((~((~relation(A!9)) | ![B: $i] : ((~in(B, A!9)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A!9) | (~((~in(tptp_fun_B_17(A!9), A!9)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A!9) = ordered_pair(C, D))))))))))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(15,plain,
% 0.65/0.81 (~((~((~relation(A!9)) | ![B: $i] : ((~in(B, A!9)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A!9) | (~((~in(tptp_fun_B_17(A!9), A!9)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A!9) = ordered_pair(C, D)))))))))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.65/0.81 tff(16,plain,
% 0.65/0.81 (((~((~relation(A!9)) | ![B: $i] : ((~in(B, A!9)) | (B = ordered_pair(tptp_fun_C_16(B), tptp_fun_D_15(B)))))) | (~(relation(A!9) | (~((~in(tptp_fun_B_17(A!9), A!9)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A!9) = ordered_pair(C, D))))))))) | (relation(A!9) | (~((~in(tptp_fun_B_17(A!9), A!9)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A!9) = ordered_pair(C, D)))))))),
% 0.65/0.81 inference(tautology,[status(thm)],[])).
% 0.65/0.81 tff(17,plain,
% 0.65/0.81 (relation(A!9) | (~((~in(tptp_fun_B_17(A!9), A!9)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A!9) = ordered_pair(C, D))))))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.65/0.81 tff(18,assumption,((~((~function(A!9)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))))) | (~(function(A!9) | (~((~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9))))))), introduced(assumption)).
% 0.65/0.81 tff(19,plain,
% 0.65/0.81 (^[A: $i] : refl((~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A)))))))) <=> (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A)))))))))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(20,plain,
% 0.65/0.81 (![A: $i] : (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A)))))))) <=> ![A: $i] : (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))))))))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[19])).
% 0.65/0.81 tff(21,plain,
% 0.65/0.81 (^[A: $i] : rewrite((~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A)))))))) <=> (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A)))))))))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(22,plain,
% 0.65/0.81 (![A: $i] : (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A)))))))) <=> ![A: $i] : (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))))))))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[21])).
% 0.65/0.81 tff(23,plain,
% 0.65/0.81 (![A: $i] : (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A)))))))) <=> ![A: $i] : (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))))))))),
% 0.65/0.81 inference(transitivity,[status(thm)],[22, 20])).
% 0.65/0.81 tff(24,plain,
% 0.65/0.81 (^[A: $i] : trans(monotonicity(rewrite(((~function(A)) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D))) <=> ((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))), rewrite((function(A) | (~((~(in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A) & in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))) | (tptp_fun_C_13(A) = tptp_fun_D_12(A))))) <=> (function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A)))))), ((((~function(A)) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D))) & (function(A) | (~((~(in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A) & in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))) | (tptp_fun_C_13(A) = tptp_fun_D_12(A)))))) <=> (((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A)))) & (function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A)))))))), rewrite((((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A)))) & (function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A)))))) <=> (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))))))))), ((((~function(A)) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D))) & (function(A) | (~((~(in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A) & in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))) | (tptp_fun_C_13(A) = tptp_fun_D_12(A)))))) <=> (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))))))))))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(25,plain,
% 0.65/0.81 (![A: $i] : (((~function(A)) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D))) & (function(A) | (~((~(in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A) & in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))) | (tptp_fun_C_13(A) = tptp_fun_D_12(A)))))) <=> ![A: $i] : (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))))))))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[24])).
% 0.65/0.81 tff(26,plain,
% 0.65/0.81 (![A: $i] : (function(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D))) <=> ![A: $i] : (function(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(27,plain,
% 0.65/0.82 (^[A: $i] : rewrite((function(A) <=> ![B: $i, C: $i, D: $i] : ((in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A)) => (C = D))) <=> (function(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D))))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(28,plain,
% 0.65/0.82 (![A: $i] : (function(A) <=> ![B: $i, C: $i, D: $i] : ((in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A)) => (C = D))) <=> ![A: $i] : (function(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D)))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[27])).
% 0.65/0.82 tff(29,axiom,(![A: $i] : (function(A) <=> ![B: $i, C: $i, D: $i] : ((in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A)) => (C = D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_funct_1')).
% 0.65/0.82 tff(30,plain,
% 0.65/0.82 (![A: $i] : (function(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.65/0.82 tff(31,plain,
% 0.65/0.82 (![A: $i] : (function(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.65/0.82 tff(32,plain,(
% 0.65/0.82 ![A: $i] : (((~function(A)) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D))) & (function(A) | (~((~(in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A) & in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))) | (tptp_fun_C_13(A) = tptp_fun_D_12(A))))))),
% 0.65/0.82 inference(skolemize,[status(sab)],[31])).
% 0.65/0.82 tff(33,plain,
% 0.65/0.82 (![A: $i] : (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))))))))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.65/0.82 tff(34,plain,
% 0.65/0.82 (![A: $i] : (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))))))))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[33, 23])).
% 0.65/0.82 tff(35,plain,
% 0.65/0.82 (((~![A: $i] : (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))))))))) | (~((~((~function(A!9)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))))) | (~(function(A!9) | (~((~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9))))))))) <=> ((~![A: $i] : (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))))))))) | (~((~((~function(A!9)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))))) | (~(function(A!9) | (~((~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)))))))))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(36,plain,
% 0.65/0.82 ((~((~((~function(A!9)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))))) | (~(function(A!9) | (~((tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)))))))) <=> (~((~((~function(A!9)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))))) | (~(function(A!9) | (~((~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9))))))))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(37,plain,
% 0.65/0.82 (((~![A: $i] : (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))))))))) | (~((~((~function(A!9)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))))) | (~(function(A!9) | (~((tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9))))))))) <=> ((~![A: $i] : (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))))))))) | (~((~((~function(A!9)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))))) | (~(function(A!9) | (~((~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)))))))))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[36])).
% 0.65/0.82 tff(38,plain,
% 0.65/0.82 (((~![A: $i] : (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))))))))) | (~((~((~function(A!9)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))))) | (~(function(A!9) | (~((tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9))))))))) <=> ((~![A: $i] : (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))))))))) | (~((~((~function(A!9)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))))) | (~(function(A!9) | (~((~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)))))))))),
% 0.65/0.82 inference(transitivity,[status(thm)],[37, 35])).
% 0.65/0.82 tff(39,plain,
% 0.65/0.82 ((~![A: $i] : (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))))))))) | (~((~((~function(A!9)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))))) | (~(function(A!9) | (~((tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9))))))))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(40,plain,
% 0.65/0.82 ((~![A: $i] : (~((~((~function(A)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(B, D), A))))) | (~(function(A) | (~((tptp_fun_C_13(A) = tptp_fun_D_12(A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_C_13(A)), A)) | (~in(ordered_pair(tptp_fun_B_14(A), tptp_fun_D_12(A)), A))))))))) | (~((~((~function(A!9)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))))) | (~(function(A!9) | (~((~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9))))))))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.65/0.82 tff(41,plain,
% 0.65/0.82 ($false),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[40, 34, 18])).
% 0.65/0.82 tff(42,plain,(~((~((~function(A!9)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))))) | (~(function(A!9) | (~((~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)))))))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.82 tff(43,plain,
% 0.65/0.82 (((~((~function(A!9)) | ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))))) | (~(function(A!9) | (~((~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9))))))) | (function(A!9) | (~((~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)))))),
% 0.65/0.82 inference(tautology,[status(thm)],[])).
% 0.65/0.82 tff(44,plain,
% 0.65/0.82 (function(A!9) | (~((~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9))))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.65/0.82 tff(45,assumption,(~((~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)))), introduced(assumption)).
% 0.65/0.82 tff(46,plain,
% 0.65/0.82 (((~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9))) | (~(tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)))),
% 0.65/0.82 inference(tautology,[status(thm)],[])).
% 0.65/0.82 tff(47,plain,
% 0.65/0.82 (~(tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.65/0.82 tff(48,plain,
% 0.65/0.82 (((~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9))) | in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)),
% 0.65/0.82 inference(tautology,[status(thm)],[])).
% 0.65/0.82 tff(49,plain,
% 0.65/0.82 (in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[48, 45])).
% 0.65/0.82 tff(50,plain,
% 0.65/0.82 (((~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9))) | in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)),
% 0.65/0.82 inference(tautology,[status(thm)],[])).
% 0.65/0.82 tff(51,plain,
% 0.65/0.82 (in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[50, 45])).
% 0.65/0.82 tff(52,plain,
% 0.65/0.82 (^[B: $i, C: $i, D: $i] : refl(((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))) <=> ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(53,plain,
% 0.65/0.82 (![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))) <=> ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9)))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[52])).
% 0.65/0.82 tff(54,plain,
% 0.65/0.82 (^[B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((in(ordered_pair(B, C), A!9) & in(ordered_pair(B, D), A!9)) <=> (~((~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))))), ((~(in(ordered_pair(B, C), A!9) & in(ordered_pair(B, D), A!9))) <=> (~(~((~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))))))), rewrite((~(~((~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))))) <=> ((~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9)))), ((~(in(ordered_pair(B, C), A!9) & in(ordered_pair(B, D), A!9))) <=> ((~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))))), (((~(in(ordered_pair(B, C), A!9) & in(ordered_pair(B, D), A!9))) | (C = D)) <=> (((~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))) | (C = D)))), rewrite((((~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9))) | (C = D)) <=> ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9)))), (((~(in(ordered_pair(B, C), A!9) & in(ordered_pair(B, D), A!9))) | (C = D)) <=> ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9)))))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(55,plain,
% 0.65/0.82 (![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!9) & in(ordered_pair(B, D), A!9))) | (C = D)) <=> ![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9)))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[54])).
% 0.65/0.82 tff(56,plain,
% 0.65/0.82 (((![B: $i] : ((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B)) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!9) & in(ordered_pair(B, D), A!9))) | (C = D))) & (~(relation(A!9) & function(A!9)))) <=> (![B: $i] : ((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B)) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!9) & in(ordered_pair(B, D), A!9))) | (C = D)) & (~(relation(A!9) & function(A!9))))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(57,plain,
% 0.65/0.82 ((![B: $i] : ((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B)) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!9) & in(ordered_pair(B, D), A!9))) | (C = D))) <=> (![B: $i] : ((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B)) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!9) & in(ordered_pair(B, D), A!9))) | (C = D)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(58,plain,
% 0.65/0.82 (((![B: $i] : ((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B)) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!9) & in(ordered_pair(B, D), A!9))) | (C = D))) & (~(relation(A!9) & function(A!9)))) <=> ((![B: $i] : ((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B)) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!9) & in(ordered_pair(B, D), A!9))) | (C = D))) & (~(relation(A!9) & function(A!9))))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[57])).
% 0.65/0.82 tff(59,plain,
% 0.65/0.82 (((![B: $i] : ((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B)) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!9) & in(ordered_pair(B, D), A!9))) | (C = D))) & (~(relation(A!9) & function(A!9)))) <=> (![B: $i] : ((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B)) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!9) & in(ordered_pair(B, D), A!9))) | (C = D)) & (~(relation(A!9) & function(A!9))))),
% 0.65/0.82 inference(transitivity,[status(thm)],[58, 56])).
% 0.65/0.82 tff(60,plain,
% 0.65/0.82 ((~![A: $i] : ((~(![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(ordered_pair(C, D) = B)))) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D)))) | (relation(A) & function(A)))) <=> (~![A: $i] : ((~(![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(ordered_pair(C, D) = B)))) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D)))) | (relation(A) & function(A))))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(61,plain,
% 0.65/0.82 ((~![A: $i] : ((![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(ordered_pair(C, D) = B)))) & ![B: $i, C: $i, D: $i] : ((in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A)) => (C = D))) => (relation(A) & function(A)))) <=> (~![A: $i] : ((~(![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(ordered_pair(C, D) = B)))) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D)))) | (relation(A) & function(A))))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(62,axiom,(~![A: $i] : ((![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(ordered_pair(C, D) = B)))) & ![B: $i, C: $i, D: $i] : ((in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A)) => (C = D))) => (relation(A) & function(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2_funct_1')).
% 0.65/0.82 tff(63,plain,
% 0.65/0.82 (~![A: $i] : ((~(![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(ordered_pair(C, D) = B)))) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D)))) | (relation(A) & function(A)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.65/0.82 tff(64,plain,
% 0.65/0.82 (~![A: $i] : ((~(![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(ordered_pair(C, D) = B)))) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D)))) | (relation(A) & function(A)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[63, 60])).
% 0.65/0.82 tff(65,plain,
% 0.65/0.82 (~![A: $i] : ((~(![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(ordered_pair(C, D) = B)))) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D)))) | (relation(A) & function(A)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.65/0.82 tff(66,plain,
% 0.65/0.82 (~![A: $i] : ((~(![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(ordered_pair(C, D) = B)))) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(B, D), A))) | (C = D)))) | (relation(A) & function(A)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[65, 60])).
% 0.65/0.82 tff(67,plain,
% 0.65/0.82 (![B: $i] : ((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B)) & ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!9) & in(ordered_pair(B, D), A!9))) | (C = D)) & (~(relation(A!9) & function(A!9)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.65/0.82 tff(68,plain,
% 0.65/0.82 (![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!9) & in(ordered_pair(B, D), A!9))) | (C = D))),
% 0.65/0.82 inference(and_elim,[status(thm)],[67])).
% 0.65/0.82 tff(69,plain,
% 0.65/0.82 (![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[68, 55])).
% 0.65/0.82 tff(70,plain,
% 0.65/0.82 (![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[69, 53])).
% 0.65/0.82 tff(71,plain,
% 0.65/0.82 (((~![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9)))) | ((~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)))) <=> ((~![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9)))) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(72,plain,
% 0.65/0.82 (((tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9))) <=> ((~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(73,plain,
% 0.65/0.82 (((~![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9)))) | ((tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)))) <=> ((~![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9)))) | ((~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9))))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[72])).
% 0.65/0.82 tff(74,plain,
% 0.65/0.82 (((~![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9)))) | ((tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)))) <=> ((~![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9)))) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)))),
% 0.65/0.82 inference(transitivity,[status(thm)],[73, 71])).
% 0.65/0.82 tff(75,plain,
% 0.65/0.82 ((~![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9)))) | ((tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(76,plain,
% 0.65/0.82 ((~![B: $i, C: $i, D: $i] : ((C = D) | (~in(ordered_pair(B, C), A!9)) | (~in(ordered_pair(B, D), A!9)))) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.65/0.82 tff(77,plain,
% 0.65/0.82 ($false),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[76, 70, 51, 49, 47])).
% 0.65/0.82 tff(78,plain,((~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.82 tff(79,plain,
% 0.65/0.82 ((~(function(A!9) | (~((~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)))))) | function(A!9) | (~((~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9))))),
% 0.65/0.82 inference(tautology,[status(thm)],[])).
% 0.65/0.82 tff(80,plain,
% 0.65/0.82 ((~(function(A!9) | (~((~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_D_12(A!9)), A!9)) | (~in(ordered_pair(tptp_fun_B_14(A!9), tptp_fun_C_13(A!9)), A!9)) | (tptp_fun_C_13(A!9) = tptp_fun_D_12(A!9)))))) | function(A!9)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.65/0.82 tff(81,plain,
% 0.65/0.82 (function(A!9)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[80, 44])).
% 0.65/0.82 tff(82,plain,
% 0.65/0.82 ((~(~((~relation(A!9)) | (~function(A!9))))) <=> ((~relation(A!9)) | (~function(A!9)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(83,plain,
% 0.65/0.82 ((relation(A!9) & function(A!9)) <=> (~((~relation(A!9)) | (~function(A!9))))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(84,plain,
% 0.65/0.82 ((~(relation(A!9) & function(A!9))) <=> (~(~((~relation(A!9)) | (~function(A!9)))))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[83])).
% 0.65/0.82 tff(85,plain,
% 0.65/0.82 ((~(relation(A!9) & function(A!9))) <=> ((~relation(A!9)) | (~function(A!9)))),
% 0.65/0.82 inference(transitivity,[status(thm)],[84, 82])).
% 0.65/0.82 tff(86,plain,
% 0.65/0.82 (~(relation(A!9) & function(A!9))),
% 0.65/0.82 inference(and_elim,[status(thm)],[67])).
% 0.65/0.82 tff(87,plain,
% 0.65/0.82 ((~relation(A!9)) | (~function(A!9))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.65/0.82 tff(88,plain,
% 0.65/0.82 (~relation(A!9)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[87, 81])).
% 0.65/0.82 tff(89,plain,
% 0.65/0.82 ((~(relation(A!9) | (~((~in(tptp_fun_B_17(A!9), A!9)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A!9) = ordered_pair(C, D)))))))) | relation(A!9) | (~((~in(tptp_fun_B_17(A!9), A!9)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A!9) = ordered_pair(C, D))))))),
% 0.65/0.82 inference(tautology,[status(thm)],[])).
% 0.65/0.82 tff(90,plain,
% 0.65/0.82 ((~(relation(A!9) | (~((~in(tptp_fun_B_17(A!9), A!9)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A!9) = ordered_pair(C, D)))))))) | (~((~in(tptp_fun_B_17(A!9), A!9)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A!9) = ordered_pair(C, D))))))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.65/0.83 tff(91,plain,
% 0.65/0.83 (~((~in(tptp_fun_B_17(A!9), A!9)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A!9) = ordered_pair(C, D)))))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[90, 17])).
% 0.65/0.83 tff(92,plain,
% 0.65/0.83 (((~in(tptp_fun_B_17(A!9), A!9)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A!9) = ordered_pair(C, D))))) | in(tptp_fun_B_17(A!9), A!9)),
% 0.65/0.83 inference(tautology,[status(thm)],[])).
% 0.65/0.83 tff(93,plain,
% 0.65/0.83 (in(tptp_fun_B_17(A!9), A!9)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.65/0.83 tff(94,plain,
% 0.65/0.83 (^[B: $i] : refl(((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B)) <=> ((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B)))),
% 0.65/0.83 inference(bind,[status(th)],[])).
% 0.65/0.83 tff(95,plain,
% 0.65/0.83 (![B: $i] : ((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B)) <=> ![B: $i] : ((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B))),
% 0.65/0.83 inference(quant_intro,[status(thm)],[94])).
% 0.65/0.83 tff(96,plain,
% 0.65/0.83 (![B: $i] : ((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B))),
% 0.65/0.83 inference(and_elim,[status(thm)],[67])).
% 0.65/0.83 tff(97,plain,
% 0.65/0.83 (![B: $i] : ((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.65/0.83 tff(98,plain,
% 0.65/0.83 (((~![B: $i] : ((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B))) | ((~in(tptp_fun_B_17(A!9), A!9)) | (ordered_pair(tptp_fun_C_11(tptp_fun_B_17(A!9)), tptp_fun_D_10(tptp_fun_B_17(A!9))) = tptp_fun_B_17(A!9)))) <=> ((~![B: $i] : ((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B))) | (~in(tptp_fun_B_17(A!9), A!9)) | (ordered_pair(tptp_fun_C_11(tptp_fun_B_17(A!9)), tptp_fun_D_10(tptp_fun_B_17(A!9))) = tptp_fun_B_17(A!9)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(99,plain,
% 0.65/0.83 ((~![B: $i] : ((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B))) | ((~in(tptp_fun_B_17(A!9), A!9)) | (ordered_pair(tptp_fun_C_11(tptp_fun_B_17(A!9)), tptp_fun_D_10(tptp_fun_B_17(A!9))) = tptp_fun_B_17(A!9)))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(100,plain,
% 0.65/0.83 ((~![B: $i] : ((~in(B, A!9)) | (ordered_pair(tptp_fun_C_11(B), tptp_fun_D_10(B)) = B))) | (~in(tptp_fun_B_17(A!9), A!9)) | (ordered_pair(tptp_fun_C_11(tptp_fun_B_17(A!9)), tptp_fun_D_10(tptp_fun_B_17(A!9))) = tptp_fun_B_17(A!9))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.65/0.83 tff(101,plain,
% 0.65/0.83 (ordered_pair(tptp_fun_C_11(tptp_fun_B_17(A!9)), tptp_fun_D_10(tptp_fun_B_17(A!9))) = tptp_fun_B_17(A!9)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[100, 97, 93])).
% 0.65/0.83 tff(102,plain,
% 0.65/0.83 (tptp_fun_B_17(A!9) = ordered_pair(tptp_fun_C_11(tptp_fun_B_17(A!9)), tptp_fun_D_10(tptp_fun_B_17(A!9)))),
% 0.65/0.83 inference(symmetry,[status(thm)],[101])).
% 0.65/0.83 tff(103,plain,
% 0.65/0.83 (((~in(tptp_fun_B_17(A!9), A!9)) | (~![C: $i, D: $i] : (~(tptp_fun_B_17(A!9) = ordered_pair(C, D))))) | ![C: $i, D: $i] : (~(tptp_fun_B_17(A!9) = ordered_pair(C, D)))),
% 0.65/0.83 inference(tautology,[status(thm)],[])).
% 0.65/0.83 tff(104,plain,
% 0.65/0.83 (![C: $i, D: $i] : (~(tptp_fun_B_17(A!9) = ordered_pair(C, D)))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[103, 91])).
% 0.65/0.83 tff(105,plain,
% 0.65/0.83 ((~![C: $i, D: $i] : (~(tptp_fun_B_17(A!9) = ordered_pair(C, D)))) | (~(tptp_fun_B_17(A!9) = ordered_pair(tptp_fun_C_11(tptp_fun_B_17(A!9)), tptp_fun_D_10(tptp_fun_B_17(A!9)))))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(106,plain,
% 0.65/0.83 ($false),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[105, 104, 102])).
% 0.65/0.83 % SZS output end Proof
% 0.65/0.83 % E exiting
%------------------------------------------------------------------------------