%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU075+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:52 AM UTC 2025
% Result : Theorem 4.01s 4.22s
% Output : Proof 4.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SEU075+1 : TPTP v9.0.0. Released v3.2.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 06:01:56 EDT 2025
% 0.13/0.36 % CPUTime :
% 4.01/4.22 % SZS status Theorem
% 4.01/4.22 % SZS output start Proof
% 4.01/4.22 tff(apply_type, type, (
% 4.01/4.22 apply: ( $i * $i ) > $i)).
% 4.01/4.22 tff(tptp_fun_C_18_type, type, (
% 4.01/4.22 tptp_fun_C_18: ( $i * $i ) > $i)).
% 4.01/4.22 tff(tptp_fun_C_16_type, type, (
% 4.01/4.22 tptp_fun_C_16: $i)).
% 4.01/4.22 tff(tptp_fun_D_17_type, type, (
% 4.01/4.22 tptp_fun_D_17: $i)).
% 4.01/4.22 tff(tptp_fun_D_0_type, type, (
% 4.01/4.22 tptp_fun_D_0: ( $i * $i ) > $i)).
% 4.01/4.22 tff(tptp_fun_B_14_type, type, (
% 4.01/4.22 tptp_fun_B_14: $i)).
% 4.01/4.22 tff(in_type, type, (
% 4.01/4.22 in: ( $i * $i ) > $o)).
% 4.01/4.22 tff(relation_dom_type, type, (
% 4.01/4.22 relation_dom: $i > $i)).
% 4.01/4.22 tff(relation_rng_type, type, (
% 4.01/4.22 relation_rng: $i > $i)).
% 4.01/4.22 tff(tptp_fun_C_1_type, type, (
% 4.01/4.22 tptp_fun_C_1: ( $i * $i ) > $i)).
% 4.01/4.22 tff(tptp_fun_D_2_type, type, (
% 4.01/4.22 tptp_fun_D_2: ( $i * $i ) > $i)).
% 4.01/4.22 tff(function_type, type, (
% 4.01/4.22 function: $i > $o)).
% 4.01/4.22 tff(relation_composition_type, type, (
% 4.01/4.22 relation_composition: ( $i * $i ) > $i)).
% 4.01/4.22 tff(tptp_fun_A_15_type, type, (
% 4.01/4.22 tptp_fun_A_15: $i)).
% 4.01/4.22 tff(relation_type, type, (
% 4.01/4.22 relation: $i > $o)).
% 4.01/4.22 tff(1,plain,
% 4.01/4.22 (((relation(B!14) & function(B!14)) & (relation(C!16) & function(C!16) & (~((C!16 = D!17) | (~(relation(D!17) & function(D!17))) | (~((A!15 = relation_rng(B!14)) & (relation_dom(C!16) = A!15) & (relation_dom(D!17) = A!15) & (relation_composition(B!14, C!16) = relation_composition(B!14, D!17)))))))) <=> (relation(B!14) & function(B!14) & relation(C!16) & function(C!16) & (~((C!16 = D!17) | (~(relation(D!17) & function(D!17))) | (~((A!15 = relation_rng(B!14)) & (relation_dom(C!16) = A!15) & (relation_dom(D!17) = A!15) & (relation_composition(B!14, C!16) = relation_composition(B!14, D!17)))))))),
% 4.01/4.22 inference(rewrite,[status(thm)],[])).
% 4.01/4.22 tff(2,plain,
% 4.01/4.22 (((relation(C!16) & function(C!16)) & (~((C!16 = D!17) | (~(relation(D!17) & function(D!17))) | (~((A!15 = relation_rng(B!14)) & (relation_dom(C!16) = A!15) & (relation_dom(D!17) = A!15) & (relation_composition(B!14, C!16) = relation_composition(B!14, D!17))))))) <=> (relation(C!16) & function(C!16) & (~((C!16 = D!17) | (~(relation(D!17) & function(D!17))) | (~((A!15 = relation_rng(B!14)) & (relation_dom(C!16) = A!15) & (relation_dom(D!17) = A!15) & (relation_composition(B!14, C!16) = relation_composition(B!14, D!17)))))))),
% 4.01/4.22 inference(rewrite,[status(thm)],[])).
% 4.01/4.22 tff(3,plain,
% 4.01/4.22 ((~((C!16 = D!17) | (~(relation(D!17) & function(D!17))) | (~((A!15 = relation_rng(B!14)) & (relation_dom(C!16) = A!15) & (relation_dom(D!17) = A!15) & (relation_composition(B!14, C!16) = relation_composition(B!14, D!17)))))) <=> (~((C!16 = D!17) | (~(relation(D!17) & function(D!17))) | (~((A!15 = relation_rng(B!14)) & (relation_dom(C!16) = A!15) & (relation_dom(D!17) = A!15) & (relation_composition(B!14, C!16) = relation_composition(B!14, D!17))))))),
% 4.01/4.22 inference(rewrite,[status(thm)],[])).
% 4.01/4.22 tff(4,plain,
% 4.01/4.22 (((relation(C!16) & function(C!16)) & (~((C!16 = D!17) | (~(relation(D!17) & function(D!17))) | (~((A!15 = relation_rng(B!14)) & (relation_dom(C!16) = A!15) & (relation_dom(D!17) = A!15) & (relation_composition(B!14, C!16) = relation_composition(B!14, D!17))))))) <=> ((relation(C!16) & function(C!16)) & (~((C!16 = D!17) | (~(relation(D!17) & function(D!17))) | (~((A!15 = relation_rng(B!14)) & (relation_dom(C!16) = A!15) & (relation_dom(D!17) = A!15) & (relation_composition(B!14, C!16) = relation_composition(B!14, D!17)))))))),
% 4.01/4.22 inference(monotonicity,[status(thm)],[3])).
% 4.01/4.22 tff(5,plain,
% 4.01/4.22 (((relation(C!16) & function(C!16)) & (~((C!16 = D!17) | (~(relation(D!17) & function(D!17))) | (~((A!15 = relation_rng(B!14)) & (relation_dom(C!16) = A!15) & (relation_dom(D!17) = A!15) & (relation_composition(B!14, C!16) = relation_composition(B!14, D!17))))))) <=> (relation(C!16) & function(C!16) & (~((C!16 = D!17) | (~(relation(D!17) & function(D!17))) | (~((A!15 = relation_rng(B!14)) & (relation_dom(C!16) = A!15) & (relation_dom(D!17) = A!15) & (relation_composition(B!14, C!16) = relation_composition(B!14, D!17)))))))),
% 4.01/4.22 inference(transitivity,[status(thm)],[4, 2])).
% 4.01/4.22 tff(6,plain,
% 4.01/4.22 (((relation(B!14) & function(B!14)) & ((relation(C!16) & function(C!16)) & (~((C!16 = D!17) | (~(relation(D!17) & function(D!17))) | (~((A!15 = relation_rng(B!14)) & (relation_dom(C!16) = A!15) & (relation_dom(D!17) = A!15) & (relation_composition(B!14, C!16) = relation_composition(B!14, D!17)))))))) <=> ((relation(B!14) & function(B!14)) & (relation(C!16) & function(C!16) & (~((C!16 = D!17) | (~(relation(D!17) & function(D!17))) | (~((A!15 = relation_rng(B!14)) & (relation_dom(C!16) = A!15) & (relation_dom(D!17) = A!15) & (relation_composition(B!14, C!16) = relation_composition(B!14, D!17))))))))),
% 4.01/4.22 inference(monotonicity,[status(thm)],[5])).
% 4.01/4.22 tff(7,plain,
% 4.01/4.22 (((relation(B!14) & function(B!14)) & ((relation(C!16) & function(C!16)) & (~((C!16 = D!17) | (~(relation(D!17) & function(D!17))) | (~((A!15 = relation_rng(B!14)) & (relation_dom(C!16) = A!15) & (relation_dom(D!17) = A!15) & (relation_composition(B!14, C!16) = relation_composition(B!14, D!17)))))))) <=> (relation(B!14) & function(B!14) & relation(C!16) & function(C!16) & (~((C!16 = D!17) | (~(relation(D!17) & function(D!17))) | (~((A!15 = relation_rng(B!14)) & (relation_dom(C!16) = A!15) & (relation_dom(D!17) = A!15) & (relation_composition(B!14, C!16) = relation_composition(B!14, D!17)))))))),
% 4.01/4.22 inference(transitivity,[status(thm)],[6, 1])).
% 4.01/4.22 tff(8,plain,
% 4.01/4.22 ((~![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | ![D: $i] : ((C = D) | (~(relation(D) & function(D))) | (~((A = relation_rng(B)) & (relation_dom(C) = A) & (relation_dom(D) = A) & (relation_composition(B, C) = relation_composition(B, D)))))))) <=> (~![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | ![D: $i] : ((C = D) | (~(relation(D) & function(D))) | (~((A = relation_rng(B)) & (relation_dom(C) = A) & (relation_dom(D) = A) & (relation_composition(B, C) = relation_composition(B, D))))))))),
% 4.01/4.22 inference(rewrite,[status(thm)],[])).
% 4.01/4.22 tff(9,plain,
% 4.01/4.22 ((~![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => ![D: $i] : ((relation(D) & function(D)) => (((((A = relation_rng(B)) & (relation_dom(C) = A)) & (relation_dom(D) = A)) & (relation_composition(B, C) = relation_composition(B, D))) => (C = D)))))) <=> (~![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | ![D: $i] : ((C = D) | (~(relation(D) & function(D))) | (~((A = relation_rng(B)) & (relation_dom(C) = A) & (relation_dom(D) = A) & (relation_composition(B, C) = relation_composition(B, D))))))))),
% 4.01/4.22 inference(rewrite,[status(thm)],[])).
% 4.01/4.22 tff(10,axiom,(~![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => ![D: $i] : ((relation(D) & function(D)) => (((((A = relation_rng(B)) & (relation_dom(C) = A)) & (relation_dom(D) = A)) & (relation_composition(B, C) = relation_composition(B, D))) => (C = D)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t156_funct_1')).
% 4.01/4.22 tff(11,plain,
% 4.01/4.22 (~![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | ![D: $i] : ((C = D) | (~(relation(D) & function(D))) | (~((A = relation_rng(B)) & (relation_dom(C) = A) & (relation_dom(D) = A) & (relation_composition(B, C) = relation_composition(B, D)))))))),
% 4.01/4.22 inference(modus_ponens,[status(thm)],[10, 9])).
% 4.01/4.22 tff(12,plain,
% 4.01/4.22 (~![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | ![D: $i] : ((C = D) | (~(relation(D) & function(D))) | (~((A = relation_rng(B)) & (relation_dom(C) = A) & (relation_dom(D) = A) & (relation_composition(B, C) = relation_composition(B, D)))))))),
% 4.01/4.22 inference(modus_ponens,[status(thm)],[11, 8])).
% 4.01/4.22 tff(13,plain,
% 4.01/4.22 (~![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | ![D: $i] : ((C = D) | (~(relation(D) & function(D))) | (~((A = relation_rng(B)) & (relation_dom(C) = A) & (relation_dom(D) = A) & (relation_composition(B, C) = relation_composition(B, D)))))))),
% 4.01/4.22 inference(modus_ponens,[status(thm)],[12, 8])).
% 4.01/4.22 tff(14,plain,
% 4.01/4.22 (~![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | ![D: $i] : ((C = D) | (~(relation(D) & function(D))) | (~((A = relation_rng(B)) & (relation_dom(C) = A) & (relation_dom(D) = A) & (relation_composition(B, C) = relation_composition(B, D)))))))),
% 4.01/4.22 inference(modus_ponens,[status(thm)],[13, 8])).
% 4.01/4.22 tff(15,plain,
% 4.01/4.22 (relation(B!14) & function(B!14) & relation(C!16) & function(C!16) & (~((C!16 = D!17) | (~(relation(D!17) & function(D!17))) | (~((A!15 = relation_rng(B!14)) & (relation_dom(C!16) = A!15) & (relation_dom(D!17) = A!15) & (relation_composition(B!14, C!16) = relation_composition(B!14, D!17))))))),
% 4.01/4.22 inference(modus_ponens,[status(thm)],[14, 7])).
% 4.01/4.22 tff(16,plain,
% 4.01/4.22 (function(B!14)),
% 4.01/4.22 inference(and_elim,[status(thm)],[15])).
% 4.01/4.22 tff(17,plain,
% 4.01/4.22 (relation(B!14)),
% 4.01/4.22 inference(and_elim,[status(thm)],[15])).
% 4.01/4.22 tff(18,plain,
% 4.01/4.22 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i, D_19: $i, C: $i, D: $i] : rewrite((~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19)))))))))))) <=> (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))), (![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19)))))))))))) <=> ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))), (((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19)))))))))))))), rewrite(((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19)))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))), (((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))))),
% 4.01/4.22 inference(bind,[status(th)],[])).
% 4.01/4.22 tff(19,plain,
% 4.01/4.22 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))),
% 4.01/4.22 inference(quant_intro,[status(thm)],[18])).
% 4.01/4.22 tff(20,plain,
% 4.01/4.22 (^[A: $i] : refl(((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))))),
% 4.01/4.22 inference(bind,[status(th)],[])).
% 4.01/4.22 tff(21,plain,
% 4.01/4.22 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19)))))))))))))),
% 4.01/4.22 inference(quant_intro,[status(thm)],[20])).
% 4.01/4.22 tff(22,plain,
% 4.01/4.22 (^[A: $i] : rewrite(((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))))),
% 4.01/4.22 inference(bind,[status(th)],[])).
% 4.01/4.22 tff(23,plain,
% 4.01/4.22 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19)))))))))))))),
% 4.01/4.22 inference(quant_intro,[status(thm)],[22])).
% 4.01/4.22 tff(24,plain,
% 4.01/4.22 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19)))))))))))))),
% 4.01/4.22 inference(transitivity,[status(thm)],[23, 21])).
% 4.01/4.22 tff(25,plain,
% 4.01/4.22 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & function(A)) <=> (~((~relation(A)) | (~function(A))))), ((~(relation(A) & function(A))) <=> (~(~((~relation(A)) | (~function(A))))))), rewrite((~(~((~relation(A)) | (~function(A))))) <=> ((~relation(A)) | (~function(A)))), ((~(relation(A) & function(A))) <=> ((~relation(A)) | (~function(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite(((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_0(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_0(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) <=> ((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))) <=> (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))))), ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) <=> (in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))))))), rewrite((in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))))) <=> (in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))), ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) <=> (in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))))))), rewrite(((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D))))) <=> ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))), (((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D)))))) <=> ((in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))), rewrite(((in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))) <=> (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))), (((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D)))))) <=> (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))), (((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D))))))) <=> ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))))), rewrite(((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))) <=> ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))), (((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D))))))) <=> ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))))), ((((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_0(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_0(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D)))))))) <=> (((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) & ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))))), rewrite((((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) & ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))) <=> (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))))))), ((((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_0(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_0(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D)))))))) <=> (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))))))))), (![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_0(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_0(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D)))))))) <=> ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))))))), (((~(relation(A) & function(A))) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_0(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_0(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D))))))))) <=> (((~relation(A)) | (~function(A))) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))))))))), rewrite((((~relation(A)) | (~function(A))) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))))))), (((~(relation(A) & function(A))) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_0(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_0(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))))))))),
% 4.01/4.23 inference(bind,[status(th)],[])).
% 4.01/4.23 tff(26,plain,
% 4.01/4.23 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_0(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_0(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))))))),
% 4.01/4.23 inference(quant_intro,[status(thm)],[25])).
% 4.01/4.23 tff(27,plain,
% 4.01/4.23 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D)))))) <=> ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D))))))),
% 4.01/4.23 inference(rewrite,[status(thm)],[])).
% 4.01/4.23 tff(28,plain,
% 4.01/4.23 (^[A: $i] : rewrite(((relation(A) & function(A)) => ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D)))))) <=> ((~(relation(A) & function(A))) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D)))))))),
% 4.01/4.23 inference(bind,[status(th)],[])).
% 4.01/4.23 tff(29,plain,
% 4.01/4.23 (![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D)))))) <=> ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D))))))),
% 4.01/4.23 inference(quant_intro,[status(thm)],[28])).
% 4.01/4.23 tff(30,axiom,(![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d5_funct_1')).
% 4.01/4.23 tff(31,plain,
% 4.01/4.23 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D))))))),
% 4.01/4.23 inference(modus_ponens,[status(thm)],[30, 29])).
% 4.01/4.23 tff(32,plain,
% 4.01/4.23 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D))))))),
% 4.01/4.23 inference(modus_ponens,[status(thm)],[31, 27])).
% 4.01/4.23 tff(33,plain,(
% 4.01/4.23 ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_0(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_0(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D)))))))))),
% 4.01/4.23 inference(skolemize,[status(sab)],[32])).
% 4.01/4.23 tff(34,plain,
% 4.01/4.23 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))))))),
% 4.01/4.23 inference(modus_ponens,[status(thm)],[33, 26])).
% 4.01/4.23 tff(35,plain,
% 4.01/4.23 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19)))))))))))))),
% 4.01/4.23 inference(modus_ponens,[status(thm)],[34, 24])).
% 4.01/4.23 tff(36,plain,
% 4.01/4.23 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))),
% 4.01/4.23 inference(modus_ponens,[status(thm)],[35, 19])).
% 4.01/4.23 tff(37,plain,
% 4.01/4.23 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))) | ((~function(B!14)) | (~relation(B!14)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!14))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!14), relation_dom(B!14))) | (~(C = apply(B!14, tptp_fun_D_0(C, B!14)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!14))) | (~(C = apply(B!14, D))))))))) | (~((B = relation_rng(B!14)) | (~((~(in(tptp_fun_C_1(B, B!14), B) | (~((~in(tptp_fun_D_2(B, B!14), relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, tptp_fun_D_2(B, B!14)))))))) | (~((~in(tptp_fun_C_1(B, B!14), B)) | (~in(D_19, relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, D_19))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))) | (~function(B!14)) | (~relation(B!14)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!14))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!14), relation_dom(B!14))) | (~(C = apply(B!14, tptp_fun_D_0(C, B!14)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!14))) | (~(C = apply(B!14, D))))))))) | (~((B = relation_rng(B!14)) | (~((~(in(tptp_fun_C_1(B, B!14), B) | (~((~in(tptp_fun_D_2(B, B!14), relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, tptp_fun_D_2(B, B!14)))))))) | (~((~in(tptp_fun_C_1(B, B!14), B)) | (~in(D_19, relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, D_19))))))))))))),
% 4.01/4.23 inference(rewrite,[status(thm)],[])).
% 4.01/4.23 tff(38,plain,
% 4.01/4.23 (((~relation(B!14)) | (~function(B!14)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!14))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!14), relation_dom(B!14))) | (~(C = apply(B!14, tptp_fun_D_0(C, B!14)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!14))) | (~(C = apply(B!14, D))))))))) | (~((B = relation_rng(B!14)) | (~((~(in(tptp_fun_C_1(B, B!14), B) | (~((~in(tptp_fun_D_2(B, B!14), relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, tptp_fun_D_2(B, B!14)))))))) | (~((~in(tptp_fun_C_1(B, B!14), B)) | (~in(D_19, relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, D_19)))))))))))) <=> ((~function(B!14)) | (~relation(B!14)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!14))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!14), relation_dom(B!14))) | (~(C = apply(B!14, tptp_fun_D_0(C, B!14)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!14))) | (~(C = apply(B!14, D))))))))) | (~((B = relation_rng(B!14)) | (~((~(in(tptp_fun_C_1(B, B!14), B) | (~((~in(tptp_fun_D_2(B, B!14), relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, tptp_fun_D_2(B, B!14)))))))) | (~((~in(tptp_fun_C_1(B, B!14), B)) | (~in(D_19, relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, D_19))))))))))))),
% 4.01/4.23 inference(rewrite,[status(thm)],[])).
% 4.01/4.23 tff(39,plain,
% 4.01/4.23 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))) | ((~relation(B!14)) | (~function(B!14)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!14))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!14), relation_dom(B!14))) | (~(C = apply(B!14, tptp_fun_D_0(C, B!14)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!14))) | (~(C = apply(B!14, D))))))))) | (~((B = relation_rng(B!14)) | (~((~(in(tptp_fun_C_1(B, B!14), B) | (~((~in(tptp_fun_D_2(B, B!14), relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, tptp_fun_D_2(B, B!14)))))))) | (~((~in(tptp_fun_C_1(B, B!14), B)) | (~in(D_19, relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, D_19))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))) | ((~function(B!14)) | (~relation(B!14)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!14))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!14), relation_dom(B!14))) | (~(C = apply(B!14, tptp_fun_D_0(C, B!14)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!14))) | (~(C = apply(B!14, D))))))))) | (~((B = relation_rng(B!14)) | (~((~(in(tptp_fun_C_1(B, B!14), B) | (~((~in(tptp_fun_D_2(B, B!14), relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, tptp_fun_D_2(B, B!14)))))))) | (~((~in(tptp_fun_C_1(B, B!14), B)) | (~in(D_19, relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, D_19)))))))))))))),
% 4.01/4.23 inference(monotonicity,[status(thm)],[38])).
% 4.01/4.23 tff(40,plain,
% 4.01/4.23 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))) | ((~relation(B!14)) | (~function(B!14)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!14))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!14), relation_dom(B!14))) | (~(C = apply(B!14, tptp_fun_D_0(C, B!14)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!14))) | (~(C = apply(B!14, D))))))))) | (~((B = relation_rng(B!14)) | (~((~(in(tptp_fun_C_1(B, B!14), B) | (~((~in(tptp_fun_D_2(B, B!14), relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, tptp_fun_D_2(B, B!14)))))))) | (~((~in(tptp_fun_C_1(B, B!14), B)) | (~in(D_19, relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, D_19))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))) | (~function(B!14)) | (~relation(B!14)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!14))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!14), relation_dom(B!14))) | (~(C = apply(B!14, tptp_fun_D_0(C, B!14)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!14))) | (~(C = apply(B!14, D))))))))) | (~((B = relation_rng(B!14)) | (~((~(in(tptp_fun_C_1(B, B!14), B) | (~((~in(tptp_fun_D_2(B, B!14), relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, tptp_fun_D_2(B, B!14)))))))) | (~((~in(tptp_fun_C_1(B, B!14), B)) | (~in(D_19, relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, D_19))))))))))))),
% 4.01/4.23 inference(transitivity,[status(thm)],[39, 37])).
% 4.01/4.23 tff(41,plain,
% 4.01/4.23 ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))) | ((~relation(B!14)) | (~function(B!14)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!14))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!14), relation_dom(B!14))) | (~(C = apply(B!14, tptp_fun_D_0(C, B!14)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!14))) | (~(C = apply(B!14, D))))))))) | (~((B = relation_rng(B!14)) | (~((~(in(tptp_fun_C_1(B, B!14), B) | (~((~in(tptp_fun_D_2(B, B!14), relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, tptp_fun_D_2(B, B!14)))))))) | (~((~in(tptp_fun_C_1(B, B!14), B)) | (~in(D_19, relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, D_19))))))))))))),
% 4.01/4.23 inference(quant_inst,[status(thm)],[])).
% 4.01/4.23 tff(42,plain,
% 4.01/4.23 ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_19, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_19))))))))))))) | (~function(B!14)) | (~relation(B!14)) | ![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!14))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!14), relation_dom(B!14))) | (~(C = apply(B!14, tptp_fun_D_0(C, B!14)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!14))) | (~(C = apply(B!14, D))))))))) | (~((B = relation_rng(B!14)) | (~((~(in(tptp_fun_C_1(B, B!14), B) | (~((~in(tptp_fun_D_2(B, B!14), relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, tptp_fun_D_2(B, B!14)))))))) | (~((~in(tptp_fun_C_1(B, B!14), B)) | (~in(D_19, relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, D_19)))))))))))),
% 4.01/4.23 inference(modus_ponens,[status(thm)],[41, 40])).
% 4.01/4.23 tff(43,plain,
% 4.01/4.23 (![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!14))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!14), relation_dom(B!14))) | (~(C = apply(B!14, tptp_fun_D_0(C, B!14)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!14))) | (~(C = apply(B!14, D))))))))) | (~((B = relation_rng(B!14)) | (~((~(in(tptp_fun_C_1(B, B!14), B) | (~((~in(tptp_fun_D_2(B, B!14), relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, tptp_fun_D_2(B, B!14)))))))) | (~((~in(tptp_fun_C_1(B, B!14), B)) | (~in(D_19, relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, D_19)))))))))))),
% 4.01/4.23 inference(unit_resolution,[status(thm)],[42, 36, 17, 16])).
% 4.01/4.23 tff(44,plain,
% 4.01/4.23 (((~![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!14))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!14), relation_dom(B!14))) | (~(C = apply(B!14, tptp_fun_D_0(C, B!14)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!14))) | (~(C = apply(B!14, D))))))))) | (~((B = relation_rng(B!14)) | (~((~(in(tptp_fun_C_1(B, B!14), B) | (~((~in(tptp_fun_D_2(B, B!14), relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, tptp_fun_D_2(B, B!14)))))))) | (~((~in(tptp_fun_C_1(B, B!14), B)) | (~in(D_19, relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, D_19)))))))))))) | (~((~((~in(tptp_fun_C_18(D!17, C!16), relation_rng(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (~(tptp_fun_C_18(D!17, C!16) = apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))))) | (~(in(tptp_fun_C_18(D!17, C!16), relation_rng(B!14)) | (~in(apply(D!17, tptp_fun_C_18(D!17, C!16)), relation_dom(B!14))) | (~(tptp_fun_C_18(D!17, C!16) = apply(B!14, apply(D!17, tptp_fun_C_18(D!17, C!16)))))))))) <=> ((~![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!14))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!14), relation_dom(B!14))) | (~(C = apply(B!14, tptp_fun_D_0(C, B!14)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!14))) | (~(C = apply(B!14, D))))))))) | (~((B = relation_rng(B!14)) | (~((~(in(tptp_fun_C_1(B, B!14), B) | (~((~in(tptp_fun_D_2(B, B!14), relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, tptp_fun_D_2(B, B!14)))))))) | (~((~in(tptp_fun_C_1(B, B!14), B)) | (~in(D_19, relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, D_19)))))))))))) | (~((~((~in(tptp_fun_C_18(D!17, C!16), relation_rng(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (~(tptp_fun_C_18(D!17, C!16) = apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))))) | (~(in(tptp_fun_C_18(D!17, C!16), relation_rng(B!14)) | (~in(apply(D!17, tptp_fun_C_18(D!17, C!16)), relation_dom(B!14))) | (~(tptp_fun_C_18(D!17, C!16) = apply(B!14, apply(D!17, tptp_fun_C_18(D!17, C!16))))))))))),
% 4.01/4.23 inference(rewrite,[status(thm)],[])).
% 4.01/4.23 tff(45,plain,
% 4.01/4.23 ((~((~((~(relation_rng(B!14) = relation_rng(B!14))) | (~((~((~in(tptp_fun_C_18(D!17, C!16), relation_rng(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (~(tptp_fun_C_18(D!17, C!16) = apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))))) | (~(in(tptp_fun_C_18(D!17, C!16), relation_rng(B!14)) | (~in(apply(D!17, tptp_fun_C_18(D!17, C!16)), relation_dom(B!14))) | (~(tptp_fun_C_18(D!17, C!16) = apply(B!14, apply(D!17, tptp_fun_C_18(D!17, C!16))))))))))) | (~((relation_rng(B!14) = relation_rng(B!14)) | (~((~(in(tptp_fun_C_1(relation_rng(B!14), B!14), relation_rng(B!14)) | (~((~in(tptp_fun_D_2(relation_rng(B!14), B!14), relation_dom(B!14))) | (~(tptp_fun_C_1(relation_rng(B!14), B!14) = apply(B!14, tptp_fun_D_2(relation_rng(B!14), B!14)))))))) | (~((~in(tptp_fun_C_1(relation_rng(B!14), B!14), relation_rng(B!14))) | (~in(apply(D!17, tptp_fun_C_18(D!17, C!16)), relation_dom(B!14))) | (~(tptp_fun_C_1(relation_rng(B!14), B!14) = apply(B!14, apply(D!17, tptp_fun_C_18(D!17, C!16))))))))))))) <=> (~((~((~in(tptp_fun_C_18(D!17, C!16), relation_rng(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (~(tptp_fun_C_18(D!17, C!16) = apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))))) | (~(in(tptp_fun_C_18(D!17, C!16), relation_rng(B!14)) | (~in(apply(D!17, tptp_fun_C_18(D!17, C!16)), relation_dom(B!14))) | (~(tptp_fun_C_18(D!17, C!16) = apply(B!14, apply(D!17, tptp_fun_C_18(D!17, C!16)))))))))),
% 4.01/4.23 inference(rewrite,[status(thm)],[])).
% 4.01/4.23 tff(46,plain,
% 4.01/4.23 (((~![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!14))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!14), relation_dom(B!14))) | (~(C = apply(B!14, tptp_fun_D_0(C, B!14)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!14))) | (~(C = apply(B!14, D))))))))) | (~((B = relation_rng(B!14)) | (~((~(in(tptp_fun_C_1(B, B!14), B) | (~((~in(tptp_fun_D_2(B, B!14), relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, tptp_fun_D_2(B, B!14)))))))) | (~((~in(tptp_fun_C_1(B, B!14), B)) | (~in(D_19, relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, D_19)))))))))))) | (~((~((~(relation_rng(B!14) = relation_rng(B!14))) | (~((~((~in(tptp_fun_C_18(D!17, C!16), relation_rng(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (~(tptp_fun_C_18(D!17, C!16) = apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))))) | (~(in(tptp_fun_C_18(D!17, C!16), relation_rng(B!14)) | (~in(apply(D!17, tptp_fun_C_18(D!17, C!16)), relation_dom(B!14))) | (~(tptp_fun_C_18(D!17, C!16) = apply(B!14, apply(D!17, tptp_fun_C_18(D!17, C!16))))))))))) | (~((relation_rng(B!14) = relation_rng(B!14)) | (~((~(in(tptp_fun_C_1(relation_rng(B!14), B!14), relation_rng(B!14)) | (~((~in(tptp_fun_D_2(relation_rng(B!14), B!14), relation_dom(B!14))) | (~(tptp_fun_C_1(relation_rng(B!14), B!14) = apply(B!14, tptp_fun_D_2(relation_rng(B!14), B!14)))))))) | (~((~in(tptp_fun_C_1(relation_rng(B!14), B!14), relation_rng(B!14))) | (~in(apply(D!17, tptp_fun_C_18(D!17, C!16)), relation_dom(B!14))) | (~(tptp_fun_C_1(relation_rng(B!14), B!14) = apply(B!14, apply(D!17, tptp_fun_C_18(D!17, C!16)))))))))))))) <=> ((~![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!14))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!14), relation_dom(B!14))) | (~(C = apply(B!14, tptp_fun_D_0(C, B!14)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!14))) | (~(C = apply(B!14, D))))))))) | (~((B = relation_rng(B!14)) | (~((~(in(tptp_fun_C_1(B, B!14), B) | (~((~in(tptp_fun_D_2(B, B!14), relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, tptp_fun_D_2(B, B!14)))))))) | (~((~in(tptp_fun_C_1(B, B!14), B)) | (~in(D_19, relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, D_19)))))))))))) | (~((~((~in(tptp_fun_C_18(D!17, C!16), relation_rng(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (~(tptp_fun_C_18(D!17, C!16) = apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))))) | (~(in(tptp_fun_C_18(D!17, C!16), relation_rng(B!14)) | (~in(apply(D!17, tptp_fun_C_18(D!17, C!16)), relation_dom(B!14))) | (~(tptp_fun_C_18(D!17, C!16) = apply(B!14, apply(D!17, tptp_fun_C_18(D!17, C!16))))))))))),
% 4.01/4.23 inference(monotonicity,[status(thm)],[45])).
% 4.01/4.23 tff(47,plain,
% 4.01/4.23 (((~![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!14))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!14), relation_dom(B!14))) | (~(C = apply(B!14, tptp_fun_D_0(C, B!14)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!14))) | (~(C = apply(B!14, D))))))))) | (~((B = relation_rng(B!14)) | (~((~(in(tptp_fun_C_1(B, B!14), B) | (~((~in(tptp_fun_D_2(B, B!14), relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, tptp_fun_D_2(B, B!14)))))))) | (~((~in(tptp_fun_C_1(B, B!14), B)) | (~in(D_19, relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, D_19)))))))))))) | (~((~((~(relation_rng(B!14) = relation_rng(B!14))) | (~((~((~in(tptp_fun_C_18(D!17, C!16), relation_rng(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (~(tptp_fun_C_18(D!17, C!16) = apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))))) | (~(in(tptp_fun_C_18(D!17, C!16), relation_rng(B!14)) | (~in(apply(D!17, tptp_fun_C_18(D!17, C!16)), relation_dom(B!14))) | (~(tptp_fun_C_18(D!17, C!16) = apply(B!14, apply(D!17, tptp_fun_C_18(D!17, C!16))))))))))) | (~((relation_rng(B!14) = relation_rng(B!14)) | (~((~(in(tptp_fun_C_1(relation_rng(B!14), B!14), relation_rng(B!14)) | (~((~in(tptp_fun_D_2(relation_rng(B!14), B!14), relation_dom(B!14))) | (~(tptp_fun_C_1(relation_rng(B!14), B!14) = apply(B!14, tptp_fun_D_2(relation_rng(B!14), B!14)))))))) | (~((~in(tptp_fun_C_1(relation_rng(B!14), B!14), relation_rng(B!14))) | (~in(apply(D!17, tptp_fun_C_18(D!17, C!16)), relation_dom(B!14))) | (~(tptp_fun_C_1(relation_rng(B!14), B!14) = apply(B!14, apply(D!17, tptp_fun_C_18(D!17, C!16)))))))))))))) <=> ((~![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!14))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!14), relation_dom(B!14))) | (~(C = apply(B!14, tptp_fun_D_0(C, B!14)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!14))) | (~(C = apply(B!14, D))))))))) | (~((B = relation_rng(B!14)) | (~((~(in(tptp_fun_C_1(B, B!14), B) | (~((~in(tptp_fun_D_2(B, B!14), relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, tptp_fun_D_2(B, B!14)))))))) | (~((~in(tptp_fun_C_1(B, B!14), B)) | (~in(D_19, relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, D_19)))))))))))) | (~((~((~in(tptp_fun_C_18(D!17, C!16), relation_rng(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (~(tptp_fun_C_18(D!17, C!16) = apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))))) | (~(in(tptp_fun_C_18(D!17, C!16), relation_rng(B!14)) | (~in(apply(D!17, tptp_fun_C_18(D!17, C!16)), relation_dom(B!14))) | (~(tptp_fun_C_18(D!17, C!16) = apply(B!14, apply(D!17, tptp_fun_C_18(D!17, C!16))))))))))),
% 4.01/4.24 inference(transitivity,[status(thm)],[46, 44])).
% 4.01/4.24 tff(48,plain,
% 4.01/4.24 ((~![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!14))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!14), relation_dom(B!14))) | (~(C = apply(B!14, tptp_fun_D_0(C, B!14)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!14))) | (~(C = apply(B!14, D))))))))) | (~((B = relation_rng(B!14)) | (~((~(in(tptp_fun_C_1(B, B!14), B) | (~((~in(tptp_fun_D_2(B, B!14), relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, tptp_fun_D_2(B, B!14)))))))) | (~((~in(tptp_fun_C_1(B, B!14), B)) | (~in(D_19, relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, D_19)))))))))))) | (~((~((~(relation_rng(B!14) = relation_rng(B!14))) | (~((~((~in(tptp_fun_C_18(D!17, C!16), relation_rng(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (~(tptp_fun_C_18(D!17, C!16) = apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))))) | (~(in(tptp_fun_C_18(D!17, C!16), relation_rng(B!14)) | (~in(apply(D!17, tptp_fun_C_18(D!17, C!16)), relation_dom(B!14))) | (~(tptp_fun_C_18(D!17, C!16) = apply(B!14, apply(D!17, tptp_fun_C_18(D!17, C!16))))))))))) | (~((relation_rng(B!14) = relation_rng(B!14)) | (~((~(in(tptp_fun_C_1(relation_rng(B!14), B!14), relation_rng(B!14)) | (~((~in(tptp_fun_D_2(relation_rng(B!14), B!14), relation_dom(B!14))) | (~(tptp_fun_C_1(relation_rng(B!14), B!14) = apply(B!14, tptp_fun_D_2(relation_rng(B!14), B!14)))))))) | (~((~in(tptp_fun_C_1(relation_rng(B!14), B!14), relation_rng(B!14))) | (~in(apply(D!17, tptp_fun_C_18(D!17, C!16)), relation_dom(B!14))) | (~(tptp_fun_C_1(relation_rng(B!14), B!14) = apply(B!14, apply(D!17, tptp_fun_C_18(D!17, C!16)))))))))))))),
% 4.01/4.24 inference(quant_inst,[status(thm)],[])).
% 4.01/4.24 tff(49,plain,
% 4.01/4.24 ((~![B: $i, D_19: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!14))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!14), relation_dom(B!14))) | (~(C = apply(B!14, tptp_fun_D_0(C, B!14)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!14))) | (~(C = apply(B!14, D))))))))) | (~((B = relation_rng(B!14)) | (~((~(in(tptp_fun_C_1(B, B!14), B) | (~((~in(tptp_fun_D_2(B, B!14), relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, tptp_fun_D_2(B, B!14)))))))) | (~((~in(tptp_fun_C_1(B, B!14), B)) | (~in(D_19, relation_dom(B!14))) | (~(tptp_fun_C_1(B, B!14) = apply(B!14, D_19)))))))))))) | (~((~((~in(tptp_fun_C_18(D!17, C!16), relation_rng(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (~(tptp_fun_C_18(D!17, C!16) = apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))))) | (~(in(tptp_fun_C_18(D!17, C!16), relation_rng(B!14)) | (~in(apply(D!17, tptp_fun_C_18(D!17, C!16)), relation_dom(B!14))) | (~(tptp_fun_C_18(D!17, C!16) = apply(B!14, apply(D!17, tptp_fun_C_18(D!17, C!16)))))))))),
% 4.01/4.24 inference(modus_ponens,[status(thm)],[48, 47])).
% 4.01/4.24 tff(50,plain,
% 4.01/4.24 (~((~((~in(tptp_fun_C_18(D!17, C!16), relation_rng(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (~(tptp_fun_C_18(D!17, C!16) = apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))))) | (~(in(tptp_fun_C_18(D!17, C!16), relation_rng(B!14)) | (~in(apply(D!17, tptp_fun_C_18(D!17, C!16)), relation_dom(B!14))) | (~(tptp_fun_C_18(D!17, C!16) = apply(B!14, apply(D!17, tptp_fun_C_18(D!17, C!16))))))))),
% 4.01/4.24 inference(unit_resolution,[status(thm)],[49, 43])).
% 4.01/4.24 tff(51,plain,
% 4.01/4.24 (((~((~in(tptp_fun_C_18(D!17, C!16), relation_rng(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (~(tptp_fun_C_18(D!17, C!16) = apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))))) | (~(in(tptp_fun_C_18(D!17, C!16), relation_rng(B!14)) | (~in(apply(D!17, tptp_fun_C_18(D!17, C!16)), relation_dom(B!14))) | (~(tptp_fun_C_18(D!17, C!16) = apply(B!14, apply(D!17, tptp_fun_C_18(D!17, C!16)))))))) | ((~in(tptp_fun_C_18(D!17, C!16), relation_rng(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (~(tptp_fun_C_18(D!17, C!16) = apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))))),
% 4.01/4.24 inference(tautology,[status(thm)],[])).
% 4.01/4.24 tff(52,plain,
% 4.01/4.24 ((~in(tptp_fun_C_18(D!17, C!16), relation_rng(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (~(tptp_fun_C_18(D!17, C!16) = apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14))))))),
% 4.01/4.24 inference(unit_resolution,[status(thm)],[51, 50])).
% 4.01/4.24 tff(53,plain,
% 4.01/4.24 (~((C!16 = D!17) | (~(relation(D!17) & function(D!17))) | (~((A!15 = relation_rng(B!14)) & (relation_dom(C!16) = A!15) & (relation_dom(D!17) = A!15) & (relation_composition(B!14, C!16) = relation_composition(B!14, D!17)))))),
% 4.01/4.24 inference(and_elim,[status(thm)],[15])).
% 4.01/4.24 tff(54,plain,
% 4.01/4.24 ((A!15 = relation_rng(B!14)) & (relation_dom(C!16) = A!15) & (relation_dom(D!17) = A!15) & (relation_composition(B!14, C!16) = relation_composition(B!14, D!17))),
% 4.01/4.24 inference(or_elim,[status(thm)],[53])).
% 4.01/4.24 tff(55,plain,
% 4.01/4.24 (relation_dom(C!16) = A!15),
% 4.01/4.24 inference(and_elim,[status(thm)],[54])).
% 4.01/4.24 tff(56,plain,
% 4.01/4.24 (A!15 = relation_dom(C!16)),
% 4.01/4.24 inference(symmetry,[status(thm)],[55])).
% 4.01/4.24 tff(57,plain,
% 4.01/4.24 (A!15 = relation_rng(B!14)),
% 4.01/4.24 inference(and_elim,[status(thm)],[54])).
% 4.01/4.24 tff(58,plain,
% 4.01/4.24 (relation_rng(B!14) = A!15),
% 4.01/4.24 inference(symmetry,[status(thm)],[57])).
% 4.01/4.24 tff(59,plain,
% 4.01/4.24 (relation_rng(B!14) = relation_dom(C!16)),
% 4.01/4.24 inference(transitivity,[status(thm)],[58, 56])).
% 4.01/4.24 tff(60,plain,
% 4.01/4.24 (in(tptp_fun_C_18(D!17, C!16), relation_rng(B!14)) <=> in(tptp_fun_C_18(D!17, C!16), relation_dom(C!16))),
% 4.01/4.24 inference(monotonicity,[status(thm)],[59])).
% 4.01/4.24 tff(61,plain,
% 4.01/4.24 (in(tptp_fun_C_18(D!17, C!16), relation_dom(C!16)) <=> in(tptp_fun_C_18(D!17, C!16), relation_rng(B!14))),
% 4.01/4.24 inference(symmetry,[status(thm)],[60])).
% 4.01/4.24 tff(62,plain,
% 4.01/4.24 (relation_dom(D!17) = A!15),
% 4.01/4.24 inference(and_elim,[status(thm)],[54])).
% 4.01/4.24 tff(63,plain,
% 4.01/4.24 (A!15 = relation_dom(D!17)),
% 4.01/4.24 inference(symmetry,[status(thm)],[62])).
% 4.01/4.24 tff(64,plain,
% 4.01/4.24 (relation_dom(C!16) = relation_dom(D!17)),
% 4.01/4.24 inference(transitivity,[status(thm)],[55, 63])).
% 4.01/4.24 tff(65,plain,
% 4.01/4.24 (^[A: $i] : refl(((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))))))),
% 4.01/4.24 inference(bind,[status(th)],[])).
% 4.01/4.24 tff(66,plain,
% 4.01/4.24 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))))),
% 4.01/4.24 inference(quant_intro,[status(thm)],[65])).
% 4.01/4.24 tff(67,plain,
% 4.01/4.24 (^[A: $i] : rewrite(((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))))))),
% 4.01/4.24 inference(bind,[status(th)],[])).
% 4.01/4.24 tff(68,plain,
% 4.01/4.24 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))))),
% 4.01/4.24 inference(quant_intro,[status(thm)],[67])).
% 4.01/4.24 tff(69,plain,
% 4.01/4.24 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))))),
% 4.01/4.24 inference(transitivity,[status(thm)],[68, 66])).
% 4.01/4.24 tff(70,plain,
% 4.01/4.24 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & function(A)) <=> (~((~relation(A)) | (~function(A))))), ((~(relation(A) & function(A))) <=> (~(~((~relation(A)) | (~function(A))))))), rewrite((~(~((~relation(A)) | (~function(A))))) <=> ((~relation(A)) | (~function(A)))), ((~(relation(A) & function(A))) <=> ((~relation(A)) | (~function(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B))))), ((~(relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B))))))), rewrite((~(~((~relation(B)) | (~function(B))))) <=> ((~relation(B)) | (~function(B)))), ((~(relation(B) & function(B))) <=> ((~relation(B)) | (~function(B))))), (((A = B) | (~(relation(B) & function(B))) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))) <=> ((A = B) | ((~relation(B)) | (~function(B))) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))))), rewrite(((A = B) | ((~relation(B)) | (~function(B))) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))) <=> ((A = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))))), (((A = B) | (~(relation(B) & function(B))) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))) <=> ((A = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))))))), (![B: $i] : ((A = B) | (~(relation(B) & function(B))) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))) <=> ![B: $i] : ((A = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))))), (((~(relation(A) & function(A))) | ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))))) <=> (((~relation(A)) | (~function(A))) | ![B: $i] : ((A = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))))))), rewrite((((~relation(A)) | (~function(A))) | ![B: $i] : ((A = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))))), (((~(relation(A) & function(A))) | ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))))))),
% 4.01/4.24 inference(bind,[status(th)],[])).
% 4.01/4.24 tff(71,plain,
% 4.01/4.24 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))))),
% 4.01/4.24 inference(quant_intro,[status(thm)],[70])).
% 4.01/4.24 tff(72,plain,
% 4.01/4.24 (^[A: $i] : rewrite(((~(relation(A) & function(A))) | ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | ((~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))))) <=> ((~(relation(A) & function(A))) | ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))))))),
% 4.01/4.24 inference(bind,[status(th)],[])).
% 4.01/4.24 tff(73,plain,
% 4.01/4.24 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | ((~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))))) <=> ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))))),
% 4.01/4.24 inference(quant_intro,[status(thm)],[72])).
% 4.01/4.24 tff(74,plain,
% 4.01/4.24 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | (~((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C))))))) <=> ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | (~((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C)))))))),
% 4.01/4.24 inference(rewrite,[status(thm)],[])).
% 4.01/4.24 tff(75,plain,
% 4.01/4.24 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((relation_dom(A) = relation_dom(B)) & ![C: $i] : (in(C, relation_dom(A)) => (apply(A, C) = apply(B, C)))) <=> ((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C))))), ((((relation_dom(A) = relation_dom(B)) & ![C: $i] : (in(C, relation_dom(A)) => (apply(A, C) = apply(B, C)))) => (A = B)) <=> (((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C)))) => (A = B)))), rewrite((((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C)))) => (A = B)) <=> ((~((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C))))) | (A = B))), ((((relation_dom(A) = relation_dom(B)) & ![C: $i] : (in(C, relation_dom(A)) => (apply(A, C) = apply(B, C)))) => (A = B)) <=> ((~((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C))))) | (A = B)))), (((relation(B) & function(B)) => (((relation_dom(A) = relation_dom(B)) & ![C: $i] : (in(C, relation_dom(A)) => (apply(A, C) = apply(B, C)))) => (A = B))) <=> ((relation(B) & function(B)) => ((~((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C))))) | (A = B))))), rewrite(((relation(B) & function(B)) => ((~((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C))))) | (A = B))) <=> ((A = B) | (~(relation(B) & function(B))) | (~((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C))))))), (((relation(B) & function(B)) => (((relation_dom(A) = relation_dom(B)) & ![C: $i] : (in(C, relation_dom(A)) => (apply(A, C) = apply(B, C)))) => (A = B))) <=> ((A = B) | (~(relation(B) & function(B))) | (~((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C))))))))), (![B: $i] : ((relation(B) & function(B)) => (((relation_dom(A) = relation_dom(B)) & ![C: $i] : (in(C, relation_dom(A)) => (apply(A, C) = apply(B, C)))) => (A = B))) <=> ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | (~((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C)))))))), (((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => (((relation_dom(A) = relation_dom(B)) & ![C: $i] : (in(C, relation_dom(A)) => (apply(A, C) = apply(B, C)))) => (A = B)))) <=> ((relation(A) & function(A)) => ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | (~((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C))))))))), rewrite(((relation(A) & function(A)) => ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | (~((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C))))))) <=> ((~(relation(A) & function(A))) | ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | (~((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C)))))))), (((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => (((relation_dom(A) = relation_dom(B)) & ![C: $i] : (in(C, relation_dom(A)) => (apply(A, C) = apply(B, C)))) => (A = B)))) <=> ((~(relation(A) & function(A))) | ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | (~((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C)))))))))),
% 4.01/4.24 inference(bind,[status(th)],[])).
% 4.01/4.24 tff(76,plain,
% 4.01/4.24 (![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => (((relation_dom(A) = relation_dom(B)) & ![C: $i] : (in(C, relation_dom(A)) => (apply(A, C) = apply(B, C)))) => (A = B)))) <=> ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | (~((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C)))))))),
% 4.01/4.24 inference(quant_intro,[status(thm)],[75])).
% 4.01/4.24 tff(77,axiom,(![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => (((relation_dom(A) = relation_dom(B)) & ![C: $i] : (in(C, relation_dom(A)) => (apply(A, C) = apply(B, C)))) => (A = B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t9_funct_1')).
% 4.01/4.24 tff(78,plain,
% 4.01/4.24 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | (~((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C)))))))),
% 4.01/4.24 inference(modus_ponens,[status(thm)],[77, 76])).
% 4.01/4.24 tff(79,plain,
% 4.01/4.24 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | (~((relation_dom(A) = relation_dom(B)) & ![C: $i] : ((~in(C, relation_dom(A))) | (apply(A, C) = apply(B, C)))))))),
% 4.01/4.24 inference(modus_ponens,[status(thm)],[78, 74])).
% 4.01/4.24 tff(80,plain,(
% 4.01/4.24 ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | ((~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A))))))))),
% 4.01/4.24 inference(skolemize,[status(sab)],[79])).
% 4.01/4.24 tff(81,plain,
% 4.01/4.24 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((A = B) | (~(relation(B) & function(B))) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))))),
% 4.01/4.24 inference(modus_ponens,[status(thm)],[80, 73])).
% 4.01/4.24 tff(82,plain,
% 4.01/4.24 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))))),
% 4.01/4.24 inference(modus_ponens,[status(thm)],[81, 71])).
% 4.01/4.24 tff(83,plain,
% 4.01/4.24 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))))),
% 4.01/4.24 inference(modus_ponens,[status(thm)],[82, 69])).
% 4.01/4.24 tff(84,plain,
% 4.01/4.24 (function(C!16)),
% 4.01/4.24 inference(and_elim,[status(thm)],[15])).
% 4.01/4.24 tff(85,plain,
% 4.01/4.24 (relation(C!16)),
% 4.01/4.24 inference(and_elim,[status(thm)],[15])).
% 4.01/4.24 tff(86,plain,
% 4.01/4.24 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))))) | (![B: $i] : ((C!16 = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(C!16) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, C!16), relation_dom(C!16))) | (apply(C!16, tptp_fun_C_18(B, C!16)) = apply(B, tptp_fun_C_18(B, C!16)))))) | (~function(C!16)) | (~relation(C!16)))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))))) | ![B: $i] : ((C!16 = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(C!16) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, C!16), relation_dom(C!16))) | (apply(C!16, tptp_fun_C_18(B, C!16)) = apply(B, tptp_fun_C_18(B, C!16)))))) | (~function(C!16)) | (~relation(C!16)))),
% 4.01/4.24 inference(rewrite,[status(thm)],[])).
% 4.01/4.24 tff(87,plain,
% 4.01/4.24 (((~relation(C!16)) | (~function(C!16)) | ![B: $i] : ((C!16 = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(C!16) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, C!16), relation_dom(C!16))) | (apply(C!16, tptp_fun_C_18(B, C!16)) = apply(B, tptp_fun_C_18(B, C!16))))))) <=> (![B: $i] : ((C!16 = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(C!16) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, C!16), relation_dom(C!16))) | (apply(C!16, tptp_fun_C_18(B, C!16)) = apply(B, tptp_fun_C_18(B, C!16)))))) | (~function(C!16)) | (~relation(C!16)))),
% 4.01/4.24 inference(rewrite,[status(thm)],[])).
% 4.01/4.24 tff(88,plain,
% 4.01/4.24 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))))) | ((~relation(C!16)) | (~function(C!16)) | ![B: $i] : ((C!16 = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(C!16) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, C!16), relation_dom(C!16))) | (apply(C!16, tptp_fun_C_18(B, C!16)) = apply(B, tptp_fun_C_18(B, C!16)))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))))) | (![B: $i] : ((C!16 = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(C!16) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, C!16), relation_dom(C!16))) | (apply(C!16, tptp_fun_C_18(B, C!16)) = apply(B, tptp_fun_C_18(B, C!16)))))) | (~function(C!16)) | (~relation(C!16))))),
% 4.01/4.24 inference(monotonicity,[status(thm)],[87])).
% 4.01/4.24 tff(89,plain,
% 4.01/4.24 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))))) | ((~relation(C!16)) | (~function(C!16)) | ![B: $i] : ((C!16 = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(C!16) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, C!16), relation_dom(C!16))) | (apply(C!16, tptp_fun_C_18(B, C!16)) = apply(B, tptp_fun_C_18(B, C!16)))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))))) | ![B: $i] : ((C!16 = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(C!16) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, C!16), relation_dom(C!16))) | (apply(C!16, tptp_fun_C_18(B, C!16)) = apply(B, tptp_fun_C_18(B, C!16)))))) | (~function(C!16)) | (~relation(C!16)))),
% 4.01/4.24 inference(transitivity,[status(thm)],[88, 86])).
% 4.01/4.24 tff(90,plain,
% 4.01/4.24 ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))))) | ((~relation(C!16)) | (~function(C!16)) | ![B: $i] : ((C!16 = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(C!16) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, C!16), relation_dom(C!16))) | (apply(C!16, tptp_fun_C_18(B, C!16)) = apply(B, tptp_fun_C_18(B, C!16)))))))),
% 4.01/4.24 inference(quant_inst,[status(thm)],[])).
% 4.01/4.24 tff(91,plain,
% 4.01/4.24 ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((A = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(A) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, A), relation_dom(A))) | (apply(A, tptp_fun_C_18(B, A)) = apply(B, tptp_fun_C_18(B, A)))))))) | ![B: $i] : ((C!16 = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(C!16) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, C!16), relation_dom(C!16))) | (apply(C!16, tptp_fun_C_18(B, C!16)) = apply(B, tptp_fun_C_18(B, C!16)))))) | (~function(C!16)) | (~relation(C!16))),
% 4.01/4.24 inference(modus_ponens,[status(thm)],[90, 89])).
% 4.01/4.24 tff(92,plain,
% 4.01/4.24 (![B: $i] : ((C!16 = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(C!16) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, C!16), relation_dom(C!16))) | (apply(C!16, tptp_fun_C_18(B, C!16)) = apply(B, tptp_fun_C_18(B, C!16))))))),
% 4.01/4.24 inference(unit_resolution,[status(thm)],[91, 85, 84, 83])).
% 4.01/4.24 tff(93,plain,
% 4.01/4.24 (relation(D!17) & function(D!17)),
% 4.01/4.24 inference(or_elim,[status(thm)],[53])).
% 4.01/4.24 tff(94,plain,
% 4.01/4.24 (function(D!17)),
% 4.01/4.24 inference(and_elim,[status(thm)],[93])).
% 4.01/4.24 tff(95,plain,
% 4.01/4.24 (relation(D!17)),
% 4.01/4.24 inference(and_elim,[status(thm)],[93])).
% 4.01/4.24 tff(96,plain,
% 4.01/4.24 (~(C!16 = D!17)),
% 4.01/4.24 inference(or_elim,[status(thm)],[53])).
% 4.01/4.24 tff(97,plain,
% 4.01/4.24 (((~![B: $i] : ((C!16 = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(C!16) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, C!16), relation_dom(C!16))) | (apply(C!16, tptp_fun_C_18(B, C!16)) = apply(B, tptp_fun_C_18(B, C!16))))))) | ((C!16 = D!17) | (~function(D!17)) | (~relation(D!17)) | (~(relation_dom(C!16) = relation_dom(D!17))) | (~((~in(tptp_fun_C_18(D!17, C!16), relation_dom(C!16))) | (apply(C!16, tptp_fun_C_18(D!17, C!16)) = apply(D!17, tptp_fun_C_18(D!17, C!16))))))) <=> ((~![B: $i] : ((C!16 = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(C!16) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, C!16), relation_dom(C!16))) | (apply(C!16, tptp_fun_C_18(B, C!16)) = apply(B, tptp_fun_C_18(B, C!16))))))) | (C!16 = D!17) | (~function(D!17)) | (~relation(D!17)) | (~(relation_dom(C!16) = relation_dom(D!17))) | (~((~in(tptp_fun_C_18(D!17, C!16), relation_dom(C!16))) | (apply(C!16, tptp_fun_C_18(D!17, C!16)) = apply(D!17, tptp_fun_C_18(D!17, C!16))))))),
% 4.01/4.24 inference(rewrite,[status(thm)],[])).
% 4.01/4.24 tff(98,plain,
% 4.01/4.24 (((C!16 = D!17) | (~relation(D!17)) | (~function(D!17)) | (~(relation_dom(C!16) = relation_dom(D!17))) | (~((~in(tptp_fun_C_18(D!17, C!16), relation_dom(C!16))) | (apply(C!16, tptp_fun_C_18(D!17, C!16)) = apply(D!17, tptp_fun_C_18(D!17, C!16)))))) <=> ((C!16 = D!17) | (~function(D!17)) | (~relation(D!17)) | (~(relation_dom(C!16) = relation_dom(D!17))) | (~((~in(tptp_fun_C_18(D!17, C!16), relation_dom(C!16))) | (apply(C!16, tptp_fun_C_18(D!17, C!16)) = apply(D!17, tptp_fun_C_18(D!17, C!16))))))),
% 4.01/4.24 inference(rewrite,[status(thm)],[])).
% 4.01/4.24 tff(99,plain,
% 4.01/4.24 (((~![B: $i] : ((C!16 = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(C!16) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, C!16), relation_dom(C!16))) | (apply(C!16, tptp_fun_C_18(B, C!16)) = apply(B, tptp_fun_C_18(B, C!16))))))) | ((C!16 = D!17) | (~relation(D!17)) | (~function(D!17)) | (~(relation_dom(C!16) = relation_dom(D!17))) | (~((~in(tptp_fun_C_18(D!17, C!16), relation_dom(C!16))) | (apply(C!16, tptp_fun_C_18(D!17, C!16)) = apply(D!17, tptp_fun_C_18(D!17, C!16))))))) <=> ((~![B: $i] : ((C!16 = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(C!16) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, C!16), relation_dom(C!16))) | (apply(C!16, tptp_fun_C_18(B, C!16)) = apply(B, tptp_fun_C_18(B, C!16))))))) | ((C!16 = D!17) | (~function(D!17)) | (~relation(D!17)) | (~(relation_dom(C!16) = relation_dom(D!17))) | (~((~in(tptp_fun_C_18(D!17, C!16), relation_dom(C!16))) | (apply(C!16, tptp_fun_C_18(D!17, C!16)) = apply(D!17, tptp_fun_C_18(D!17, C!16)))))))),
% 4.01/4.24 inference(monotonicity,[status(thm)],[98])).
% 4.01/4.24 tff(100,plain,
% 4.01/4.24 (((~![B: $i] : ((C!16 = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(C!16) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, C!16), relation_dom(C!16))) | (apply(C!16, tptp_fun_C_18(B, C!16)) = apply(B, tptp_fun_C_18(B, C!16))))))) | ((C!16 = D!17) | (~relation(D!17)) | (~function(D!17)) | (~(relation_dom(C!16) = relation_dom(D!17))) | (~((~in(tptp_fun_C_18(D!17, C!16), relation_dom(C!16))) | (apply(C!16, tptp_fun_C_18(D!17, C!16)) = apply(D!17, tptp_fun_C_18(D!17, C!16))))))) <=> ((~![B: $i] : ((C!16 = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(C!16) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, C!16), relation_dom(C!16))) | (apply(C!16, tptp_fun_C_18(B, C!16)) = apply(B, tptp_fun_C_18(B, C!16))))))) | (C!16 = D!17) | (~function(D!17)) | (~relation(D!17)) | (~(relation_dom(C!16) = relation_dom(D!17))) | (~((~in(tptp_fun_C_18(D!17, C!16), relation_dom(C!16))) | (apply(C!16, tptp_fun_C_18(D!17, C!16)) = apply(D!17, tptp_fun_C_18(D!17, C!16))))))),
% 4.01/4.24 inference(transitivity,[status(thm)],[99, 97])).
% 4.01/4.24 tff(101,plain,
% 4.01/4.24 ((~![B: $i] : ((C!16 = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(C!16) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, C!16), relation_dom(C!16))) | (apply(C!16, tptp_fun_C_18(B, C!16)) = apply(B, tptp_fun_C_18(B, C!16))))))) | ((C!16 = D!17) | (~relation(D!17)) | (~function(D!17)) | (~(relation_dom(C!16) = relation_dom(D!17))) | (~((~in(tptp_fun_C_18(D!17, C!16), relation_dom(C!16))) | (apply(C!16, tptp_fun_C_18(D!17, C!16)) = apply(D!17, tptp_fun_C_18(D!17, C!16))))))),
% 4.01/4.24 inference(quant_inst,[status(thm)],[])).
% 4.01/4.24 tff(102,plain,
% 4.01/4.24 ((~![B: $i] : ((C!16 = B) | (~relation(B)) | (~function(B)) | (~(relation_dom(C!16) = relation_dom(B))) | (~((~in(tptp_fun_C_18(B, C!16), relation_dom(C!16))) | (apply(C!16, tptp_fun_C_18(B, C!16)) = apply(B, tptp_fun_C_18(B, C!16))))))) | (C!16 = D!17) | (~function(D!17)) | (~relation(D!17)) | (~(relation_dom(C!16) = relation_dom(D!17))) | (~((~in(tptp_fun_C_18(D!17, C!16), relation_dom(C!16))) | (apply(C!16, tptp_fun_C_18(D!17, C!16)) = apply(D!17, tptp_fun_C_18(D!17, C!16)))))),
% 4.01/4.24 inference(modus_ponens,[status(thm)],[101, 100])).
% 4.01/4.24 tff(103,plain,
% 4.01/4.24 (~((~in(tptp_fun_C_18(D!17, C!16), relation_dom(C!16))) | (apply(C!16, tptp_fun_C_18(D!17, C!16)) = apply(D!17, tptp_fun_C_18(D!17, C!16))))),
% 4.01/4.24 inference(unit_resolution,[status(thm)],[102, 96, 95, 94, 92, 64])).
% 4.01/4.24 tff(104,plain,
% 4.01/4.24 (((~in(tptp_fun_C_18(D!17, C!16), relation_dom(C!16))) | (apply(C!16, tptp_fun_C_18(D!17, C!16)) = apply(D!17, tptp_fun_C_18(D!17, C!16)))) | in(tptp_fun_C_18(D!17, C!16), relation_dom(C!16))),
% 4.01/4.24 inference(tautology,[status(thm)],[])).
% 4.01/4.24 tff(105,plain,
% 4.01/4.24 (in(tptp_fun_C_18(D!17, C!16), relation_dom(C!16))),
% 4.01/4.24 inference(unit_resolution,[status(thm)],[104, 103])).
% 4.01/4.24 tff(106,plain,
% 4.01/4.24 (in(tptp_fun_C_18(D!17, C!16), relation_rng(B!14))),
% 4.01/4.24 inference(modus_ponens,[status(thm)],[105, 61])).
% 4.01/4.24 tff(107,plain,
% 4.01/4.24 ((~((~in(tptp_fun_C_18(D!17, C!16), relation_rng(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (~(tptp_fun_C_18(D!17, C!16) = apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))))) | (~in(tptp_fun_C_18(D!17, C!16), relation_rng(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (~(tptp_fun_C_18(D!17, C!16) = apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14))))))),
% 4.01/4.24 inference(tautology,[status(thm)],[])).
% 4.01/4.24 tff(108,plain,
% 4.01/4.24 ((~((~in(tptp_fun_C_18(D!17, C!16), relation_rng(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (~(tptp_fun_C_18(D!17, C!16) = apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))))) | (~((~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (~(tptp_fun_C_18(D!17, C!16) = apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14))))))),
% 4.01/4.24 inference(unit_resolution,[status(thm)],[107, 106])).
% 4.01/4.24 tff(109,plain,
% 4.01/4.24 (~((~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (~(tptp_fun_C_18(D!17, C!16) = apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))),
% 4.01/4.24 inference(unit_resolution,[status(thm)],[108, 52])).
% 4.01/4.24 tff(110,plain,
% 4.01/4.24 (((~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (~(tptp_fun_C_18(D!17, C!16) = apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14))))) | (tptp_fun_C_18(D!17, C!16) = apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))),
% 4.01/4.24 inference(tautology,[status(thm)],[])).
% 4.01/4.24 tff(111,plain,
% 4.01/4.24 (tptp_fun_C_18(D!17, C!16) = apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14))),
% 4.01/4.24 inference(unit_resolution,[status(thm)],[110, 109])).
% 4.01/4.24 tff(112,plain,
% 4.01/4.24 (apply(D!17, tptp_fun_C_18(D!17, C!16)) = apply(D!17, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))),
% 4.01/4.24 inference(monotonicity,[status(thm)],[111])).
% 4.01/4.24 tff(113,plain,
% 4.01/4.24 (apply(D!17, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14))) = apply(D!17, tptp_fun_C_18(D!17, C!16))),
% 4.01/4.24 inference(symmetry,[status(thm)],[112])).
% 4.01/4.24 tff(114,plain,
% 4.01/4.24 (^[A: $i, B: $i] : refl(((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))))),
% 4.01/4.24 inference(bind,[status(th)],[])).
% 4.01/4.24 tff(115,plain,
% 4.01/4.24 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 4.01/4.25 inference(quant_intro,[status(thm)],[114])).
% 4.01/4.25 tff(116,plain,
% 4.01/4.25 (^[A: $i, B: $i] : rewrite(((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))))),
% 4.01/4.25 inference(bind,[status(th)],[])).
% 4.01/4.25 tff(117,plain,
% 4.01/4.25 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 4.01/4.25 inference(quant_intro,[status(thm)],[116])).
% 4.01/4.25 tff(118,plain,
% 4.01/4.25 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 4.01/4.25 inference(transitivity,[status(thm)],[117, 115])).
% 4.01/4.25 tff(119,plain,
% 4.01/4.25 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B))))), ((~(relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B))))))), rewrite((~(~((~relation(B)) | (~function(B))))) <=> ((~relation(B)) | (~function(B)))), ((~(relation(B) & function(B))) <=> ((~relation(B)) | (~function(B))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(C) & function(C)) <=> (~((~relation(C)) | (~function(C))))), ((~(relation(C) & function(C))) <=> (~(~((~relation(C)) | (~function(C))))))), rewrite((~(~((~relation(C)) | (~function(C))))) <=> ((~relation(C)) | (~function(C)))), ((~(relation(C) & function(C))) <=> ((~relation(C)) | (~function(C))))), (((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | ((~relation(C)) | (~function(C))) | (~in(A, relation_dom(B)))))), rewrite(((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | ((~relation(C)) | (~function(C))) | (~in(A, relation_dom(B)))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))), (((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))))), (![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))) <=> ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))), (((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))) <=> (((~relation(B)) | (~function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))))), rewrite((((~relation(B)) | (~function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))), (((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))))),
% 4.01/4.25 inference(bind,[status(th)],[])).
% 4.01/4.25 tff(120,plain,
% 4.01/4.25 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 4.01/4.25 inference(quant_intro,[status(thm)],[119])).
% 4.01/4.25 tff(121,plain,
% 4.01/4.25 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))),
% 4.01/4.25 inference(rewrite,[status(thm)],[])).
% 4.01/4.25 tff(122,plain,
% 4.01/4.25 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))) <=> ((~in(A, relation_dom(B))) | (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))), (((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ((relation(C) & function(C)) => ((~in(A, relation_dom(B))) | (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))))), rewrite(((relation(C) & function(C)) => ((~in(A, relation_dom(B))) | (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))), (((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))))), (![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))))) <=> ((relation(B) & function(B)) => ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))))), rewrite(((relation(B) & function(B)) => ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))))),
% 4.01/4.25 inference(bind,[status(th)],[])).
% 4.01/4.25 tff(123,plain,
% 4.01/4.25 (![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))),
% 4.01/4.25 inference(quant_intro,[status(thm)],[122])).
% 4.01/4.25 tff(124,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t23_funct_1')).
% 4.01/4.25 tff(125,plain,
% 4.01/4.25 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))),
% 4.01/4.25 inference(modus_ponens,[status(thm)],[124, 123])).
% 4.01/4.25 tff(126,plain,
% 4.01/4.25 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))),
% 4.01/4.25 inference(modus_ponens,[status(thm)],[125, 121])).
% 4.01/4.25 tff(127,plain,(
% 4.01/4.25 ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))),
% 4.01/4.25 inference(skolemize,[status(sab)],[126])).
% 4.01/4.25 tff(128,plain,
% 4.01/4.25 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 4.01/4.25 inference(modus_ponens,[status(thm)],[127, 120])).
% 4.01/4.25 tff(129,plain,
% 4.01/4.25 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 4.01/4.25 inference(modus_ponens,[status(thm)],[128, 118])).
% 4.01/4.25 tff(130,plain,
% 4.01/4.25 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~function(B!14)) | (~relation(B!14)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | (~function(B!14)) | (~relation(B!14)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14))))))),
% 4.01/4.25 inference(rewrite,[status(thm)],[])).
% 4.01/4.25 tff(131,plain,
% 4.01/4.25 (((~relation(B!14)) | (~function(B!14)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))) <=> ((~function(B!14)) | (~relation(B!14)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14))))))),
% 4.01/4.25 inference(rewrite,[status(thm)],[])).
% 4.01/4.25 tff(132,plain,
% 4.01/4.25 (^[C: $i] : rewrite(((apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (~relation(C)) | (~function(C))) <=> ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14))))))),
% 4.01/4.25 inference(bind,[status(th)],[])).
% 4.01/4.25 tff(133,plain,
% 4.01/4.25 (![C: $i] : ((apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (~relation(C)) | (~function(C))) <=> ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))),
% 4.01/4.25 inference(quant_intro,[status(thm)],[132])).
% 4.01/4.25 tff(134,plain,
% 4.01/4.25 (((~relation(B!14)) | (~function(B!14)) | ![C: $i] : ((apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B!14)) | (~function(B!14)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14))))))),
% 4.01/4.25 inference(monotonicity,[status(thm)],[133])).
% 4.01/4.25 tff(135,plain,
% 4.01/4.25 (((~relation(B!14)) | (~function(B!14)) | ![C: $i] : ((apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (~relation(C)) | (~function(C)))) <=> ((~function(B!14)) | (~relation(B!14)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14))))))),
% 4.01/4.25 inference(transitivity,[status(thm)],[134, 131])).
% 4.01/4.25 tff(136,plain,
% 4.01/4.25 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(B!14)) | (~function(B!14)) | ![C: $i] : ((apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (~relation(C)) | (~function(C))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~function(B!14)) | (~relation(B!14)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))))),
% 4.01/4.25 inference(monotonicity,[status(thm)],[135])).
% 4.01/4.25 tff(137,plain,
% 4.01/4.25 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(B!14)) | (~function(B!14)) | ![C: $i] : ((apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (~relation(C)) | (~function(C))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | (~function(B!14)) | (~relation(B!14)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14))))))),
% 4.01/4.25 inference(transitivity,[status(thm)],[136, 130])).
% 4.01/4.25 tff(138,plain,
% 4.01/4.25 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(B!14)) | (~function(B!14)) | ![C: $i] : ((apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (~relation(C)) | (~function(C))))),
% 4.01/4.25 inference(quant_inst,[status(thm)],[])).
% 4.01/4.25 tff(139,plain,
% 4.01/4.25 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | (~function(B!14)) | (~relation(B!14)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))),
% 4.01/4.25 inference(modus_ponens,[status(thm)],[138, 137])).
% 4.01/4.25 tff(140,plain,
% 4.01/4.25 (![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))),
% 4.01/4.25 inference(unit_resolution,[status(thm)],[139, 17, 16, 129])).
% 4.01/4.25 tff(141,plain,
% 4.01/4.25 (((~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (~(tptp_fun_C_18(D!17, C!16) = apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14))))) | in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))),
% 4.01/4.25 inference(tautology,[status(thm)],[])).
% 4.01/4.25 tff(142,plain,
% 4.01/4.25 (in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))),
% 4.01/4.25 inference(unit_resolution,[status(thm)],[141, 109])).
% 4.01/4.25 tff(143,plain,
% 4.01/4.25 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))) | ((~function(D!17)) | (~relation(D!17)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, D!17), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(D!17, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))) | (~function(D!17)) | (~relation(D!17)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, D!17), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(D!17, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))),
% 4.01/4.25 inference(rewrite,[status(thm)],[])).
% 4.01/4.25 tff(144,plain,
% 4.01/4.25 (((~relation(D!17)) | (~function(D!17)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, D!17), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(D!17, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14))))) <=> ((~function(D!17)) | (~relation(D!17)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, D!17), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(D!17, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))),
% 4.01/4.25 inference(rewrite,[status(thm)],[])).
% 4.01/4.25 tff(145,plain,
% 4.01/4.25 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))) | ((~relation(D!17)) | (~function(D!17)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, D!17), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(D!17, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))) | ((~function(D!17)) | (~relation(D!17)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, D!17), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(D!17, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14))))))),
% 4.01/4.25 inference(monotonicity,[status(thm)],[144])).
% 4.01/4.25 tff(146,plain,
% 4.01/4.25 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))) | ((~relation(D!17)) | (~function(D!17)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, D!17), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(D!17, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))) | (~function(D!17)) | (~relation(D!17)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, D!17), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(D!17, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))),
% 4.01/4.25 inference(transitivity,[status(thm)],[145, 143])).
% 4.01/4.25 tff(147,plain,
% 4.01/4.25 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))) | ((~relation(D!17)) | (~function(D!17)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, D!17), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(D!17, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))),
% 4.01/4.25 inference(quant_inst,[status(thm)],[])).
% 4.01/4.25 tff(148,plain,
% 4.01/4.25 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))) | (~function(D!17)) | (~relation(D!17)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, D!17), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(D!17, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14))))),
% 4.01/4.25 inference(modus_ponens,[status(thm)],[147, 146])).
% 4.01/4.25 tff(149,plain,
% 4.01/4.25 (apply(relation_composition(B!14, D!17), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(D!17, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))),
% 4.01/4.25 inference(unit_resolution,[status(thm)],[148, 95, 94, 142, 140])).
% 4.01/4.25 tff(150,plain,
% 4.01/4.25 (relation_composition(B!14, C!16) = relation_composition(B!14, D!17)),
% 4.01/4.25 inference(and_elim,[status(thm)],[54])).
% 4.01/4.25 tff(151,plain,
% 4.01/4.25 (relation_composition(B!14, D!17) = relation_composition(B!14, C!16)),
% 4.01/4.25 inference(symmetry,[status(thm)],[150])).
% 4.01/4.25 tff(152,plain,
% 4.01/4.25 (apply(relation_composition(B!14, D!17), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(relation_composition(B!14, C!16), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14))),
% 4.01/4.25 inference(monotonicity,[status(thm)],[151])).
% 4.01/4.25 tff(153,plain,
% 4.01/4.25 (apply(relation_composition(B!14, C!16), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(relation_composition(B!14, D!17), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14))),
% 4.01/4.25 inference(symmetry,[status(thm)],[152])).
% 4.01/4.25 tff(154,plain,
% 4.01/4.25 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))) | ((~function(C!16)) | (~relation(C!16)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C!16), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C!16, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))) | (~function(C!16)) | (~relation(C!16)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C!16), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C!16, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))),
% 4.01/4.25 inference(rewrite,[status(thm)],[])).
% 4.01/4.25 tff(155,plain,
% 4.01/4.25 (((~relation(C!16)) | (~function(C!16)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C!16), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C!16, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14))))) <=> ((~function(C!16)) | (~relation(C!16)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C!16), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C!16, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))),
% 4.01/4.25 inference(rewrite,[status(thm)],[])).
% 4.01/4.25 tff(156,plain,
% 4.01/4.25 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))) | ((~relation(C!16)) | (~function(C!16)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C!16), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C!16, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))) | ((~function(C!16)) | (~relation(C!16)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C!16), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C!16, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14))))))),
% 4.01/4.25 inference(monotonicity,[status(thm)],[155])).
% 4.01/4.25 tff(157,plain,
% 4.01/4.25 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))) | ((~relation(C!16)) | (~function(C!16)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C!16), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C!16, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))) | (~function(C!16)) | (~relation(C!16)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C!16), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C!16, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))),
% 4.12/4.28 inference(transitivity,[status(thm)],[156, 154])).
% 4.12/4.28 tff(158,plain,
% 4.12/4.28 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))) | ((~relation(C!16)) | (~function(C!16)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C!16), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C!16, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))),
% 4.12/4.28 inference(quant_inst,[status(thm)],[])).
% 4.12/4.28 tff(159,plain,
% 4.12/4.28 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))))) | (~function(C!16)) | (~relation(C!16)) | (~in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))) | (apply(relation_composition(B!14, C!16), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C!16, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14))))),
% 4.12/4.28 inference(modus_ponens,[status(thm)],[158, 157])).
% 4.12/4.28 tff(160,plain,
% 4.12/4.28 (apply(relation_composition(B!14, C!16), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = apply(C!16, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))),
% 4.12/4.28 inference(unit_resolution,[status(thm)],[159, 85, 84, 142, 140])).
% 4.12/4.28 tff(161,plain,
% 4.12/4.28 (apply(C!16, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14))) = apply(relation_composition(B!14, C!16), tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14))),
% 4.12/4.28 inference(symmetry,[status(thm)],[160])).
% 4.12/4.28 tff(162,plain,
% 4.12/4.28 (apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)) = tptp_fun_C_18(D!17, C!16)),
% 4.12/4.28 inference(symmetry,[status(thm)],[111])).
% 4.12/4.28 tff(163,plain,
% 4.12/4.28 (apply(C!16, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14))) = apply(C!16, tptp_fun_C_18(D!17, C!16))),
% 4.12/4.28 inference(monotonicity,[status(thm)],[162])).
% 4.12/4.28 tff(164,plain,
% 4.12/4.28 (apply(C!16, tptp_fun_C_18(D!17, C!16)) = apply(C!16, apply(B!14, tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14)))),
% 4.12/4.28 inference(symmetry,[status(thm)],[163])).
% 4.12/4.28 tff(165,plain,
% 4.12/4.28 (apply(C!16, tptp_fun_C_18(D!17, C!16)) = apply(D!17, tptp_fun_C_18(D!17, C!16))),
% 4.12/4.28 inference(transitivity,[status(thm)],[164, 161, 153, 149, 113])).
% 4.12/4.28 tff(166,plain,
% 4.12/4.28 (((~in(tptp_fun_C_18(D!17, C!16), relation_dom(C!16))) | (apply(C!16, tptp_fun_C_18(D!17, C!16)) = apply(D!17, tptp_fun_C_18(D!17, C!16)))) | (~(apply(C!16, tptp_fun_C_18(D!17, C!16)) = apply(D!17, tptp_fun_C_18(D!17, C!16))))),
% 4.12/4.28 inference(tautology,[status(thm)],[])).
% 4.12/4.28 tff(167,plain,
% 4.12/4.28 (~(apply(C!16, tptp_fun_C_18(D!17, C!16)) = apply(D!17, tptp_fun_C_18(D!17, C!16)))),
% 4.12/4.28 inference(unit_resolution,[status(thm)],[166, 103])).
% 4.12/4.28 tff(168,plain,
% 4.12/4.28 ($false),
% 4.12/4.28 inference(unit_resolution,[status(thm)],[167, 165])).
% 4.12/4.28 % SZS output end Proof
% 4.12/4.28 % E exiting
%------------------------------------------------------------------------------