TSTP Solution File: SEU014+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU014+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 07:27:17 EDT 2022
% Result : Theorem 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU014+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n016.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 09:21:37 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44 % SZS output start Proof
% 0.20/0.44 tff(tptp_fun_B_1_type, type, (
% 0.20/0.44 tptp_fun_B_1: $i > $i)).
% 0.20/0.44 tff(tptp_fun_B_12_type, type, (
% 0.20/0.44 tptp_fun_B_12: $i)).
% 0.20/0.44 tff(tptp_fun_C_0_type, type, (
% 0.20/0.44 tptp_fun_C_0: $i > $i)).
% 0.20/0.44 tff(apply_type, type, (
% 0.20/0.44 apply: ( $i * $i ) > $i)).
% 0.20/0.44 tff(in_type, type, (
% 0.20/0.44 in: ( $i * $i ) > $o)).
% 0.20/0.44 tff(relation_dom_type, type, (
% 0.20/0.44 relation_dom: $i > $i)).
% 0.20/0.44 tff(one_to_one_type, type, (
% 0.20/0.44 one_to_one: $i > $o)).
% 0.20/0.44 tff(function_type, type, (
% 0.20/0.44 function: $i > $o)).
% 0.20/0.44 tff(relation_type, type, (
% 0.20/0.44 relation: $i > $o)).
% 0.20/0.44 tff(subset_type, type, (
% 0.20/0.44 subset: ( $i * $i ) > $o)).
% 0.20/0.44 tff(tptp_fun_A_11_type, type, (
% 0.20/0.44 tptp_fun_A_11: $i)).
% 0.20/0.44 tff(relation_rng_type, type, (
% 0.20/0.44 relation_rng: $i > $i)).
% 0.20/0.44 tff(relation_composition_type, type, (
% 0.20/0.44 relation_composition: ( $i * $i ) > $i)).
% 0.20/0.44 tff(1,plain,
% 0.20/0.44 ((tptp_fun_C_0(B!12) = tptp_fun_B_1(B!12)) <=> (tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12))),
% 0.20/0.44 inference(commutativity,[status(thm)],[])).
% 0.20/0.44 tff(2,plain,
% 0.20/0.44 ((tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)) <=> (tptp_fun_C_0(B!12) = tptp_fun_B_1(B!12))),
% 0.20/0.44 inference(symmetry,[status(thm)],[1])).
% 0.20/0.44 tff(3,plain,
% 0.20/0.44 ((~(tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12))) <=> (~(tptp_fun_C_0(B!12) = tptp_fun_B_1(B!12)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[2])).
% 0.20/0.44 tff(4,plain,
% 0.20/0.44 (((relation(A!11) & function(A!11)) & (~(one_to_one(B!12) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(relation_composition(B!12, A!11)) & subset(relation_rng(B!12), relation_dom(A!11))))))) <=> (relation(A!11) & function(A!11) & (~(one_to_one(B!12) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(relation_composition(B!12, A!11)) & subset(relation_rng(B!12), relation_dom(A!11)))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(5,plain,
% 0.20/0.44 ((~(~(relation(A!11) & function(A!11)))) <=> (relation(A!11) & function(A!11))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(6,plain,
% 0.20/0.44 (((~(~(relation(A!11) & function(A!11)))) & (~(one_to_one(B!12) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(relation_composition(B!12, A!11)) & subset(relation_rng(B!12), relation_dom(A!11))))))) <=> ((relation(A!11) & function(A!11)) & (~(one_to_one(B!12) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(relation_composition(B!12, A!11)) & subset(relation_rng(B!12), relation_dom(A!11)))))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[5])).
% 0.20/0.44 tff(7,plain,
% 0.20/0.44 (((~(~(relation(A!11) & function(A!11)))) & (~(one_to_one(B!12) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(relation_composition(B!12, A!11)) & subset(relation_rng(B!12), relation_dom(A!11))))))) <=> (relation(A!11) & function(A!11) & (~(one_to_one(B!12) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(relation_composition(B!12, A!11)) & subset(relation_rng(B!12), relation_dom(A!11)))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[6, 4])).
% 0.20/0.44 tff(8,plain,
% 0.20/0.44 ((~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))))) <=> (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A)))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(9,plain,
% 0.20/0.44 ((~![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => ((one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))) => one_to_one(B))))) <=> (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A)))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(10,axiom,(~![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => ((one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))) => one_to_one(B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t47_funct_1')).
% 0.20/0.44 tff(11,plain,
% 0.20/0.44 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.20/0.44 tff(12,plain,
% 0.20/0.44 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[11, 8])).
% 0.20/0.44 tff(13,plain,
% 0.20/0.44 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.20/0.44 tff(14,plain,
% 0.20/0.44 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[13, 8])).
% 0.20/0.44 tff(15,plain,
% 0.20/0.44 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[14, 8])).
% 0.20/0.44 tff(16,plain,
% 0.20/0.44 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.20/0.44 tff(17,plain,
% 0.20/0.44 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[16, 8])).
% 0.20/0.44 tff(18,plain,
% 0.20/0.44 (relation(A!11) & function(A!11) & (~(one_to_one(B!12) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(relation_composition(B!12, A!11)) & subset(relation_rng(B!12), relation_dom(A!11))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[17, 7])).
% 0.20/0.44 tff(19,plain,
% 0.20/0.44 (~(one_to_one(B!12) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(relation_composition(B!12, A!11)) & subset(relation_rng(B!12), relation_dom(A!11)))))),
% 0.20/0.44 inference(and_elim,[status(thm)],[18])).
% 0.20/0.44 tff(20,plain,
% 0.20/0.44 (relation(B!12) & function(B!12)),
% 0.20/0.44 inference(or_elim,[status(thm)],[19])).
% 0.20/0.44 tff(21,plain,
% 0.20/0.44 (function(B!12)),
% 0.20/0.44 inference(and_elim,[status(thm)],[20])).
% 0.20/0.44 tff(22,plain,
% 0.20/0.44 (relation(B!12)),
% 0.20/0.44 inference(and_elim,[status(thm)],[20])).
% 0.20/0.44 tff(23,plain,
% 0.20/0.44 (^[A: $i] : refl(((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))) <=> ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(24,plain,
% 0.20/0.44 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[23])).
% 0.20/0.45 tff(25,plain,
% 0.20/0.45 (^[A: $i] : rewrite(((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))) <=> ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(26,plain,
% 0.20/0.45 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.45 tff(27,plain,
% 0.20/0.45 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[26, 24])).
% 0.20/0.45 tff(28,plain,
% 0.20/0.45 (^[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))))), trans(monotonicity(rewrite(((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) <=> ((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))), rewrite((one_to_one(A) | (~((~(in(tptp_fun_B_1(A), relation_dom(A)) & in(tptp_fun_C_0(A), relation_dom(A)) & (apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))) | (tptp_fun_B_1(A) = tptp_fun_C_0(A))))) <=> (one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))), ((((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_1(A), relation_dom(A)) & in(tptp_fun_C_0(A), relation_dom(A)) & (apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))) | (tptp_fun_B_1(A) = tptp_fun_C_0(A)))))) <=> (((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C))))) & (one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))), rewrite((((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C))))) & (one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))) <=> (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))), ((((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_1(A), relation_dom(A)) & in(tptp_fun_C_0(A), relation_dom(A)) & (apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))) | (tptp_fun_B_1(A) = tptp_fun_C_0(A)))))) <=> (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))), (((~(relation(A) & function(A))) | (((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_1(A), relation_dom(A)) & in(tptp_fun_C_0(A), relation_dom(A)) & (apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))) | (tptp_fun_B_1(A) = tptp_fun_C_0(A))))))) <=> (((~relation(A)) | (~function(A))) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))))), rewrite((((~relation(A)) | (~function(A))) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))) <=> ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))), (((~(relation(A) & function(A))) | (((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_1(A), relation_dom(A)) & in(tptp_fun_C_0(A), relation_dom(A)) & (apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))) | (tptp_fun_B_1(A) = tptp_fun_C_0(A))))))) <=> ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(29,plain,
% 0.20/0.45 (![A: $i] : ((~(relation(A) & function(A))) | (((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_1(A), relation_dom(A)) & in(tptp_fun_C_0(A), relation_dom(A)) & (apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))) | (tptp_fun_B_1(A) = tptp_fun_C_0(A))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.45 tff(30,plain,
% 0.20/0.45 (![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C)))) <=> ![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(31,plain,
% 0.20/0.45 (^[A: $i] : trans(monotonicity(rewrite((one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C))) <=> (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C)))), (((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C)))) <=> ((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C)))))), rewrite(((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C)))) <=> ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))), (((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C)))) <=> ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(32,plain,
% 0.20/0.45 (![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C)))) <=> ![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.45 tff(33,axiom,(![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d8_funct_1')).
% 0.20/0.45 tff(34,plain,
% 0.20/0.45 (![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.45 tff(35,plain,
% 0.20/0.45 (![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.20/0.45 tff(36,plain,(
% 0.20/0.45 ![A: $i] : ((~(relation(A) & function(A))) | (((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_1(A), relation_dom(A)) & in(tptp_fun_C_0(A), relation_dom(A)) & (apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))) | (tptp_fun_B_1(A) = tptp_fun_C_0(A)))))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[35])).
% 0.20/0.45 tff(37,plain,
% 0.20/0.45 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.20/0.45 tff(38,plain,
% 0.20/0.45 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[37, 27])).
% 0.20/0.45 tff(39,plain,
% 0.20/0.45 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | ((~relation(B!12)) | (~function(B!12)) | (~((~((~one_to_one(B!12)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(B!12))) | (~in(C, relation_dom(B!12))) | (~(apply(B!12, B) = apply(B!12, C)))))) | (~(one_to_one(B!12) | (~((tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | (~relation(B!12)) | (~function(B!12)) | (~((~((~one_to_one(B!12)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(B!12))) | (~in(C, relation_dom(B!12))) | (~(apply(B!12, B) = apply(B!12, C)))))) | (~(one_to_one(B!12) | (~((tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))))))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(40,plain,
% 0.20/0.45 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | ((~relation(B!12)) | (~function(B!12)) | (~((~((~one_to_one(B!12)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(B!12))) | (~in(C, relation_dom(B!12))) | (~(apply(B!12, B) = apply(B!12, C)))))) | (~(one_to_one(B!12) | (~((tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))))))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(41,plain,
% 0.20/0.46 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | (~relation(B!12)) | (~function(B!12)) | (~((~((~one_to_one(B!12)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(B!12))) | (~in(C, relation_dom(B!12))) | (~(apply(B!12, B) = apply(B!12, C)))))) | (~(one_to_one(B!12) | (~((tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12))))))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.46 tff(42,plain,
% 0.20/0.46 (~((~((~one_to_one(B!12)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(B!12))) | (~in(C, relation_dom(B!12))) | (~(apply(B!12, B) = apply(B!12, C)))))) | (~(one_to_one(B!12) | (~((tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[41, 38, 22, 21])).
% 0.20/0.46 tff(43,plain,
% 0.20/0.46 (((~((~one_to_one(B!12)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(B!12))) | (~in(C, relation_dom(B!12))) | (~(apply(B!12, B) = apply(B!12, C)))))) | (~(one_to_one(B!12) | (~((tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12))))))))) | (one_to_one(B!12) | (~((tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(44,plain,
% 0.20/0.46 (one_to_one(B!12) | (~((tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.20/0.46 tff(45,plain,
% 0.20/0.46 (~one_to_one(B!12)),
% 0.20/0.46 inference(or_elim,[status(thm)],[19])).
% 0.20/0.46 tff(46,plain,
% 0.20/0.46 ((~(one_to_one(B!12) | (~((tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))))))) | one_to_one(B!12) | (~((tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12))))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(47,plain,
% 0.20/0.46 ((~(one_to_one(B!12) | (~((tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))))))) | (~((tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.20/0.46 tff(48,plain,
% 0.20/0.46 (~((tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[47, 44])).
% 0.20/0.46 tff(49,plain,
% 0.20/0.46 (((tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12))))) | (~(tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(50,plain,
% 0.20/0.46 (~(tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.20/0.46 tff(51,plain,
% 0.20/0.46 (~(tptp_fun_C_0(B!12) = tptp_fun_B_1(B!12))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[50, 3])).
% 0.20/0.46 tff(52,plain,
% 0.20/0.46 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))) <=> ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(53,plain,
% 0.20/0.46 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.46 tff(54,plain,
% 0.20/0.46 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))) <=> ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(55,plain,
% 0.20/0.46 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[54])).
% 0.20/0.46 tff(56,plain,
% 0.20/0.46 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[55, 53])).
% 0.20/0.46 tff(57,plain,
% 0.20/0.46 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(58,plain,
% 0.20/0.46 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((subset(relation_rng(A), relation_dom(B)) => (relation_dom(relation_composition(A, B)) = relation_dom(A))) <=> ((~subset(relation_rng(A), relation_dom(B))) | (relation_dom(relation_composition(A, B)) = relation_dom(A)))), ((relation(B) => (subset(relation_rng(A), relation_dom(B)) => (relation_dom(relation_composition(A, B)) = relation_dom(A)))) <=> (relation(B) => ((~subset(relation_rng(A), relation_dom(B))) | (relation_dom(relation_composition(A, B)) = relation_dom(A)))))), rewrite((relation(B) => ((~subset(relation_rng(A), relation_dom(B))) | (relation_dom(relation_composition(A, B)) = relation_dom(A)))) <=> ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))), ((relation(B) => (subset(relation_rng(A), relation_dom(B)) => (relation_dom(relation_composition(A, B)) = relation_dom(A)))) <=> ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))))), (![B: $i] : (relation(B) => (subset(relation_rng(A), relation_dom(B)) => (relation_dom(relation_composition(A, B)) = relation_dom(A)))) <=> ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))), ((relation(A) => ![B: $i] : (relation(B) => (subset(relation_rng(A), relation_dom(B)) => (relation_dom(relation_composition(A, B)) = relation_dom(A))))) <=> (relation(A) => ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))))), rewrite((relation(A) => ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))) <=> ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))), ((relation(A) => ![B: $i] : (relation(B) => (subset(relation_rng(A), relation_dom(B)) => (relation_dom(relation_composition(A, B)) = relation_dom(A))))) <=> ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(59,plain,
% 0.20/0.46 (![A: $i] : (relation(A) => ![B: $i] : (relation(B) => (subset(relation_rng(A), relation_dom(B)) => (relation_dom(relation_composition(A, B)) = relation_dom(A))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[58])).
% 0.20/0.46 tff(60,axiom,(![A: $i] : (relation(A) => ![B: $i] : (relation(B) => (subset(relation_rng(A), relation_dom(B)) => (relation_dom(relation_composition(A, B)) = relation_dom(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t46_relat_1')).
% 0.20/0.46 tff(61,plain,
% 0.20/0.46 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.46 tff(62,plain,
% 0.20/0.46 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.20/0.46 tff(63,plain,(
% 0.20/0.46 ![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[62])).
% 0.20/0.46 tff(64,plain,
% 0.20/0.46 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.20/0.46 tff(65,plain,
% 0.20/0.46 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))) | ((~relation(B!12)) | ![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B)))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))) | (~relation(B!12)) | ![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(66,plain,
% 0.20/0.46 (((~relation(B!12)) | ![B: $i] : ((relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B))) | (~relation(B)))) <=> ((~relation(B!12)) | ![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(67,plain,
% 0.20/0.46 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))) | ((~relation(B!12)) | ![B: $i] : ((relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B))) | (~relation(B))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))) | ((~relation(B!12)) | ![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B))))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[66])).
% 0.20/0.46 tff(68,plain,
% 0.20/0.46 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))) | ((~relation(B!12)) | ![B: $i] : ((relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B))) | (~relation(B))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))) | (~relation(B!12)) | ![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B)))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[67, 65])).
% 0.20/0.46 tff(69,plain,
% 0.20/0.46 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))) | ((~relation(B!12)) | ![B: $i] : ((relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B))) | (~relation(B))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(70,plain,
% 0.20/0.46 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))) | (~relation(B!12)) | ![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.46 tff(71,plain,
% 0.20/0.46 (![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[70, 64, 22])).
% 0.20/0.46 tff(72,plain,
% 0.20/0.46 (one_to_one(relation_composition(B!12, A!11)) & subset(relation_rng(B!12), relation_dom(A!11))),
% 0.20/0.46 inference(or_elim,[status(thm)],[19])).
% 0.20/0.46 tff(73,plain,
% 0.20/0.46 (subset(relation_rng(B!12), relation_dom(A!11))),
% 0.20/0.46 inference(and_elim,[status(thm)],[72])).
% 0.20/0.46 tff(74,plain,
% 0.20/0.46 (relation(A!11)),
% 0.20/0.46 inference(and_elim,[status(thm)],[18])).
% 0.20/0.46 tff(75,plain,
% 0.20/0.46 (((~![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B))))) | ((~relation(A!11)) | (~subset(relation_rng(B!12), relation_dom(A!11))) | (relation_dom(relation_composition(B!12, A!11)) = relation_dom(B!12)))) <=> ((~![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B))))) | (~relation(A!11)) | (~subset(relation_rng(B!12), relation_dom(A!11))) | (relation_dom(relation_composition(B!12, A!11)) = relation_dom(B!12)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(76,plain,
% 0.20/0.46 (((~relation(A!11)) | (relation_dom(relation_composition(B!12, A!11)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(A!11)))) <=> ((~relation(A!11)) | (~subset(relation_rng(B!12), relation_dom(A!11))) | (relation_dom(relation_composition(B!12, A!11)) = relation_dom(B!12)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(77,plain,
% 0.20/0.46 (((~![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B))))) | ((~relation(A!11)) | (relation_dom(relation_composition(B!12, A!11)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(A!11))))) <=> ((~![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B))))) | ((~relation(A!11)) | (~subset(relation_rng(B!12), relation_dom(A!11))) | (relation_dom(relation_composition(B!12, A!11)) = relation_dom(B!12))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[76])).
% 0.20/0.46 tff(78,plain,
% 0.20/0.46 (((~![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B))))) | ((~relation(A!11)) | (relation_dom(relation_composition(B!12, A!11)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(A!11))))) <=> ((~![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B))))) | (~relation(A!11)) | (~subset(relation_rng(B!12), relation_dom(A!11))) | (relation_dom(relation_composition(B!12, A!11)) = relation_dom(B!12)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[77, 75])).
% 0.20/0.46 tff(79,plain,
% 0.20/0.46 ((~![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B))))) | ((~relation(A!11)) | (relation_dom(relation_composition(B!12, A!11)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(A!11))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(80,plain,
% 0.20/0.46 ((~![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!12, B)) = relation_dom(B!12)) | (~subset(relation_rng(B!12), relation_dom(B))))) | (~relation(A!11)) | (~subset(relation_rng(B!12), relation_dom(A!11))) | (relation_dom(relation_composition(B!12, A!11)) = relation_dom(B!12))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.46 tff(81,plain,
% 0.20/0.46 (relation_dom(relation_composition(B!12, A!11)) = relation_dom(B!12)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[80, 74, 73, 71])).
% 0.20/0.46 tff(82,plain,
% 0.20/0.46 (in(tptp_fun_B_1(B!12), relation_dom(relation_composition(B!12, A!11))) <=> in(tptp_fun_B_1(B!12), relation_dom(B!12))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[81])).
% 0.20/0.46 tff(83,plain,
% 0.20/0.46 (in(tptp_fun_B_1(B!12), relation_dom(B!12)) <=> in(tptp_fun_B_1(B!12), relation_dom(relation_composition(B!12, A!11)))),
% 0.20/0.46 inference(symmetry,[status(thm)],[82])).
% 0.20/0.46 tff(84,plain,
% 0.20/0.46 (((tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12))))) | in(tptp_fun_B_1(B!12), relation_dom(B!12))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(85,plain,
% 0.20/0.46 (in(tptp_fun_B_1(B!12), relation_dom(B!12))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[84, 48])).
% 0.20/0.46 tff(86,plain,
% 0.20/0.46 (in(tptp_fun_B_1(B!12), relation_dom(relation_composition(B!12, A!11)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[85, 83])).
% 0.20/0.46 tff(87,plain,
% 0.20/0.46 (in(tptp_fun_C_0(B!12), relation_dom(relation_composition(B!12, A!11))) <=> in(tptp_fun_C_0(B!12), relation_dom(B!12))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[81])).
% 0.20/0.46 tff(88,plain,
% 0.20/0.46 (in(tptp_fun_C_0(B!12), relation_dom(B!12)) <=> in(tptp_fun_C_0(B!12), relation_dom(relation_composition(B!12, A!11)))),
% 0.20/0.46 inference(symmetry,[status(thm)],[87])).
% 0.20/0.46 tff(89,plain,
% 0.20/0.46 (((tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12))))) | in(tptp_fun_C_0(B!12), relation_dom(B!12))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(90,plain,
% 0.20/0.46 (in(tptp_fun_C_0(B!12), relation_dom(B!12))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[89, 48])).
% 0.20/0.46 tff(91,plain,
% 0.20/0.46 (in(tptp_fun_C_0(B!12), relation_dom(relation_composition(B!12, A!11)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[90, 88])).
% 0.20/0.46 tff(92,plain,
% 0.20/0.46 (^[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)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(93,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[92])).
% 0.20/0.47 tff(94,plain,
% 0.20/0.47 (^[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)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(95,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[94])).
% 0.20/0.47 tff(96,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[95, 93])).
% 0.20/0.47 tff(97,plain,
% 0.20/0.47 (^[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))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(98,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[97])).
% 0.20/0.47 tff(99,plain,
% 0.20/0.47 (![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)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(100,plain,
% 0.20/0.47 (^[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)))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(101,plain,
% 0.20/0.47 (![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)))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[100])).
% 0.20/0.47 tff(102,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/sandbox/benchmark/theBenchmark.p','t23_funct_1')).
% 0.20/0.47 tff(103,plain,
% 0.20/0.47 (![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)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.20/0.47 tff(104,plain,
% 0.20/0.47 (![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)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.20/0.47 tff(105,plain,(
% 0.20/0.47 ![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)))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[104])).
% 0.20/0.47 tff(106,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.20/0.47 tff(107,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[106, 96])).
% 0.20/0.47 tff(108,plain,
% 0.20/0.47 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | (~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(109,plain,
% 0.20/0.47 (((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))))) <=> ((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(110,plain,
% 0.20/0.47 (^[C: $i] : rewrite(((apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~relation(C)) | (~function(C))) <=> ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(111,plain,
% 0.20/0.47 (![C: $i] : ((apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~relation(C)) | (~function(C))) <=> ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[110])).
% 0.20/0.47 tff(112,plain,
% 0.20/0.47 (((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[111])).
% 0.20/0.47 tff(113,plain,
% 0.20/0.47 (((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[112, 109])).
% 0.20/0.47 tff(114,plain,
% 0.20/0.47 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~relation(C)) | (~function(C))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[113])).
% 0.20/0.47 tff(115,plain,
% 0.20/0.47 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~relation(C)) | (~function(C))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | (~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[114, 108])).
% 0.20/0.47 tff(116,plain,
% 0.20/0.47 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~relation(C)) | (~function(C))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(117,plain,
% 0.20/0.47 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | (~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.20/0.47 tff(118,plain,
% 0.20/0.47 (![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[117, 107, 22, 21])).
% 0.20/0.47 tff(119,plain,
% 0.20/0.47 (function(A!11)),
% 0.20/0.47 inference(and_elim,[status(thm)],[18])).
% 0.20/0.47 tff(120,plain,
% 0.20/0.47 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))))) | ((~relation(A!11)) | (~function(A!11)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12)) = apply(A!11, apply(B!12, tptp_fun_B_1(B!12)))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))))) | (~relation(A!11)) | (~function(A!11)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12)) = apply(A!11, apply(B!12, tptp_fun_B_1(B!12)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(121,plain,
% 0.20/0.47 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))))) | ((~relation(A!11)) | (~function(A!11)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12)) = apply(A!11, apply(B!12, tptp_fun_B_1(B!12)))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(122,plain,
% 0.20/0.47 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_B_1(B!12)) = apply(C, apply(B!12, tptp_fun_B_1(B!12)))))) | (~relation(A!11)) | (~function(A!11)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12)) = apply(A!11, apply(B!12, tptp_fun_B_1(B!12))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.20/0.47 tff(123,plain,
% 0.20/0.47 (apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12)) = apply(A!11, apply(B!12, tptp_fun_B_1(B!12)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[122, 74, 119, 85, 118])).
% 0.20/0.47 tff(124,plain,
% 0.20/0.47 (apply(A!11, apply(B!12, tptp_fun_B_1(B!12))) = apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12))),
% 0.20/0.47 inference(symmetry,[status(thm)],[123])).
% 0.20/0.47 tff(125,plain,
% 0.20/0.47 (((tptp_fun_B_1(B!12) = tptp_fun_C_0(B!12)) | (~in(tptp_fun_B_1(B!12), relation_dom(B!12))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~(apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12))))) | (apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12)))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(126,plain,
% 0.20/0.47 (apply(B!12, tptp_fun_B_1(B!12)) = apply(B!12, tptp_fun_C_0(B!12))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[125, 48])).
% 0.20/0.47 tff(127,plain,
% 0.20/0.47 (apply(A!11, apply(B!12, tptp_fun_B_1(B!12))) = apply(A!11, apply(B!12, tptp_fun_C_0(B!12)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[126])).
% 0.20/0.47 tff(128,plain,
% 0.20/0.47 (apply(A!11, apply(B!12, tptp_fun_C_0(B!12))) = apply(A!11, apply(B!12, tptp_fun_B_1(B!12)))),
% 0.20/0.47 inference(symmetry,[status(thm)],[127])).
% 0.20/0.47 tff(129,plain,
% 0.20/0.47 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | (~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(130,plain,
% 0.20/0.48 (((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))))) <=> ((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(131,plain,
% 0.20/0.48 (^[C: $i] : rewrite(((apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~relation(C)) | (~function(C))) <=> ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(132,plain,
% 0.20/0.48 (![C: $i] : ((apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~relation(C)) | (~function(C))) <=> ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[131])).
% 0.20/0.48 tff(133,plain,
% 0.20/0.48 (((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[132])).
% 0.20/0.48 tff(134,plain,
% 0.20/0.48 (((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[133, 130])).
% 0.20/0.48 tff(135,plain,
% 0.20/0.48 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~relation(C)) | (~function(C))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[134])).
% 0.20/0.48 tff(136,plain,
% 0.20/0.48 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~relation(C)) | (~function(C))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | (~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[135, 129])).
% 0.20/0.48 tff(137,plain,
% 0.20/0.48 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (~relation(C)) | (~function(C))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(138,plain,
% 0.20/0.48 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | (~relation(B!12)) | (~function(B!12)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.20/0.48 tff(139,plain,
% 0.20/0.48 (![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[138, 107, 22, 21])).
% 0.20/0.48 tff(140,plain,
% 0.20/0.48 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))))) | ((~relation(A!11)) | (~function(A!11)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12)) = apply(A!11, apply(B!12, tptp_fun_C_0(B!12)))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))))) | (~relation(A!11)) | (~function(A!11)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12)) = apply(A!11, apply(B!12, tptp_fun_C_0(B!12)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(141,plain,
% 0.20/0.48 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))))) | ((~relation(A!11)) | (~function(A!11)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12)) = apply(A!11, apply(B!12, tptp_fun_C_0(B!12)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(142,plain,
% 0.20/0.48 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, C), tptp_fun_C_0(B!12)) = apply(C, apply(B!12, tptp_fun_C_0(B!12)))))) | (~relation(A!11)) | (~function(A!11)) | (~in(tptp_fun_C_0(B!12), relation_dom(B!12))) | (apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12)) = apply(A!11, apply(B!12, tptp_fun_C_0(B!12))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.20/0.48 tff(143,plain,
% 0.20/0.48 (apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12)) = apply(A!11, apply(B!12, tptp_fun_C_0(B!12)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[142, 74, 119, 90, 139])).
% 0.20/0.48 tff(144,plain,
% 0.20/0.48 (apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12)) = apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12))),
% 0.20/0.48 inference(transitivity,[status(thm)],[143, 128, 124])).
% 0.20/0.48 tff(145,plain,
% 0.20/0.48 (^[A: $i, B: $i] : refl((relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A))) <=> (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(146,plain,
% 0.20/0.48 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A))) <=> ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[145])).
% 0.20/0.48 tff(147,plain,
% 0.20/0.48 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & relation(B)) <=> (~((~relation(B)) | (~relation(A))))), ((~(relation(A) & relation(B))) <=> (~(~((~relation(B)) | (~relation(A))))))), rewrite((~(~((~relation(B)) | (~relation(A))))) <=> ((~relation(B)) | (~relation(A)))), ((~(relation(A) & relation(B))) <=> ((~relation(B)) | (~relation(A))))), ((relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))) <=> (relation(relation_composition(A, B)) | ((~relation(B)) | (~relation(A)))))), rewrite((relation(relation_composition(A, B)) | ((~relation(B)) | (~relation(A)))) <=> (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))), ((relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))) <=> (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(148,plain,
% 0.20/0.48 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))) <=> ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[147])).
% 0.20/0.48 tff(149,plain,
% 0.20/0.48 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))) <=> ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(150,plain,
% 0.20/0.48 (^[A: $i, B: $i] : rewrite(((relation(A) & relation(B)) => relation(relation_composition(A, B))) <=> (relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(151,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((relation(A) & relation(B)) => relation(relation_composition(A, B))) <=> ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[150])).
% 0.20/0.48 tff(152,axiom,(![A: $i, B: $i] : ((relation(A) & relation(B)) => relation(relation_composition(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k5_relat_1')).
% 0.20/0.48 tff(153,plain,
% 0.20/0.48 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.20/0.48 tff(154,plain,
% 0.20/0.48 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[153, 149])).
% 0.20/0.48 tff(155,plain,(
% 0.20/0.48 ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[154])).
% 0.20/0.48 tff(156,plain,
% 0.20/0.48 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[155, 148])).
% 0.20/0.48 tff(157,plain,
% 0.20/0.48 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[156, 146])).
% 0.20/0.48 tff(158,plain,
% 0.20/0.48 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | ((~relation(A!11)) | (~relation(B!12)) | relation(relation_composition(B!12, A!11)))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (~relation(A!11)) | (~relation(B!12)) | relation(relation_composition(B!12, A!11)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(159,plain,
% 0.20/0.48 ((relation(relation_composition(B!12, A!11)) | (~relation(A!11)) | (~relation(B!12))) <=> ((~relation(A!11)) | (~relation(B!12)) | relation(relation_composition(B!12, A!11)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(160,plain,
% 0.20/0.48 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (relation(relation_composition(B!12, A!11)) | (~relation(A!11)) | (~relation(B!12)))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | ((~relation(A!11)) | (~relation(B!12)) | relation(relation_composition(B!12, A!11))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[159])).
% 0.20/0.48 tff(161,plain,
% 0.20/0.48 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (relation(relation_composition(B!12, A!11)) | (~relation(A!11)) | (~relation(B!12)))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (~relation(A!11)) | (~relation(B!12)) | relation(relation_composition(B!12, A!11)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[160, 158])).
% 0.20/0.48 tff(162,plain,
% 0.20/0.48 ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (relation(relation_composition(B!12, A!11)) | (~relation(A!11)) | (~relation(B!12)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(163,plain,
% 0.20/0.48 ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (~relation(A!11)) | (~relation(B!12)) | relation(relation_composition(B!12, A!11))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.20/0.48 tff(164,plain,
% 0.20/0.48 (relation(relation_composition(B!12, A!11))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[163, 157, 74, 22])).
% 0.20/0.48 tff(165,plain,
% 0.20/0.48 (^[A: $i, B: $i] : refl(((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))) <=> ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(166,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[165])).
% 0.20/0.48 tff(167,plain,
% 0.20/0.48 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & function(A) & relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A))))), ((~(relation(A) & function(A) & relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A))))))), rewrite((~(~((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A))))) <=> ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)))), ((~(relation(A) & function(A) & relation(B) & function(B))) <=> ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A))))), rewrite((relation(relation_composition(A, B)) & function(relation_composition(A, B))) <=> (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))), (((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> (((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A))) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))))), rewrite((((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A))) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))) <=> ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))), (((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(168,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[167])).
% 0.20/0.48 tff(169,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(170,plain,
% 0.20/0.48 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((relation(A) & function(A)) & relation(B)) <=> (relation(A) & function(A) & relation(B))), ((((relation(A) & function(A)) & relation(B)) & function(B)) <=> ((relation(A) & function(A) & relation(B)) & function(B)))), rewrite(((relation(A) & function(A) & relation(B)) & function(B)) <=> (relation(A) & function(A) & relation(B) & function(B))), ((((relation(A) & function(A)) & relation(B)) & function(B)) <=> (relation(A) & function(A) & relation(B) & function(B)))), (((((relation(A) & function(A)) & relation(B)) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ((relation(A) & function(A) & relation(B) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B)))))), rewrite(((relation(A) & function(A) & relation(B) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))), (((((relation(A) & function(A)) & relation(B)) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(171,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((((relation(A) & function(A)) & relation(B)) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[170])).
% 0.20/0.48 tff(172,axiom,(![A: $i, B: $i] : ((((relation(A) & function(A)) & relation(B)) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_funct_1')).
% 0.20/0.48 tff(173,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.20/0.48 tff(174,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[173, 169])).
% 0.20/0.48 tff(175,plain,(
% 0.20/0.48 ![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[174])).
% 0.20/0.48 tff(176,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[175, 168])).
% 0.20/0.48 tff(177,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[176, 166])).
% 0.20/0.48 tff(178,plain,
% 0.20/0.48 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~((~relation(relation_composition(B!12, A!11))) | (~function(relation_composition(B!12, A!11))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | (~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~((~relation(relation_composition(B!12, A!11))) | (~function(relation_composition(B!12, A!11))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(179,plain,
% 0.20/0.48 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~((~relation(relation_composition(B!12, A!11))) | (~function(relation_composition(B!12, A!11))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(180,plain,
% 0.20/0.48 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | (~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~((~relation(relation_composition(B!12, A!11))) | (~function(relation_composition(B!12, A!11)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.20/0.48 tff(181,plain,
% 0.20/0.48 (~((~relation(relation_composition(B!12, A!11))) | (~function(relation_composition(B!12, A!11))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[180, 177, 74, 119, 22, 21])).
% 0.20/0.48 tff(182,plain,
% 0.20/0.48 (((~relation(relation_composition(B!12, A!11))) | (~function(relation_composition(B!12, A!11)))) | function(relation_composition(B!12, A!11))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(183,plain,
% 0.20/0.48 (function(relation_composition(B!12, A!11))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[182, 181])).
% 0.20/0.48 tff(184,plain,
% 0.20/0.48 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | ((~relation(relation_composition(B!12, A!11))) | (~function(relation_composition(B!12, A!11))) | (~((~((~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C)))))) | (~(one_to_one(relation_composition(B!12, A!11)) | (~((tptp_fun_B_1(relation_composition(B!12, A!11)) = tptp_fun_C_0(relation_composition(B!12, A!11))) | (~in(tptp_fun_B_1(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_C_0(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(relation_composition(B!12, A!11))) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(relation_composition(B!12, A!11))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | (~relation(relation_composition(B!12, A!11))) | (~function(relation_composition(B!12, A!11))) | (~((~((~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C)))))) | (~(one_to_one(relation_composition(B!12, A!11)) | (~((tptp_fun_B_1(relation_composition(B!12, A!11)) = tptp_fun_C_0(relation_composition(B!12, A!11))) | (~in(tptp_fun_B_1(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_C_0(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(relation_composition(B!12, A!11))) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(relation_composition(B!12, A!11))))))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(185,plain,
% 0.20/0.48 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | ((~relation(relation_composition(B!12, A!11))) | (~function(relation_composition(B!12, A!11))) | (~((~((~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C)))))) | (~(one_to_one(relation_composition(B!12, A!11)) | (~((tptp_fun_B_1(relation_composition(B!12, A!11)) = tptp_fun_C_0(relation_composition(B!12, A!11))) | (~in(tptp_fun_B_1(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_C_0(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(relation_composition(B!12, A!11))) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(relation_composition(B!12, A!11))))))))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(186,plain,
% 0.20/0.48 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | (~relation(relation_composition(B!12, A!11))) | (~function(relation_composition(B!12, A!11))) | (~((~((~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C)))))) | (~(one_to_one(relation_composition(B!12, A!11)) | (~((tptp_fun_B_1(relation_composition(B!12, A!11)) = tptp_fun_C_0(relation_composition(B!12, A!11))) | (~in(tptp_fun_B_1(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_C_0(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(relation_composition(B!12, A!11))) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(relation_composition(B!12, A!11)))))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.20/0.49 tff(187,plain,
% 0.20/0.49 ((~relation(relation_composition(B!12, A!11))) | (~function(relation_composition(B!12, A!11))) | (~((~((~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C)))))) | (~(one_to_one(relation_composition(B!12, A!11)) | (~((tptp_fun_B_1(relation_composition(B!12, A!11)) = tptp_fun_C_0(relation_composition(B!12, A!11))) | (~in(tptp_fun_B_1(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_C_0(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(relation_composition(B!12, A!11))) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(relation_composition(B!12, A!11)))))))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[186, 38])).
% 0.20/0.49 tff(188,plain,
% 0.20/0.49 (~((~((~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C)))))) | (~(one_to_one(relation_composition(B!12, A!11)) | (~((tptp_fun_B_1(relation_composition(B!12, A!11)) = tptp_fun_C_0(relation_composition(B!12, A!11))) | (~in(tptp_fun_B_1(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_C_0(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(relation_composition(B!12, A!11))) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(relation_composition(B!12, A!11))))))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[187, 183, 164])).
% 0.20/0.49 tff(189,plain,
% 0.20/0.49 (((~((~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C)))))) | (~(one_to_one(relation_composition(B!12, A!11)) | (~((tptp_fun_B_1(relation_composition(B!12, A!11)) = tptp_fun_C_0(relation_composition(B!12, A!11))) | (~in(tptp_fun_B_1(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_C_0(relation_composition(B!12, A!11)), relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), tptp_fun_B_1(relation_composition(B!12, A!11))) = apply(relation_composition(B!12, A!11), tptp_fun_C_0(relation_composition(B!12, A!11)))))))))) | ((~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C)))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(190,plain,
% 0.20/0.49 ((~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[189, 188])).
% 0.20/0.49 tff(191,plain,
% 0.20/0.49 (one_to_one(relation_composition(B!12, A!11))),
% 0.20/0.49 inference(and_elim,[status(thm)],[72])).
% 0.20/0.49 tff(192,plain,
% 0.20/0.49 ((~((~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C)))))) | (~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(193,plain,
% 0.20/0.49 ((~((~one_to_one(relation_composition(B!12, A!11))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C)))))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[192, 191])).
% 0.20/0.49 tff(194,plain,
% 0.20/0.49 (![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[193, 190])).
% 0.20/0.49 tff(195,plain,
% 0.20/0.49 (((~![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C))))) | ((~in(tptp_fun_B_1(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_C_0(B!12), relation_dom(relation_composition(B!12, A!11)))) | (tptp_fun_C_0(B!12) = tptp_fun_B_1(B!12)) | (~(apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12)) = apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12)))))) <=> ((~![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C))))) | (~in(tptp_fun_B_1(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_C_0(B!12), relation_dom(relation_composition(B!12, A!11)))) | (tptp_fun_C_0(B!12) = tptp_fun_B_1(B!12)) | (~(apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12)) = apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(196,plain,
% 0.20/0.49 (((tptp_fun_C_0(B!12) = tptp_fun_B_1(B!12)) | (~in(tptp_fun_C_0(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_B_1(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12)) = apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12))))) <=> ((~in(tptp_fun_B_1(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_C_0(B!12), relation_dom(relation_composition(B!12, A!11)))) | (tptp_fun_C_0(B!12) = tptp_fun_B_1(B!12)) | (~(apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12)) = apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(197,plain,
% 0.20/0.49 (((~![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C))))) | ((tptp_fun_C_0(B!12) = tptp_fun_B_1(B!12)) | (~in(tptp_fun_C_0(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_B_1(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12)) = apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12)))))) <=> ((~![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C))))) | ((~in(tptp_fun_B_1(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_C_0(B!12), relation_dom(relation_composition(B!12, A!11)))) | (tptp_fun_C_0(B!12) = tptp_fun_B_1(B!12)) | (~(apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12)) = apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[196])).
% 0.20/0.49 tff(198,plain,
% 0.20/0.49 (((~![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C))))) | ((tptp_fun_C_0(B!12) = tptp_fun_B_1(B!12)) | (~in(tptp_fun_C_0(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_B_1(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12)) = apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12)))))) <=> ((~![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C))))) | (~in(tptp_fun_B_1(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_C_0(B!12), relation_dom(relation_composition(B!12, A!11)))) | (tptp_fun_C_0(B!12) = tptp_fun_B_1(B!12)) | (~(apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12)) = apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12)))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[197, 195])).
% 0.20/0.49 tff(199,plain,
% 0.20/0.49 ((~![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C))))) | ((tptp_fun_C_0(B!12) = tptp_fun_B_1(B!12)) | (~in(tptp_fun_C_0(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_B_1(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12)) = apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12)))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(200,plain,
% 0.20/0.49 ((~![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(B!12, A!11)))) | (~in(C, relation_dom(relation_composition(B!12, A!11)))) | (~(apply(relation_composition(B!12, A!11), B) = apply(relation_composition(B!12, A!11), C))))) | (~in(tptp_fun_B_1(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_C_0(B!12), relation_dom(relation_composition(B!12, A!11)))) | (tptp_fun_C_0(B!12) = tptp_fun_B_1(B!12)) | (~(apply(relation_composition(B!12, A!11), tptp_fun_C_0(B!12)) = apply(relation_composition(B!12, A!11), tptp_fun_B_1(B!12))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.20/0.49 tff(201,plain,
% 0.20/0.49 ((~in(tptp_fun_B_1(B!12), relation_dom(relation_composition(B!12, A!11)))) | (~in(tptp_fun_C_0(B!12), relation_dom(relation_composition(B!12, A!11)))) | (tptp_fun_C_0(B!12) = tptp_fun_B_1(B!12))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[200, 194, 144])).
% 0.20/0.49 tff(202,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[201, 91, 86, 51])).
% 0.20/0.49 % SZS output end Proof
%------------------------------------------------------------------------------