TSTP Solution File: SEU075+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU075+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 : Tue Sep 20 07:27:26 EDT 2022
% Result : Theorem 11.22s 7.18s
% Output : Proof 11.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU075+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 09:18:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 11.22/7.18 % SZS status Theorem
% 11.22/7.18 % SZS output start Proof
% 11.22/7.18 tff(apply_type, type, (
% 11.22/7.18 apply: ( $i * $i ) > $i)).
% 11.22/7.18 tff(tptp_fun_C_18_type, type, (
% 11.22/7.18 tptp_fun_C_18: ( $i * $i ) > $i)).
% 11.22/7.18 tff(tptp_fun_C_16_type, type, (
% 11.22/7.18 tptp_fun_C_16: $i)).
% 11.22/7.18 tff(tptp_fun_D_17_type, type, (
% 11.22/7.18 tptp_fun_D_17: $i)).
% 11.22/7.18 tff(tptp_fun_D_0_type, type, (
% 11.22/7.18 tptp_fun_D_0: ( $i * $i ) > $i)).
% 11.22/7.18 tff(tptp_fun_B_14_type, type, (
% 11.22/7.18 tptp_fun_B_14: $i)).
% 11.22/7.18 tff(in_type, type, (
% 11.22/7.18 in: ( $i * $i ) > $o)).
% 11.22/7.18 tff(relation_dom_type, type, (
% 11.22/7.18 relation_dom: $i > $i)).
% 11.22/7.18 tff(relation_rng_type, type, (
% 11.22/7.18 relation_rng: $i > $i)).
% 11.22/7.18 tff(tptp_fun_C_1_type, type, (
% 11.22/7.18 tptp_fun_C_1: ( $i * $i ) > $i)).
% 11.22/7.18 tff(tptp_fun_D_2_type, type, (
% 11.22/7.18 tptp_fun_D_2: ( $i * $i ) > $i)).
% 11.22/7.18 tff(function_type, type, (
% 11.22/7.18 function: $i > $o)).
% 11.22/7.18 tff(relation_composition_type, type, (
% 11.22/7.18 relation_composition: ( $i * $i ) > $i)).
% 11.22/7.18 tff(tptp_fun_A_15_type, type, (
% 11.22/7.18 tptp_fun_A_15: $i)).
% 11.22/7.18 tff(relation_type, type, (
% 11.22/7.18 relation: $i > $o)).
% 11.22/7.18 tff(1,plain,
% 11.22/7.18 (((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)))))))),
% 11.22/7.18 inference(rewrite,[status(thm)],[])).
% 11.22/7.18 tff(2,plain,
% 11.22/7.18 (((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)))))))),
% 11.22/7.18 inference(rewrite,[status(thm)],[])).
% 11.22/7.18 tff(3,plain,
% 11.22/7.18 ((~((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))))))),
% 11.22/7.18 inference(rewrite,[status(thm)],[])).
% 11.22/7.18 tff(4,plain,
% 11.22/7.18 ((~(~(relation(C!16) & function(C!16)))) <=> (relation(C!16) & function(C!16))),
% 11.22/7.18 inference(rewrite,[status(thm)],[])).
% 11.22/7.18 tff(5,plain,
% 11.22/7.18 (((~(~(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)))))))),
% 11.22/7.18 inference(monotonicity,[status(thm)],[4, 3])).
% 11.22/7.18 tff(6,plain,
% 11.22/7.18 (((~(~(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)))))))),
% 11.22/7.18 inference(transitivity,[status(thm)],[5, 2])).
% 11.22/7.18 tff(7,plain,
% 11.22/7.18 ((~(~(relation(B!14) & function(B!14)))) <=> (relation(B!14) & function(B!14))),
% 11.22/7.18 inference(rewrite,[status(thm)],[])).
% 11.22/7.18 tff(8,plain,
% 11.22/7.18 (((~(~(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))))))))),
% 11.22/7.18 inference(monotonicity,[status(thm)],[7, 6])).
% 11.22/7.18 tff(9,plain,
% 11.22/7.18 (((~(~(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)))))))),
% 11.22/7.18 inference(transitivity,[status(thm)],[8, 1])).
% 11.22/7.18 tff(10,plain,
% 11.22/7.18 ((~![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))))))))),
% 11.22/7.18 inference(rewrite,[status(thm)],[])).
% 11.22/7.18 tff(11,plain,
% 11.22/7.18 ((~![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))))))))),
% 11.22/7.18 inference(rewrite,[status(thm)],[])).
% 11.22/7.18 tff(12,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')).
% 11.22/7.18 tff(13,plain,
% 11.22/7.18 (~![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)))))))),
% 11.22/7.18 inference(modus_ponens,[status(thm)],[12, 11])).
% 11.22/7.18 tff(14,plain,
% 11.22/7.18 (~![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)))))))),
% 11.22/7.18 inference(modus_ponens,[status(thm)],[13, 10])).
% 11.22/7.18 tff(15,plain,
% 11.22/7.18 (~![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)))))))),
% 11.22/7.18 inference(modus_ponens,[status(thm)],[14, 10])).
% 11.22/7.18 tff(16,plain,
% 11.22/7.18 (~![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)))))))),
% 11.22/7.18 inference(modus_ponens,[status(thm)],[15, 10])).
% 11.22/7.18 tff(17,plain,
% 11.22/7.18 (~![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)))))))),
% 11.22/7.18 inference(modus_ponens,[status(thm)],[16, 10])).
% 11.22/7.18 tff(18,plain,
% 11.22/7.18 (~![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)))))))),
% 11.22/7.18 inference(modus_ponens,[status(thm)],[17, 10])).
% 11.22/7.18 tff(19,plain,
% 11.22/7.18 (~![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)))))))),
% 11.22/7.18 inference(modus_ponens,[status(thm)],[18, 10])).
% 11.22/7.18 tff(20,plain,
% 11.22/7.18 (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))))))),
% 11.22/7.18 inference(modus_ponens,[status(thm)],[19, 9])).
% 11.22/7.18 tff(21,plain,
% 11.22/7.18 (function(B!14)),
% 11.22/7.18 inference(and_elim,[status(thm)],[20])).
% 11.22/7.18 tff(22,plain,
% 11.22/7.18 (relation(B!14)),
% 11.22/7.18 inference(and_elim,[status(thm)],[20])).
% 11.22/7.18 tff(23,plain,
% 11.22/7.18 (^[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))))))))))))))),
% 11.22/7.18 inference(bind,[status(th)],[])).
% 11.22/7.18 tff(24,plain,
% 11.22/7.18 (![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))))))))))))),
% 11.22/7.19 inference(quant_intro,[status(thm)],[23])).
% 11.22/7.19 tff(25,plain,
% 11.22/7.19 (^[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))))))))))))))),
% 11.22/7.19 inference(bind,[status(th)],[])).
% 11.22/7.19 tff(26,plain,
% 11.22/7.19 (![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))))))))))))) <=> ![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)))))))))))))),
% 11.22/7.19 inference(quant_intro,[status(thm)],[25])).
% 11.22/7.19 tff(27,plain,
% 11.22/7.19 (^[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))))))))))))))),
% 11.22/7.19 inference(bind,[status(th)],[])).
% 11.22/7.19 tff(28,plain,
% 11.22/7.19 (![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)))))))))))))),
% 11.22/7.19 inference(quant_intro,[status(thm)],[27])).
% 11.22/7.19 tff(29,plain,
% 11.22/7.19 (![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)))))))))))))),
% 11.22/7.19 inference(transitivity,[status(thm)],[28, 26])).
% 11.22/7.19 tff(30,plain,
% 11.22/7.19 (^[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)))))))))))))))),
% 11.22/7.19 inference(bind,[status(th)],[])).
% 11.22/7.19 tff(31,plain,
% 11.22/7.19 (![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)))))))))))))),
% 11.22/7.19 inference(quant_intro,[status(thm)],[30])).
% 11.22/7.19 tff(32,plain,
% 11.22/7.19 (![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))))))),
% 11.22/7.19 inference(rewrite,[status(thm)],[])).
% 11.22/7.19 tff(33,plain,
% 11.22/7.19 (^[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)))))))),
% 11.22/7.19 inference(bind,[status(th)],[])).
% 11.22/7.19 tff(34,plain,
% 11.22/7.19 (![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))))))),
% 11.22/7.19 inference(quant_intro,[status(thm)],[33])).
% 11.22/7.19 tff(35,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')).
% 11.22/7.19 tff(36,plain,
% 11.22/7.19 (![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))))))),
% 11.22/7.19 inference(modus_ponens,[status(thm)],[35, 34])).
% 11.22/7.19 tff(37,plain,
% 11.22/7.19 (![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))))))),
% 11.22/7.19 inference(modus_ponens,[status(thm)],[36, 32])).
% 11.22/7.19 tff(38,plain,(
% 11.22/7.19 ![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)))))))))),
% 11.22/7.19 inference(skolemize,[status(sab)],[37])).
% 11.22/7.19 tff(39,plain,
% 11.22/7.19 (![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)))))))))))))),
% 11.22/7.19 inference(modus_ponens,[status(thm)],[38, 31])).
% 11.22/7.19 tff(40,plain,
% 11.22/7.20 (![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)))))))))))))),
% 11.22/7.20 inference(modus_ponens,[status(thm)],[39, 29])).
% 11.22/7.20 tff(41,plain,
% 11.22/7.20 (![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))))))))))))),
% 11.22/7.20 inference(modus_ponens,[status(thm)],[40, 24])).
% 11.22/7.20 tff(42,plain,
% 11.22/7.20 (((~![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))))))))))))) | (~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))))))))))))),
% 11.22/7.20 inference(rewrite,[status(thm)],[])).
% 11.22/7.20 tff(43,plain,
% 11.22/7.20 ((~![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))))))))))))),
% 11.22/7.20 inference(quant_inst,[status(thm)],[])).
% 11.22/7.20 tff(44,plain,
% 11.22/7.20 ((~![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)))))))))))),
% 11.22/7.20 inference(modus_ponens,[status(thm)],[43, 42])).
% 11.22/7.20 tff(45,plain,
% 11.22/7.20 (![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)))))))))))),
% 11.22/7.20 inference(unit_resolution,[status(thm)],[44, 41, 22, 21])).
% 11.22/7.20 tff(46,plain,
% 11.22/7.20 (((~![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))))))))))),
% 11.22/7.20 inference(rewrite,[status(thm)],[])).
% 11.22/7.20 tff(47,plain,
% 11.22/7.20 ((~((~((~(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)))))))))),
% 11.22/7.20 inference(rewrite,[status(thm)],[])).
% 11.22/7.20 tff(48,plain,
% 11.22/7.20 (((~![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))))))))))),
% 11.22/7.21 inference(monotonicity,[status(thm)],[47])).
% 11.22/7.21 tff(49,plain,
% 11.22/7.21 (((~![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))))))))))),
% 11.22/7.21 inference(transitivity,[status(thm)],[48, 46])).
% 11.22/7.21 tff(50,plain,
% 11.22/7.21 ((~![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)))))))))))))),
% 11.22/7.21 inference(quant_inst,[status(thm)],[])).
% 11.22/7.21 tff(51,plain,
% 11.22/7.21 ((~![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)))))))))),
% 11.22/7.21 inference(modus_ponens,[status(thm)],[50, 49])).
% 11.22/7.21 tff(52,plain,
% 11.22/7.21 (~((~((~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))))))))),
% 11.22/7.21 inference(unit_resolution,[status(thm)],[51, 45])).
% 11.22/7.21 tff(53,plain,
% 11.22/7.21 (((~((~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)))))))),
% 11.22/7.21 inference(tautology,[status(thm)],[])).
% 11.22/7.21 tff(54,plain,
% 11.22/7.21 ((~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))))))),
% 11.22/7.21 inference(unit_resolution,[status(thm)],[53, 52])).
% 11.22/7.21 tff(55,plain,
% 11.22/7.21 (~((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)))))),
% 11.22/7.21 inference(and_elim,[status(thm)],[20])).
% 11.22/7.21 tff(56,plain,
% 11.22/7.21 ((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))),
% 11.22/7.21 inference(or_elim,[status(thm)],[55])).
% 11.22/7.21 tff(57,plain,
% 11.22/7.21 (relation_dom(C!16) = A!15),
% 11.22/7.21 inference(and_elim,[status(thm)],[56])).
% 11.22/7.21 tff(58,plain,
% 11.22/7.21 (A!15 = relation_dom(C!16)),
% 11.22/7.21 inference(symmetry,[status(thm)],[57])).
% 11.22/7.21 tff(59,plain,
% 11.22/7.21 (A!15 = relation_rng(B!14)),
% 11.22/7.21 inference(and_elim,[status(thm)],[56])).
% 11.22/7.21 tff(60,plain,
% 11.22/7.21 (relation_rng(B!14) = A!15),
% 11.22/7.21 inference(symmetry,[status(thm)],[59])).
% 11.22/7.21 tff(61,plain,
% 11.22/7.21 (relation_rng(B!14) = relation_dom(C!16)),
% 11.22/7.21 inference(transitivity,[status(thm)],[60, 58])).
% 11.22/7.21 tff(62,plain,
% 11.22/7.21 (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))),
% 11.22/7.21 inference(monotonicity,[status(thm)],[61])).
% 11.22/7.21 tff(63,plain,
% 11.22/7.21 (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))),
% 11.22/7.21 inference(symmetry,[status(thm)],[62])).
% 11.22/7.21 tff(64,plain,
% 11.22/7.21 (relation_dom(D!17) = A!15),
% 11.22/7.21 inference(and_elim,[status(thm)],[56])).
% 11.22/7.21 tff(65,plain,
% 11.22/7.21 (A!15 = relation_dom(D!17)),
% 11.22/7.21 inference(symmetry,[status(thm)],[64])).
% 11.22/7.21 tff(66,plain,
% 11.22/7.21 (relation_dom(C!16) = relation_dom(D!17)),
% 11.22/7.21 inference(transitivity,[status(thm)],[57, 65])).
% 11.22/7.21 tff(67,plain,
% 11.22/7.21 (^[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))))))))),
% 11.22/7.21 inference(bind,[status(th)],[])).
% 11.22/7.21 tff(68,plain,
% 11.22/7.21 (![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)))))))),
% 11.22/7.21 inference(quant_intro,[status(thm)],[67])).
% 11.22/7.21 tff(69,plain,
% 11.22/7.21 (^[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))))))))),
% 11.22/7.21 inference(bind,[status(th)],[])).
% 11.22/7.21 tff(70,plain,
% 11.22/7.21 (![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)))))))),
% 11.22/7.21 inference(quant_intro,[status(thm)],[69])).
% 11.22/7.21 tff(71,plain,
% 11.22/7.21 (![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)))))))),
% 11.22/7.21 inference(transitivity,[status(thm)],[70, 68])).
% 11.22/7.21 tff(72,plain,
% 11.22/7.21 (^[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)))))))))),
% 11.22/7.21 inference(bind,[status(th)],[])).
% 11.22/7.21 tff(73,plain,
% 11.22/7.21 (![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)))))))),
% 11.22/7.21 inference(quant_intro,[status(thm)],[72])).
% 11.22/7.21 tff(74,plain,
% 11.22/7.21 (^[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))))))))),
% 11.22/7.21 inference(bind,[status(th)],[])).
% 11.22/7.21 tff(75,plain,
% 11.22/7.21 (![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)))))))),
% 11.22/7.21 inference(quant_intro,[status(thm)],[74])).
% 11.22/7.21 tff(76,plain,
% 11.22/7.21 (![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)))))))),
% 11.22/7.21 inference(rewrite,[status(thm)],[])).
% 11.22/7.21 tff(77,plain,
% 11.22/7.21 (^[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)))))))))),
% 11.22/7.22 inference(bind,[status(th)],[])).
% 11.22/7.22 tff(78,plain,
% 11.22/7.22 (![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)))))))),
% 11.22/7.22 inference(quant_intro,[status(thm)],[77])).
% 11.22/7.22 tff(79,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')).
% 11.22/7.22 tff(80,plain,
% 11.22/7.22 (![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)))))))),
% 11.22/7.22 inference(modus_ponens,[status(thm)],[79, 78])).
% 11.22/7.22 tff(81,plain,
% 11.22/7.22 (![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)))))))),
% 11.22/7.22 inference(modus_ponens,[status(thm)],[80, 76])).
% 11.22/7.22 tff(82,plain,(
% 11.22/7.22 ![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))))))))),
% 11.22/7.22 inference(skolemize,[status(sab)],[81])).
% 11.22/7.22 tff(83,plain,
% 11.22/7.22 (![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)))))))),
% 11.22/7.22 inference(modus_ponens,[status(thm)],[82, 75])).
% 11.22/7.22 tff(84,plain,
% 11.22/7.22 (![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)))))))),
% 11.22/7.22 inference(modus_ponens,[status(thm)],[83, 73])).
% 11.22/7.22 tff(85,plain,
% 11.22/7.22 (![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)))))))),
% 11.22/7.22 inference(modus_ponens,[status(thm)],[84, 71])).
% 11.22/7.22 tff(86,plain,
% 11.22/7.22 (function(C!16)),
% 11.22/7.22 inference(and_elim,[status(thm)],[20])).
% 11.22/7.22 tff(87,plain,
% 11.22/7.22 (relation(C!16)),
% 11.22/7.22 inference(and_elim,[status(thm)],[20])).
% 11.22/7.22 tff(88,plain,
% 11.22/7.22 (((~![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)))))))) | (~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)))))))),
% 11.22/7.22 inference(rewrite,[status(thm)],[])).
% 11.22/7.22 tff(89,plain,
% 11.22/7.22 ((~![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)))))))),
% 11.22/7.22 inference(quant_inst,[status(thm)],[])).
% 11.22/7.22 tff(90,plain,
% 11.22/7.22 ((~![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))))))),
% 11.22/7.22 inference(modus_ponens,[status(thm)],[89, 88])).
% 11.22/7.22 tff(91,plain,
% 11.22/7.22 (![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))))))),
% 11.22/7.22 inference(unit_resolution,[status(thm)],[90, 87, 86, 85])).
% 11.22/7.22 tff(92,plain,
% 11.22/7.22 (relation(D!17) & function(D!17)),
% 11.22/7.22 inference(or_elim,[status(thm)],[55])).
% 11.22/7.22 tff(93,plain,
% 11.22/7.22 (function(D!17)),
% 11.22/7.22 inference(and_elim,[status(thm)],[92])).
% 11.22/7.22 tff(94,plain,
% 11.27/7.22 (relation(D!17)),
% 11.27/7.22 inference(and_elim,[status(thm)],[92])).
% 11.27/7.22 tff(95,plain,
% 11.27/7.22 (~(C!16 = D!17)),
% 11.27/7.22 inference(or_elim,[status(thm)],[55])).
% 11.27/7.22 tff(96,plain,
% 11.27/7.22 (((~![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) | (~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))))))),
% 11.27/7.22 inference(rewrite,[status(thm)],[])).
% 11.27/7.22 tff(97,plain,
% 11.27/7.22 ((~![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))))))),
% 11.27/7.22 inference(quant_inst,[status(thm)],[])).
% 11.27/7.22 tff(98,plain,
% 11.27/7.22 ((~![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)))))),
% 11.27/7.22 inference(modus_ponens,[status(thm)],[97, 96])).
% 11.27/7.22 tff(99,plain,
% 11.27/7.22 (~((~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))))),
% 11.27/7.22 inference(unit_resolution,[status(thm)],[98, 95, 94, 93, 91, 66])).
% 11.27/7.22 tff(100,plain,
% 11.27/7.22 (((~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))),
% 11.27/7.22 inference(tautology,[status(thm)],[])).
% 11.27/7.22 tff(101,plain,
% 11.27/7.22 (in(tptp_fun_C_18(D!17, C!16), relation_dom(C!16))),
% 11.27/7.22 inference(unit_resolution,[status(thm)],[100, 99])).
% 11.27/7.22 tff(102,plain,
% 11.27/7.22 (in(tptp_fun_C_18(D!17, C!16), relation_rng(B!14))),
% 11.27/7.22 inference(modus_ponens,[status(thm)],[101, 63])).
% 11.27/7.22 tff(103,plain,
% 11.27/7.22 ((~((~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))))))),
% 11.27/7.22 inference(tautology,[status(thm)],[])).
% 11.27/7.22 tff(104,plain,
% 11.27/7.22 ((~((~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))))))),
% 11.27/7.22 inference(unit_resolution,[status(thm)],[103, 102])).
% 11.27/7.22 tff(105,plain,
% 11.27/7.22 (~((~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)))))),
% 11.27/7.22 inference(unit_resolution,[status(thm)],[104, 54])).
% 11.27/7.22 tff(106,plain,
% 11.27/7.22 (((~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)))),
% 11.27/7.22 inference(tautology,[status(thm)],[])).
% 11.27/7.22 tff(107,plain,
% 11.27/7.22 (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))),
% 11.27/7.22 inference(unit_resolution,[status(thm)],[106, 105])).
% 11.27/7.22 tff(108,plain,
% 11.27/7.22 (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)))),
% 11.27/7.22 inference(monotonicity,[status(thm)],[107])).
% 11.27/7.22 tff(109,plain,
% 11.27/7.22 (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))),
% 11.27/7.22 inference(symmetry,[status(thm)],[108])).
% 11.27/7.22 tff(110,plain,
% 11.27/7.22 (^[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)))))),
% 11.27/7.22 inference(bind,[status(th)],[])).
% 11.27/7.22 tff(111,plain,
% 11.27/7.22 (![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))))),
% 11.27/7.22 inference(quant_intro,[status(thm)],[110])).
% 11.27/7.22 tff(112,plain,
% 11.27/7.22 (^[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)))))),
% 11.27/7.22 inference(bind,[status(th)],[])).
% 11.27/7.22 tff(113,plain,
% 11.27/7.22 (![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))))),
% 11.27/7.22 inference(quant_intro,[status(thm)],[112])).
% 11.27/7.22 tff(114,plain,
% 11.27/7.22 (![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))))),
% 11.27/7.22 inference(transitivity,[status(thm)],[113, 111])).
% 11.27/7.22 tff(115,plain,
% 11.27/7.22 (^[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))))))),
% 11.27/7.23 inference(bind,[status(th)],[])).
% 11.27/7.23 tff(116,plain,
% 11.27/7.23 (![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))))),
% 11.27/7.23 inference(quant_intro,[status(thm)],[115])).
% 11.27/7.23 tff(117,plain,
% 11.27/7.23 (![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)))))),
% 11.27/7.23 inference(rewrite,[status(thm)],[])).
% 11.27/7.23 tff(118,plain,
% 11.27/7.23 (^[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)))))))),
% 11.27/7.23 inference(bind,[status(th)],[])).
% 11.27/7.23 tff(119,plain,
% 11.27/7.23 (![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)))))),
% 11.27/7.23 inference(quant_intro,[status(thm)],[118])).
% 11.27/7.23 tff(120,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')).
% 11.27/7.23 tff(121,plain,
% 11.27/7.23 (![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)))))),
% 11.27/7.23 inference(modus_ponens,[status(thm)],[120, 119])).
% 11.27/7.23 tff(122,plain,
% 11.27/7.23 (![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)))))),
% 11.27/7.23 inference(modus_ponens,[status(thm)],[121, 117])).
% 11.27/7.23 tff(123,plain,(
% 11.27/7.23 ![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)))))),
% 11.27/7.23 inference(skolemize,[status(sab)],[122])).
% 11.27/7.23 tff(124,plain,
% 11.27/7.23 (![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))))),
% 11.27/7.23 inference(modus_ponens,[status(thm)],[123, 116])).
% 11.27/7.23 tff(125,plain,
% 11.27/7.23 (![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))))),
% 11.27/7.23 inference(modus_ponens,[status(thm)],[124, 114])).
% 11.27/7.23 tff(126,plain,
% 11.27/7.23 (((~![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] : ((~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))))) | (~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))))))),
% 11.27/7.23 inference(rewrite,[status(thm)],[])).
% 11.27/7.23 tff(127,plain,
% 11.27/7.23 (((~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)))))) <=> ((~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))))))),
% 11.27/7.23 inference(rewrite,[status(thm)],[])).
% 11.27/7.23 tff(128,plain,
% 11.27/7.23 (^[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))))))),
% 11.27/7.23 inference(bind,[status(th)],[])).
% 11.27/7.23 tff(129,plain,
% 11.27/7.23 (![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)))))),
% 11.27/7.23 inference(quant_intro,[status(thm)],[128])).
% 11.27/7.23 tff(130,plain,
% 11.27/7.23 (((~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))))))),
% 11.27/7.23 inference(monotonicity,[status(thm)],[129])).
% 11.27/7.23 tff(131,plain,
% 11.27/7.23 (((~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))))))),
% 11.27/7.23 inference(transitivity,[status(thm)],[130, 127])).
% 11.27/7.23 tff(132,plain,
% 11.27/7.23 (((~![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))))) | ((~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)))))))),
% 11.27/7.23 inference(monotonicity,[status(thm)],[131])).
% 11.27/7.23 tff(133,plain,
% 11.27/7.23 (((~![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))))) | (~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))))))),
% 11.27/7.23 inference(transitivity,[status(thm)],[132, 126])).
% 11.27/7.23 tff(134,plain,
% 11.27/7.23 ((~![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))))),
% 11.27/7.23 inference(quant_inst,[status(thm)],[])).
% 11.27/7.23 tff(135,plain,
% 11.27/7.23 ((~![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] : ((~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)))))),
% 11.27/7.23 inference(modus_ponens,[status(thm)],[134, 133])).
% 11.27/7.23 tff(136,plain,
% 11.27/7.23 (![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)))))),
% 11.27/7.23 inference(unit_resolution,[status(thm)],[135, 22, 21, 125])).
% 11.27/7.23 tff(137,plain,
% 11.27/7.23 (((~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))),
% 11.27/7.23 inference(tautology,[status(thm)],[])).
% 11.27/7.23 tff(138,plain,
% 11.27/7.23 (in(tptp_fun_D_0(tptp_fun_C_18(D!17, C!16), B!14), relation_dom(B!14))),
% 11.27/7.23 inference(unit_resolution,[status(thm)],[137, 105])).
% 11.27/7.24 tff(139,plain,
% 11.27/7.24 (((~![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)))))) | (~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)))))),
% 11.27/7.24 inference(rewrite,[status(thm)],[])).
% 11.27/7.24 tff(140,plain,
% 11.27/7.24 ((~![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)))))),
% 11.27/7.24 inference(quant_inst,[status(thm)],[])).
% 11.27/7.24 tff(141,plain,
% 11.27/7.24 ((~![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))))),
% 11.27/7.24 inference(modus_ponens,[status(thm)],[140, 139])).
% 11.27/7.24 tff(142,plain,
% 11.27/7.24 (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)))),
% 11.27/7.24 inference(unit_resolution,[status(thm)],[141, 94, 93, 138, 136])).
% 11.27/7.24 tff(143,plain,
% 11.27/7.24 (relation_composition(B!14, C!16) = relation_composition(B!14, D!17)),
% 11.27/7.24 inference(and_elim,[status(thm)],[56])).
% 11.27/7.24 tff(144,plain,
% 11.27/7.24 (relation_composition(B!14, D!17) = relation_composition(B!14, C!16)),
% 11.27/7.24 inference(symmetry,[status(thm)],[143])).
% 11.27/7.24 tff(145,plain,
% 11.27/7.24 (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))),
% 11.27/7.24 inference(monotonicity,[status(thm)],[144])).
% 11.27/7.24 tff(146,plain,
% 11.27/7.24 (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))),
% 11.27/7.24 inference(symmetry,[status(thm)],[145])).
% 11.27/7.24 tff(147,plain,
% 11.27/7.24 (((~![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)))))) | (~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)))))),
% 11.29/7.28 inference(rewrite,[status(thm)],[])).
% 11.29/7.28 tff(148,plain,
% 11.29/7.28 ((~![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)))))),
% 11.29/7.28 inference(quant_inst,[status(thm)],[])).
% 11.29/7.28 tff(149,plain,
% 11.29/7.28 ((~![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))))),
% 11.29/7.28 inference(modus_ponens,[status(thm)],[148, 147])).
% 11.29/7.28 tff(150,plain,
% 11.29/7.28 (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)))),
% 11.29/7.28 inference(unit_resolution,[status(thm)],[149, 87, 86, 138, 136])).
% 11.29/7.28 tff(151,plain,
% 11.29/7.28 (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))),
% 11.29/7.28 inference(symmetry,[status(thm)],[150])).
% 11.29/7.28 tff(152,plain,
% 11.29/7.28 (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)),
% 11.29/7.28 inference(symmetry,[status(thm)],[107])).
% 11.29/7.28 tff(153,plain,
% 11.29/7.28 (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))),
% 11.29/7.28 inference(monotonicity,[status(thm)],[152])).
% 11.29/7.28 tff(154,plain,
% 11.29/7.28 (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)))),
% 11.29/7.28 inference(symmetry,[status(thm)],[153])).
% 11.29/7.28 tff(155,plain,
% 11.29/7.28 (apply(C!16, tptp_fun_C_18(D!17, C!16)) = apply(D!17, tptp_fun_C_18(D!17, C!16))),
% 11.29/7.28 inference(transitivity,[status(thm)],[154, 151, 146, 142, 109])).
% 11.29/7.28 tff(156,plain,
% 11.29/7.28 (((~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))))),
% 11.29/7.28 inference(tautology,[status(thm)],[])).
% 11.29/7.28 tff(157,plain,
% 11.29/7.28 (~(apply(C!16, tptp_fun_C_18(D!17, C!16)) = apply(D!17, tptp_fun_C_18(D!17, C!16)))),
% 11.29/7.28 inference(unit_resolution,[status(thm)],[156, 99])).
% 11.29/7.28 tff(158,plain,
% 11.29/7.28 ($false),
% 11.29/7.28 inference(unit_resolution,[status(thm)],[157, 155])).
% 11.29/7.28 % SZS output end Proof
%------------------------------------------------------------------------------