TSTP Solution File: SEU012+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU012+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 07:27:16 EDT 2022
% Result : Theorem 0.77s 0.76s
% Output : Proof 0.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU012+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n018.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 09:02:29 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.21/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.21/0.35 Usage: tptp [options] [-file:]file
% 0.21/0.35 -h, -? prints this message.
% 0.21/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.21/0.35 -m, -model generate model.
% 0.21/0.35 -p, -proof generate proof.
% 0.21/0.35 -c, -core generate unsat core of named formulas.
% 0.21/0.35 -st, -statistics display statistics.
% 0.21/0.35 -t:timeout set timeout (in second).
% 0.21/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.21/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.21/0.35 -<param>:<value> configuration parameter and value.
% 0.21/0.35 -o:<output-file> file to place output in.
% 0.77/0.76 % SZS status Theorem
% 0.77/0.76 % SZS output start Proof
% 0.77/0.76 tff(tptp_fun_C_12_type, type, (
% 0.77/0.76 tptp_fun_C_12: ( $i * $i ) > $i)).
% 0.77/0.76 tff(relation_dom_type, type, (
% 0.77/0.76 relation_dom: $i > $i)).
% 0.77/0.76 tff(tptp_fun_B_14_type, type, (
% 0.77/0.76 tptp_fun_B_14: $i)).
% 0.77/0.76 tff(apply_type, type, (
% 0.77/0.76 apply: ( $i * $i ) > $i)).
% 0.77/0.76 tff(tptp_fun_D_0_type, type, (
% 0.77/0.76 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.77/0.76 tff(tptp_fun_A_13_type, type, (
% 0.77/0.76 tptp_fun_A_13: $i)).
% 0.77/0.76 tff(in_type, type, (
% 0.77/0.76 in: ( $i * $i ) > $o)).
% 0.77/0.76 tff(relation_rng_type, type, (
% 0.77/0.76 relation_rng: $i > $i)).
% 0.77/0.76 tff(tptp_fun_C_1_type, type, (
% 0.77/0.76 tptp_fun_C_1: ( $i * $i ) > $i)).
% 0.77/0.76 tff(tptp_fun_D_2_type, type, (
% 0.77/0.76 tptp_fun_D_2: ( $i * $i ) > $i)).
% 0.77/0.76 tff(function_type, type, (
% 0.77/0.76 function: $i > $o)).
% 0.77/0.76 tff(relation_composition_type, type, (
% 0.77/0.76 relation_composition: ( $i * $i ) > $i)).
% 0.77/0.76 tff(relation_type, type, (
% 0.77/0.76 relation: $i > $o)).
% 0.77/0.76 tff(identity_relation_type, type, (
% 0.77/0.76 identity_relation: $i > $i)).
% 0.77/0.76 tff(1,plain,
% 0.77/0.76 (((relation(A!13) & function(A!13)) & (~((B!14 = identity_relation(relation_dom(B!14))) | (~(relation(B!14) & function(B!14))) | (~((relation_rng(A!13) = relation_dom(B!14)) & (relation_composition(A!13, B!14) = A!13)))))) <=> (relation(A!13) & function(A!13) & (~((B!14 = identity_relation(relation_dom(B!14))) | (~(relation(B!14) & function(B!14))) | (~((relation_rng(A!13) = relation_dom(B!14)) & (relation_composition(A!13, B!14) = A!13))))))),
% 0.77/0.76 inference(rewrite,[status(thm)],[])).
% 0.77/0.76 tff(2,plain,
% 0.77/0.76 ((~((B!14 = identity_relation(relation_dom(B!14))) | (~(relation(B!14) & function(B!14))) | (~((relation_rng(A!13) = relation_dom(B!14)) & (relation_composition(A!13, B!14) = A!13))))) <=> (~((B!14 = identity_relation(relation_dom(B!14))) | (~(relation(B!14) & function(B!14))) | (~((relation_rng(A!13) = relation_dom(B!14)) & (relation_composition(A!13, B!14) = A!13)))))),
% 0.77/0.76 inference(rewrite,[status(thm)],[])).
% 0.77/0.76 tff(3,plain,
% 0.77/0.76 ((~(~(relation(A!13) & function(A!13)))) <=> (relation(A!13) & function(A!13))),
% 0.77/0.76 inference(rewrite,[status(thm)],[])).
% 0.77/0.76 tff(4,plain,
% 0.77/0.76 (((~(~(relation(A!13) & function(A!13)))) & (~((B!14 = identity_relation(relation_dom(B!14))) | (~(relation(B!14) & function(B!14))) | (~((relation_rng(A!13) = relation_dom(B!14)) & (relation_composition(A!13, B!14) = A!13)))))) <=> ((relation(A!13) & function(A!13)) & (~((B!14 = identity_relation(relation_dom(B!14))) | (~(relation(B!14) & function(B!14))) | (~((relation_rng(A!13) = relation_dom(B!14)) & (relation_composition(A!13, B!14) = A!13))))))),
% 0.77/0.76 inference(monotonicity,[status(thm)],[3, 2])).
% 0.77/0.76 tff(5,plain,
% 0.77/0.76 (((~(~(relation(A!13) & function(A!13)))) & (~((B!14 = identity_relation(relation_dom(B!14))) | (~(relation(B!14) & function(B!14))) | (~((relation_rng(A!13) = relation_dom(B!14)) & (relation_composition(A!13, B!14) = A!13)))))) <=> (relation(A!13) & function(A!13) & (~((B!14 = identity_relation(relation_dom(B!14))) | (~(relation(B!14) & function(B!14))) | (~((relation_rng(A!13) = relation_dom(B!14)) & (relation_composition(A!13, B!14) = A!13))))))),
% 0.77/0.76 inference(transitivity,[status(thm)],[4, 1])).
% 0.77/0.76 tff(6,plain,
% 0.77/0.76 ((~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)))))) <=> (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A))))))),
% 0.77/0.76 inference(rewrite,[status(thm)],[])).
% 0.77/0.76 tff(7,plain,
% 0.77/0.76 ((~![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => (((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)) => (B = identity_relation(relation_dom(B))))))) <=> (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A))))))),
% 0.77/0.76 inference(rewrite,[status(thm)],[])).
% 0.77/0.76 tff(8,axiom,(~![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => (((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)) => (B = identity_relation(relation_dom(B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t44_funct_1')).
% 0.77/0.76 tff(9,plain,
% 0.77/0.76 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)))))),
% 0.77/0.76 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.77/0.76 tff(10,plain,
% 0.77/0.76 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)))))),
% 0.77/0.76 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.77/0.76 tff(11,plain,
% 0.77/0.76 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)))))),
% 0.77/0.76 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.77/0.76 tff(12,plain,
% 0.77/0.76 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)))))),
% 0.77/0.76 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.77/0.76 tff(13,plain,
% 0.77/0.76 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)))))),
% 0.77/0.76 inference(modus_ponens,[status(thm)],[12, 6])).
% 0.77/0.76 tff(14,plain,
% 0.77/0.76 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)))))),
% 0.77/0.76 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.77/0.76 tff(15,plain,
% 0.77/0.76 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)))))),
% 0.77/0.76 inference(modus_ponens,[status(thm)],[14, 6])).
% 0.77/0.76 tff(16,plain,
% 0.77/0.76 (relation(A!13) & function(A!13) & (~((B!14 = identity_relation(relation_dom(B!14))) | (~(relation(B!14) & function(B!14))) | (~((relation_rng(A!13) = relation_dom(B!14)) & (relation_composition(A!13, B!14) = A!13)))))),
% 0.77/0.76 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.77/0.76 tff(17,plain,
% 0.77/0.76 (function(A!13)),
% 0.77/0.76 inference(and_elim,[status(thm)],[16])).
% 0.77/0.76 tff(18,plain,
% 0.77/0.76 (relation(A!13)),
% 0.77/0.76 inference(and_elim,[status(thm)],[16])).
% 0.77/0.76 tff(19,plain,
% 0.77/0.76 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15)))))))))))) <=> (~((~((~(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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))), (![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15)))))))))))) <=> ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))), (((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15)))))))))))))), rewrite(((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15)))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))), (((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))))),
% 0.84/0.76 inference(bind,[status(th)],[])).
% 0.84/0.76 tff(20,plain,
% 0.84/0.76 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))),
% 0.84/0.76 inference(quant_intro,[status(thm)],[19])).
% 0.84/0.76 tff(21,plain,
% 0.84/0.76 (^[A: $i] : refl(((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))))),
% 0.84/0.76 inference(bind,[status(th)],[])).
% 0.84/0.76 tff(22,plain,
% 0.84/0.76 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15)))))))))))))),
% 0.84/0.76 inference(quant_intro,[status(thm)],[21])).
% 0.84/0.76 tff(23,plain,
% 0.84/0.76 (^[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_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))))),
% 0.84/0.76 inference(bind,[status(th)],[])).
% 0.84/0.76 tff(24,plain,
% 0.84/0.76 (![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_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15)))))))))))))),
% 0.84/0.76 inference(quant_intro,[status(thm)],[23])).
% 0.84/0.76 tff(25,plain,
% 0.84/0.76 (![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_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15)))))))))))))),
% 0.84/0.76 inference(transitivity,[status(thm)],[24, 22])).
% 0.84/0.76 tff(26,plain,
% 0.84/0.76 (^[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)))))))))))))))),
% 0.84/0.77 inference(bind,[status(th)],[])).
% 0.84/0.77 tff(27,plain,
% 0.84/0.77 (![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)))))))))))))),
% 0.84/0.77 inference(quant_intro,[status(thm)],[26])).
% 0.84/0.77 tff(28,plain,
% 0.84/0.77 (![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))))))),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(29,plain,
% 0.84/0.77 (^[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)))))))),
% 0.84/0.77 inference(bind,[status(th)],[])).
% 0.84/0.77 tff(30,plain,
% 0.84/0.77 (![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))))))),
% 0.84/0.77 inference(quant_intro,[status(thm)],[29])).
% 0.84/0.77 tff(31,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')).
% 0.84/0.77 tff(32,plain,
% 0.84/0.77 (![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))))))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.84/0.77 tff(33,plain,
% 0.84/0.77 (![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))))))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.84/0.77 tff(34,plain,(
% 0.84/0.77 ![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)))))))))),
% 0.84/0.77 inference(skolemize,[status(sab)],[33])).
% 0.84/0.77 tff(35,plain,
% 0.84/0.77 (![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)))))))))))))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.84/0.77 tff(36,plain,
% 0.84/0.77 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15)))))))))))))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[35, 25])).
% 0.84/0.77 tff(37,plain,
% 0.84/0.77 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[36, 20])).
% 0.84/0.77 tff(38,plain,
% 0.84/0.77 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))) | ((~relation(A!13)) | (~function(A!13)) | ![B: $i, D_15: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!13))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!13), relation_dom(A!13))) | (~(C = apply(A!13, tptp_fun_D_0(C, A!13)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!13))) | (~(C = apply(A!13, D))))))))) | (~((B = relation_rng(A!13)) | (~((~(in(tptp_fun_C_1(B, A!13), B) | (~((~in(tptp_fun_D_2(B, A!13), relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, tptp_fun_D_2(B, A!13)))))))) | (~((~in(tptp_fun_C_1(B, A!13), B)) | (~in(D_15, relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, D_15))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))) | (~relation(A!13)) | (~function(A!13)) | ![B: $i, D_15: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!13))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!13), relation_dom(A!13))) | (~(C = apply(A!13, tptp_fun_D_0(C, A!13)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!13))) | (~(C = apply(A!13, D))))))))) | (~((B = relation_rng(A!13)) | (~((~(in(tptp_fun_C_1(B, A!13), B) | (~((~in(tptp_fun_D_2(B, A!13), relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, tptp_fun_D_2(B, A!13)))))))) | (~((~in(tptp_fun_C_1(B, A!13), B)) | (~in(D_15, relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, D_15))))))))))))),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(39,plain,
% 0.84/0.77 ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))) | ((~relation(A!13)) | (~function(A!13)) | ![B: $i, D_15: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!13))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!13), relation_dom(A!13))) | (~(C = apply(A!13, tptp_fun_D_0(C, A!13)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!13))) | (~(C = apply(A!13, D))))))))) | (~((B = relation_rng(A!13)) | (~((~(in(tptp_fun_C_1(B, A!13), B) | (~((~in(tptp_fun_D_2(B, A!13), relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, tptp_fun_D_2(B, A!13)))))))) | (~((~in(tptp_fun_C_1(B, A!13), B)) | (~in(D_15, relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, D_15))))))))))))),
% 0.84/0.77 inference(quant_inst,[status(thm)],[])).
% 0.84/0.77 tff(40,plain,
% 0.84/0.77 ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))) | (~relation(A!13)) | (~function(A!13)) | ![B: $i, D_15: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!13))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!13), relation_dom(A!13))) | (~(C = apply(A!13, tptp_fun_D_0(C, A!13)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!13))) | (~(C = apply(A!13, D))))))))) | (~((B = relation_rng(A!13)) | (~((~(in(tptp_fun_C_1(B, A!13), B) | (~((~in(tptp_fun_D_2(B, A!13), relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, tptp_fun_D_2(B, A!13)))))))) | (~((~in(tptp_fun_C_1(B, A!13), B)) | (~in(D_15, relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, D_15)))))))))))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.84/0.77 tff(41,plain,
% 0.84/0.77 (![B: $i, D_15: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!13))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!13), relation_dom(A!13))) | (~(C = apply(A!13, tptp_fun_D_0(C, A!13)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!13))) | (~(C = apply(A!13, D))))))))) | (~((B = relation_rng(A!13)) | (~((~(in(tptp_fun_C_1(B, A!13), B) | (~((~in(tptp_fun_D_2(B, A!13), relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, tptp_fun_D_2(B, A!13)))))))) | (~((~in(tptp_fun_C_1(B, A!13), B)) | (~in(D_15, relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, D_15)))))))))))),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[40, 37, 18, 17])).
% 0.84/0.77 tff(42,plain,
% 0.84/0.77 ((~![B: $i, D_15: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!13))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!13), relation_dom(A!13))) | (~(C = apply(A!13, tptp_fun_D_0(C, A!13)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!13))) | (~(C = apply(A!13, D))))))))) | (~((B = relation_rng(A!13)) | (~((~(in(tptp_fun_C_1(B, A!13), B) | (~((~in(tptp_fun_D_2(B, A!13), relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, tptp_fun_D_2(B, A!13)))))))) | (~((~in(tptp_fun_C_1(B, A!13), B)) | (~in(D_15, relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, D_15)))))))))))) | (~((~((~(relation_dom(B!14) = relation_rng(A!13))) | (~((~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))))) | (~(in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14)) | (~in(apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14)))))))))))) | (~((relation_dom(B!14) = relation_rng(A!13)) | (~((~(in(tptp_fun_C_1(relation_dom(B!14), A!13), relation_dom(B!14)) | (~((~in(tptp_fun_D_2(relation_dom(B!14), A!13), relation_dom(A!13))) | (~(tptp_fun_C_1(relation_dom(B!14), A!13) = apply(A!13, tptp_fun_D_2(relation_dom(B!14), A!13)))))))) | (~((~in(tptp_fun_C_1(relation_dom(B!14), A!13), relation_dom(B!14))) | (~in(apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))), relation_dom(A!13))) | (~(tptp_fun_C_1(relation_dom(B!14), A!13) = apply(A!13, apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))))))))))))))),
% 0.84/0.77 inference(quant_inst,[status(thm)],[])).
% 0.84/0.77 tff(43,plain,
% 0.84/0.77 (~((~((~(relation_dom(B!14) = relation_rng(A!13))) | (~((~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))))) | (~(in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14)) | (~in(apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14)))))))))))) | (~((relation_dom(B!14) = relation_rng(A!13)) | (~((~(in(tptp_fun_C_1(relation_dom(B!14), A!13), relation_dom(B!14)) | (~((~in(tptp_fun_D_2(relation_dom(B!14), A!13), relation_dom(A!13))) | (~(tptp_fun_C_1(relation_dom(B!14), A!13) = apply(A!13, tptp_fun_D_2(relation_dom(B!14), A!13)))))))) | (~((~in(tptp_fun_C_1(relation_dom(B!14), A!13), relation_dom(B!14))) | (~in(apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))), relation_dom(A!13))) | (~(tptp_fun_C_1(relation_dom(B!14), A!13) = apply(A!13, apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14)))))))))))))),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.84/0.77 tff(44,plain,
% 0.84/0.77 (((~((~(relation_dom(B!14) = relation_rng(A!13))) | (~((~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))))) | (~(in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14)) | (~in(apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14)))))))))))) | (~((relation_dom(B!14) = relation_rng(A!13)) | (~((~(in(tptp_fun_C_1(relation_dom(B!14), A!13), relation_dom(B!14)) | (~((~in(tptp_fun_D_2(relation_dom(B!14), A!13), relation_dom(A!13))) | (~(tptp_fun_C_1(relation_dom(B!14), A!13) = apply(A!13, tptp_fun_D_2(relation_dom(B!14), A!13)))))))) | (~((~in(tptp_fun_C_1(relation_dom(B!14), A!13), relation_dom(B!14))) | (~in(apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))), relation_dom(A!13))) | (~(tptp_fun_C_1(relation_dom(B!14), A!13) = apply(A!13, apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))))))))))))) | ((~(relation_dom(B!14) = relation_rng(A!13))) | (~((~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))))) | (~(in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14)) | (~in(apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14)))))))))))),
% 0.84/0.77 inference(tautology,[status(thm)],[])).
% 0.84/0.77 tff(45,plain,
% 0.84/0.77 ((~(relation_dom(B!14) = relation_rng(A!13))) | (~((~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))))) | (~(in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14)) | (~in(apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))))))))))),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.84/0.77 tff(46,plain,
% 0.84/0.77 (~((B!14 = identity_relation(relation_dom(B!14))) | (~(relation(B!14) & function(B!14))) | (~((relation_rng(A!13) = relation_dom(B!14)) & (relation_composition(A!13, B!14) = A!13))))),
% 0.84/0.77 inference(and_elim,[status(thm)],[16])).
% 0.84/0.77 tff(47,plain,
% 0.84/0.77 ((relation_rng(A!13) = relation_dom(B!14)) & (relation_composition(A!13, B!14) = A!13)),
% 0.84/0.77 inference(or_elim,[status(thm)],[46])).
% 0.84/0.77 tff(48,plain,
% 0.84/0.77 (relation_rng(A!13) = relation_dom(B!14)),
% 0.84/0.77 inference(and_elim,[status(thm)],[47])).
% 0.84/0.77 tff(49,plain,
% 0.84/0.77 (relation_dom(B!14) = relation_rng(A!13)),
% 0.84/0.77 inference(symmetry,[status(thm)],[48])).
% 0.84/0.77 tff(50,plain,
% 0.84/0.77 ((~((~(relation_dom(B!14) = relation_rng(A!13))) | (~((~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))))) | (~(in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14)) | (~in(apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14)))))))))))) | (~(relation_dom(B!14) = relation_rng(A!13))) | (~((~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))))) | (~(in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14)) | (~in(apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))))))))))),
% 0.84/0.77 inference(tautology,[status(thm)],[])).
% 0.84/0.77 tff(51,plain,
% 0.84/0.77 ((~((~(relation_dom(B!14) = relation_rng(A!13))) | (~((~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))))) | (~(in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14)) | (~in(apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14)))))))))))) | (~((~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))))) | (~(in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14)) | (~in(apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))))))))))),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.84/0.77 tff(52,plain,
% 0.84/0.77 (~((~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))))) | (~(in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14)) | (~in(apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14)))))))))),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[51, 45])).
% 0.84/0.77 tff(53,plain,
% 0.84/0.77 (((~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))))) | (~(in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14)) | (~in(apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))))))))) | ((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))))),
% 0.84/0.77 inference(tautology,[status(thm)],[])).
% 0.84/0.77 tff(54,plain,
% 0.84/0.77 ((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))))))),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.84/0.77 tff(55,plain,
% 0.84/0.77 (relation(B!14) & function(B!14)),
% 0.84/0.77 inference(or_elim,[status(thm)],[46])).
% 0.84/0.77 tff(56,plain,
% 0.84/0.77 (function(B!14)),
% 0.84/0.77 inference(and_elim,[status(thm)],[55])).
% 0.84/0.77 tff(57,plain,
% 0.84/0.77 (relation(B!14)),
% 0.84/0.77 inference(and_elim,[status(thm)],[55])).
% 0.84/0.77 tff(58,plain,
% 0.84/0.77 (^[A: $i, B: $i] : trans(monotonicity(rewrite((~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))))) <=> (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))))))), (((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))))))))), rewrite(((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))), (((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))))),
% 0.84/0.78 inference(bind,[status(th)],[])).
% 0.84/0.78 tff(59,plain,
% 0.84/0.78 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))),
% 0.84/0.78 inference(quant_intro,[status(thm)],[58])).
% 0.84/0.78 tff(60,plain,
% 0.84/0.78 (^[A: $i, B: $i] : refl(((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))))))),
% 0.84/0.78 inference(bind,[status(th)],[])).
% 0.84/0.78 tff(61,plain,
% 0.84/0.78 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))))))),
% 0.84/0.78 inference(quant_intro,[status(thm)],[60])).
% 0.84/0.78 tff(62,plain,
% 0.84/0.78 (^[A: $i, B: $i] : rewrite(((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))))))),
% 0.84/0.78 inference(bind,[status(th)],[])).
% 0.84/0.78 tff(63,plain,
% 0.84/0.78 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))))))),
% 0.84/0.78 inference(quant_intro,[status(thm)],[62])).
% 0.84/0.78 tff(64,plain,
% 0.84/0.78 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))))))),
% 0.84/0.78 inference(transitivity,[status(thm)],[63, 61])).
% 0.84/0.78 tff(65,plain,
% 0.84/0.78 (^[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))))), trans(monotonicity(rewrite(((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) <=> ((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))), rewrite(((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))) <=> ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))), ((((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) <=> (((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))))), rewrite((((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) <=> (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))))), ((((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) <=> (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))))))), (((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))) <=> (((~relation(B)) | (~function(B))) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))))))), rewrite((((~relation(B)) | (~function(B))) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))))))), (((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))))))))),
% 0.84/0.78 inference(bind,[status(th)],[])).
% 0.84/0.78 tff(66,plain,
% 0.84/0.78 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))))))),
% 0.84/0.78 inference(quant_intro,[status(thm)],[65])).
% 0.84/0.78 tff(67,plain,
% 0.84/0.78 (^[A: $i, B: $i] : rewrite(((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | ((~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))))) <=> ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))))),
% 0.84/0.78 inference(bind,[status(th)],[])).
% 0.84/0.78 tff(68,plain,
% 0.84/0.78 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | ((~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))))),
% 0.84/0.78 inference(quant_intro,[status(thm)],[67])).
% 0.84/0.78 tff(69,plain,
% 0.84/0.78 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(70,plain,
% 0.84/0.78 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C)))) <=> ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))), (((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C))))) <=> ((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))), rewrite(((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))) <=> ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))), (((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C))))) <=> ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))))),
% 0.84/0.78 inference(bind,[status(th)],[])).
% 0.84/0.78 tff(71,plain,
% 0.84/0.78 (![A: $i, B: $i] : ((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))),
% 0.84/0.78 inference(quant_intro,[status(thm)],[70])).
% 0.84/0.78 tff(72,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t34_funct_1')).
% 0.84/0.78 tff(73,plain,
% 0.84/0.78 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.84/0.78 tff(74,plain,
% 0.84/0.78 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.84/0.78 tff(75,plain,(
% 0.84/0.78 ![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | ((~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))))),
% 0.84/0.78 inference(skolemize,[status(sab)],[74])).
% 0.84/0.78 tff(76,plain,
% 0.84/0.78 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.84/0.78 tff(77,plain,
% 0.84/0.78 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))))))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[76, 66])).
% 0.84/0.78 tff(78,plain,
% 0.84/0.78 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))))))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[77, 64])).
% 0.84/0.78 tff(79,plain,
% 0.84/0.78 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[78, 59])).
% 0.84/0.78 tff(80,plain,
% 0.84/0.78 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(B!14)) | (~function(B!14)) | (~((~((B!14 = identity_relation(relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))) | (~((~(B!14 = identity_relation(relation_dom(B!14)))) | ![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C)))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~relation(B!14)) | (~function(B!14)) | (~((~((B!14 = identity_relation(relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))) | (~((~(B!14 = identity_relation(relation_dom(B!14)))) | ![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C)))))))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(81,plain,
% 0.84/0.78 (((~relation(B!14)) | (~function(B!14)) | (~((~((B!14 = identity_relation(relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))) | (~((~(B!14 = identity_relation(relation_dom(B!14)))) | ![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C))))))) <=> ((~relation(B!14)) | (~function(B!14)) | (~((~((B!14 = identity_relation(relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))) | (~((~(B!14 = identity_relation(relation_dom(B!14)))) | ![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C)))))))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(82,plain,
% 0.84/0.78 ((~((~((B!14 = identity_relation(relation_dom(B!14))) | (~(relation_dom(B!14) = relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))) | (~((~(B!14 = identity_relation(relation_dom(B!14)))) | (~((~(relation_dom(B!14) = relation_dom(B!14))) | (~![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C))))))))) <=> (~((~((B!14 = identity_relation(relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))) | (~((~(B!14 = identity_relation(relation_dom(B!14)))) | ![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C))))))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(83,plain,
% 0.84/0.78 (((~relation(B!14)) | (~function(B!14)) | (~((~((B!14 = identity_relation(relation_dom(B!14))) | (~(relation_dom(B!14) = relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))) | (~((~(B!14 = identity_relation(relation_dom(B!14)))) | (~((~(relation_dom(B!14) = relation_dom(B!14))) | (~![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C)))))))))) <=> ((~relation(B!14)) | (~function(B!14)) | (~((~((B!14 = identity_relation(relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))) | (~((~(B!14 = identity_relation(relation_dom(B!14)))) | ![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C)))))))),
% 0.84/0.78 inference(monotonicity,[status(thm)],[82])).
% 0.84/0.78 tff(84,plain,
% 0.84/0.78 (((~relation(B!14)) | (~function(B!14)) | (~((~((B!14 = identity_relation(relation_dom(B!14))) | (~(relation_dom(B!14) = relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))) | (~((~(B!14 = identity_relation(relation_dom(B!14)))) | (~((~(relation_dom(B!14) = relation_dom(B!14))) | (~![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C)))))))))) <=> ((~relation(B!14)) | (~function(B!14)) | (~((~((B!14 = identity_relation(relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))) | (~((~(B!14 = identity_relation(relation_dom(B!14)))) | ![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C)))))))),
% 0.84/0.78 inference(transitivity,[status(thm)],[83, 81])).
% 0.84/0.78 tff(85,plain,
% 0.84/0.78 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(B!14)) | (~function(B!14)) | (~((~((B!14 = identity_relation(relation_dom(B!14))) | (~(relation_dom(B!14) = relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))) | (~((~(B!14 = identity_relation(relation_dom(B!14)))) | (~((~(relation_dom(B!14) = relation_dom(B!14))) | (~![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(B!14)) | (~function(B!14)) | (~((~((B!14 = identity_relation(relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))) | (~((~(B!14 = identity_relation(relation_dom(B!14)))) | ![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C))))))))),
% 0.84/0.78 inference(monotonicity,[status(thm)],[84])).
% 0.84/0.78 tff(86,plain,
% 0.84/0.78 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(B!14)) | (~function(B!14)) | (~((~((B!14 = identity_relation(relation_dom(B!14))) | (~(relation_dom(B!14) = relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))) | (~((~(B!14 = identity_relation(relation_dom(B!14)))) | (~((~(relation_dom(B!14) = relation_dom(B!14))) | (~![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~relation(B!14)) | (~function(B!14)) | (~((~((B!14 = identity_relation(relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))) | (~((~(B!14 = identity_relation(relation_dom(B!14)))) | ![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C)))))))),
% 0.84/0.78 inference(transitivity,[status(thm)],[85, 80])).
% 0.84/0.78 tff(87,plain,
% 0.84/0.78 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(B!14)) | (~function(B!14)) | (~((~((B!14 = identity_relation(relation_dom(B!14))) | (~(relation_dom(B!14) = relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))) | (~((~(B!14 = identity_relation(relation_dom(B!14)))) | (~((~(relation_dom(B!14) = relation_dom(B!14))) | (~![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C))))))))))),
% 0.84/0.78 inference(quant_inst,[status(thm)],[])).
% 0.84/0.78 tff(88,plain,
% 0.84/0.78 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~relation(B!14)) | (~function(B!14)) | (~((~((B!14 = identity_relation(relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))) | (~((~(B!14 = identity_relation(relation_dom(B!14)))) | ![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C))))))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.84/0.78 tff(89,plain,
% 0.84/0.78 (~((~((B!14 = identity_relation(relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))) | (~((~(B!14 = identity_relation(relation_dom(B!14)))) | ![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C)))))),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[88, 79, 57, 56])).
% 0.84/0.78 tff(90,plain,
% 0.84/0.78 (((~((B!14 = identity_relation(relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))) | (~((~(B!14 = identity_relation(relation_dom(B!14)))) | ![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C))))) | ((B!14 = identity_relation(relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))),
% 0.84/0.78 inference(tautology,[status(thm)],[])).
% 0.84/0.78 tff(91,plain,
% 0.84/0.78 ((B!14 = identity_relation(relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14)))))),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.84/0.78 tff(92,plain,
% 0.84/0.78 (~(B!14 = identity_relation(relation_dom(B!14)))),
% 0.84/0.78 inference(or_elim,[status(thm)],[46])).
% 0.84/0.78 tff(93,plain,
% 0.84/0.78 ((~((B!14 = identity_relation(relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))) | (B!14 = identity_relation(relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14)))))),
% 0.84/0.78 inference(tautology,[status(thm)],[])).
% 0.84/0.78 tff(94,plain,
% 0.84/0.78 ((~((B!14 = identity_relation(relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14)))))),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.84/0.78 tff(95,plain,
% 0.84/0.78 (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[94, 91])).
% 0.84/0.78 tff(96,plain,
% 0.84/0.78 (((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14)))) | in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))),
% 0.84/0.78 inference(tautology,[status(thm)],[])).
% 0.84/0.78 tff(97,plain,
% 0.84/0.78 (in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.84/0.78 tff(98,plain,
% 0.84/0.78 ((~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))))) | (~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))))))),
% 0.84/0.78 inference(tautology,[status(thm)],[])).
% 0.84/0.78 tff(99,plain,
% 0.84/0.78 ((~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))))) | (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))))))),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.84/0.78 tff(100,plain,
% 0.84/0.78 (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[99, 54])).
% 0.84/0.78 tff(101,plain,
% 0.84/0.78 (((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))))) | (tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))),
% 0.84/0.78 inference(tautology,[status(thm)],[])).
% 0.84/0.78 tff(102,plain,
% 0.84/0.78 (tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.84/0.78 tff(103,plain,
% 0.84/0.78 (apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = tptp_fun_C_12(B!14, relation_dom(B!14))),
% 0.84/0.78 inference(symmetry,[status(thm)],[102])).
% 0.84/0.78 tff(104,plain,
% 0.84/0.78 (relation_composition(A!13, B!14) = A!13),
% 0.84/0.78 inference(and_elim,[status(thm)],[47])).
% 0.84/0.78 tff(105,plain,
% 0.84/0.78 (apply(relation_composition(A!13, B!14), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))),
% 0.84/0.78 inference(monotonicity,[status(thm)],[104])).
% 0.84/0.78 tff(106,plain,
% 0.84/0.78 (^[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)))))),
% 0.84/0.78 inference(bind,[status(th)],[])).
% 0.84/0.78 tff(107,plain,
% 0.84/0.78 (![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))))),
% 0.84/0.78 inference(quant_intro,[status(thm)],[106])).
% 0.84/0.78 tff(108,plain,
% 0.84/0.78 (^[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)))))),
% 0.84/0.78 inference(bind,[status(th)],[])).
% 0.84/0.78 tff(109,plain,
% 0.84/0.78 (![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))))),
% 0.84/0.78 inference(quant_intro,[status(thm)],[108])).
% 0.84/0.78 tff(110,plain,
% 0.84/0.78 (![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))))),
% 0.84/0.78 inference(transitivity,[status(thm)],[109, 107])).
% 0.84/0.78 tff(111,plain,
% 0.84/0.78 (^[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))))))),
% 0.84/0.78 inference(bind,[status(th)],[])).
% 0.84/0.78 tff(112,plain,
% 0.84/0.78 (![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))))),
% 0.84/0.78 inference(quant_intro,[status(thm)],[111])).
% 0.84/0.78 tff(113,plain,
% 0.84/0.78 (![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)))))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(114,plain,
% 0.84/0.78 (^[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)))))))),
% 0.84/0.78 inference(bind,[status(th)],[])).
% 0.84/0.78 tff(115,plain,
% 0.84/0.78 (![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)))))),
% 0.84/0.79 inference(quant_intro,[status(thm)],[114])).
% 0.84/0.79 tff(116,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')).
% 0.84/0.79 tff(117,plain,
% 0.84/0.79 (![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)))))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.84/0.79 tff(118,plain,
% 0.84/0.79 (![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)))))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.84/0.79 tff(119,plain,(
% 0.84/0.79 ![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)))))),
% 0.84/0.79 inference(skolemize,[status(sab)],[118])).
% 0.84/0.79 tff(120,plain,
% 0.84/0.79 (![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))))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[119, 112])).
% 0.84/0.79 tff(121,plain,
% 0.84/0.79 (![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))))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[120, 110])).
% 0.84/0.79 tff(122,plain,
% 0.84/0.79 (((~![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(A!13)) | (~function(A!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))))))) <=> ((~![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(A!13)) | (~function(A!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))))))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(123,plain,
% 0.84/0.79 (((~relation(A!13)) | (~function(A!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))) <=> ((~relation(A!13)) | (~function(A!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))))))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(124,plain,
% 0.84/0.79 (^[C: $i] : rewrite(((apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~relation(C)) | (~function(C))) <=> ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))))))),
% 0.84/0.79 inference(bind,[status(th)],[])).
% 0.84/0.79 tff(125,plain,
% 0.84/0.79 (![C: $i] : ((apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~relation(C)) | (~function(C))) <=> ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))),
% 0.84/0.79 inference(quant_intro,[status(thm)],[124])).
% 0.84/0.79 tff(126,plain,
% 0.84/0.79 (((~relation(A!13)) | (~function(A!13)) | ![C: $i] : ((apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~relation(C)) | (~function(C)))) <=> ((~relation(A!13)) | (~function(A!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))))))),
% 0.84/0.79 inference(monotonicity,[status(thm)],[125])).
% 0.84/0.79 tff(127,plain,
% 0.84/0.79 (((~relation(A!13)) | (~function(A!13)) | ![C: $i] : ((apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~relation(C)) | (~function(C)))) <=> ((~relation(A!13)) | (~function(A!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))))))),
% 0.84/0.79 inference(transitivity,[status(thm)],[126, 123])).
% 0.84/0.79 tff(128,plain,
% 0.84/0.79 (((~![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(A!13)) | (~function(A!13)) | ![C: $i] : ((apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~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(A!13)) | (~function(A!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))))),
% 0.84/0.79 inference(monotonicity,[status(thm)],[127])).
% 0.84/0.79 tff(129,plain,
% 0.84/0.79 (((~![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(A!13)) | (~function(A!13)) | ![C: $i] : ((apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~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(A!13)) | (~function(A!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))))))),
% 0.84/0.79 inference(transitivity,[status(thm)],[128, 122])).
% 0.84/0.79 tff(130,plain,
% 0.84/0.79 ((~![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(A!13)) | (~function(A!13)) | ![C: $i] : ((apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~relation(C)) | (~function(C))))),
% 0.84/0.79 inference(quant_inst,[status(thm)],[])).
% 0.84/0.79 tff(131,plain,
% 0.84/0.79 ((~![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(A!13)) | (~function(A!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.84/0.79 tff(132,plain,
% 0.84/0.79 (![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[131, 121, 18, 17])).
% 0.84/0.79 tff(133,plain,
% 0.84/0.79 (((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))))) | in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))),
% 0.84/0.79 inference(tautology,[status(thm)],[])).
% 0.84/0.79 tff(134,plain,
% 0.84/0.79 (in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[133, 100])).
% 0.84/0.79 tff(135,plain,
% 0.84/0.79 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))) | ((~relation(B!14)) | (~function(B!14)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, B!14), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(B!14, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))) | (~relation(B!14)) | (~function(B!14)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, B!14), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(B!14, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(136,plain,
% 0.84/0.79 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))) | ((~relation(B!14)) | (~function(B!14)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, B!14), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(B!14, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))),
% 0.84/0.79 inference(quant_inst,[status(thm)],[])).
% 0.84/0.79 tff(137,plain,
% 0.84/0.79 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))) | (~relation(B!14)) | (~function(B!14)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, B!14), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(B!14, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.84/0.79 tff(138,plain,
% 0.84/0.79 (apply(relation_composition(A!13, B!14), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(B!14, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[137, 57, 56, 134, 132])).
% 0.84/0.79 tff(139,plain,
% 0.84/0.79 (apply(B!14, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))) = apply(relation_composition(A!13, B!14), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))),
% 0.84/0.79 inference(symmetry,[status(thm)],[138])).
% 0.84/0.79 tff(140,plain,
% 0.84/0.79 (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = apply(B!14, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))),
% 0.84/0.79 inference(monotonicity,[status(thm)],[102])).
% 0.84/0.79 tff(141,plain,
% 0.84/0.79 (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))),
% 0.84/0.79 inference(transitivity,[status(thm)],[140, 139, 105, 103])).
% 0.84/0.79 tff(142,plain,
% 0.84/0.79 (((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14)))) | (~(apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))),
% 0.84/0.79 inference(tautology,[status(thm)],[])).
% 0.84/0.79 tff(143,plain,
% 0.84/0.79 (~(apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14)))),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[142, 95])).
% 0.84/0.79 tff(144,plain,
% 0.84/0.79 ($false),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[143, 141])).
% 0.84/0.79 % SZS output end Proof
%------------------------------------------------------------------------------