%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU191+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:27:11 AM UTC 2025
% Result : Theorem 0.22s 0.47s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU191+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 06:18:35 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.22/0.47 % SZS status Theorem
% 0.22/0.47 % SZS output start Proof
% 0.22/0.47 tff(in_type, type, (
% 0.22/0.47 in: ( $i * $i ) > $o)).
% 0.22/0.47 tff(tptp_fun_D_11_type, type, (
% 0.22/0.47 tptp_fun_D_11: $i)).
% 0.22/0.47 tff(ordered_pair_type, type, (
% 0.22/0.47 ordered_pair: ( $i * $i ) > $i)).
% 0.22/0.47 tff(tptp_fun_B_13_type, type, (
% 0.22/0.47 tptp_fun_B_13: $i)).
% 0.22/0.47 tff(tptp_fun_F_2_type, type, (
% 0.22/0.47 tptp_fun_F_2: ( $i * $i * $i * $i ) > $i)).
% 0.22/0.47 tff(identity_relation_type, type, (
% 0.22/0.47 identity_relation: $i > $i)).
% 0.22/0.47 tff(tptp_fun_C_12_type, type, (
% 0.22/0.47 tptp_fun_C_12: $i)).
% 0.22/0.47 tff(tptp_fun_A_14_type, type, (
% 0.22/0.47 tptp_fun_A_14: $i)).
% 0.22/0.47 tff(relation_type, type, (
% 0.22/0.47 relation: $i > $o)).
% 0.22/0.47 tff(tptp_fun_D_0_type, type, (
% 0.22/0.47 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.22/0.47 tff(tptp_fun_C_1_type, type, (
% 0.22/0.47 tptp_fun_C_1: ( $i * $i ) > $i)).
% 0.22/0.47 tff(relation_composition_type, type, (
% 0.22/0.47 relation_composition: ( $i * $i ) > $i)).
% 0.22/0.47 tff(tptp_fun_E_3_type, type, (
% 0.22/0.47 tptp_fun_E_3: ( $i * $i * $i ) > $i)).
% 0.22/0.47 tff(tptp_fun_D_4_type, type, (
% 0.22/0.47 tptp_fun_D_4: ( $i * $i * $i ) > $i)).
% 0.22/0.47 tff(tptp_fun_F_5_type, type, (
% 0.22/0.47 tptp_fun_F_5: ( $i * $i * $i ) > $i)).
% 0.22/0.47 tff(1,plain,
% 0.22/0.47 (^[A: $i] : refl(relation(identity_relation(A)) <=> relation(identity_relation(A)))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(2,plain,
% 0.22/0.47 (![A: $i] : relation(identity_relation(A)) <=> ![A: $i] : relation(identity_relation(A))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.47 tff(3,plain,
% 0.22/0.47 (![A: $i] : relation(identity_relation(A)) <=> ![A: $i] : relation(identity_relation(A))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(4,axiom,(![A: $i] : relation(identity_relation(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k6_relat_1')).
% 0.22/0.47 tff(5,plain,
% 0.22/0.47 (![A: $i] : relation(identity_relation(A))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.22/0.47 tff(6,plain,(
% 0.22/0.47 ![A: $i] : relation(identity_relation(A))),
% 0.22/0.47 inference(skolemize,[status(sab)],[5])).
% 0.22/0.47 tff(7,plain,
% 0.22/0.47 (![A: $i] : relation(identity_relation(A))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.22/0.47 tff(8,plain,
% 0.22/0.47 ((~![A: $i] : relation(identity_relation(A))) | relation(identity_relation(C!12))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(9,plain,
% 0.22/0.47 (relation(identity_relation(C!12))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.22/0.47 tff(10,plain,
% 0.22/0.47 (^[A: $i, B: $i] : rewrite(((~relation(B)) | (~((~((~(B = identity_relation(A))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, A))) <=> in(ordered_pair(C, D), B))))) | (~((B = identity_relation(A)) | (((~in(tptp_fun_C_1(B, A), A)) | (~(tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)))) <=> in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B))))))) <=> ((~relation(B)) | (~((~((B = identity_relation(A)) | (((~in(tptp_fun_C_1(B, A), A)) | (~(tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)))) <=> in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B)))) | (~((~(B = identity_relation(A))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, A))) <=> in(ordered_pair(C, D), B)))))))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(11,plain,
% 0.22/0.47 (![A: $i, B: $i] : ((~relation(B)) | (~((~((~(B = identity_relation(A))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, A))) <=> in(ordered_pair(C, D), B))))) | (~((B = identity_relation(A)) | (((~in(tptp_fun_C_1(B, A), A)) | (~(tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)))) <=> in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~((~((B = identity_relation(A)) | (((~in(tptp_fun_C_1(B, A), A)) | (~(tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)))) <=> in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B)))) | (~((~(B = identity_relation(A))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, A))) <=> in(ordered_pair(C, D), B))))))))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[10])).
% 0.22/0.47 tff(12,plain,
% 0.22/0.47 (^[A: $i, B: $i] : refl(((~relation(B)) | (~((~((~(B = identity_relation(A))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, A))) <=> in(ordered_pair(C, D), B))))) | (~((B = identity_relation(A)) | (((~in(tptp_fun_C_1(B, A), A)) | (~(tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)))) <=> in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B))))))) <=> ((~relation(B)) | (~((~((~(B = identity_relation(A))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, A))) <=> in(ordered_pair(C, D), B))))) | (~((B = identity_relation(A)) | (((~in(tptp_fun_C_1(B, A), A)) | (~(tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)))) <=> in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B))))))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(13,plain,
% 0.22/0.47 (![A: $i, B: $i] : ((~relation(B)) | (~((~((~(B = identity_relation(A))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, A))) <=> in(ordered_pair(C, D), B))))) | (~((B = identity_relation(A)) | (((~in(tptp_fun_C_1(B, A), A)) | (~(tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)))) <=> in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~((~((~(B = identity_relation(A))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, A))) <=> in(ordered_pair(C, D), B))))) | (~((B = identity_relation(A)) | (((~in(tptp_fun_C_1(B, A), A)) | (~(tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)))) <=> in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B)))))))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[12])).
% 0.22/0.47 tff(14,plain,
% 0.22/0.47 (^[A: $i, B: $i] : rewrite(((~relation(B)) | (~((~((~(B = identity_relation(A))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, A))) <=> in(ordered_pair(C, D), B))))) | (~((B = identity_relation(A)) | (((~in(tptp_fun_C_1(B, A), A)) | (~(tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)))) <=> in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B))))))) <=> ((~relation(B)) | (~((~((~(B = identity_relation(A))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, A))) <=> in(ordered_pair(C, D), B))))) | (~((B = identity_relation(A)) | (((~in(tptp_fun_C_1(B, A), A)) | (~(tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)))) <=> in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B))))))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(15,plain,
% 0.22/0.47 (![A: $i, B: $i] : ((~relation(B)) | (~((~((~(B = identity_relation(A))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, A))) <=> in(ordered_pair(C, D), B))))) | (~((B = identity_relation(A)) | (((~in(tptp_fun_C_1(B, A), A)) | (~(tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)))) <=> in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~((~((~(B = identity_relation(A))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, A))) <=> in(ordered_pair(C, D), B))))) | (~((B = identity_relation(A)) | (((~in(tptp_fun_C_1(B, A), A)) | (~(tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)))) <=> in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B)))))))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[14])).
% 0.22/0.47 tff(16,plain,
% 0.22/0.47 (![A: $i, B: $i] : ((~relation(B)) | (~((~((~(B = identity_relation(A))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, A))) <=> in(ordered_pair(C, D), B))))) | (~((B = identity_relation(A)) | (((~in(tptp_fun_C_1(B, A), A)) | (~(tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)))) <=> in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~((~((~(B = identity_relation(A))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, A))) <=> in(ordered_pair(C, D), B))))) | (~((B = identity_relation(A)) | (((~in(tptp_fun_C_1(B, A), A)) | (~(tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)))) <=> in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B)))))))),
% 0.22/0.47 inference(transitivity,[status(thm)],[15, 13])).
% 0.22/0.47 tff(17,plain,
% 0.22/0.47 (^[A: $i, B: $i] : rewrite(((~relation(B)) | (((~(B = identity_relation(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> (in(C, A) & (C = D)))) & ((B = identity_relation(A)) | (~(in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> (in(tptp_fun_C_1(B, A), A) & (tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)))))))) <=> ((~relation(B)) | (~((~((~(B = identity_relation(A))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, A))) <=> in(ordered_pair(C, D), B))))) | (~((B = identity_relation(A)) | (((~in(tptp_fun_C_1(B, A), A)) | (~(tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)))) <=> in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B))))))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(18,plain,
% 0.22/0.47 (![A: $i, B: $i] : ((~relation(B)) | (((~(B = identity_relation(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> (in(C, A) & (C = D)))) & ((B = identity_relation(A)) | (~(in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> (in(tptp_fun_C_1(B, A), A) & (tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~((~((~(B = identity_relation(A))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, A))) <=> in(ordered_pair(C, D), B))))) | (~((B = identity_relation(A)) | (((~in(tptp_fun_C_1(B, A), A)) | (~(tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)))) <=> in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B)))))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[17])).
% 0.22/0.48 tff(19,plain,
% 0.22/0.48 (![A: $i, B: $i] : ((~relation(B)) | ((B = identity_relation(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> (in(C, A) & (C = D))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ((B = identity_relation(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> (in(C, A) & (C = D)))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(20,plain,
% 0.22/0.48 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((B = identity_relation(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> (in(C, A) & (C = D)))) <=> ((B = identity_relation(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> (in(C, A) & (C = D))))), ((relation(B) => ((B = identity_relation(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> (in(C, A) & (C = D))))) <=> (relation(B) => ((B = identity_relation(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> (in(C, A) & (C = D))))))), rewrite((relation(B) => ((B = identity_relation(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> (in(C, A) & (C = D))))) <=> ((~relation(B)) | ((B = identity_relation(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> (in(C, A) & (C = D)))))), ((relation(B) => ((B = identity_relation(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> (in(C, A) & (C = D))))) <=> ((~relation(B)) | ((B = identity_relation(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> (in(C, A) & (C = D)))))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(21,plain,
% 0.22/0.48 (![A: $i, B: $i] : (relation(B) => ((B = identity_relation(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> (in(C, A) & (C = D))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ((B = identity_relation(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> (in(C, A) & (C = D)))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[20])).
% 0.22/0.48 tff(22,axiom,(![A: $i, B: $i] : (relation(B) => ((B = identity_relation(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> (in(C, A) & (C = D)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d10_relat_1')).
% 0.22/0.48 tff(23,plain,
% 0.22/0.48 (![A: $i, B: $i] : ((~relation(B)) | ((B = identity_relation(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> (in(C, A) & (C = D)))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.22/0.48 tff(24,plain,
% 0.22/0.48 (![A: $i, B: $i] : ((~relation(B)) | ((B = identity_relation(A)) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> (in(C, A) & (C = D)))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.22/0.48 tff(25,plain,(
% 0.22/0.48 ![A: $i, B: $i] : ((~relation(B)) | (((~(B = identity_relation(A))) | ![C: $i, D: $i] : (in(ordered_pair(C, D), B) <=> (in(C, A) & (C = D)))) & ((B = identity_relation(A)) | (~(in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> (in(tptp_fun_C_1(B, A), A) & (tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A))))))))),
% 0.22/0.48 inference(skolemize,[status(sab)],[24])).
% 0.22/0.48 tff(26,plain,
% 0.22/0.48 (![A: $i, B: $i] : ((~relation(B)) | (~((~((~(B = identity_relation(A))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, A))) <=> in(ordered_pair(C, D), B))))) | (~((B = identity_relation(A)) | (((~in(tptp_fun_C_1(B, A), A)) | (~(tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)))) <=> in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B)))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.22/0.48 tff(27,plain,
% 0.22/0.48 (![A: $i, B: $i] : ((~relation(B)) | (~((~((~(B = identity_relation(A))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, A))) <=> in(ordered_pair(C, D), B))))) | (~((B = identity_relation(A)) | (((~in(tptp_fun_C_1(B, A), A)) | (~(tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)))) <=> in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B)))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.22/0.48 tff(28,plain,
% 0.22/0.48 (![A: $i, B: $i] : ((~relation(B)) | (~((~((B = identity_relation(A)) | (((~in(tptp_fun_C_1(B, A), A)) | (~(tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)))) <=> in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B)))) | (~((~(B = identity_relation(A))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, A))) <=> in(ordered_pair(C, D), B))))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[27, 11])).
% 0.22/0.48 tff(29,plain,
% 0.22/0.48 (((~![A: $i, B: $i] : ((~relation(B)) | (~((~((B = identity_relation(A)) | (((~in(tptp_fun_C_1(B, A), A)) | (~(tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)))) <=> in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B)))) | (~((~(B = identity_relation(A))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, A))) <=> in(ordered_pair(C, D), B))))))))) | ((~relation(identity_relation(C!12))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, C!12))) <=> in(ordered_pair(C, D), identity_relation(C!12)))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~((~((B = identity_relation(A)) | (((~in(tptp_fun_C_1(B, A), A)) | (~(tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)))) <=> in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B)))) | (~((~(B = identity_relation(A))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, A))) <=> in(ordered_pair(C, D), B))))))))) | (~relation(identity_relation(C!12))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, C!12))) <=> in(ordered_pair(C, D), identity_relation(C!12)))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(30,plain,
% 0.22/0.48 (((~relation(identity_relation(C!12))) | (~((~((identity_relation(C!12) = identity_relation(C!12)) | (((~in(tptp_fun_C_1(identity_relation(C!12), C!12), C!12)) | (~(tptp_fun_C_1(identity_relation(C!12), C!12) = tptp_fun_D_0(identity_relation(C!12), C!12)))) <=> in(ordered_pair(tptp_fun_C_1(identity_relation(C!12), C!12), tptp_fun_D_0(identity_relation(C!12), C!12)), identity_relation(C!12))))) | (~((~(identity_relation(C!12) = identity_relation(C!12))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, C!12))) <=> in(ordered_pair(C, D), identity_relation(C!12))))))))) <=> ((~relation(identity_relation(C!12))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, C!12))) <=> in(ordered_pair(C, D), identity_relation(C!12)))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(31,plain,
% 0.22/0.48 (((~![A: $i, B: $i] : ((~relation(B)) | (~((~((B = identity_relation(A)) | (((~in(tptp_fun_C_1(B, A), A)) | (~(tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)))) <=> in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B)))) | (~((~(B = identity_relation(A))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, A))) <=> in(ordered_pair(C, D), B))))))))) | ((~relation(identity_relation(C!12))) | (~((~((identity_relation(C!12) = identity_relation(C!12)) | (((~in(tptp_fun_C_1(identity_relation(C!12), C!12), C!12)) | (~(tptp_fun_C_1(identity_relation(C!12), C!12) = tptp_fun_D_0(identity_relation(C!12), C!12)))) <=> in(ordered_pair(tptp_fun_C_1(identity_relation(C!12), C!12), tptp_fun_D_0(identity_relation(C!12), C!12)), identity_relation(C!12))))) | (~((~(identity_relation(C!12) = identity_relation(C!12))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, C!12))) <=> in(ordered_pair(C, D), identity_relation(C!12)))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~((~((B = identity_relation(A)) | (((~in(tptp_fun_C_1(B, A), A)) | (~(tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)))) <=> in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B)))) | (~((~(B = identity_relation(A))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, A))) <=> in(ordered_pair(C, D), B))))))))) | ((~relation(identity_relation(C!12))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, C!12))) <=> in(ordered_pair(C, D), identity_relation(C!12))))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[30])).
% 0.22/0.48 tff(32,plain,
% 0.22/0.48 (((~![A: $i, B: $i] : ((~relation(B)) | (~((~((B = identity_relation(A)) | (((~in(tptp_fun_C_1(B, A), A)) | (~(tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)))) <=> in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B)))) | (~((~(B = identity_relation(A))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, A))) <=> in(ordered_pair(C, D), B))))))))) | ((~relation(identity_relation(C!12))) | (~((~((identity_relation(C!12) = identity_relation(C!12)) | (((~in(tptp_fun_C_1(identity_relation(C!12), C!12), C!12)) | (~(tptp_fun_C_1(identity_relation(C!12), C!12) = tptp_fun_D_0(identity_relation(C!12), C!12)))) <=> in(ordered_pair(tptp_fun_C_1(identity_relation(C!12), C!12), tptp_fun_D_0(identity_relation(C!12), C!12)), identity_relation(C!12))))) | (~((~(identity_relation(C!12) = identity_relation(C!12))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, C!12))) <=> in(ordered_pair(C, D), identity_relation(C!12)))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~((~((B = identity_relation(A)) | (((~in(tptp_fun_C_1(B, A), A)) | (~(tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)))) <=> in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B)))) | (~((~(B = identity_relation(A))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, A))) <=> in(ordered_pair(C, D), B))))))))) | (~relation(identity_relation(C!12))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, C!12))) <=> in(ordered_pair(C, D), identity_relation(C!12)))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[31, 29])).
% 0.22/0.48 tff(33,plain,
% 0.22/0.48 ((~![A: $i, B: $i] : ((~relation(B)) | (~((~((B = identity_relation(A)) | (((~in(tptp_fun_C_1(B, A), A)) | (~(tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)))) <=> in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B)))) | (~((~(B = identity_relation(A))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, A))) <=> in(ordered_pair(C, D), B))))))))) | ((~relation(identity_relation(C!12))) | (~((~((identity_relation(C!12) = identity_relation(C!12)) | (((~in(tptp_fun_C_1(identity_relation(C!12), C!12), C!12)) | (~(tptp_fun_C_1(identity_relation(C!12), C!12) = tptp_fun_D_0(identity_relation(C!12), C!12)))) <=> in(ordered_pair(tptp_fun_C_1(identity_relation(C!12), C!12), tptp_fun_D_0(identity_relation(C!12), C!12)), identity_relation(C!12))))) | (~((~(identity_relation(C!12) = identity_relation(C!12))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, C!12))) <=> in(ordered_pair(C, D), identity_relation(C!12)))))))))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(34,plain,
% 0.22/0.48 ((~![A: $i, B: $i] : ((~relation(B)) | (~((~((B = identity_relation(A)) | (((~in(tptp_fun_C_1(B, A), A)) | (~(tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)))) <=> in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B)))) | (~((~(B = identity_relation(A))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, A))) <=> in(ordered_pair(C, D), B))))))))) | (~relation(identity_relation(C!12))) | ![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, C!12))) <=> in(ordered_pair(C, D), identity_relation(C!12))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.22/0.48 tff(35,plain,
% 0.22/0.48 (![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, C!12))) <=> in(ordered_pair(C, D), identity_relation(C!12))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[34, 28, 9])).
% 0.22/0.48 tff(36,plain,
% 0.22/0.48 (((~![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, C!12))) <=> in(ordered_pair(C, D), identity_relation(C!12))))) | (~(((~in(A!14, C!12)) | (~(A!14 = tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))))) <=> in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12))))) <=> ((~![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, C!12))) <=> in(ordered_pair(C, D), identity_relation(C!12))))) | (~(((~in(A!14, C!12)) | (~(A!14 = tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))))) <=> in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12)))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(37,plain,
% 0.22/0.48 ((~(((~in(A!14, C!12)) | (~(A!14 = tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))))) <=> in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12)))) <=> (~(((~in(A!14, C!12)) | (~(A!14 = tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))))) <=> in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(38,plain,
% 0.22/0.48 ((((~(A!14 = tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)))) | (~in(A!14, C!12))) <=> in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12))) <=> (((~in(A!14, C!12)) | (~(A!14 = tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))))) <=> in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(39,plain,
% 0.22/0.48 ((~(((~(A!14 = tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)))) | (~in(A!14, C!12))) <=> in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12)))) <=> (~(((~in(A!14, C!12)) | (~(A!14 = tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))))) <=> in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[38])).
% 0.22/0.48 tff(40,plain,
% 0.22/0.48 ((~(((~(A!14 = tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)))) | (~in(A!14, C!12))) <=> in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12)))) <=> (~(((~in(A!14, C!12)) | (~(A!14 = tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))))) <=> in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[39, 37])).
% 0.22/0.48 tff(41,plain,
% 0.22/0.48 (((~![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, C!12))) <=> in(ordered_pair(C, D), identity_relation(C!12))))) | (~(((~(A!14 = tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)))) | (~in(A!14, C!12))) <=> in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12))))) <=> ((~![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, C!12))) <=> in(ordered_pair(C, D), identity_relation(C!12))))) | (~(((~in(A!14, C!12)) | (~(A!14 = tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))))) <=> in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12)))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[40])).
% 0.22/0.48 tff(42,plain,
% 0.22/0.48 (((~![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, C!12))) <=> in(ordered_pair(C, D), identity_relation(C!12))))) | (~(((~(A!14 = tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)))) | (~in(A!14, C!12))) <=> in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12))))) <=> ((~![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, C!12))) <=> in(ordered_pair(C, D), identity_relation(C!12))))) | (~(((~in(A!14, C!12)) | (~(A!14 = tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))))) <=> in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12)))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[41, 36])).
% 0.22/0.48 tff(43,plain,
% 0.22/0.48 ((~![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, C!12))) <=> in(ordered_pair(C, D), identity_relation(C!12))))) | (~(((~(A!14 = tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)))) | (~in(A!14, C!12))) <=> in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12))))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(44,plain,
% 0.22/0.48 ((~![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, C!12))) <=> in(ordered_pair(C, D), identity_relation(C!12))))) | (~(((~in(A!14, C!12)) | (~(A!14 = tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))))) <=> in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.22/0.48 tff(45,plain,
% 0.22/0.48 (~(((~in(A!14, C!12)) | (~(A!14 = tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))))) <=> in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12)))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[44, 35])).
% 0.22/0.48 tff(46,assumption,(~(in(A!14, C!12) <=> in(ordered_pair(A!14, A!14), identity_relation(C!12)))), introduced(assumption)).
% 0.22/0.48 tff(47,plain,
% 0.22/0.48 (((~![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, C!12))) <=> in(ordered_pair(C, D), identity_relation(C!12))))) | (in(A!14, C!12) <=> in(ordered_pair(A!14, A!14), identity_relation(C!12)))) <=> ((~![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, C!12))) <=> in(ordered_pair(C, D), identity_relation(C!12))))) | (in(A!14, C!12) <=> in(ordered_pair(A!14, A!14), identity_relation(C!12))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(48,plain,
% 0.22/0.48 ((~(~(in(A!14, C!12) <=> in(ordered_pair(A!14, A!14), identity_relation(C!12))))) <=> (in(A!14, C!12) <=> in(ordered_pair(A!14, A!14), identity_relation(C!12)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(49,plain,
% 0.22/0.48 ((~(in(A!14, C!12) <=> in(ordered_pair(A!14, A!14), identity_relation(C!12)))) <=> (~(in(A!14, C!12) <=> in(ordered_pair(A!14, A!14), identity_relation(C!12))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(50,plain,
% 0.22/0.48 (((~in(A!14, C!12)) <=> in(ordered_pair(A!14, A!14), identity_relation(C!12))) <=> (~(in(A!14, C!12) <=> in(ordered_pair(A!14, A!14), identity_relation(C!12))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(51,plain,
% 0.22/0.48 (($false | (~in(A!14, C!12))) <=> (~in(A!14, C!12))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(52,plain,
% 0.22/0.48 ((~$true) <=> $false),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(53,plain,
% 0.22/0.48 ((A!14 = A!14) <=> $true),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(54,plain,
% 0.22/0.48 ((~(A!14 = A!14)) <=> (~$true)),
% 0.22/0.48 inference(monotonicity,[status(thm)],[53])).
% 0.22/0.48 tff(55,plain,
% 0.22/0.48 ((~(A!14 = A!14)) <=> $false),
% 0.22/0.48 inference(transitivity,[status(thm)],[54, 52])).
% 0.22/0.48 tff(56,plain,
% 0.22/0.48 (((~(A!14 = A!14)) | (~in(A!14, C!12))) <=> ($false | (~in(A!14, C!12)))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[55])).
% 0.22/0.48 tff(57,plain,
% 0.22/0.48 (((~(A!14 = A!14)) | (~in(A!14, C!12))) <=> (~in(A!14, C!12))),
% 0.22/0.48 inference(transitivity,[status(thm)],[56, 51])).
% 0.22/0.48 tff(58,plain,
% 0.22/0.48 ((((~(A!14 = A!14)) | (~in(A!14, C!12))) <=> in(ordered_pair(A!14, A!14), identity_relation(C!12))) <=> ((~in(A!14, C!12)) <=> in(ordered_pair(A!14, A!14), identity_relation(C!12)))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[57])).
% 0.22/0.48 tff(59,plain,
% 0.22/0.48 ((((~(A!14 = A!14)) | (~in(A!14, C!12))) <=> in(ordered_pair(A!14, A!14), identity_relation(C!12))) <=> (~(in(A!14, C!12) <=> in(ordered_pair(A!14, A!14), identity_relation(C!12))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[58, 50])).
% 0.22/0.48 tff(60,plain,
% 0.22/0.48 ((((~(A!14 = A!14)) | (~in(A!14, C!12))) <=> in(ordered_pair(A!14, A!14), identity_relation(C!12))) <=> (~(in(A!14, C!12) <=> in(ordered_pair(A!14, A!14), identity_relation(C!12))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[59, 49])).
% 0.22/0.48 tff(61,plain,
% 0.22/0.48 ((~(((~(A!14 = A!14)) | (~in(A!14, C!12))) <=> in(ordered_pair(A!14, A!14), identity_relation(C!12)))) <=> (~(~(in(A!14, C!12) <=> in(ordered_pair(A!14, A!14), identity_relation(C!12)))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[60])).
% 0.22/0.48 tff(62,plain,
% 0.22/0.48 ((~(((~(A!14 = A!14)) | (~in(A!14, C!12))) <=> in(ordered_pair(A!14, A!14), identity_relation(C!12)))) <=> (in(A!14, C!12) <=> in(ordered_pair(A!14, A!14), identity_relation(C!12)))),
% 0.22/0.48 inference(transitivity,[status(thm)],[61, 48])).
% 0.22/0.48 tff(63,plain,
% 0.22/0.48 (((~![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, C!12))) <=> in(ordered_pair(C, D), identity_relation(C!12))))) | (~(((~(A!14 = A!14)) | (~in(A!14, C!12))) <=> in(ordered_pair(A!14, A!14), identity_relation(C!12))))) <=> ((~![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, C!12))) <=> in(ordered_pair(C, D), identity_relation(C!12))))) | (in(A!14, C!12) <=> in(ordered_pair(A!14, A!14), identity_relation(C!12))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[62])).
% 0.22/0.48 tff(64,plain,
% 0.22/0.48 (((~![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, C!12))) <=> in(ordered_pair(C, D), identity_relation(C!12))))) | (~(((~(A!14 = A!14)) | (~in(A!14, C!12))) <=> in(ordered_pair(A!14, A!14), identity_relation(C!12))))) <=> ((~![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, C!12))) <=> in(ordered_pair(C, D), identity_relation(C!12))))) | (in(A!14, C!12) <=> in(ordered_pair(A!14, A!14), identity_relation(C!12))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[63, 47])).
% 0.22/0.48 tff(65,plain,
% 0.22/0.48 ((~![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, C!12))) <=> in(ordered_pair(C, D), identity_relation(C!12))))) | (~(((~(A!14 = A!14)) | (~in(A!14, C!12))) <=> in(ordered_pair(A!14, A!14), identity_relation(C!12))))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(66,plain,
% 0.22/0.48 ((~![C: $i, D: $i] : (~(((~(C = D)) | (~in(C, C!12))) <=> in(ordered_pair(C, D), identity_relation(C!12))))) | (in(A!14, C!12) <=> in(ordered_pair(A!14, A!14), identity_relation(C!12)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.22/0.48 tff(67,plain,
% 0.22/0.48 ($false),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[66, 35, 46])).
% 0.22/0.48 tff(68,plain,(in(A!14, C!12) <=> in(ordered_pair(A!14, A!14), identity_relation(C!12))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.48 tff(69,assumption,(~((~in(A!14, C!12)) | (~in(ordered_pair(A!14, B!13), D!11)))), introduced(assumption)).
% 0.22/0.48 tff(70,plain,
% 0.22/0.48 (((~in(A!14, C!12)) | (~in(ordered_pair(A!14, B!13), D!11))) | in(A!14, C!12)),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(71,plain,
% 0.22/0.48 (in(A!14, C!12)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.22/0.48 tff(72,plain,
% 0.22/0.48 ((~(in(A!14, C!12) <=> in(ordered_pair(A!14, A!14), identity_relation(C!12)))) | (~in(A!14, C!12)) | in(ordered_pair(A!14, A!14), identity_relation(C!12))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(73,plain,
% 0.22/0.48 (in(ordered_pair(A!14, A!14), identity_relation(C!12))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[72, 71, 68])).
% 0.22/0.48 tff(74,plain,
% 0.22/0.48 ((~(~(((~in(A!14, C!12)) | (~in(ordered_pair(A!14, B!13), D!11))) <=> in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11))))) <=> (((~in(A!14, C!12)) | (~in(ordered_pair(A!14, B!13), D!11))) <=> in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(75,plain,
% 0.22/0.48 ((~(((~in(A!14, C!12)) | (~in(ordered_pair(A!14, B!13), D!11))) <=> in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11)))) <=> (~(((~in(A!14, C!12)) | (~in(ordered_pair(A!14, B!13), D!11))) <=> in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(76,plain,
% 0.22/0.48 ((in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11)) <=> (~((~in(A!14, C!12)) | (~in(ordered_pair(A!14, B!13), D!11))))) <=> (~(((~in(A!14, C!12)) | (~in(ordered_pair(A!14, B!13), D!11))) <=> in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(77,plain,
% 0.22/0.48 ((in(A!14, C!12) & in(ordered_pair(A!14, B!13), D!11)) <=> (~((~in(A!14, C!12)) | (~in(ordered_pair(A!14, B!13), D!11))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(78,plain,
% 0.22/0.48 ((in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11)) <=> (in(A!14, C!12) & in(ordered_pair(A!14, B!13), D!11))) <=> (in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11)) <=> (~((~in(A!14, C!12)) | (~in(ordered_pair(A!14, B!13), D!11)))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[77])).
% 0.22/0.48 tff(79,plain,
% 0.22/0.48 ((in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11)) <=> (in(A!14, C!12) & in(ordered_pair(A!14, B!13), D!11))) <=> (~(((~in(A!14, C!12)) | (~in(ordered_pair(A!14, B!13), D!11))) <=> in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[78, 76])).
% 0.22/0.48 tff(80,plain,
% 0.22/0.48 ((in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11)) <=> (in(A!14, C!12) & in(ordered_pair(A!14, B!13), D!11))) <=> (~(((~in(A!14, C!12)) | (~in(ordered_pair(A!14, B!13), D!11))) <=> in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[79, 75])).
% 0.22/0.48 tff(81,plain,
% 0.22/0.48 ((~(in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11)) <=> (in(A!14, C!12) & in(ordered_pair(A!14, B!13), D!11)))) <=> (~(~(((~in(A!14, C!12)) | (~in(ordered_pair(A!14, B!13), D!11))) <=> in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11)))))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[80])).
% 0.22/0.49 tff(82,plain,
% 0.22/0.49 ((~(in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11)) <=> (in(A!14, C!12) & in(ordered_pair(A!14, B!13), D!11)))) <=> (((~in(A!14, C!12)) | (~in(ordered_pair(A!14, B!13), D!11))) <=> in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11)))),
% 0.22/0.49 inference(transitivity,[status(thm)],[81, 74])).
% 0.22/0.49 tff(83,plain,
% 0.22/0.49 ((~![A: $i, B: $i, C: $i, D: $i] : ((~relation(D)) | (in(ordered_pair(A, B), relation_composition(identity_relation(C), D)) <=> (in(A, C) & in(ordered_pair(A, B), D))))) <=> (~![A: $i, B: $i, C: $i, D: $i] : ((~relation(D)) | (in(ordered_pair(A, B), relation_composition(identity_relation(C), D)) <=> (in(A, C) & in(ordered_pair(A, B), D)))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(84,plain,
% 0.22/0.49 ((~![A: $i, B: $i, C: $i, D: $i] : (relation(D) => (in(ordered_pair(A, B), relation_composition(identity_relation(C), D)) <=> (in(A, C) & in(ordered_pair(A, B), D))))) <=> (~![A: $i, B: $i, C: $i, D: $i] : ((~relation(D)) | (in(ordered_pair(A, B), relation_composition(identity_relation(C), D)) <=> (in(A, C) & in(ordered_pair(A, B), D)))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(85,axiom,(~![A: $i, B: $i, C: $i, D: $i] : (relation(D) => (in(ordered_pair(A, B), relation_composition(identity_relation(C), D)) <=> (in(A, C) & in(ordered_pair(A, B), D))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t74_relat_1')).
% 0.22/0.49 tff(86,plain,
% 0.22/0.49 (~![A: $i, B: $i, C: $i, D: $i] : ((~relation(D)) | (in(ordered_pair(A, B), relation_composition(identity_relation(C), D)) <=> (in(A, C) & in(ordered_pair(A, B), D))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.22/0.49 tff(87,plain,
% 0.22/0.49 (~![A: $i, B: $i, C: $i, D: $i] : ((~relation(D)) | (in(ordered_pair(A, B), relation_composition(identity_relation(C), D)) <=> (in(A, C) & in(ordered_pair(A, B), D))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[86, 83])).
% 0.22/0.49 tff(88,plain,
% 0.22/0.49 (~![A: $i, B: $i, C: $i, D: $i] : ((~relation(D)) | (in(ordered_pair(A, B), relation_composition(identity_relation(C), D)) <=> (in(A, C) & in(ordered_pair(A, B), D))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.22/0.49 tff(89,plain,
% 0.22/0.49 (~![A: $i, B: $i, C: $i, D: $i] : ((~relation(D)) | (in(ordered_pair(A, B), relation_composition(identity_relation(C), D)) <=> (in(A, C) & in(ordered_pair(A, B), D))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[88, 83])).
% 0.22/0.49 tff(90,plain,(
% 0.22/0.49 ~((~relation(D!11)) | (in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11)) <=> (in(A!14, C!12) & in(ordered_pair(A!14, B!13), D!11))))),
% 0.22/0.49 inference(skolemize,[status(sab)],[89])).
% 0.22/0.49 tff(91,plain,
% 0.22/0.49 (~(in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11)) <=> (in(A!14, C!12) & in(ordered_pair(A!14, B!13), D!11)))),
% 0.22/0.49 inference(or_elim,[status(thm)],[90])).
% 0.22/0.49 tff(92,plain,
% 0.22/0.49 (((~in(A!14, C!12)) | (~in(ordered_pair(A!14, B!13), D!11))) <=> in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[91, 82])).
% 0.22/0.49 tff(93,plain,
% 0.22/0.49 (((~in(A!14, C!12)) | (~in(ordered_pair(A!14, B!13), D!11))) | (~in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11))) | (~(((~in(A!14, C!12)) | (~in(ordered_pair(A!14, B!13), D!11))) <=> in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11))))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(94,plain,
% 0.22/0.49 (((~in(A!14, C!12)) | (~in(ordered_pair(A!14, B!13), D!11))) | (~in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11)))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.22/0.49 tff(95,plain,
% 0.22/0.49 (~in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[94, 69])).
% 0.22/0.49 tff(96,plain,
% 0.22/0.49 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_composition(A, B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(D, tptp_fun_F_2(E, D, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_2(E, D, B, A), E), B)))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(D, F), A)) | (~in(ordered_pair(F, E), B))))))))) | (~((C = relation_composition(A, B)) | (~((~(in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_F_5(C, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_5(C, B, A), tptp_fun_E_3(C, B, A)), B)))))) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, A), F), A)) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, A)), B)))))))))))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(A, B)) | (~((~(in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_F_5(C, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_5(C, B, A), tptp_fun_E_3(C, B, A)), B)))))) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, A), F), A)) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, A)), B))))))))) | (~((~(C = relation_composition(A, B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(D, tptp_fun_F_2(E, D, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_2(E, D, B, A), E), B)))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(D, F), A)) | (~in(ordered_pair(F, E), B)))))))))))))))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(97,plain,
% 0.22/0.49 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_composition(A, B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(D, tptp_fun_F_2(E, D, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_2(E, D, B, A), E), B)))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(D, F), A)) | (~in(ordered_pair(F, E), B))))))))) | (~((C = relation_composition(A, B)) | (~((~(in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_F_5(C, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_5(C, B, A), tptp_fun_E_3(C, B, A)), B)))))) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, A), F), A)) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, A)), B)))))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(A, B)) | (~((~(in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_F_5(C, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_5(C, B, A), tptp_fun_E_3(C, B, A)), B)))))) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, A), F), A)) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, A)), B))))))))) | (~((~(C = relation_composition(A, B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(D, tptp_fun_F_2(E, D, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_2(E, D, B, A), E), B)))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(D, F), A)) | (~in(ordered_pair(F, E), B))))))))))))))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[96])).
% 0.22/0.49 tff(98,plain,
% 0.22/0.49 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_composition(A, B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(D, tptp_fun_F_2(E, D, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_2(E, D, B, A), E), B)))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(D, F), A)) | (~in(ordered_pair(F, E), B))))))))) | (~((C = relation_composition(A, B)) | (~((~(in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_F_5(C, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_5(C, B, A), tptp_fun_E_3(C, B, A)), B)))))) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, A), F), A)) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, A)), B)))))))))))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_composition(A, B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(D, tptp_fun_F_2(E, D, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_2(E, D, B, A), E), B)))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(D, F), A)) | (~in(ordered_pair(F, E), B))))))))) | (~((C = relation_composition(A, B)) | (~((~(in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_F_5(C, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_5(C, B, A), tptp_fun_E_3(C, B, A)), B)))))) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, A), F), A)) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, A)), B)))))))))))))))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(99,plain,
% 0.22/0.49 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_composition(A, B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(D, tptp_fun_F_2(E, D, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_2(E, D, B, A), E), B)))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(D, F), A)) | (~in(ordered_pair(F, E), B))))))))) | (~((C = relation_composition(A, B)) | (~((~(in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_F_5(C, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_5(C, B, A), tptp_fun_E_3(C, B, A)), B)))))) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, A), F), A)) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, A)), B)))))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_composition(A, B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(D, tptp_fun_F_2(E, D, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_2(E, D, B, A), E), B)))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(D, F), A)) | (~in(ordered_pair(F, E), B))))))))) | (~((C = relation_composition(A, B)) | (~((~(in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_F_5(C, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_5(C, B, A), tptp_fun_E_3(C, B, A)), B)))))) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, A), F), A)) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, A)), B))))))))))))))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[98])).
% 0.22/0.49 tff(100,plain,
% 0.22/0.49 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_composition(A, B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(D, tptp_fun_F_2(E, D, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_2(E, D, B, A), E), B)))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(D, F), A)) | (~in(ordered_pair(F, E), B))))))))) | (~((C = relation_composition(A, B)) | (~((~(in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_F_5(C, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_5(C, B, A), tptp_fun_E_3(C, B, A)), B)))))) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, A), F), A)) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, A)), B)))))))))))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_composition(A, B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(D, tptp_fun_F_2(E, D, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_2(E, D, B, A), E), B)))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(D, F), A)) | (~in(ordered_pair(F, E), B))))))))) | (~((C = relation_composition(A, B)) | (~((~(in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_F_5(C, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_5(C, B, A), tptp_fun_E_3(C, B, A)), B)))))) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, A), F), A)) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, A)), B)))))))))))))))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(101,plain,
% 0.22/0.49 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_composition(A, B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(D, tptp_fun_F_2(E, D, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_2(E, D, B, A), E), B)))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(D, F), A)) | (~in(ordered_pair(F, E), B))))))))) | (~((C = relation_composition(A, B)) | (~((~(in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_F_5(C, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_5(C, B, A), tptp_fun_E_3(C, B, A)), B)))))) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, A), F), A)) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, A)), B)))))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_composition(A, B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(D, tptp_fun_F_2(E, D, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_2(E, D, B, A), E), B)))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(D, F), A)) | (~in(ordered_pair(F, E), B))))))))) | (~((C = relation_composition(A, B)) | (~((~(in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_F_5(C, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_5(C, B, A), tptp_fun_E_3(C, B, A)), B)))))) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, A), F), A)) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, A)), B))))))))))))))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[100])).
% 0.22/0.49 tff(102,plain,
% 0.22/0.49 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_composition(A, B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(D, tptp_fun_F_2(E, D, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_2(E, D, B, A), E), B)))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(D, F), A)) | (~in(ordered_pair(F, E), B))))))))) | (~((C = relation_composition(A, B)) | (~((~(in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_F_5(C, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_5(C, B, A), tptp_fun_E_3(C, B, A)), B)))))) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, A), F), A)) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, A)), B)))))))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_composition(A, B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(D, tptp_fun_F_2(E, D, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_2(E, D, B, A), E), B)))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(D, F), A)) | (~in(ordered_pair(F, E), B))))))))) | (~((C = relation_composition(A, B)) | (~((~(in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_F_5(C, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_5(C, B, A), tptp_fun_E_3(C, B, A)), B)))))) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, A), F), A)) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, A)), B))))))))))))))),
% 0.22/0.49 inference(transitivity,[status(thm)],[101, 99])).
% 0.22/0.49 tff(103,plain,
% 0.22/0.49 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (((~(C = relation_composition(A, B))) | ![D: $i, E: $i] : (((~in(ordered_pair(D, E), C)) | (in(ordered_pair(D, tptp_fun_F_2(E, D, B, A)), A) & in(ordered_pair(tptp_fun_F_2(E, D, B, A), E), B))) & (in(ordered_pair(D, E), C) | ![F: $i] : (~(in(ordered_pair(D, F), A) & in(ordered_pair(F, E), B)))))) & ((C = relation_composition(A, B)) | ((in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C) | (in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_F_5(C, B, A)), A) & in(ordered_pair(tptp_fun_F_5(C, B, A), tptp_fun_E_3(C, B, A)), B))) & ((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C)) | ![F: $i] : (~(in(ordered_pair(tptp_fun_D_4(C, B, A), F), A) & in(ordered_pair(F, tptp_fun_E_3(C, B, A)), B)))))))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_composition(A, B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(D, tptp_fun_F_2(E, D, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_2(E, D, B, A), E), B)))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(D, F), A)) | (~in(ordered_pair(F, E), B))))))))) | (~((C = relation_composition(A, B)) | (~((~(in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_F_5(C, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_5(C, B, A), tptp_fun_E_3(C, B, A)), B)))))) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, A), F), A)) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, A)), B)))))))))))))))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(104,plain,
% 0.22/0.49 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (((~(C = relation_composition(A, B))) | ![D: $i, E: $i] : (((~in(ordered_pair(D, E), C)) | (in(ordered_pair(D, tptp_fun_F_2(E, D, B, A)), A) & in(ordered_pair(tptp_fun_F_2(E, D, B, A), E), B))) & (in(ordered_pair(D, E), C) | ![F: $i] : (~(in(ordered_pair(D, F), A) & in(ordered_pair(F, E), B)))))) & ((C = relation_composition(A, B)) | ((in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C) | (in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_F_5(C, B, A)), A) & in(ordered_pair(tptp_fun_F_5(C, B, A), tptp_fun_E_3(C, B, A)), B))) & ((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C)) | ![F: $i] : (~(in(ordered_pair(tptp_fun_D_4(C, B, A), F), A) & in(ordered_pair(F, tptp_fun_E_3(C, B, A)), B)))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_composition(A, B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(D, tptp_fun_F_2(E, D, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_2(E, D, B, A), E), B)))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(D, F), A)) | (~in(ordered_pair(F, E), B))))))))) | (~((C = relation_composition(A, B)) | (~((~(in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_F_5(C, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_5(C, B, A), tptp_fun_E_3(C, B, A)), B)))))) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, A), F), A)) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, A)), B))))))))))))))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[103])).
% 0.22/0.49 tff(105,plain,
% 0.22/0.49 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_composition(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> ?[F: $i] : (in(ordered_pair(D, F), A) & in(ordered_pair(F, E), B))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_composition(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> ?[F: $i] : (in(ordered_pair(D, F), A) & in(ordered_pair(F, E), B)))))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(106,plain,
% 0.22/0.49 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((C = relation_composition(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> ?[F: $i] : (in(ordered_pair(D, F), A) & in(ordered_pair(F, E), B)))) <=> ((C = relation_composition(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> ?[F: $i] : (in(ordered_pair(D, F), A) & in(ordered_pair(F, E), B))))), ((relation(C) => ((C = relation_composition(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> ?[F: $i] : (in(ordered_pair(D, F), A) & in(ordered_pair(F, E), B))))) <=> (relation(C) => ((C = relation_composition(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> ?[F: $i] : (in(ordered_pair(D, F), A) & in(ordered_pair(F, E), B))))))), rewrite((relation(C) => ((C = relation_composition(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> ?[F: $i] : (in(ordered_pair(D, F), A) & in(ordered_pair(F, E), B))))) <=> ((~relation(C)) | ((C = relation_composition(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> ?[F: $i] : (in(ordered_pair(D, F), A) & in(ordered_pair(F, E), B)))))), ((relation(C) => ((C = relation_composition(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> ?[F: $i] : (in(ordered_pair(D, F), A) & in(ordered_pair(F, E), B))))) <=> ((~relation(C)) | ((C = relation_composition(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> ?[F: $i] : (in(ordered_pair(D, F), A) & in(ordered_pair(F, E), B)))))))), (![C: $i] : (relation(C) => ((C = relation_composition(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> ?[F: $i] : (in(ordered_pair(D, F), A) & in(ordered_pair(F, E), B))))) <=> ![C: $i] : ((~relation(C)) | ((C = relation_composition(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> ?[F: $i] : (in(ordered_pair(D, F), A) & in(ordered_pair(F, E), B))))))), ((relation(B) => ![C: $i] : (relation(C) => ((C = relation_composition(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> ?[F: $i] : (in(ordered_pair(D, F), A) & in(ordered_pair(F, E), B)))))) <=> (relation(B) => ![C: $i] : ((~relation(C)) | ((C = relation_composition(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> ?[F: $i] : (in(ordered_pair(D, F), A) & in(ordered_pair(F, E), B)))))))), rewrite((relation(B) => ![C: $i] : ((~relation(C)) | ((C = relation_composition(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> ?[F: $i] : (in(ordered_pair(D, F), A) & in(ordered_pair(F, E), B)))))) <=> ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_composition(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> ?[F: $i] : (in(ordered_pair(D, F), A) & in(ordered_pair(F, E), B))))))), ((relation(B) => ![C: $i] : (relation(C) => ((C = relation_composition(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> ?[F: $i] : (in(ordered_pair(D, F), A) & in(ordered_pair(F, E), B)))))) <=> ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_composition(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> ?[F: $i] : (in(ordered_pair(D, F), A) & in(ordered_pair(F, E), B))))))))), (![B: $i] : (relation(B) => ![C: $i] : (relation(C) => ((C = relation_composition(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> ?[F: $i] : (in(ordered_pair(D, F), A) & in(ordered_pair(F, E), B)))))) <=> ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_composition(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> ?[F: $i] : (in(ordered_pair(D, F), A) & in(ordered_pair(F, E), B)))))))), ((relation(A) => ![B: $i] : (relation(B) => ![C: $i] : (relation(C) => ((C = relation_composition(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> ?[F: $i] : (in(ordered_pair(D, F), A) & in(ordered_pair(F, E), B))))))) <=> (relation(A) => ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_composition(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> ?[F: $i] : (in(ordered_pair(D, F), A) & in(ordered_pair(F, E), B))))))))), rewrite((relation(A) => ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_composition(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> ?[F: $i] : (in(ordered_pair(D, F), A) & in(ordered_pair(F, E), B))))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_composition(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> ?[F: $i] : (in(ordered_pair(D, F), A) & in(ordered_pair(F, E), B)))))))), ((relation(A) => ![B: $i] : (relation(B) => ![C: $i] : (relation(C) => ((C = relation_composition(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> ?[F: $i] : (in(ordered_pair(D, F), A) & in(ordered_pair(F, E), B))))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_composition(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> ?[F: $i] : (in(ordered_pair(D, F), A) & in(ordered_pair(F, E), B)))))))))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(107,plain,
% 0.22/0.49 (![A: $i] : (relation(A) => ![B: $i] : (relation(B) => ![C: $i] : (relation(C) => ((C = relation_composition(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> ?[F: $i] : (in(ordered_pair(D, F), A) & in(ordered_pair(F, E), B))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_composition(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> ?[F: $i] : (in(ordered_pair(D, F), A) & in(ordered_pair(F, E), B)))))))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[106])).
% 0.22/0.49 tff(108,axiom,(![A: $i] : (relation(A) => ![B: $i] : (relation(B) => ![C: $i] : (relation(C) => ((C = relation_composition(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> ?[F: $i] : (in(ordered_pair(D, F), A) & in(ordered_pair(F, E), B)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d8_relat_1')).
% 0.22/0.49 tff(109,plain,
% 0.22/0.49 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_composition(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> ?[F: $i] : (in(ordered_pair(D, F), A) & in(ordered_pair(F, E), B)))))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.22/0.49 tff(110,plain,
% 0.22/0.49 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_composition(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> ?[F: $i] : (in(ordered_pair(D, F), A) & in(ordered_pair(F, E), B)))))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.22/0.49 tff(111,plain,(
% 0.22/0.49 ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (((~(C = relation_composition(A, B))) | ![D: $i, E: $i] : (((~in(ordered_pair(D, E), C)) | (in(ordered_pair(D, tptp_fun_F_2(E, D, B, A)), A) & in(ordered_pair(tptp_fun_F_2(E, D, B, A), E), B))) & (in(ordered_pair(D, E), C) | ![F: $i] : (~(in(ordered_pair(D, F), A) & in(ordered_pair(F, E), B)))))) & ((C = relation_composition(A, B)) | ((in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C) | (in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_F_5(C, B, A)), A) & in(ordered_pair(tptp_fun_F_5(C, B, A), tptp_fun_E_3(C, B, A)), B))) & ((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C)) | ![F: $i] : (~(in(ordered_pair(tptp_fun_D_4(C, B, A), F), A) & in(ordered_pair(F, tptp_fun_E_3(C, B, A)), B))))))))))),
% 0.22/0.49 inference(skolemize,[status(sab)],[110])).
% 0.22/0.49 tff(112,plain,
% 0.22/0.49 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_composition(A, B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(D, tptp_fun_F_2(E, D, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_2(E, D, B, A), E), B)))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(D, F), A)) | (~in(ordered_pair(F, E), B))))))))) | (~((C = relation_composition(A, B)) | (~((~(in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_F_5(C, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_5(C, B, A), tptp_fun_E_3(C, B, A)), B)))))) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, A), F), A)) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, A)), B))))))))))))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.22/0.49 tff(113,plain,
% 0.22/0.49 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_composition(A, B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(D, tptp_fun_F_2(E, D, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_2(E, D, B, A), E), B)))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(D, F), A)) | (~in(ordered_pair(F, E), B))))))))) | (~((C = relation_composition(A, B)) | (~((~(in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_F_5(C, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_5(C, B, A), tptp_fun_E_3(C, B, A)), B)))))) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, A), F), A)) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, A)), B))))))))))))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[112, 102])).
% 0.22/0.49 tff(114,plain,
% 0.22/0.49 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(A, B)) | (~((~(in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_F_5(C, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_5(C, B, A), tptp_fun_E_3(C, B, A)), B)))))) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, A), F), A)) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, A)), B))))))))) | (~((~(C = relation_composition(A, B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(D, tptp_fun_F_2(E, D, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_2(E, D, B, A), E), B)))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(D, F), A)) | (~in(ordered_pair(F, E), B))))))))))))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[113, 97])).
% 0.22/0.49 tff(115,plain,
% 0.22/0.49 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(A, B)) | (~((~(in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_F_5(C, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_5(C, B, A), tptp_fun_E_3(C, B, A)), B)))))) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, A), F), A)) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, A)), B))))))))) | (~((~(C = relation_composition(A, B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(D, tptp_fun_F_2(E, D, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_2(E, D, B, A), E), B)))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(D, F), A)) | (~in(ordered_pair(F, E), B))))))))))))))) | ((~relation(identity_relation(C!12))) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), B)) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, identity_relation(C!12))), B))))) | (~(in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_F_5(C, B, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), B)))))))))) | (~((~(C = relation_composition(identity_relation(C!12), B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, B, identity_relation(C!12)), E), B)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, B, identity_relation(C!12))), identity_relation(C!12))))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(F, E), B)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(A, B)) | (~((~(in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_F_5(C, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_5(C, B, A), tptp_fun_E_3(C, B, A)), B)))))) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, A), F), A)) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, A)), B))))))))) | (~((~(C = relation_composition(A, B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(D, tptp_fun_F_2(E, D, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_2(E, D, B, A), E), B)))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(D, F), A)) | (~in(ordered_pair(F, E), B))))))))))))))) | (~relation(identity_relation(C!12))) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), B)) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, identity_relation(C!12))), B))))) | (~(in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_F_5(C, B, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), B)))))))))) | (~((~(C = relation_composition(identity_relation(C!12), B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, B, identity_relation(C!12)), E), B)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, B, identity_relation(C!12))), identity_relation(C!12))))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(F, E), B)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))))))))))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(116,plain,
% 0.22/0.49 (((~relation(identity_relation(C!12))) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), B)) | (~((~(in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_F_5(C, B, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), B)))))) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, identity_relation(C!12))), B))))))))) | (~((~(C = relation_composition(identity_relation(C!12), B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(D, tptp_fun_F_2(E, D, B, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_2(E, D, B, identity_relation(C!12)), E), B)))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(D, F), identity_relation(C!12))) | (~in(ordered_pair(F, E), B)))))))))))))) <=> ((~relation(identity_relation(C!12))) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), B)) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, identity_relation(C!12))), B))))) | (~(in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_F_5(C, B, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), B)))))))))) | (~((~(C = relation_composition(identity_relation(C!12), B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, B, identity_relation(C!12)), E), B)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, B, identity_relation(C!12))), identity_relation(C!12))))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(F, E), B)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))))))))))))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(117,plain,
% 0.22/0.50 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(A, B)) | (~((~(in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_F_5(C, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_5(C, B, A), tptp_fun_E_3(C, B, A)), B)))))) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, A), F), A)) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, A)), B))))))))) | (~((~(C = relation_composition(A, B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(D, tptp_fun_F_2(E, D, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_2(E, D, B, A), E), B)))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(D, F), A)) | (~in(ordered_pair(F, E), B))))))))))))))) | ((~relation(identity_relation(C!12))) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), B)) | (~((~(in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_F_5(C, B, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), B)))))) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, identity_relation(C!12))), B))))))))) | (~((~(C = relation_composition(identity_relation(C!12), B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(D, tptp_fun_F_2(E, D, B, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_2(E, D, B, identity_relation(C!12)), E), B)))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(D, F), identity_relation(C!12))) | (~in(ordered_pair(F, E), B))))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(A, B)) | (~((~(in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_F_5(C, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_5(C, B, A), tptp_fun_E_3(C, B, A)), B)))))) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, A), F), A)) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, A)), B))))))))) | (~((~(C = relation_composition(A, B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(D, tptp_fun_F_2(E, D, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_2(E, D, B, A), E), B)))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(D, F), A)) | (~in(ordered_pair(F, E), B))))))))))))))) | ((~relation(identity_relation(C!12))) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), B)) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, identity_relation(C!12))), B))))) | (~(in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_F_5(C, B, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), B)))))))))) | (~((~(C = relation_composition(identity_relation(C!12), B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, B, identity_relation(C!12)), E), B)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, B, identity_relation(C!12))), identity_relation(C!12))))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(F, E), B)) | (~in(ordered_pair(D, F), identity_relation(C!12))))))))))))))))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[116])).
% 0.22/0.50 tff(118,plain,
% 0.22/0.50 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(A, B)) | (~((~(in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_F_5(C, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_5(C, B, A), tptp_fun_E_3(C, B, A)), B)))))) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, A), F), A)) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, A)), B))))))))) | (~((~(C = relation_composition(A, B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(D, tptp_fun_F_2(E, D, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_2(E, D, B, A), E), B)))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(D, F), A)) | (~in(ordered_pair(F, E), B))))))))))))))) | ((~relation(identity_relation(C!12))) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), B)) | (~((~(in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_F_5(C, B, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), B)))))) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, identity_relation(C!12))), B))))))))) | (~((~(C = relation_composition(identity_relation(C!12), B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(D, tptp_fun_F_2(E, D, B, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_2(E, D, B, identity_relation(C!12)), E), B)))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(D, F), identity_relation(C!12))) | (~in(ordered_pair(F, E), B))))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(A, B)) | (~((~(in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_F_5(C, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_5(C, B, A), tptp_fun_E_3(C, B, A)), B)))))) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, A), F), A)) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, A)), B))))))))) | (~((~(C = relation_composition(A, B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(D, tptp_fun_F_2(E, D, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_2(E, D, B, A), E), B)))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(D, F), A)) | (~in(ordered_pair(F, E), B))))))))))))))) | (~relation(identity_relation(C!12))) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), B)) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, identity_relation(C!12))), B))))) | (~(in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_F_5(C, B, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), B)))))))))) | (~((~(C = relation_composition(identity_relation(C!12), B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, B, identity_relation(C!12)), E), B)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, B, identity_relation(C!12))), identity_relation(C!12))))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(F, E), B)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))))))))))))),
% 0.22/0.50 inference(transitivity,[status(thm)],[117, 115])).
% 0.22/0.50 tff(119,plain,
% 0.22/0.50 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(A, B)) | (~((~(in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_F_5(C, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_5(C, B, A), tptp_fun_E_3(C, B, A)), B)))))) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, A), F), A)) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, A)), B))))))))) | (~((~(C = relation_composition(A, B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(D, tptp_fun_F_2(E, D, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_2(E, D, B, A), E), B)))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(D, F), A)) | (~in(ordered_pair(F, E), B))))))))))))))) | ((~relation(identity_relation(C!12))) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), B)) | (~((~(in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_F_5(C, B, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), B)))))) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, identity_relation(C!12))), B))))))))) | (~((~(C = relation_composition(identity_relation(C!12), B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(D, tptp_fun_F_2(E, D, B, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_2(E, D, B, identity_relation(C!12)), E), B)))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(D, F), identity_relation(C!12))) | (~in(ordered_pair(F, E), B))))))))))))))),
% 0.22/0.50 inference(quant_inst,[status(thm)],[])).
% 0.22/0.50 tff(120,plain,
% 0.22/0.50 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(A, B)) | (~((~(in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_F_5(C, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_5(C, B, A), tptp_fun_E_3(C, B, A)), B)))))) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, A), tptp_fun_E_3(C, B, A)), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, A), F), A)) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, A)), B))))))))) | (~((~(C = relation_composition(A, B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(D, tptp_fun_F_2(E, D, B, A)), A)) | (~in(ordered_pair(tptp_fun_F_2(E, D, B, A), E), B)))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(D, F), A)) | (~in(ordered_pair(F, E), B))))))))))))))) | (~relation(identity_relation(C!12))) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), B)) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, identity_relation(C!12))), B))))) | (~(in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_F_5(C, B, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), B)))))))))) | (~((~(C = relation_composition(identity_relation(C!12), B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, B, identity_relation(C!12)), E), B)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, B, identity_relation(C!12))), identity_relation(C!12))))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(F, E), B)) | (~in(ordered_pair(D, F), identity_relation(C!12))))))))))))))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.22/0.50 tff(121,plain,
% 0.22/0.50 (![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), B)) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, identity_relation(C!12))), B))))) | (~(in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_F_5(C, B, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), B)))))))))) | (~((~(C = relation_composition(identity_relation(C!12), B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, B, identity_relation(C!12)), E), B)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, B, identity_relation(C!12))), identity_relation(C!12))))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(F, E), B)) | (~in(ordered_pair(D, F), identity_relation(C!12))))))))))))))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[120, 114, 9])).
% 0.22/0.50 tff(122,plain,
% 0.22/0.50 (relation(D!11)),
% 0.22/0.50 inference(or_elim,[status(thm)],[90])).
% 0.22/0.50 tff(123,plain,
% 0.22/0.50 (((~![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), B)) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, identity_relation(C!12))), B))))) | (~(in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_F_5(C, B, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), B)))))))))) | (~((~(C = relation_composition(identity_relation(C!12), B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, B, identity_relation(C!12)), E), B)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, B, identity_relation(C!12))), identity_relation(C!12))))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(F, E), B)) | (~in(ordered_pair(D, F), identity_relation(C!12))))))))))))))) | ((~relation(D!11)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), D!11)) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11))))) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_F_5(C, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11)))) | in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C))))))) | (~((~(C = relation_composition(identity_relation(C!12), D!11))) | ![D: $i, E: $i] : (~((~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12)))))))))))))))) <=> ((~![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), B)) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, identity_relation(C!12))), B))))) | (~(in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_F_5(C, B, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), B)))))))))) | (~((~(C = relation_composition(identity_relation(C!12), B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, B, identity_relation(C!12)), E), B)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, B, identity_relation(C!12))), identity_relation(C!12))))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(F, E), B)) | (~in(ordered_pair(D, F), identity_relation(C!12))))))))))))))) | (~relation(D!11)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), D!11)) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11))))) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_F_5(C, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11)))) | in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C))))))) | (~((~(C = relation_composition(identity_relation(C!12), D!11))) | ![D: $i, E: $i] : (~((~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12)))))))))))))))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(124,plain,
% 0.22/0.50 (((~relation(D!11)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), D!11)) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11))))) | (~(in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_F_5(C, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11)))))))))) | (~((~(C = relation_composition(identity_relation(C!12), D!11))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12))))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))))))))))) <=> ((~relation(D!11)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), D!11)) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11))))) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_F_5(C, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11)))) | in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C))))))) | (~((~(C = relation_composition(identity_relation(C!12), D!11))) | ![D: $i, E: $i] : (~((~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12)))))))))))))))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(125,plain,
% 0.22/0.50 (((~![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), B)) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, identity_relation(C!12))), B))))) | (~(in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_F_5(C, B, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), B)))))))))) | (~((~(C = relation_composition(identity_relation(C!12), B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, B, identity_relation(C!12)), E), B)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, B, identity_relation(C!12))), identity_relation(C!12))))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(F, E), B)) | (~in(ordered_pair(D, F), identity_relation(C!12))))))))))))))) | ((~relation(D!11)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), D!11)) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11))))) | (~(in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_F_5(C, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11)))))))))) | (~((~(C = relation_composition(identity_relation(C!12), D!11))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12))))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12))))))))))))))) <=> ((~![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), B)) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, identity_relation(C!12))), B))))) | (~(in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_F_5(C, B, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), B)))))))))) | (~((~(C = relation_composition(identity_relation(C!12), B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, B, identity_relation(C!12)), E), B)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, B, identity_relation(C!12))), identity_relation(C!12))))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(F, E), B)) | (~in(ordered_pair(D, F), identity_relation(C!12))))))))))))))) | ((~relation(D!11)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), D!11)) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11))))) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_F_5(C, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11)))) | in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C))))))) | (~((~(C = relation_composition(identity_relation(C!12), D!11))) | ![D: $i, E: $i] : (~((~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12))))))))))))))))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[124])).
% 0.22/0.51 tff(126,plain,
% 0.22/0.51 (((~![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), B)) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, identity_relation(C!12))), B))))) | (~(in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_F_5(C, B, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), B)))))))))) | (~((~(C = relation_composition(identity_relation(C!12), B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, B, identity_relation(C!12)), E), B)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, B, identity_relation(C!12))), identity_relation(C!12))))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(F, E), B)) | (~in(ordered_pair(D, F), identity_relation(C!12))))))))))))))) | ((~relation(D!11)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), D!11)) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11))))) | (~(in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_F_5(C, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11)))))))))) | (~((~(C = relation_composition(identity_relation(C!12), D!11))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12))))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12))))))))))))))) <=> ((~![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), B)) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, identity_relation(C!12))), B))))) | (~(in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_F_5(C, B, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), B)))))))))) | (~((~(C = relation_composition(identity_relation(C!12), B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, B, identity_relation(C!12)), E), B)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, B, identity_relation(C!12))), identity_relation(C!12))))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(F, E), B)) | (~in(ordered_pair(D, F), identity_relation(C!12))))))))))))))) | (~relation(D!11)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), D!11)) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11))))) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_F_5(C, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11)))) | in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C))))))) | (~((~(C = relation_composition(identity_relation(C!12), D!11))) | ![D: $i, E: $i] : (~((~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12)))))))))))))))),
% 0.22/0.51 inference(transitivity,[status(thm)],[125, 123])).
% 0.22/0.51 tff(127,plain,
% 0.22/0.51 ((~![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), B)) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, identity_relation(C!12))), B))))) | (~(in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_F_5(C, B, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), B)))))))))) | (~((~(C = relation_composition(identity_relation(C!12), B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, B, identity_relation(C!12)), E), B)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, B, identity_relation(C!12))), identity_relation(C!12))))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(F, E), B)) | (~in(ordered_pair(D, F), identity_relation(C!12))))))))))))))) | ((~relation(D!11)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), D!11)) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11))))) | (~(in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_F_5(C, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11)))))))))) | (~((~(C = relation_composition(identity_relation(C!12), D!11))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12))))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12))))))))))))))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(128,plain,
% 0.22/0.51 ((~![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), B)) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, B, identity_relation(C!12))), B))))) | (~(in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), C) | (~((~in(ordered_pair(tptp_fun_D_4(C, B, identity_relation(C!12)), tptp_fun_F_5(C, B, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, B, identity_relation(C!12)), tptp_fun_E_3(C, B, identity_relation(C!12))), B)))))))))) | (~((~(C = relation_composition(identity_relation(C!12), B))) | ![D: $i, E: $i] : (~((~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, B, identity_relation(C!12)), E), B)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, B, identity_relation(C!12))), identity_relation(C!12))))))) | (~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(F, E), B)) | (~in(ordered_pair(D, F), identity_relation(C!12))))))))))))))) | (~relation(D!11)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), D!11)) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11))))) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_F_5(C, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11)))) | in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C))))))) | (~((~(C = relation_composition(identity_relation(C!12), D!11))) | ![D: $i, E: $i] : (~((~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12))))))))))))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.22/0.51 tff(129,plain,
% 0.22/0.51 (![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), D!11)) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11))))) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_F_5(C, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11)))) | in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C))))))) | (~((~(C = relation_composition(identity_relation(C!12), D!11))) | ![D: $i, E: $i] : (~((~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12))))))))))))))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[128, 122, 121])).
% 0.22/0.51 tff(130,plain,
% 0.22/0.51 (^[A: $i, B: $i] : refl((relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A))) <=> (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A))))),
% 0.22/0.51 inference(bind,[status(th)],[])).
% 0.22/0.51 tff(131,plain,
% 0.22/0.51 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A))) <=> ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))),
% 0.22/0.51 inference(quant_intro,[status(thm)],[130])).
% 0.22/0.51 tff(132,plain,
% 0.22/0.51 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & relation(B)) <=> (~((~relation(B)) | (~relation(A))))), ((~(relation(A) & relation(B))) <=> (~(~((~relation(B)) | (~relation(A))))))), rewrite((~(~((~relation(B)) | (~relation(A))))) <=> ((~relation(B)) | (~relation(A)))), ((~(relation(A) & relation(B))) <=> ((~relation(B)) | (~relation(A))))), ((relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))) <=> (relation(relation_composition(A, B)) | ((~relation(B)) | (~relation(A)))))), rewrite((relation(relation_composition(A, B)) | ((~relation(B)) | (~relation(A)))) <=> (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))), ((relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))) <=> (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))))),
% 0.22/0.51 inference(bind,[status(th)],[])).
% 0.22/0.51 tff(133,plain,
% 0.22/0.51 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))) <=> ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))),
% 0.22/0.51 inference(quant_intro,[status(thm)],[132])).
% 0.22/0.51 tff(134,plain,
% 0.22/0.51 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))) <=> ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(135,plain,
% 0.22/0.51 (^[A: $i, B: $i] : rewrite(((relation(A) & relation(B)) => relation(relation_composition(A, B))) <=> (relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))))),
% 0.22/0.51 inference(bind,[status(th)],[])).
% 0.22/0.51 tff(136,plain,
% 0.22/0.51 (![A: $i, B: $i] : ((relation(A) & relation(B)) => relation(relation_composition(A, B))) <=> ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 0.22/0.51 inference(quant_intro,[status(thm)],[135])).
% 0.22/0.51 tff(137,axiom,(![A: $i, B: $i] : ((relation(A) & relation(B)) => relation(relation_composition(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k5_relat_1')).
% 0.22/0.51 tff(138,plain,
% 0.22/0.51 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.22/0.51 tff(139,plain,
% 0.22/0.51 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[138, 134])).
% 0.22/0.51 tff(140,plain,(
% 0.22/0.51 ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 0.22/0.51 inference(skolemize,[status(sab)],[139])).
% 0.22/0.51 tff(141,plain,
% 0.22/0.51 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[140, 133])).
% 0.22/0.51 tff(142,plain,
% 0.22/0.51 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[141, 131])).
% 0.22/0.51 tff(143,plain,
% 0.22/0.51 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | ((~relation(D!11)) | relation(relation_composition(identity_relation(C!12), D!11)) | (~relation(identity_relation(C!12))))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (~relation(D!11)) | relation(relation_composition(identity_relation(C!12), D!11)) | (~relation(identity_relation(C!12))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(144,plain,
% 0.22/0.51 ((relation(relation_composition(identity_relation(C!12), D!11)) | (~relation(D!11)) | (~relation(identity_relation(C!12)))) <=> ((~relation(D!11)) | relation(relation_composition(identity_relation(C!12), D!11)) | (~relation(identity_relation(C!12))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(145,plain,
% 0.22/0.51 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (relation(relation_composition(identity_relation(C!12), D!11)) | (~relation(D!11)) | (~relation(identity_relation(C!12))))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | ((~relation(D!11)) | relation(relation_composition(identity_relation(C!12), D!11)) | (~relation(identity_relation(C!12)))))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[144])).
% 0.22/0.51 tff(146,plain,
% 0.22/0.51 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (relation(relation_composition(identity_relation(C!12), D!11)) | (~relation(D!11)) | (~relation(identity_relation(C!12))))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (~relation(D!11)) | relation(relation_composition(identity_relation(C!12), D!11)) | (~relation(identity_relation(C!12))))),
% 0.22/0.51 inference(transitivity,[status(thm)],[145, 143])).
% 0.22/0.51 tff(147,plain,
% 0.22/0.51 ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (relation(relation_composition(identity_relation(C!12), D!11)) | (~relation(D!11)) | (~relation(identity_relation(C!12))))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(148,plain,
% 0.22/0.51 ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (~relation(D!11)) | relation(relation_composition(identity_relation(C!12), D!11)) | (~relation(identity_relation(C!12)))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.22/0.51 tff(149,plain,
% 0.22/0.51 (relation(relation_composition(identity_relation(C!12), D!11)) | (~relation(identity_relation(C!12)))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[148, 142, 122])).
% 0.22/0.51 tff(150,plain,
% 0.22/0.51 (relation(relation_composition(identity_relation(C!12), D!11))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[149, 9])).
% 0.22/0.51 tff(151,plain,
% 0.22/0.51 (((~![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), D!11)) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11))))) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_F_5(C, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11)))) | in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C))))))) | (~((~(C = relation_composition(identity_relation(C!12), D!11))) | ![D: $i, E: $i] : (~((~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12))))))))))))))) | ((~relation(relation_composition(identity_relation(C!12), D!11))) | ![D: $i, E: $i] : (~((~(in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12))))))))))) <=> ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), D!11)) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11))))) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_F_5(C, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11)))) | in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C))))))) | (~((~(C = relation_composition(identity_relation(C!12), D!11))) | ![D: $i, E: $i] : (~((~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12))))))))))))))) | (~relation(relation_composition(identity_relation(C!12), D!11))) | ![D: $i, E: $i] : (~((~(in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12))))))))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(152,plain,
% 0.22/0.51 (((~relation(relation_composition(identity_relation(C!12), D!11))) | (~((~((relation_composition(identity_relation(C!12), D!11) = relation_composition(identity_relation(C!12), D!11)) | (~((~((~in(ordered_pair(tptp_fun_D_4(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12)), tptp_fun_E_3(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12))), relation_composition(identity_relation(C!12), D!11))) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12))), D!11))))) | (~((~((~in(ordered_pair(tptp_fun_D_4(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12)), tptp_fun_F_5(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12)), tptp_fun_E_3(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12))), D!11)))) | in(ordered_pair(tptp_fun_D_4(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12)), tptp_fun_E_3(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12))), relation_composition(identity_relation(C!12), D!11)))))))) | (~((~(relation_composition(identity_relation(C!12), D!11) = relation_composition(identity_relation(C!12), D!11))) | ![D: $i, E: $i] : (~((~(in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12)))))))))))))) <=> ((~relation(relation_composition(identity_relation(C!12), D!11))) | ![D: $i, E: $i] : (~((~(in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12))))))))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(153,plain,
% 0.22/0.51 (((~![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), D!11)) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11))))) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_F_5(C, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11)))) | in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C))))))) | (~((~(C = relation_composition(identity_relation(C!12), D!11))) | ![D: $i, E: $i] : (~((~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12))))))))))))))) | ((~relation(relation_composition(identity_relation(C!12), D!11))) | (~((~((relation_composition(identity_relation(C!12), D!11) = relation_composition(identity_relation(C!12), D!11)) | (~((~((~in(ordered_pair(tptp_fun_D_4(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12)), tptp_fun_E_3(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12))), relation_composition(identity_relation(C!12), D!11))) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12))), D!11))))) | (~((~((~in(ordered_pair(tptp_fun_D_4(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12)), tptp_fun_F_5(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12)), tptp_fun_E_3(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12))), D!11)))) | in(ordered_pair(tptp_fun_D_4(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12)), tptp_fun_E_3(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12))), relation_composition(identity_relation(C!12), D!11)))))))) | (~((~(relation_composition(identity_relation(C!12), D!11) = relation_composition(identity_relation(C!12), D!11))) | ![D: $i, E: $i] : (~((~(in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12))))))))))))))) <=> ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), D!11)) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11))))) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_F_5(C, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11)))) | in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C))))))) | (~((~(C = relation_composition(identity_relation(C!12), D!11))) | ![D: $i, E: $i] : (~((~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12))))))))))))))) | ((~relation(relation_composition(identity_relation(C!12), D!11))) | ![D: $i, E: $i] : (~((~(in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12)))))))))))),
% 0.22/0.52 inference(monotonicity,[status(thm)],[152])).
% 0.22/0.52 tff(154,plain,
% 0.22/0.52 (((~![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), D!11)) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11))))) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_F_5(C, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11)))) | in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C))))))) | (~((~(C = relation_composition(identity_relation(C!12), D!11))) | ![D: $i, E: $i] : (~((~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12))))))))))))))) | ((~relation(relation_composition(identity_relation(C!12), D!11))) | (~((~((relation_composition(identity_relation(C!12), D!11) = relation_composition(identity_relation(C!12), D!11)) | (~((~((~in(ordered_pair(tptp_fun_D_4(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12)), tptp_fun_E_3(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12))), relation_composition(identity_relation(C!12), D!11))) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12))), D!11))))) | (~((~((~in(ordered_pair(tptp_fun_D_4(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12)), tptp_fun_F_5(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12)), tptp_fun_E_3(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12))), D!11)))) | in(ordered_pair(tptp_fun_D_4(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12)), tptp_fun_E_3(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12))), relation_composition(identity_relation(C!12), D!11)))))))) | (~((~(relation_composition(identity_relation(C!12), D!11) = relation_composition(identity_relation(C!12), D!11))) | ![D: $i, E: $i] : (~((~(in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12))))))))))))))) <=> ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), D!11)) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11))))) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_F_5(C, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11)))) | in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C))))))) | (~((~(C = relation_composition(identity_relation(C!12), D!11))) | ![D: $i, E: $i] : (~((~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12))))))))))))))) | (~relation(relation_composition(identity_relation(C!12), D!11))) | ![D: $i, E: $i] : (~((~(in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12))))))))))),
% 0.22/0.52 inference(transitivity,[status(thm)],[153, 151])).
% 0.22/0.52 tff(155,plain,
% 0.22/0.52 ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), D!11)) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11))))) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_F_5(C, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11)))) | in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C))))))) | (~((~(C = relation_composition(identity_relation(C!12), D!11))) | ![D: $i, E: $i] : (~((~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12))))))))))))))) | ((~relation(relation_composition(identity_relation(C!12), D!11))) | (~((~((relation_composition(identity_relation(C!12), D!11) = relation_composition(identity_relation(C!12), D!11)) | (~((~((~in(ordered_pair(tptp_fun_D_4(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12)), tptp_fun_E_3(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12))), relation_composition(identity_relation(C!12), D!11))) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12))), D!11))))) | (~((~((~in(ordered_pair(tptp_fun_D_4(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12)), tptp_fun_F_5(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12)), tptp_fun_E_3(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12))), D!11)))) | in(ordered_pair(tptp_fun_D_4(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12)), tptp_fun_E_3(relation_composition(identity_relation(C!12), D!11), D!11, identity_relation(C!12))), relation_composition(identity_relation(C!12), D!11)))))))) | (~((~(relation_composition(identity_relation(C!12), D!11) = relation_composition(identity_relation(C!12), D!11))) | ![D: $i, E: $i] : (~((~(in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12))))))))))))))),
% 0.22/0.52 inference(quant_inst,[status(thm)],[])).
% 0.22/0.52 tff(156,plain,
% 0.22/0.52 ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_composition(identity_relation(C!12), D!11)) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C)) | ![F: $i] : ((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), F), identity_relation(C!12))) | (~in(ordered_pair(F, tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11))))) | (~((~((~in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_F_5(C, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_5(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), D!11)))) | in(ordered_pair(tptp_fun_D_4(C, D!11, identity_relation(C!12)), tptp_fun_E_3(C, D!11, identity_relation(C!12))), C))))))) | (~((~(C = relation_composition(identity_relation(C!12), D!11))) | ![D: $i, E: $i] : (~((~(in(ordered_pair(D, E), C) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(D, E), C)) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12))))))))))))))) | (~relation(relation_composition(identity_relation(C!12), D!11))) | ![D: $i, E: $i] : (~((~(in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12)))))))))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.22/0.52 tff(157,plain,
% 0.22/0.52 (![D: $i, E: $i] : (~((~(in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12)))))))))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[156, 150, 129])).
% 0.22/0.52 tff(158,plain,
% 0.22/0.52 (((~![D: $i, E: $i] : (~((~(in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12)))))))))) | (~((~(in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, B!13), D!11)) | (~in(ordered_pair(A!14, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)), B!13), D!11))))))))) <=> ((~![D: $i, E: $i] : (~((~(in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12)))))))))) | (~((~(in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, B!13), D!11)) | (~in(ordered_pair(A!14, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)), B!13), D!11)))))))))),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(159,plain,
% 0.22/0.52 ((~((~(in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, B!13), D!11)) | (~in(ordered_pair(A!14, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)), B!13), D!11)) | (~in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12))))))))) <=> (~((~(in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, B!13), D!11)) | (~in(ordered_pair(A!14, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)), B!13), D!11))))))))),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(160,plain,
% 0.22/0.52 (((~![D: $i, E: $i] : (~((~(in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12)))))))))) | (~((~(in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, B!13), D!11)) | (~in(ordered_pair(A!14, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)), B!13), D!11)) | (~in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12)))))))))) <=> ((~![D: $i, E: $i] : (~((~(in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12)))))))))) | (~((~(in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, B!13), D!11)) | (~in(ordered_pair(A!14, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)), B!13), D!11)))))))))),
% 0.22/0.52 inference(monotonicity,[status(thm)],[159])).
% 0.22/0.52 tff(161,plain,
% 0.22/0.52 (((~![D: $i, E: $i] : (~((~(in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12)))))))))) | (~((~(in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, B!13), D!11)) | (~in(ordered_pair(A!14, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)), B!13), D!11)) | (~in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12)))))))))) <=> ((~![D: $i, E: $i] : (~((~(in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12)))))))))) | (~((~(in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, B!13), D!11)) | (~in(ordered_pair(A!14, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)), B!13), D!11)))))))))),
% 0.22/0.52 inference(transitivity,[status(thm)],[160, 158])).
% 0.22/0.52 tff(162,plain,
% 0.22/0.52 ((~![D: $i, E: $i] : (~((~(in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12)))))))))) | (~((~(in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, B!13), D!11)) | (~in(ordered_pair(A!14, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)), B!13), D!11)) | (~in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12)))))))))),
% 0.22/0.52 inference(quant_inst,[status(thm)],[])).
% 0.22/0.52 tff(163,plain,
% 0.22/0.52 ((~![D: $i, E: $i] : (~((~(in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, E), D!11)) | (~in(ordered_pair(D, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(D, E), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(tptp_fun_F_2(E, D, D!11, identity_relation(C!12)), E), D!11)) | (~in(ordered_pair(D, tptp_fun_F_2(E, D, D!11, identity_relation(C!12))), identity_relation(C!12)))))))))) | (~((~(in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, B!13), D!11)) | (~in(ordered_pair(A!14, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)), B!13), D!11))))))))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.22/0.52 tff(164,plain,
% 0.22/0.52 (~((~(in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, B!13), D!11)) | (~in(ordered_pair(A!14, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)), B!13), D!11)))))))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[163, 157])).
% 0.22/0.52 tff(165,plain,
% 0.22/0.52 (((~(in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, B!13), D!11)) | (~in(ordered_pair(A!14, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)), B!13), D!11))))))) | (in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, B!13), D!11)) | (~in(ordered_pair(A!14, F), identity_relation(C!12)))))),
% 0.22/0.52 inference(tautology,[status(thm)],[])).
% 0.22/0.52 tff(166,plain,
% 0.22/0.52 (in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, B!13), D!11)) | (~in(ordered_pair(A!14, F), identity_relation(C!12))))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[165, 164])).
% 0.22/0.52 tff(167,plain,
% 0.22/0.52 ((~(in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, B!13), D!11)) | (~in(ordered_pair(A!14, F), identity_relation(C!12)))))) | in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, B!13), D!11)) | (~in(ordered_pair(A!14, F), identity_relation(C!12))))),
% 0.22/0.52 inference(tautology,[status(thm)],[])).
% 0.22/0.52 tff(168,plain,
% 0.22/0.52 (in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, B!13), D!11)) | (~in(ordered_pair(A!14, F), identity_relation(C!12))))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.22/0.52 tff(169,plain,
% 0.22/0.52 (![F: $i] : ((~in(ordered_pair(F, B!13), D!11)) | (~in(ordered_pair(A!14, F), identity_relation(C!12))))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[168, 95])).
% 0.22/0.52 tff(170,plain,
% 0.22/0.52 (((~in(A!14, C!12)) | (~in(ordered_pair(A!14, B!13), D!11))) | in(ordered_pair(A!14, B!13), D!11)),
% 0.22/0.52 inference(tautology,[status(thm)],[])).
% 0.22/0.52 tff(171,plain,
% 0.22/0.52 (in(ordered_pair(A!14, B!13), D!11)),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[170, 69])).
% 0.22/0.52 tff(172,plain,
% 0.22/0.52 (((~![F: $i] : ((~in(ordered_pair(F, B!13), D!11)) | (~in(ordered_pair(A!14, F), identity_relation(C!12))))) | ((~in(ordered_pair(A!14, B!13), D!11)) | (~in(ordered_pair(A!14, A!14), identity_relation(C!12))))) <=> ((~![F: $i] : ((~in(ordered_pair(F, B!13), D!11)) | (~in(ordered_pair(A!14, F), identity_relation(C!12))))) | (~in(ordered_pair(A!14, B!13), D!11)) | (~in(ordered_pair(A!14, A!14), identity_relation(C!12))))),
% 0.22/0.53 inference(rewrite,[status(thm)],[])).
% 0.22/0.53 tff(173,plain,
% 0.22/0.53 ((~![F: $i] : ((~in(ordered_pair(F, B!13), D!11)) | (~in(ordered_pair(A!14, F), identity_relation(C!12))))) | ((~in(ordered_pair(A!14, B!13), D!11)) | (~in(ordered_pair(A!14, A!14), identity_relation(C!12))))),
% 0.22/0.53 inference(quant_inst,[status(thm)],[])).
% 0.22/0.53 tff(174,plain,
% 0.22/0.53 ((~![F: $i] : ((~in(ordered_pair(F, B!13), D!11)) | (~in(ordered_pair(A!14, F), identity_relation(C!12))))) | (~in(ordered_pair(A!14, B!13), D!11)) | (~in(ordered_pair(A!14, A!14), identity_relation(C!12)))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.22/0.53 tff(175,plain,
% 0.22/0.53 ($false),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[174, 171, 169, 73])).
% 0.22/0.53 tff(176,plain,((~in(A!14, C!12)) | (~in(ordered_pair(A!14, B!13), D!11))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.53 tff(177,plain,
% 0.22/0.53 ((~((~in(A!14, C!12)) | (~in(ordered_pair(A!14, B!13), D!11)))) | in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11)) | (~(((~in(A!14, C!12)) | (~in(ordered_pair(A!14, B!13), D!11))) <=> in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11))))),
% 0.22/0.53 inference(tautology,[status(thm)],[])).
% 0.22/0.53 tff(178,plain,
% 0.22/0.53 ((~((~in(A!14, C!12)) | (~in(ordered_pair(A!14, B!13), D!11)))) | in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11))),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[177, 92])).
% 0.22/0.53 tff(179,plain,
% 0.22/0.53 (in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11))),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[178, 176])).
% 0.22/0.53 tff(180,plain,
% 0.22/0.53 (((~(in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11)) | ![F: $i] : ((~in(ordered_pair(F, B!13), D!11)) | (~in(ordered_pair(A!14, F), identity_relation(C!12)))))) | (~((~in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)), B!13), D!11))))))) | ((~in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)), B!13), D!11)))))),
% 0.22/0.53 inference(tautology,[status(thm)],[])).
% 0.22/0.53 tff(181,plain,
% 0.22/0.53 ((~in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)), B!13), D!11))))),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[180, 164])).
% 0.22/0.53 tff(182,plain,
% 0.22/0.53 ((~((~in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)), B!13), D!11)))))) | (~in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)), B!13), D!11))))),
% 0.22/0.53 inference(tautology,[status(thm)],[])).
% 0.22/0.53 tff(183,plain,
% 0.22/0.53 ((~in(ordered_pair(A!14, B!13), relation_composition(identity_relation(C!12), D!11))) | (~((~in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)), B!13), D!11))))),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[182, 181])).
% 0.22/0.53 tff(184,plain,
% 0.22/0.53 (~((~in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)), B!13), D!11)))),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[183, 179])).
% 0.22/0.53 tff(185,plain,
% 0.22/0.53 (((~in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)), B!13), D!11))) | in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12))),
% 0.22/0.53 inference(tautology,[status(thm)],[])).
% 0.22/0.53 tff(186,plain,
% 0.22/0.53 (in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12))),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[185, 184])).
% 0.22/0.53 tff(187,plain,
% 0.22/0.53 ((((~in(A!14, C!12)) | (~(A!14 = tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))))) <=> in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~((~in(A!14, C!12)) | (~(A!14 = tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)))))) | (~in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12)))),
% 0.22/0.53 inference(tautology,[status(thm)],[])).
% 0.22/0.53 tff(188,plain,
% 0.22/0.53 ((((~in(A!14, C!12)) | (~(A!14 = tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))))) <=> in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~((~in(A!14, C!12)) | (~(A!14 = tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))))))),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[187, 186])).
% 0.22/0.53 tff(189,plain,
% 0.22/0.53 (~((~in(A!14, C!12)) | (~(A!14 = tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)))))),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[188, 45])).
% 0.22/0.53 tff(190,plain,
% 0.22/0.53 (((~in(A!14, C!12)) | (~(A!14 = tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))))) | (A!14 = tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)))),
% 0.22/0.53 inference(tautology,[status(thm)],[])).
% 0.22/0.53 tff(191,plain,
% 0.22/0.53 (A!14 = tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[190, 189])).
% 0.22/0.53 tff(192,plain,
% 0.22/0.53 (tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)) = A!14),
% 0.22/0.53 inference(symmetry,[status(thm)],[191])).
% 0.22/0.53 tff(193,plain,
% 0.22/0.53 (ordered_pair(tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)), B!13) = ordered_pair(A!14, B!13)),
% 0.22/0.53 inference(monotonicity,[status(thm)],[192])).
% 0.22/0.53 tff(194,plain,
% 0.22/0.53 (in(ordered_pair(tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)), B!13), D!11) <=> in(ordered_pair(A!14, B!13), D!11)),
% 0.22/0.53 inference(monotonicity,[status(thm)],[193])).
% 0.22/0.53 tff(195,plain,
% 0.22/0.53 (in(ordered_pair(A!14, B!13), D!11) <=> in(ordered_pair(tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)), B!13), D!11)),
% 0.22/0.53 inference(symmetry,[status(thm)],[194])).
% 0.22/0.53 tff(196,plain,
% 0.22/0.53 ((~in(ordered_pair(A!14, B!13), D!11)) <=> (~in(ordered_pair(tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)), B!13), D!11))),
% 0.22/0.53 inference(monotonicity,[status(thm)],[195])).
% 0.22/0.53 tff(197,plain,
% 0.22/0.53 (((~in(A!14, C!12)) | (~(A!14 = tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))))) | in(A!14, C!12)),
% 0.22/0.53 inference(tautology,[status(thm)],[])).
% 0.22/0.53 tff(198,plain,
% 0.22/0.53 (in(A!14, C!12)),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[197, 189])).
% 0.22/0.53 tff(199,plain,
% 0.22/0.53 ((~((~in(A!14, C!12)) | (~in(ordered_pair(A!14, B!13), D!11)))) | (~in(A!14, C!12)) | (~in(ordered_pair(A!14, B!13), D!11))),
% 0.22/0.53 inference(tautology,[status(thm)],[])).
% 0.22/0.53 tff(200,plain,
% 0.22/0.53 (~in(ordered_pair(A!14, B!13), D!11)),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[199, 198, 176])).
% 0.22/0.53 tff(201,plain,
% 0.22/0.53 (~in(ordered_pair(tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)), B!13), D!11)),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[200, 196])).
% 0.22/0.53 tff(202,plain,
% 0.22/0.53 (((~in(ordered_pair(A!14, tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12))), identity_relation(C!12))) | (~in(ordered_pair(tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)), B!13), D!11))) | in(ordered_pair(tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)), B!13), D!11)),
% 0.22/0.53 inference(tautology,[status(thm)],[])).
% 0.22/0.53 tff(203,plain,
% 0.22/0.53 (in(ordered_pair(tptp_fun_F_2(B!13, A!14, D!11, identity_relation(C!12)), B!13), D!11)),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[202, 184])).
% 0.22/0.53 tff(204,plain,
% 0.22/0.53 ($false),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[203, 201])).
% 0.22/0.53 % SZS output end Proof
% 0.22/0.53 % E exiting
%------------------------------------------------------------------------------