TSTP Solution File: SEU013+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU013+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 0.13s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU013+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n026.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 09:13:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(apply_type, type, (
% 0.13/0.40 apply: ( $i * $i ) > $i)).
% 0.13/0.40 tff(tptp_fun_C_0_type, type, (
% 0.13/0.40 tptp_fun_C_0: $i > $i)).
% 0.13/0.40 tff(relation_composition_type, type, (
% 0.13/0.40 relation_composition: ( $i * $i ) > $i)).
% 0.13/0.40 tff(tptp_fun_B_12_type, type, (
% 0.13/0.40 tptp_fun_B_12: $i)).
% 0.13/0.40 tff(tptp_fun_A_11_type, type, (
% 0.13/0.40 tptp_fun_A_11: $i)).
% 0.13/0.40 tff(tptp_fun_B_1_type, type, (
% 0.13/0.40 tptp_fun_B_1: $i > $i)).
% 0.13/0.40 tff(in_type, type, (
% 0.13/0.40 in: ( $i * $i ) > $o)).
% 0.13/0.40 tff(relation_dom_type, type, (
% 0.13/0.40 relation_dom: $i > $i)).
% 0.13/0.40 tff(one_to_one_type, type, (
% 0.13/0.40 one_to_one: $i > $o)).
% 0.13/0.40 tff(relation_type, type, (
% 0.13/0.40 relation: $i > $o)).
% 0.13/0.40 tff(function_type, type, (
% 0.13/0.40 function: $i > $o)).
% 0.13/0.40 tff(1,plain,
% 0.13/0.40 (((relation(A!11) & function(A!11)) & (~(one_to_one(relation_composition(A!11, B!12)) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(A!11) & one_to_one(B!12)))))) <=> (relation(A!11) & function(A!11) & (~(one_to_one(relation_composition(A!11, B!12)) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(A!11) & one_to_one(B!12))))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 ((~(one_to_one(relation_composition(A!11, B!12)) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(A!11) & one_to_one(B!12))))) <=> (~(one_to_one(relation_composition(A!11, B!12)) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(A!11) & one_to_one(B!12)))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 ((~(~(relation(A!11) & function(A!11)))) <=> (relation(A!11) & function(A!11))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(4,plain,
% 0.13/0.40 (((~(~(relation(A!11) & function(A!11)))) & (~(one_to_one(relation_composition(A!11, B!12)) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(A!11) & one_to_one(B!12)))))) <=> ((relation(A!11) & function(A!11)) & (~(one_to_one(relation_composition(A!11, B!12)) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(A!11) & one_to_one(B!12))))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[3, 2])).
% 0.13/0.40 tff(5,plain,
% 0.13/0.40 (((~(~(relation(A!11) & function(A!11)))) & (~(one_to_one(relation_composition(A!11, B!12)) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(A!11) & one_to_one(B!12)))))) <=> (relation(A!11) & function(A!11) & (~(one_to_one(relation_composition(A!11, B!12)) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(A!11) & one_to_one(B!12))))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[4, 1])).
% 0.13/0.40 tff(6,plain,
% 0.13/0.40 ((~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(relation_composition(A, B)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & one_to_one(B)))))) <=> (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(relation_composition(A, B)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & one_to_one(B))))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 ((~![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => ((one_to_one(A) & one_to_one(B)) => one_to_one(relation_composition(A, B)))))) <=> (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(relation_composition(A, B)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & one_to_one(B))))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(8,axiom,(~![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => ((one_to_one(A) & one_to_one(B)) => one_to_one(relation_composition(A, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t46_funct_1')).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(relation_composition(A, B)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & one_to_one(B)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(relation_composition(A, B)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & one_to_one(B)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(relation_composition(A, B)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & one_to_one(B)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(relation_composition(A, B)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & one_to_one(B)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(relation_composition(A, B)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & one_to_one(B)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[12, 6])).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(relation_composition(A, B)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & one_to_one(B)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(relation_composition(A, B)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & one_to_one(B)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[14, 6])).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 (relation(A!11) & function(A!11) & (~(one_to_one(relation_composition(A!11, B!12)) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(A!11) & one_to_one(B!12)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 (~(one_to_one(relation_composition(A!11, B!12)) | (~(relation(B!12) & function(B!12))) | (~(one_to_one(A!11) & one_to_one(B!12))))),
% 0.13/0.40 inference(and_elim,[status(thm)],[16])).
% 0.13/0.40 tff(18,plain,
% 0.13/0.40 (relation(B!12) & function(B!12)),
% 0.13/0.40 inference(or_elim,[status(thm)],[17])).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 (relation(B!12)),
% 0.13/0.40 inference(and_elim,[status(thm)],[18])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 (relation(A!11)),
% 0.13/0.40 inference(and_elim,[status(thm)],[16])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 (^[A: $i, B: $i] : refl((relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A))) <=> (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 (![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)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[21])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 (^[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)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 (![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)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[23])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 (![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))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(26,plain,
% 0.13/0.40 (^[A: $i, B: $i] : rewrite(((relation(A) & relation(B)) => relation(relation_composition(A, B))) <=> (relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(27,plain,
% 0.13/0.40 (![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))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[26])).
% 0.13/0.40 tff(28,axiom,(![A: $i, B: $i] : ((relation(A) & relation(B)) => relation(relation_composition(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k5_relat_1')).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.13/0.40 tff(31,plain,(
% 0.13/0.40 ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[30])).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.13/0.40 tff(33,plain,
% 0.13/0.40 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[32, 22])).
% 0.13/0.40 tff(34,plain,
% 0.13/0.40 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | ((~relation(A!11)) | (~relation(B!12)) | relation(relation_composition(A!11, B!12)))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (~relation(A!11)) | (~relation(B!12)) | relation(relation_composition(A!11, B!12)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(35,plain,
% 0.13/0.40 ((relation(relation_composition(A!11, B!12)) | (~relation(B!12)) | (~relation(A!11))) <=> ((~relation(A!11)) | (~relation(B!12)) | relation(relation_composition(A!11, B!12)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(36,plain,
% 0.13/0.40 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (relation(relation_composition(A!11, B!12)) | (~relation(B!12)) | (~relation(A!11)))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | ((~relation(A!11)) | (~relation(B!12)) | relation(relation_composition(A!11, B!12))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[35])).
% 0.13/0.40 tff(37,plain,
% 0.13/0.40 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (relation(relation_composition(A!11, B!12)) | (~relation(B!12)) | (~relation(A!11)))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (~relation(A!11)) | (~relation(B!12)) | relation(relation_composition(A!11, B!12)))),
% 0.13/0.40 inference(transitivity,[status(thm)],[36, 34])).
% 0.13/0.40 tff(38,plain,
% 0.13/0.40 ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (relation(relation_composition(A!11, B!12)) | (~relation(B!12)) | (~relation(A!11)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(39,plain,
% 0.13/0.40 ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (~relation(A!11)) | (~relation(B!12)) | relation(relation_composition(A!11, B!12))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.13/0.40 tff(40,plain,
% 0.13/0.40 (relation(relation_composition(A!11, B!12))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[39, 33, 20, 19])).
% 0.13/0.40 tff(41,plain,
% 0.13/0.40 (function(B!12)),
% 0.13/0.40 inference(and_elim,[status(thm)],[18])).
% 0.13/0.40 tff(42,plain,
% 0.13/0.40 (function(A!11)),
% 0.13/0.40 inference(and_elim,[status(thm)],[16])).
% 0.13/0.40 tff(43,plain,
% 0.13/0.40 (^[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)))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(44,plain,
% 0.13/0.40 (![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))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[43])).
% 0.13/0.41 tff(45,plain,
% 0.13/0.41 (^[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))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(46,plain,
% 0.13/0.41 (![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))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[45])).
% 0.13/0.41 tff(47,plain,
% 0.13/0.41 (![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))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(48,plain,
% 0.13/0.41 (^[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))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(49,plain,
% 0.13/0.41 (![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))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[48])).
% 0.13/0.41 tff(50,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/sandbox2/benchmark/theBenchmark.p','fc1_funct_1')).
% 0.13/0.41 tff(51,plain,
% 0.13/0.41 (![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.13/0.41 tff(52,plain,
% 0.13/0.41 (![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.13/0.41 tff(53,plain,(
% 0.13/0.41 ![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 0.13/0.41 inference(skolemize,[status(sab)],[52])).
% 0.13/0.41 tff(54,plain,
% 0.13/0.41 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.13/0.41 tff(55,plain,
% 0.13/0.41 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[54, 44])).
% 0.13/0.41 tff(56,plain,
% 0.13/0.41 (((~![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(A!11, B!12))) | (~function(relation_composition(A!11, B!12))))))) <=> ((~![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(A!11, B!12))) | (~function(relation_composition(A!11, B!12))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(57,plain,
% 0.13/0.41 (((~relation(B!12)) | (~function(B!12)) | (~relation(A!11)) | (~function(A!11)) | (~((~relation(relation_composition(A!11, B!12))) | (~function(relation_composition(A!11, B!12)))))) <=> ((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~((~relation(relation_composition(A!11, B!12))) | (~function(relation_composition(A!11, B!12))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(58,plain,
% 0.13/0.41 ((~((~relation(relation_composition(A!11, B!12))) | (~function(relation_composition(A!11, B!12))))) <=> (~((~relation(relation_composition(A!11, B!12))) | (~function(relation_composition(A!11, B!12)))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(59,plain,
% 0.13/0.41 (((~relation(B!12)) | (~function(B!12)) | (~relation(A!11)) | (~function(A!11)) | (~((~relation(relation_composition(A!11, B!12))) | (~function(relation_composition(A!11, B!12)))))) <=> ((~relation(B!12)) | (~function(B!12)) | (~relation(A!11)) | (~function(A!11)) | (~((~relation(relation_composition(A!11, B!12))) | (~function(relation_composition(A!11, B!12))))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[58])).
% 0.13/0.41 tff(60,plain,
% 0.13/0.41 (((~relation(B!12)) | (~function(B!12)) | (~relation(A!11)) | (~function(A!11)) | (~((~relation(relation_composition(A!11, B!12))) | (~function(relation_composition(A!11, B!12)))))) <=> ((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~((~relation(relation_composition(A!11, B!12))) | (~function(relation_composition(A!11, B!12))))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[59, 57])).
% 0.13/0.41 tff(61,plain,
% 0.13/0.41 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(B!12)) | (~function(B!12)) | (~relation(A!11)) | (~function(A!11)) | (~((~relation(relation_composition(A!11, B!12))) | (~function(relation_composition(A!11, B!12))))))) <=> ((~![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(A!11, B!12))) | (~function(relation_composition(A!11, B!12)))))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[60])).
% 0.13/0.41 tff(62,plain,
% 0.13/0.41 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(B!12)) | (~function(B!12)) | (~relation(A!11)) | (~function(A!11)) | (~((~relation(relation_composition(A!11, B!12))) | (~function(relation_composition(A!11, B!12))))))) <=> ((~![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(A!11, B!12))) | (~function(relation_composition(A!11, B!12))))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[61, 56])).
% 0.13/0.41 tff(63,plain,
% 0.13/0.41 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(B!12)) | (~function(B!12)) | (~relation(A!11)) | (~function(A!11)) | (~((~relation(relation_composition(A!11, B!12))) | (~function(relation_composition(A!11, B!12))))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(64,plain,
% 0.13/0.41 ((~![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(A!11, B!12))) | (~function(relation_composition(A!11, B!12)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.13/0.41 tff(65,plain,
% 0.13/0.41 (~((~relation(relation_composition(A!11, B!12))) | (~function(relation_composition(A!11, B!12))))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[64, 55, 20, 42, 19, 41])).
% 0.13/0.41 tff(66,plain,
% 0.13/0.41 (((~relation(relation_composition(A!11, B!12))) | (~function(relation_composition(A!11, B!12)))) | function(relation_composition(A!11, B!12))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(67,plain,
% 0.13/0.41 (function(relation_composition(A!11, B!12))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.13/0.41 tff(68,plain,
% 0.13/0.41 (^[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))))))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(69,plain,
% 0.13/0.41 (![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)))))))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[68])).
% 0.13/0.41 tff(70,plain,
% 0.13/0.41 (^[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))))))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(71,plain,
% 0.13/0.41 (![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)))))))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[70])).
% 0.13/0.41 tff(72,plain,
% 0.13/0.41 (![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)))))))))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[71, 69])).
% 0.13/0.41 tff(73,plain,
% 0.13/0.41 (^[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)))))))))))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(74,plain,
% 0.13/0.42 (![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)))))))))))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[73])).
% 0.13/0.42 tff(75,plain,
% 0.13/0.42 (![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))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(76,plain,
% 0.13/0.42 (^[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))))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(77,plain,
% 0.13/0.42 (![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))))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[76])).
% 0.13/0.42 tff(78,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/sandbox2/benchmark/theBenchmark.p','d8_funct_1')).
% 0.13/0.42 tff(79,plain,
% 0.13/0.42 (![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))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.13/0.42 tff(80,plain,
% 0.13/0.42 (![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))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.13/0.42 tff(81,plain,(
% 0.13/0.42 ![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)))))))),
% 0.13/0.42 inference(skolemize,[status(sab)],[80])).
% 0.13/0.42 tff(82,plain,
% 0.13/0.42 (![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)))))))))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.13/0.42 tff(83,plain,
% 0.13/0.42 (![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)))))))))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[82, 72])).
% 0.13/0.42 tff(84,plain,
% 0.13/0.42 (((~![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(A!11, B!12))) | (~function(relation_composition(A!11, B!12))) | (~((~((~one_to_one(relation_composition(A!11, B!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(A!11, B!12)))) | (~in(C, relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), B) = apply(relation_composition(A!11, B!12), C)))))) | (~(one_to_one(relation_composition(A!11, B!12)) | (~((tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, 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(relation_composition(A!11, B!12))) | (~function(relation_composition(A!11, B!12))) | (~((~((~one_to_one(relation_composition(A!11, B!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(A!11, B!12)))) | (~in(C, relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), B) = apply(relation_composition(A!11, B!12), C)))))) | (~(one_to_one(relation_composition(A!11, B!12)) | (~((tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))))))))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(85,plain,
% 0.13/0.42 ((~![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(A!11, B!12))) | (~function(relation_composition(A!11, B!12))) | (~((~((~one_to_one(relation_composition(A!11, B!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(A!11, B!12)))) | (~in(C, relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), B) = apply(relation_composition(A!11, B!12), C)))))) | (~(one_to_one(relation_composition(A!11, B!12)) | (~((tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))))))))))),
% 0.13/0.42 inference(quant_inst,[status(thm)],[])).
% 0.13/0.42 tff(86,plain,
% 0.13/0.42 ((~![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(A!11, B!12))) | (~function(relation_composition(A!11, B!12))) | (~((~((~one_to_one(relation_composition(A!11, B!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(A!11, B!12)))) | (~in(C, relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), B) = apply(relation_composition(A!11, B!12), C)))))) | (~(one_to_one(relation_composition(A!11, B!12)) | (~((tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12)))))))))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.13/0.42 tff(87,plain,
% 0.13/0.42 ((~relation(relation_composition(A!11, B!12))) | (~function(relation_composition(A!11, B!12))) | (~((~((~one_to_one(relation_composition(A!11, B!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(A!11, B!12)))) | (~in(C, relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), B) = apply(relation_composition(A!11, B!12), C)))))) | (~(one_to_one(relation_composition(A!11, B!12)) | (~((tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12)))))))))))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[86, 83])).
% 0.13/0.42 tff(88,plain,
% 0.13/0.42 (~((~((~one_to_one(relation_composition(A!11, B!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(A!11, B!12)))) | (~in(C, relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), B) = apply(relation_composition(A!11, B!12), C)))))) | (~(one_to_one(relation_composition(A!11, B!12)) | (~((tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))))))))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[87, 67, 40])).
% 0.13/0.42 tff(89,plain,
% 0.13/0.42 (((~((~one_to_one(relation_composition(A!11, B!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(relation_composition(A!11, B!12)))) | (~in(C, relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), B) = apply(relation_composition(A!11, B!12), C)))))) | (~(one_to_one(relation_composition(A!11, B!12)) | (~((tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12)))))))))) | (one_to_one(relation_composition(A!11, B!12)) | (~((tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))))))),
% 0.13/0.42 inference(tautology,[status(thm)],[])).
% 0.13/0.42 tff(90,plain,
% 0.13/0.42 (one_to_one(relation_composition(A!11, B!12)) | (~((tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12)))))))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.13/0.42 tff(91,plain,
% 0.13/0.42 (~one_to_one(relation_composition(A!11, B!12))),
% 0.13/0.42 inference(or_elim,[status(thm)],[17])).
% 0.13/0.42 tff(92,plain,
% 0.13/0.42 ((~(one_to_one(relation_composition(A!11, B!12)) | (~((tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))))))) | one_to_one(relation_composition(A!11, B!12)) | (~((tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12)))))))),
% 0.13/0.43 inference(tautology,[status(thm)],[])).
% 0.13/0.43 tff(93,plain,
% 0.13/0.43 ((~(one_to_one(relation_composition(A!11, B!12)) | (~((tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))))))) | (~((tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12)))))))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.13/0.43 tff(94,plain,
% 0.13/0.43 (~((tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[93, 90])).
% 0.13/0.43 tff(95,plain,
% 0.13/0.43 (((tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12)))))) | in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))),
% 0.13/0.43 inference(tautology,[status(thm)],[])).
% 0.13/0.43 tff(96,plain,
% 0.13/0.43 (in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.13/0.43 tff(97,plain,
% 0.13/0.43 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))) <=> ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))), (((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))))), rewrite(((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))), (((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(98,plain,
% 0.13/0.43 (![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[97])).
% 0.13/0.43 tff(99,plain,
% 0.13/0.43 (^[A: $i, B: $i, C: $i] : refl(((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(100,plain,
% 0.13/0.43 (![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[99])).
% 0.13/0.43 tff(101,plain,
% 0.13/0.43 (![A: $i, B: $i] : ![C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 0.13/0.43 inference(pull_quant,[status(thm)],[])).
% 0.13/0.43 tff(102,plain,
% 0.13/0.43 (^[A: $i, B: $i] : pull_quant(((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(103,plain,
% 0.13/0.43 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i] : ![C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[102])).
% 0.13/0.43 tff(104,plain,
% 0.13/0.43 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 0.13/0.43 inference(transitivity,[status(thm)],[103, 101])).
% 0.19/0.43 tff(105,plain,
% 0.19/0.43 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[104, 100])).
% 0.19/0.43 tff(106,plain,
% 0.19/0.43 (^[A: $i, B: $i] : rewrite(((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(107,plain,
% 0.19/0.43 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[106])).
% 0.19/0.43 tff(108,plain,
% 0.19/0.43 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[107, 105])).
% 0.19/0.43 tff(109,plain,
% 0.19/0.43 (^[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(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B))))) <=> ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | ((~relation(C)) | (~function(C))) | (~in(A, relation_dom(relation_composition(C, B))))))), rewrite(((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | ((~relation(C)) | (~function(C))) | (~in(A, relation_dom(relation_composition(C, B))))) <=> ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))), (((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B))))) <=> ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))))), (![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B))))) <=> ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))), (((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B)))))) <=> (((~relation(B)) | (~function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))))), rewrite((((~relation(B)) | (~function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))), (((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B)))))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(110,plain,
% 0.19/0.43 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B)))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[109])).
% 0.19/0.43 tff(111,plain,
% 0.19/0.43 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B)))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(112,plain,
% 0.19/0.43 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((in(A, relation_dom(relation_composition(C, B))) => (apply(relation_composition(C, B), A) = apply(B, apply(C, A)))) <=> ((~in(A, relation_dom(relation_composition(C, B)))) | (apply(relation_composition(C, B), A) = apply(B, apply(C, A))))), (((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) => (apply(relation_composition(C, B), A) = apply(B, apply(C, A))))) <=> ((relation(C) & function(C)) => ((~in(A, relation_dom(relation_composition(C, B)))) | (apply(relation_composition(C, B), A) = apply(B, apply(C, A))))))), rewrite(((relation(C) & function(C)) => ((~in(A, relation_dom(relation_composition(C, B)))) | (apply(relation_composition(C, B), A) = apply(B, apply(C, A))))) <=> ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B)))))), (((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) => (apply(relation_composition(C, B), A) = apply(B, apply(C, A))))) <=> ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B)))))))), (![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) => (apply(relation_composition(C, B), A) = apply(B, apply(C, A))))) <=> ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B))))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) => (apply(relation_composition(C, B), A) = apply(B, apply(C, A)))))) <=> ((relation(B) & function(B)) => ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B)))))))), rewrite(((relation(B) & function(B)) => ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B)))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B))))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) => (apply(relation_composition(C, B), A) = apply(B, apply(C, A)))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(113,plain,
% 0.19/0.43 (![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) => (apply(relation_composition(C, B), A) = apply(B, apply(C, A)))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[112])).
% 0.19/0.43 tff(114,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) => (apply(relation_composition(C, B), A) = apply(B, apply(C, A))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t22_funct_1')).
% 0.19/0.43 tff(115,plain,
% 0.19/0.43 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.19/0.43 tff(116,plain,
% 0.19/0.43 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[115, 111])).
% 0.19/0.43 tff(117,plain,(
% 0.19/0.43 ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(relation_composition(C, B))))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[116])).
% 0.19/0.43 tff(118,plain,
% 0.19/0.43 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[117, 110])).
% 0.19/0.43 tff(119,plain,
% 0.19/0.43 (![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[118, 108])).
% 0.19/0.43 tff(120,plain,
% 0.19/0.43 (![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[119, 98])).
% 0.19/0.43 tff(121,plain,
% 0.19/0.43 (((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))) | ((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))))) <=> ((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))) | (~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(122,plain,
% 0.19/0.44 (((apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12))) <=> ((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(123,plain,
% 0.19/0.44 (((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))) | ((apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)))) <=> ((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))) | ((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[122])).
% 0.19/0.44 tff(124,plain,
% 0.19/0.44 (((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))) | ((apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)))) <=> ((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))) | (~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[123, 121])).
% 0.19/0.44 tff(125,plain,
% 0.19/0.44 ((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))) | ((apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(126,plain,
% 0.19/0.44 ((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))) | (~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.19/0.44 tff(127,plain,
% 0.19/0.44 (apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[126, 120, 20, 42, 19, 41, 96])).
% 0.19/0.44 tff(128,plain,
% 0.19/0.44 (((tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12)))))) | (apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(129,plain,
% 0.19/0.44 (apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[128, 94])).
% 0.19/0.44 tff(130,plain,
% 0.19/0.44 (((tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12)))))) | in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(131,plain,
% 0.19/0.44 (in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[130, 94])).
% 0.19/0.44 tff(132,plain,
% 0.19/0.44 (((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))) | ((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))))))) <=> ((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))) | (~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(133,plain,
% 0.19/0.44 (((apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12))) <=> ((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(134,plain,
% 0.19/0.44 (((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))) | ((apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)))) <=> ((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))) | ((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12)))))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[133])).
% 0.19/0.44 tff(135,plain,
% 0.19/0.44 (((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))) | ((apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)))) <=> ((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))) | (~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[134, 132])).
% 0.19/0.44 tff(136,plain,
% 0.19/0.44 ((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))) | ((apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(137,plain,
% 0.19/0.44 ((~![A: $i, B: $i, C: $i] : ((apply(relation_composition(C, B), A) = apply(B, apply(C, A))) | (~in(A, relation_dom(relation_composition(C, B)))) | (~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)))) | (~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.19/0.44 tff(138,plain,
% 0.19/0.44 (apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[137, 120, 20, 42, 19, 41, 131])).
% 0.19/0.44 tff(139,plain,
% 0.19/0.44 (apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12)))) = apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12)))),
% 0.19/0.44 inference(symmetry,[status(thm)],[138])).
% 0.19/0.44 tff(140,plain,
% 0.19/0.44 (apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12)))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[139, 129, 127])).
% 0.19/0.44 tff(141,plain,
% 0.19/0.44 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(monotonicity(rewrite((~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B))))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))), ((in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))) <=> (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))), (((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B))))))) <=> ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B))))))))), rewrite(((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B))))))) <=> ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))), (((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B))))))) <=> ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B))))))))), (((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))) <=> ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))))), rewrite(((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))) <=> ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))), (((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))) <=> ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(142,plain,
% 0.19/0.45 (![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[141])).
% 0.19/0.45 tff(143,plain,
% 0.19/0.45 (^[A: $i, B: $i, C: $i] : refl(((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))) <=> ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(144,plain,
% 0.19/0.45 (![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B))))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[143])).
% 0.19/0.45 tff(145,plain,
% 0.19/0.45 (![A: $i, B: $i] : ![C: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B))))))))),
% 0.19/0.45 inference(pull_quant,[status(thm)],[])).
% 0.19/0.45 tff(146,plain,
% 0.19/0.45 (^[A: $i, B: $i] : pull_quant(((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))) <=> ![C: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(147,plain,
% 0.19/0.45 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))) <=> ![A: $i, B: $i] : ![C: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B))))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[146])).
% 0.19/0.45 tff(148,plain,
% 0.19/0.45 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B))))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[147, 145])).
% 0.19/0.45 tff(149,plain,
% 0.19/0.45 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B))))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[148, 144])).
% 0.19/0.45 tff(150,plain,
% 0.19/0.45 (^[A: $i, B: $i] : rewrite(((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(151,plain,
% 0.19/0.45 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B))))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[150])).
% 0.19/0.45 tff(152,plain,
% 0.19/0.45 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B))))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[151, 149])).
% 0.19/0.45 tff(153,plain,
% 0.19/0.45 (^[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))))), rewrite((in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B)))) <=> (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B))))))), (((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))) <=> (((~relation(C)) | (~function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B))))))))), rewrite((((~relation(C)) | (~function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B))))))) <=> ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))), (((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))) <=> ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))))), (![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))) <=> ![C: $i] : ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B))))))))), (((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B)))))) <=> (((~relation(B)) | (~function(B))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))))), rewrite((((~relation(B)) | (~function(B))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B))))))))), (((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B)))))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B))))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(154,plain,
% 0.19/0.45 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B)))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B))))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[153])).
% 0.19/0.45 tff(155,plain,
% 0.19/0.45 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B)))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(156,plain,
% 0.19/0.45 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite(((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))) <=> ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))))), (![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))) <=> ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B)))))) <=> ((relation(B) & function(B)) => ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B)))))))), rewrite(((relation(B) & function(B)) => ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B)))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B)))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(157,plain,
% 0.19/0.45 (![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B)))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[156])).
% 0.19/0.45 tff(158,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t21_funct_1')).
% 0.19/0.45 tff(159,plain,
% 0.19/0.45 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.19/0.45 tff(160,plain,
% 0.19/0.45 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[159, 155])).
% 0.19/0.45 tff(161,plain,(
% 0.19/0.45 ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))))),
% 0.19/0.45 inference(skolemize,[status(sab)],[160])).
% 0.19/0.45 tff(162,plain,
% 0.19/0.45 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B))))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[161, 154])).
% 0.19/0.45 tff(163,plain,
% 0.19/0.45 (![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B))))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[162, 152])).
% 0.19/0.45 tff(164,plain,
% 0.19/0.45 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[163, 142])).
% 0.19/0.45 tff(165,plain,
% 0.19/0.45 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))) | ((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))) <=> (~((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))) | (~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))) <=> (~((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12)))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(166,plain,
% 0.19/0.45 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))) | ((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))) <=> (~((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12)))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(167,plain,
% 0.19/0.45 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))) | (~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))) <=> (~((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.19/0.45 tff(168,plain,
% 0.19/0.45 (in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))) <=> (~((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12)))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[167, 164, 20, 42, 19, 41])).
% 0.19/0.45 tff(169,plain,
% 0.19/0.45 ((~(in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))) <=> (~((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12))))))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12)))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(170,plain,
% 0.19/0.45 ((~(in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))) <=> (~((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12))))))) | (~((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12)))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[169, 131])).
% 0.19/0.45 tff(171,plain,
% 0.19/0.45 (~((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[170, 168])).
% 0.19/0.45 tff(172,plain,
% 0.19/0.45 (((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12)))) | in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(173,plain,
% 0.19/0.45 (in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[172, 171])).
% 0.19/0.45 tff(174,plain,
% 0.19/0.45 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))) | ((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))) <=> (~((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))) | (~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))) <=> (~((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12)))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(175,plain,
% 0.19/0.46 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))) | ((~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))) <=> (~((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12)))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(176,plain,
% 0.19/0.46 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~function(C)) | (~relation(B)) | (~function(B)) | (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))) | (~relation(A!11)) | (~function(A!11)) | (~relation(B!12)) | (~function(B!12)) | (in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))) <=> (~((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.19/0.46 tff(177,plain,
% 0.19/0.46 (in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))) <=> (~((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[176, 164, 20, 42, 19, 41])).
% 0.19/0.46 tff(178,plain,
% 0.19/0.46 ((~(in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))) <=> (~((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12))))))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12)))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(179,plain,
% 0.19/0.46 ((~(in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12))) <=> (~((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12))))))) | (~((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[178, 96])).
% 0.19/0.46 tff(180,plain,
% 0.19/0.46 (~((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[179, 177])).
% 0.19/0.46 tff(181,plain,
% 0.19/0.46 (((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12)))) | in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(182,plain,
% 0.19/0.46 (in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[181, 180])).
% 0.19/0.46 tff(183,plain,
% 0.19/0.46 (((~![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)))))))))))) <=> ((~![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)))))))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(184,plain,
% 0.19/0.46 ((~![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)))))))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(185,plain,
% 0.19/0.46 ((~![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))))))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.19/0.46 tff(186,plain,
% 0.19/0.46 (~((~((~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)))))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[185, 83, 19, 41])).
% 0.19/0.46 tff(187,plain,
% 0.19/0.46 (((~((~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)) | ![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)))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(188,plain,
% 0.19/0.46 ((~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))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[187, 186])).
% 0.19/0.46 tff(189,plain,
% 0.19/0.46 (one_to_one(A!11) & one_to_one(B!12)),
% 0.19/0.46 inference(or_elim,[status(thm)],[17])).
% 0.19/0.46 tff(190,plain,
% 0.19/0.46 (one_to_one(B!12)),
% 0.19/0.46 inference(and_elim,[status(thm)],[189])).
% 0.19/0.46 tff(191,plain,
% 0.19/0.46 ((~((~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)) | ![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))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(192,plain,
% 0.19/0.46 ((~((~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)))))) | ![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))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[191, 190])).
% 0.19/0.46 tff(193,plain,
% 0.19/0.46 (![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))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[192, 188])).
% 0.19/0.46 tff(194,plain,
% 0.19/0.46 (((~![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))))) | ((~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12))) | (apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))) | (~(apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12)))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, 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))))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12))) | (apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))) | (~(apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12)))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(195,plain,
% 0.19/0.46 (((apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12))) | (~(apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12)))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))))) <=> ((~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12))) | (apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))) | (~(apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12)))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(196,plain,
% 0.19/0.46 (((~![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))))) | ((apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12))) | (~(apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12)))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, 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))))) | ((~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12))) | (apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))) | (~(apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12)))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[195])).
% 0.19/0.46 tff(197,plain,
% 0.19/0.46 (((~![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))))) | ((apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12))) | (~(apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12)))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, 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))))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12))) | (apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))) | (~(apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12)))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[196, 194])).
% 0.19/0.46 tff(198,plain,
% 0.19/0.46 ((~![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))))) | ((apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12))) | (~(apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12)))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(199,plain,
% 0.19/0.46 ((~![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))))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12))) | (apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))) | (~(apply(B!12, apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12)))) = apply(B!12, apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.19/0.46 tff(200,plain,
% 0.19/0.46 (apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[199, 193, 182, 173, 140])).
% 0.19/0.46 tff(201,plain,
% 0.19/0.46 (((~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))), relation_dom(B!12)))) | in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(202,plain,
% 0.19/0.47 (in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[201, 171])).
% 0.19/0.47 tff(203,plain,
% 0.19/0.47 (((~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))), relation_dom(B!12)))) | in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(204,plain,
% 0.19/0.47 (in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[203, 180])).
% 0.19/0.47 tff(205,plain,
% 0.19/0.47 (((tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(relation_composition(A!11, B!12)))) | (~(apply(relation_composition(A!11, B!12), tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(relation_composition(A!11, B!12), tptp_fun_C_0(relation_composition(A!11, B!12)))))) | (~(tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(206,plain,
% 0.19/0.47 (~(tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[205, 94])).
% 0.19/0.47 tff(207,plain,
% 0.19/0.47 (((~![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(A!11)) | (~function(A!11)) | (~((~((~one_to_one(A!11)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C)))))) | (~(one_to_one(A!11) | (~((tptp_fun_B_1(A!11) = tptp_fun_C_0(A!11)) | (~in(tptp_fun_B_1(A!11), relation_dom(A!11))) | (~in(tptp_fun_C_0(A!11), relation_dom(A!11))) | (~(apply(A!11, tptp_fun_B_1(A!11)) = apply(A!11, tptp_fun_C_0(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(A!11)) | (~function(A!11)) | (~((~((~one_to_one(A!11)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C)))))) | (~(one_to_one(A!11) | (~((tptp_fun_B_1(A!11) = tptp_fun_C_0(A!11)) | (~in(tptp_fun_B_1(A!11), relation_dom(A!11))) | (~in(tptp_fun_C_0(A!11), relation_dom(A!11))) | (~(apply(A!11, tptp_fun_B_1(A!11)) = apply(A!11, tptp_fun_C_0(A!11)))))))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(208,plain,
% 0.19/0.47 ((~![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(A!11)) | (~function(A!11)) | (~((~((~one_to_one(A!11)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C)))))) | (~(one_to_one(A!11) | (~((tptp_fun_B_1(A!11) = tptp_fun_C_0(A!11)) | (~in(tptp_fun_B_1(A!11), relation_dom(A!11))) | (~in(tptp_fun_C_0(A!11), relation_dom(A!11))) | (~(apply(A!11, tptp_fun_B_1(A!11)) = apply(A!11, tptp_fun_C_0(A!11)))))))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(209,plain,
% 0.19/0.47 ((~![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(A!11)) | (~function(A!11)) | (~((~((~one_to_one(A!11)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C)))))) | (~(one_to_one(A!11) | (~((tptp_fun_B_1(A!11) = tptp_fun_C_0(A!11)) | (~in(tptp_fun_B_1(A!11), relation_dom(A!11))) | (~in(tptp_fun_C_0(A!11), relation_dom(A!11))) | (~(apply(A!11, tptp_fun_B_1(A!11)) = apply(A!11, tptp_fun_C_0(A!11))))))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.19/0.47 tff(210,plain,
% 0.19/0.47 (~((~((~one_to_one(A!11)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C)))))) | (~(one_to_one(A!11) | (~((tptp_fun_B_1(A!11) = tptp_fun_C_0(A!11)) | (~in(tptp_fun_B_1(A!11), relation_dom(A!11))) | (~in(tptp_fun_C_0(A!11), relation_dom(A!11))) | (~(apply(A!11, tptp_fun_B_1(A!11)) = apply(A!11, tptp_fun_C_0(A!11)))))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[209, 83, 20, 42])).
% 0.19/0.47 tff(211,plain,
% 0.19/0.47 (((~((~one_to_one(A!11)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C)))))) | (~(one_to_one(A!11) | (~((tptp_fun_B_1(A!11) = tptp_fun_C_0(A!11)) | (~in(tptp_fun_B_1(A!11), relation_dom(A!11))) | (~in(tptp_fun_C_0(A!11), relation_dom(A!11))) | (~(apply(A!11, tptp_fun_B_1(A!11)) = apply(A!11, tptp_fun_C_0(A!11))))))))) | ((~one_to_one(A!11)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C)))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(212,plain,
% 0.19/0.47 ((~one_to_one(A!11)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[211, 210])).
% 0.19/0.47 tff(213,plain,
% 0.19/0.47 (one_to_one(A!11)),
% 0.19/0.47 inference(and_elim,[status(thm)],[189])).
% 0.19/0.47 tff(214,plain,
% 0.19/0.47 ((~((~one_to_one(A!11)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C)))))) | (~one_to_one(A!11)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(215,plain,
% 0.19/0.47 ((~((~one_to_one(A!11)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C)))))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[214, 213])).
% 0.19/0.47 tff(216,plain,
% 0.19/0.47 (![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[215, 212])).
% 0.19/0.47 tff(217,plain,
% 0.19/0.47 (((~![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C))))) | ((tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))))) <=> ((~![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C))))) | (tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(218,plain,
% 0.19/0.47 (((tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))))) <=> ((tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(219,plain,
% 0.19/0.47 (((~![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C))))) | ((tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))))) <=> ((~![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C))))) | ((tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[218])).
% 0.19/0.47 tff(220,plain,
% 0.19/0.47 (((~![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C))))) | ((tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))))) <=> ((~![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C))))) | (tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[219, 217])).
% 0.19/0.47 tff(221,plain,
% 0.19/0.47 ((~![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C))))) | ((tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(222,plain,
% 0.19/0.48 ((~![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A!11))) | (~in(C, relation_dom(A!11))) | (~(apply(A!11, B) = apply(A!11, C))))) | (tptp_fun_B_1(relation_composition(A!11, B!12)) = tptp_fun_C_0(relation_composition(A!11, B!12))) | (~in(tptp_fun_C_0(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~in(tptp_fun_B_1(relation_composition(A!11, B!12)), relation_dom(A!11))) | (~(apply(A!11, tptp_fun_B_1(relation_composition(A!11, B!12))) = apply(A!11, tptp_fun_C_0(relation_composition(A!11, B!12)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.19/0.48 tff(223,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[222, 216, 206, 204, 202, 200])).
% 0.19/0.48 % SZS output end Proof
%------------------------------------------------------------------------------