TSTP Solution File: SEU028+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU028+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 07:27:20 EDT 2022
% Result : Theorem 1.81s 1.44s
% Output : Proof 1.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU028+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 09:11:48 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 1.81/1.44 % SZS status Theorem
% 1.81/1.44 % SZS output start Proof
% 1.81/1.44 tff(tptp_fun_C_11_type, type, (
% 1.81/1.44 tptp_fun_C_11: ( $i * $i ) > $i)).
% 1.81/1.44 tff(relation_dom_type, type, (
% 1.81/1.44 relation_dom: $i > $i)).
% 1.81/1.44 tff(tptp_fun_A_12_type, type, (
% 1.81/1.44 tptp_fun_A_12: $i)).
% 1.81/1.44 tff(relation_composition_type, type, (
% 1.81/1.44 relation_composition: ( $i * $i ) > $i)).
% 1.81/1.44 tff(function_inverse_type, type, (
% 1.81/1.44 function_inverse: $i > $i)).
% 1.81/1.44 tff(apply_type, type, (
% 1.81/1.44 apply: ( $i * $i ) > $i)).
% 1.81/1.44 tff(in_type, type, (
% 1.81/1.44 in: ( $i * $i ) > $o)).
% 1.81/1.44 tff(identity_relation_type, type, (
% 1.81/1.44 identity_relation: $i > $i)).
% 1.81/1.44 tff(function_type, type, (
% 1.81/1.44 function: $i > $o)).
% 1.81/1.44 tff(relation_type, type, (
% 1.81/1.44 relation: $i > $o)).
% 1.81/1.44 tff(one_to_one_type, type, (
% 1.81/1.44 one_to_one: $i > $o)).
% 1.81/1.44 tff(relation_rng_type, type, (
% 1.81/1.44 relation_rng: $i > $i)).
% 1.81/1.44 tff(1,plain,
% 1.81/1.44 ((~(((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) & (relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12)))) | (~(relation(A!12) & function(A!12))) | (~one_to_one(A!12)))) <=> (~(((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) & (relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12)))) | (~(relation(A!12) & function(A!12))) | (~one_to_one(A!12))))),
% 1.81/1.44 inference(rewrite,[status(thm)],[])).
% 1.81/1.44 tff(2,plain,
% 1.81/1.44 ((~![A: $i] : (((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))) <=> (~![A: $i] : (((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A))))),
% 1.81/1.44 inference(rewrite,[status(thm)],[])).
% 1.81/1.44 tff(3,plain,
% 1.81/1.44 ((~![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => ((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A))))))) <=> (~![A: $i] : (((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A))))),
% 1.81/1.44 inference(rewrite,[status(thm)],[])).
% 1.81/1.44 tff(4,axiom,(~![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => ((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t61_funct_1')).
% 1.81/1.44 tff(5,plain,
% 1.81/1.44 (~![A: $i] : (((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 1.81/1.44 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.81/1.44 tff(6,plain,
% 1.81/1.44 (~![A: $i] : (((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 1.81/1.44 inference(modus_ponens,[status(thm)],[5, 2])).
% 1.81/1.44 tff(7,plain,
% 1.81/1.44 (~![A: $i] : (((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 1.81/1.44 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.81/1.44 tff(8,plain,
% 1.81/1.44 (~![A: $i] : (((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 1.81/1.44 inference(modus_ponens,[status(thm)],[7, 2])).
% 1.81/1.44 tff(9,plain,
% 1.81/1.44 (~![A: $i] : (((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 1.81/1.44 inference(modus_ponens,[status(thm)],[8, 2])).
% 1.81/1.44 tff(10,plain,
% 1.81/1.44 (~![A: $i] : (((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 1.81/1.44 inference(modus_ponens,[status(thm)],[9, 2])).
% 1.81/1.44 tff(11,plain,
% 1.81/1.44 (~![A: $i] : (((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 1.81/1.44 inference(modus_ponens,[status(thm)],[10, 2])).
% 1.81/1.44 tff(12,plain,(
% 1.81/1.44 ~(((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) & (relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12)))) | (~(relation(A!12) & function(A!12))) | (~one_to_one(A!12)))),
% 1.81/1.44 inference(skolemize,[status(sab)],[11])).
% 1.81/1.44 tff(13,plain,
% 1.81/1.44 (~(((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) & (relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12)))) | (~(relation(A!12) & function(A!12))) | (~one_to_one(A!12)))),
% 1.81/1.44 inference(modus_ponens,[status(thm)],[12, 1])).
% 1.81/1.44 tff(14,plain,
% 1.81/1.44 (relation(A!12) & function(A!12)),
% 1.81/1.44 inference(or_elim,[status(thm)],[13])).
% 1.81/1.44 tff(15,plain,
% 1.81/1.44 (function(A!12)),
% 1.81/1.44 inference(and_elim,[status(thm)],[14])).
% 1.81/1.44 tff(16,plain,
% 1.81/1.44 (relation(A!12)),
% 1.81/1.44 inference(and_elim,[status(thm)],[14])).
% 1.81/1.44 tff(17,plain,
% 1.81/1.44 (^[A: $i] : refl(((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))) <=> ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))))),
% 1.81/1.44 inference(bind,[status(th)],[])).
% 1.81/1.44 tff(18,plain,
% 1.81/1.44 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 1.81/1.44 inference(quant_intro,[status(thm)],[17])).
% 1.81/1.44 tff(19,plain,
% 1.81/1.44 (^[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))))), rewrite((relation(function_inverse(A)) & function(function_inverse(A))) <=> (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))), (((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A)))) <=> (((~relation(A)) | (~function(A))) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))))), rewrite((((~relation(A)) | (~function(A))) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))) <=> ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))), (((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A)))) <=> ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))))),
% 1.81/1.44 inference(bind,[status(th)],[])).
% 1.81/1.44 tff(20,plain,
% 1.81/1.44 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A)))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 1.81/1.44 inference(quant_intro,[status(thm)],[19])).
% 1.81/1.44 tff(21,plain,
% 1.81/1.44 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A)))) <=> ![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 1.81/1.44 inference(rewrite,[status(thm)],[])).
% 1.81/1.44 tff(22,plain,
% 1.81/1.44 (^[A: $i] : rewrite(((relation(A) & function(A)) => (relation(function_inverse(A)) & function(function_inverse(A)))) <=> ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A)))))),
% 1.81/1.44 inference(bind,[status(th)],[])).
% 1.81/1.44 tff(23,plain,
% 1.81/1.44 (![A: $i] : ((relation(A) & function(A)) => (relation(function_inverse(A)) & function(function_inverse(A)))) <=> ![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 1.81/1.44 inference(quant_intro,[status(thm)],[22])).
% 1.81/1.44 tff(24,axiom,(![A: $i] : ((relation(A) & function(A)) => (relation(function_inverse(A)) & function(function_inverse(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k2_funct_1')).
% 1.81/1.44 tff(25,plain,
% 1.81/1.44 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 1.81/1.44 inference(modus_ponens,[status(thm)],[24, 23])).
% 1.81/1.44 tff(26,plain,
% 1.81/1.44 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 1.81/1.44 inference(modus_ponens,[status(thm)],[25, 21])).
% 1.81/1.44 tff(27,plain,(
% 1.81/1.44 ![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 1.81/1.44 inference(skolemize,[status(sab)],[26])).
% 1.81/1.44 tff(28,plain,
% 1.81/1.44 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 1.81/1.44 inference(modus_ponens,[status(thm)],[27, 20])).
% 1.81/1.44 tff(29,plain,
% 1.81/1.44 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 1.81/1.44 inference(modus_ponens,[status(thm)],[28, 18])).
% 1.81/1.44 tff(30,plain,
% 1.81/1.44 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~relation(A!12)) | (~function(A!12)) | (~((~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | (~relation(A!12)) | (~function(A!12)) | (~((~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))))))),
% 1.81/1.44 inference(rewrite,[status(thm)],[])).
% 1.81/1.44 tff(31,plain,
% 1.81/1.44 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~relation(A!12)) | (~function(A!12)) | (~((~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))))))),
% 1.81/1.44 inference(quant_inst,[status(thm)],[])).
% 1.81/1.44 tff(32,plain,
% 1.81/1.44 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | (~relation(A!12)) | (~function(A!12)) | (~((~relation(function_inverse(A!12))) | (~function(function_inverse(A!12)))))),
% 1.81/1.44 inference(modus_ponens,[status(thm)],[31, 30])).
% 1.81/1.44 tff(33,plain,
% 1.81/1.44 (~((~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))))),
% 1.81/1.44 inference(unit_resolution,[status(thm)],[32, 29, 16, 15])).
% 1.81/1.44 tff(34,plain,
% 1.81/1.44 (((~relation(function_inverse(A!12))) | (~function(function_inverse(A!12)))) | relation(function_inverse(A!12))),
% 1.81/1.44 inference(tautology,[status(thm)],[])).
% 1.81/1.44 tff(35,plain,
% 1.81/1.44 (relation(function_inverse(A!12))),
% 1.81/1.44 inference(unit_resolution,[status(thm)],[34, 33])).
% 1.81/1.44 tff(36,plain,
% 1.81/1.44 (((~relation(function_inverse(A!12))) | (~function(function_inverse(A!12)))) | function(function_inverse(A!12))),
% 1.81/1.44 inference(tautology,[status(thm)],[])).
% 1.81/1.44 tff(37,plain,
% 1.81/1.44 (function(function_inverse(A!12))),
% 1.81/1.44 inference(unit_resolution,[status(thm)],[36, 33])).
% 1.81/1.44 tff(38,plain,
% 1.81/1.44 (^[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)))))))),
% 1.81/1.44 inference(bind,[status(th)],[])).
% 1.81/1.44 tff(39,plain,
% 1.81/1.44 (![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))))))),
% 1.81/1.44 inference(quant_intro,[status(thm)],[38])).
% 1.81/1.44 tff(40,plain,
% 1.81/1.44 (^[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))))))))),
% 1.81/1.44 inference(bind,[status(th)],[])).
% 1.81/1.44 tff(41,plain,
% 1.81/1.44 (![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))))))),
% 1.81/1.44 inference(quant_intro,[status(thm)],[40])).
% 1.81/1.44 tff(42,plain,
% 1.81/1.44 (![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))))),
% 1.81/1.44 inference(rewrite,[status(thm)],[])).
% 1.81/1.44 tff(43,plain,
% 1.81/1.44 (^[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))))))),
% 1.81/1.44 inference(bind,[status(th)],[])).
% 1.81/1.44 tff(44,plain,
% 1.81/1.44 (![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))))),
% 1.81/1.44 inference(quant_intro,[status(thm)],[43])).
% 1.81/1.44 tff(45,axiom,(![A: $i, B: $i] : ((((relation(A) & function(A)) & relation(B)) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_funct_1')).
% 1.81/1.44 tff(46,plain,
% 1.81/1.44 (![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 1.81/1.44 inference(modus_ponens,[status(thm)],[45, 44])).
% 1.81/1.44 tff(47,plain,
% 1.81/1.44 (![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 1.81/1.44 inference(modus_ponens,[status(thm)],[46, 42])).
% 1.81/1.44 tff(48,plain,(
% 1.81/1.44 ![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 1.81/1.44 inference(skolemize,[status(sab)],[47])).
% 1.81/1.44 tff(49,plain,
% 1.81/1.44 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))),
% 1.81/1.44 inference(modus_ponens,[status(thm)],[48, 41])).
% 1.81/1.44 tff(50,plain,
% 1.81/1.44 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))),
% 1.81/1.44 inference(modus_ponens,[status(thm)],[49, 39])).
% 1.81/1.44 tff(51,plain,
% 1.81/1.44 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(A!12)) | (~function(A!12)) | (~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!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!12)) | (~function(A!12)) | (~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12)))))))),
% 1.81/1.44 inference(rewrite,[status(thm)],[])).
% 1.81/1.44 tff(52,plain,
% 1.81/1.44 (((~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~relation(A!12)) | (~function(A!12)) | (~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12))))))) <=> ((~relation(A!12)) | (~function(A!12)) | (~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12)))))))),
% 1.81/1.44 inference(rewrite,[status(thm)],[])).
% 1.81/1.44 tff(53,plain,
% 1.81/1.44 ((~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12)))))) <=> (~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12))))))),
% 1.81/1.44 inference(rewrite,[status(thm)],[])).
% 1.81/1.44 tff(54,plain,
% 1.81/1.44 (((~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~relation(A!12)) | (~function(A!12)) | (~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12))))))) <=> ((~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~relation(A!12)) | (~function(A!12)) | (~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12)))))))),
% 1.81/1.44 inference(monotonicity,[status(thm)],[53])).
% 1.81/1.44 tff(55,plain,
% 1.81/1.44 (((~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~relation(A!12)) | (~function(A!12)) | (~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12))))))) <=> ((~relation(A!12)) | (~function(A!12)) | (~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12)))))))),
% 1.81/1.44 inference(transitivity,[status(thm)],[54, 52])).
% 1.81/1.44 tff(56,plain,
% 1.81/1.44 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~relation(A!12)) | (~function(A!12)) | (~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!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!12)) | (~function(A!12)) | (~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12))))))))),
% 1.81/1.44 inference(monotonicity,[status(thm)],[55])).
% 1.81/1.44 tff(57,plain,
% 1.81/1.44 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~relation(A!12)) | (~function(A!12)) | (~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!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!12)) | (~function(A!12)) | (~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12)))))))),
% 1.81/1.44 inference(transitivity,[status(thm)],[56, 51])).
% 1.81/1.44 tff(58,plain,
% 1.81/1.44 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~relation(A!12)) | (~function(A!12)) | (~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12)))))))),
% 1.81/1.44 inference(quant_inst,[status(thm)],[])).
% 1.81/1.44 tff(59,plain,
% 1.81/1.44 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | (~relation(A!12)) | (~function(A!12)) | (~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12))))))),
% 1.81/1.44 inference(modus_ponens,[status(thm)],[58, 57])).
% 1.81/1.44 tff(60,plain,
% 1.81/1.44 ((~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12))))))),
% 1.81/1.45 inference(unit_resolution,[status(thm)],[59, 50, 16, 15])).
% 1.81/1.45 tff(61,plain,
% 1.81/1.45 (~((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12)))))),
% 1.81/1.45 inference(unit_resolution,[status(thm)],[60, 37, 35])).
% 1.81/1.45 tff(62,plain,
% 1.81/1.45 (((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12))))) | function(relation_composition(A!12, function_inverse(A!12)))),
% 1.81/1.45 inference(tautology,[status(thm)],[])).
% 1.81/1.45 tff(63,plain,
% 1.81/1.45 (function(relation_composition(A!12, function_inverse(A!12)))),
% 1.81/1.45 inference(unit_resolution,[status(thm)],[62, 61])).
% 1.81/1.45 tff(64,plain,
% 1.81/1.45 (^[A: $i, B: $i] : refl((relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A))) <=> (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A))))),
% 1.81/1.45 inference(bind,[status(th)],[])).
% 1.81/1.45 tff(65,plain,
% 1.81/1.45 (![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)))),
% 1.81/1.45 inference(quant_intro,[status(thm)],[64])).
% 1.81/1.45 tff(66,plain,
% 1.81/1.45 (^[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)))))),
% 1.81/1.45 inference(bind,[status(th)],[])).
% 1.81/1.45 tff(67,plain,
% 1.81/1.45 (![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)))),
% 1.81/1.45 inference(quant_intro,[status(thm)],[66])).
% 1.81/1.45 tff(68,plain,
% 1.81/1.45 (![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))))),
% 1.81/1.45 inference(rewrite,[status(thm)],[])).
% 1.81/1.45 tff(69,plain,
% 1.81/1.45 (^[A: $i, B: $i] : rewrite(((relation(A) & relation(B)) => relation(relation_composition(A, B))) <=> (relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))))),
% 1.81/1.45 inference(bind,[status(th)],[])).
% 1.81/1.45 tff(70,plain,
% 1.81/1.45 (![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))))),
% 1.81/1.45 inference(quant_intro,[status(thm)],[69])).
% 1.81/1.45 tff(71,axiom,(![A: $i, B: $i] : ((relation(A) & relation(B)) => relation(relation_composition(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k5_relat_1')).
% 1.81/1.45 tff(72,plain,
% 1.81/1.45 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 1.81/1.45 inference(modus_ponens,[status(thm)],[71, 70])).
% 1.81/1.45 tff(73,plain,
% 1.81/1.45 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 1.81/1.45 inference(modus_ponens,[status(thm)],[72, 68])).
% 1.81/1.45 tff(74,plain,(
% 1.81/1.45 ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 1.81/1.45 inference(skolemize,[status(sab)],[73])).
% 1.81/1.45 tff(75,plain,
% 1.81/1.45 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))),
% 1.81/1.45 inference(modus_ponens,[status(thm)],[74, 67])).
% 1.81/1.45 tff(76,plain,
% 1.81/1.45 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))),
% 1.81/1.45 inference(modus_ponens,[status(thm)],[75, 65])).
% 1.81/1.45 tff(77,plain,
% 1.81/1.45 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | ((~relation(A!12)) | relation(relation_composition(A!12, function_inverse(A!12))) | (~relation(function_inverse(A!12))))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (~relation(A!12)) | relation(relation_composition(A!12, function_inverse(A!12))) | (~relation(function_inverse(A!12))))),
% 1.81/1.45 inference(rewrite,[status(thm)],[])).
% 1.81/1.45 tff(78,plain,
% 1.81/1.45 ((relation(relation_composition(A!12, function_inverse(A!12))) | (~relation(function_inverse(A!12))) | (~relation(A!12))) <=> ((~relation(A!12)) | relation(relation_composition(A!12, function_inverse(A!12))) | (~relation(function_inverse(A!12))))),
% 1.81/1.45 inference(rewrite,[status(thm)],[])).
% 1.81/1.45 tff(79,plain,
% 1.81/1.45 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (relation(relation_composition(A!12, function_inverse(A!12))) | (~relation(function_inverse(A!12))) | (~relation(A!12)))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | ((~relation(A!12)) | relation(relation_composition(A!12, function_inverse(A!12))) | (~relation(function_inverse(A!12)))))),
% 1.81/1.45 inference(monotonicity,[status(thm)],[78])).
% 1.81/1.45 tff(80,plain,
% 1.81/1.45 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (relation(relation_composition(A!12, function_inverse(A!12))) | (~relation(function_inverse(A!12))) | (~relation(A!12)))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (~relation(A!12)) | relation(relation_composition(A!12, function_inverse(A!12))) | (~relation(function_inverse(A!12))))),
% 1.81/1.45 inference(transitivity,[status(thm)],[79, 77])).
% 1.81/1.45 tff(81,plain,
% 1.81/1.45 ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (relation(relation_composition(A!12, function_inverse(A!12))) | (~relation(function_inverse(A!12))) | (~relation(A!12)))),
% 1.81/1.45 inference(quant_inst,[status(thm)],[])).
% 1.81/1.45 tff(82,plain,
% 1.81/1.45 ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (~relation(A!12)) | relation(relation_composition(A!12, function_inverse(A!12))) | (~relation(function_inverse(A!12)))),
% 1.81/1.45 inference(modus_ponens,[status(thm)],[81, 80])).
% 1.81/1.45 tff(83,plain,
% 1.81/1.45 (relation(relation_composition(A!12, function_inverse(A!12))) | (~relation(function_inverse(A!12)))),
% 1.81/1.45 inference(unit_resolution,[status(thm)],[82, 76, 16])).
% 1.81/1.45 tff(84,plain,
% 1.81/1.45 (relation(relation_composition(A!12, function_inverse(A!12)))),
% 1.81/1.45 inference(unit_resolution,[status(thm)],[83, 35])).
% 1.81/1.45 tff(85,plain,
% 1.81/1.45 (^[A: $i, B: $i] : trans(monotonicity(rewrite((~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))) <=> (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))))))), (((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))))))))), rewrite(((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))), (((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))))),
% 1.81/1.45 inference(bind,[status(th)],[])).
% 1.81/1.45 tff(86,plain,
% 1.81/1.45 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))),
% 1.81/1.45 inference(quant_intro,[status(thm)],[85])).
% 1.81/1.45 tff(87,plain,
% 1.81/1.45 (^[A: $i, B: $i] : refl(((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))))),
% 1.81/1.45 inference(bind,[status(th)],[])).
% 1.81/1.45 tff(88,plain,
% 1.81/1.45 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))))),
% 1.81/1.45 inference(quant_intro,[status(thm)],[87])).
% 1.81/1.45 tff(89,plain,
% 1.81/1.45 (^[A: $i, B: $i] : rewrite(((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))))),
% 1.95/1.45 inference(bind,[status(th)],[])).
% 1.95/1.45 tff(90,plain,
% 1.95/1.45 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))))),
% 1.95/1.45 inference(quant_intro,[status(thm)],[89])).
% 1.95/1.45 tff(91,plain,
% 1.95/1.45 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))))),
% 1.95/1.45 inference(transitivity,[status(thm)],[90, 88])).
% 1.95/1.45 tff(92,plain,
% 1.95/1.45 (^[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))))), trans(monotonicity(rewrite(((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) <=> ((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))), rewrite(((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))) <=> ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))), ((((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) <=> (((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))), rewrite((((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) <=> (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))), ((((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) <=> (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))))), (((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))) <=> (((~relation(B)) | (~function(B))) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))))), rewrite((((~relation(B)) | (~function(B))) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))))), (((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))))))),
% 1.95/1.45 inference(bind,[status(th)],[])).
% 1.95/1.45 tff(93,plain,
% 1.95/1.45 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))))),
% 1.95/1.45 inference(quant_intro,[status(thm)],[92])).
% 1.95/1.45 tff(94,plain,
% 1.95/1.45 (^[A: $i, B: $i] : rewrite(((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | ((~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))) <=> ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))),
% 1.95/1.45 inference(bind,[status(th)],[])).
% 1.95/1.45 tff(95,plain,
% 1.95/1.45 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | ((~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))),
% 1.95/1.45 inference(quant_intro,[status(thm)],[94])).
% 1.95/1.45 tff(96,plain,
% 1.95/1.45 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))),
% 1.95/1.45 inference(rewrite,[status(thm)],[])).
% 1.95/1.45 tff(97,plain,
% 1.95/1.45 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C)))) <=> ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))), (((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C))))) <=> ((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))), rewrite(((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))) <=> ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))), (((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C))))) <=> ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))))),
% 1.95/1.45 inference(bind,[status(th)],[])).
% 1.95/1.45 tff(98,plain,
% 1.95/1.45 (![A: $i, B: $i] : ((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))),
% 1.95/1.45 inference(quant_intro,[status(thm)],[97])).
% 1.95/1.45 tff(99,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t34_funct_1')).
% 1.95/1.45 tff(100,plain,
% 1.95/1.45 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))),
% 1.95/1.45 inference(modus_ponens,[status(thm)],[99, 98])).
% 1.95/1.45 tff(101,plain,
% 1.95/1.45 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))),
% 1.95/1.45 inference(modus_ponens,[status(thm)],[100, 96])).
% 1.95/1.45 tff(102,plain,(
% 1.95/1.45 ![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | ((~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))),
% 1.95/1.45 inference(skolemize,[status(sab)],[101])).
% 1.95/1.45 tff(103,plain,
% 1.95/1.45 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))),
% 1.95/1.45 inference(modus_ponens,[status(thm)],[102, 95])).
% 1.95/1.45 tff(104,plain,
% 1.95/1.45 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))))),
% 1.95/1.45 inference(modus_ponens,[status(thm)],[103, 93])).
% 1.95/1.45 tff(105,plain,
% 1.95/1.45 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))))),
% 1.95/1.46 inference(modus_ponens,[status(thm)],[104, 91])).
% 1.95/1.46 tff(106,plain,
% 1.95/1.46 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))),
% 1.95/1.46 inference(modus_ponens,[status(thm)],[105, 86])).
% 1.95/1.46 tff(107,plain,
% 1.95/1.46 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12)))) | (~((~((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) | (~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))) | (~((~(relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12)))) | (~((~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~![C: $i] : ((~in(C, relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), C) = C))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12)))) | (~((~((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) | (~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))) | (~((~(relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12)))) | (~((~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~![C: $i] : ((~in(C, relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), C) = C))))))))))),
% 1.95/1.46 inference(rewrite,[status(thm)],[])).
% 1.95/1.46 tff(108,plain,
% 1.95/1.46 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12)))) | (~((~((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) | (~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))) | (~((~(relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12)))) | (~((~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~![C: $i] : ((~in(C, relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), C) = C))))))))))),
% 1.95/1.46 inference(quant_inst,[status(thm)],[])).
% 1.95/1.46 tff(109,plain,
% 1.95/1.46 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~relation(relation_composition(A!12, function_inverse(A!12)))) | (~function(relation_composition(A!12, function_inverse(A!12)))) | (~((~((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) | (~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))) | (~((~(relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12)))) | (~((~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~![C: $i] : ((~in(C, relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), C) = C)))))))))),
% 1.95/1.46 inference(modus_ponens,[status(thm)],[108, 107])).
% 1.95/1.46 tff(110,plain,
% 1.95/1.46 (~((~((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) | (~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))) | (~((~(relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12)))) | (~((~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~![C: $i] : ((~in(C, relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), C) = C))))))))),
% 1.95/1.46 inference(unit_resolution,[status(thm)],[109, 106, 84, 63])).
% 1.95/1.46 tff(111,plain,
% 1.95/1.46 (((~((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) | (~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))) | (~((~(relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12)))) | (~((~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~![C: $i] : ((~in(C, relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), C) = C)))))))) | ((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) | (~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))),
% 1.95/1.46 inference(tautology,[status(thm)],[])).
% 1.95/1.46 tff(112,plain,
% 1.95/1.46 ((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) | (~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))),
% 1.95/1.46 inference(unit_resolution,[status(thm)],[111, 110])).
% 1.95/1.46 tff(113,plain,
% 1.95/1.46 (one_to_one(A!12)),
% 1.95/1.46 inference(or_elim,[status(thm)],[13])).
% 1.95/1.46 tff(114,plain,
% 1.95/1.46 (^[A: $i] : refl(((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A)))))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A)))))))),
% 1.95/1.46 inference(bind,[status(th)],[])).
% 1.95/1.46 tff(115,plain,
% 1.95/1.46 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A)))))) <=> ![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))))),
% 1.95/1.46 inference(quant_intro,[status(thm)],[114])).
% 1.95/1.46 tff(116,plain,
% 1.95/1.46 (^[A: $i] : trans(monotonicity(rewrite(((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))) <=> (~((~(relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A)))))), 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))))), ((((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ((~((~(relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))) | ((~relation(A)) | (~function(A))) | (~one_to_one(A))))), rewrite(((~((~(relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))) | ((~relation(A)) | (~function(A))) | (~one_to_one(A))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))))), ((((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))))))),
% 1.95/1.46 inference(bind,[status(th)],[])).
% 1.95/1.46 tff(117,plain,
% 1.95/1.46 (![A: $i] : (((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))))),
% 1.95/1.46 inference(quant_intro,[status(thm)],[116])).
% 1.95/1.46 tff(118,plain,
% 1.95/1.46 (![A: $i] : (((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ![A: $i] : (((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 1.95/1.46 inference(rewrite,[status(thm)],[])).
% 1.95/1.46 tff(119,plain,
% 1.95/1.46 (^[A: $i] : trans(monotonicity(rewrite((one_to_one(A) => ((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A)))) <=> ((~one_to_one(A)) | ((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))), (((relation(A) & function(A)) => (one_to_one(A) => ((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))) <=> ((relation(A) & function(A)) => ((~one_to_one(A)) | ((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))))), rewrite(((relation(A) & function(A)) => ((~one_to_one(A)) | ((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))) <=> (((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))), (((relation(A) & function(A)) => (one_to_one(A) => ((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))) <=> (((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))))),
% 1.95/1.46 inference(bind,[status(th)],[])).
% 1.95/1.46 tff(120,plain,
% 1.95/1.46 (![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => ((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))) <=> ![A: $i] : (((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 1.95/1.46 inference(quant_intro,[status(thm)],[119])).
% 1.95/1.46 tff(121,axiom,(![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => ((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t58_funct_1')).
% 1.95/1.46 tff(122,plain,
% 1.95/1.46 (![A: $i] : (((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 1.95/1.46 inference(modus_ponens,[status(thm)],[121, 120])).
% 1.95/1.46 tff(123,plain,
% 1.95/1.46 (![A: $i] : (((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 1.95/1.46 inference(modus_ponens,[status(thm)],[122, 118])).
% 1.95/1.46 tff(124,plain,(
% 1.95/1.46 ![A: $i] : (((relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A)) & (relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 1.95/1.46 inference(skolemize,[status(sab)],[123])).
% 1.95/1.46 tff(125,plain,
% 1.95/1.46 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))))),
% 1.95/1.46 inference(modus_ponens,[status(thm)],[124, 117])).
% 1.95/1.46 tff(126,plain,
% 1.95/1.46 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))))),
% 1.95/1.46 inference(modus_ponens,[status(thm)],[125, 115])).
% 1.95/1.46 tff(127,plain,
% 1.95/1.46 (((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))))) | ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~(relation_rng(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))))))) <=> ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))))) | (~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~(relation_rng(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))))))),
% 1.95/1.46 inference(rewrite,[status(thm)],[])).
% 1.95/1.46 tff(128,plain,
% 1.95/1.46 ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))))) | ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~(relation_rng(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))))))),
% 1.95/1.46 inference(quant_inst,[status(thm)],[])).
% 1.95/1.46 tff(129,plain,
% 1.95/1.46 ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(A, function_inverse(A))) = relation_dom(A))) | (~(relation_rng(relation_composition(A, function_inverse(A))) = relation_dom(A))))))) | (~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~(relation_rng(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12)))))),
% 1.95/1.46 inference(modus_ponens,[status(thm)],[128, 127])).
% 1.95/1.46 tff(130,plain,
% 1.95/1.46 (~((~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~(relation_rng(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))))),
% 1.95/1.46 inference(unit_resolution,[status(thm)],[129, 126, 16, 15, 113])).
% 1.95/1.46 tff(131,plain,
% 1.95/1.46 (((~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~(relation_rng(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12)))) | (relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))),
% 1.95/1.46 inference(tautology,[status(thm)],[])).
% 1.95/1.47 tff(132,plain,
% 1.95/1.47 (relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12)),
% 1.95/1.47 inference(unit_resolution,[status(thm)],[131, 130])).
% 1.95/1.47 tff(133,assumption,((~((relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))) | (~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))) | (~((~(relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12)))) | (~((~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~![C: $i] : ((~in(C, relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), C) = C)))))))), introduced(assumption)).
% 1.95/1.47 tff(134,plain,
% 1.95/1.47 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(A!12)) | (~function(A!12)) | (~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~((~relation(relation_composition(function_inverse(A!12), A!12))) | (~function(relation_composition(function_inverse(A!12), A!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!12)) | (~function(A!12)) | (~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~((~relation(relation_composition(function_inverse(A!12), A!12))) | (~function(relation_composition(function_inverse(A!12), A!12))))))),
% 1.95/1.47 inference(rewrite,[status(thm)],[])).
% 1.95/1.47 tff(135,plain,
% 1.95/1.47 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(A!12)) | (~function(A!12)) | (~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~((~relation(relation_composition(function_inverse(A!12), A!12))) | (~function(relation_composition(function_inverse(A!12), A!12))))))),
% 1.95/1.47 inference(quant_inst,[status(thm)],[])).
% 1.95/1.47 tff(136,plain,
% 1.95/1.47 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | (~relation(A!12)) | (~function(A!12)) | (~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~((~relation(relation_composition(function_inverse(A!12), A!12))) | (~function(relation_composition(function_inverse(A!12), A!12)))))),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[135, 134])).
% 1.95/1.47 tff(137,plain,
% 1.95/1.47 ((~relation(function_inverse(A!12))) | (~function(function_inverse(A!12))) | (~((~relation(relation_composition(function_inverse(A!12), A!12))) | (~function(relation_composition(function_inverse(A!12), A!12)))))),
% 1.95/1.47 inference(unit_resolution,[status(thm)],[136, 50, 16, 15])).
% 1.95/1.47 tff(138,plain,
% 1.95/1.47 (~((~relation(relation_composition(function_inverse(A!12), A!12))) | (~function(relation_composition(function_inverse(A!12), A!12))))),
% 1.95/1.47 inference(unit_resolution,[status(thm)],[137, 37, 35])).
% 1.95/1.47 tff(139,plain,
% 1.95/1.47 (((~relation(relation_composition(function_inverse(A!12), A!12))) | (~function(relation_composition(function_inverse(A!12), A!12)))) | function(relation_composition(function_inverse(A!12), A!12))),
% 1.95/1.47 inference(tautology,[status(thm)],[])).
% 1.95/1.47 tff(140,plain,
% 1.95/1.47 (function(relation_composition(function_inverse(A!12), A!12))),
% 1.95/1.47 inference(unit_resolution,[status(thm)],[139, 138])).
% 1.95/1.47 tff(141,plain,
% 1.95/1.47 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | ((~relation(A!12)) | relation(relation_composition(function_inverse(A!12), A!12)) | (~relation(function_inverse(A!12))))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (~relation(A!12)) | relation(relation_composition(function_inverse(A!12), A!12)) | (~relation(function_inverse(A!12))))),
% 1.95/1.47 inference(rewrite,[status(thm)],[])).
% 1.95/1.47 tff(142,plain,
% 1.95/1.47 ((relation(relation_composition(function_inverse(A!12), A!12)) | (~relation(A!12)) | (~relation(function_inverse(A!12)))) <=> ((~relation(A!12)) | relation(relation_composition(function_inverse(A!12), A!12)) | (~relation(function_inverse(A!12))))),
% 1.95/1.47 inference(rewrite,[status(thm)],[])).
% 1.95/1.47 tff(143,plain,
% 1.95/1.47 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (relation(relation_composition(function_inverse(A!12), A!12)) | (~relation(A!12)) | (~relation(function_inverse(A!12))))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | ((~relation(A!12)) | relation(relation_composition(function_inverse(A!12), A!12)) | (~relation(function_inverse(A!12)))))),
% 1.95/1.47 inference(monotonicity,[status(thm)],[142])).
% 1.95/1.47 tff(144,plain,
% 1.95/1.47 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (relation(relation_composition(function_inverse(A!12), A!12)) | (~relation(A!12)) | (~relation(function_inverse(A!12))))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (~relation(A!12)) | relation(relation_composition(function_inverse(A!12), A!12)) | (~relation(function_inverse(A!12))))),
% 1.95/1.47 inference(transitivity,[status(thm)],[143, 141])).
% 1.95/1.47 tff(145,plain,
% 1.95/1.47 ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (relation(relation_composition(function_inverse(A!12), A!12)) | (~relation(A!12)) | (~relation(function_inverse(A!12))))),
% 1.95/1.47 inference(quant_inst,[status(thm)],[])).
% 1.95/1.47 tff(146,plain,
% 1.95/1.47 ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (~relation(A!12)) | relation(relation_composition(function_inverse(A!12), A!12)) | (~relation(function_inverse(A!12)))),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[145, 144])).
% 1.95/1.47 tff(147,plain,
% 1.95/1.47 (relation(relation_composition(function_inverse(A!12), A!12)) | (~relation(function_inverse(A!12)))),
% 1.95/1.47 inference(unit_resolution,[status(thm)],[146, 76, 16])).
% 1.95/1.47 tff(148,plain,
% 1.95/1.47 (relation(relation_composition(function_inverse(A!12), A!12))),
% 1.95/1.47 inference(unit_resolution,[status(thm)],[147, 35])).
% 1.95/1.47 tff(149,plain,
% 1.95/1.47 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(relation_composition(function_inverse(A!12), A!12))) | (~function(relation_composition(function_inverse(A!12), A!12))) | (~((~((relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))) | (~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))) | (~((~(relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12)))) | (~((~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~![C: $i] : ((~in(C, relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), C) = C))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~relation(relation_composition(function_inverse(A!12), A!12))) | (~function(relation_composition(function_inverse(A!12), A!12))) | (~((~((relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))) | (~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))) | (~((~(relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12)))) | (~((~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~![C: $i] : ((~in(C, relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), C) = C))))))))))),
% 1.95/1.47 inference(rewrite,[status(thm)],[])).
% 1.95/1.47 tff(150,plain,
% 1.95/1.47 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(relation_composition(function_inverse(A!12), A!12))) | (~function(relation_composition(function_inverse(A!12), A!12))) | (~((~((relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))) | (~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))) | (~((~(relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12)))) | (~((~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~![C: $i] : ((~in(C, relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), C) = C))))))))))),
% 1.95/1.47 inference(quant_inst,[status(thm)],[])).
% 1.95/1.47 tff(151,plain,
% 1.95/1.47 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~relation(relation_composition(function_inverse(A!12), A!12))) | (~function(relation_composition(function_inverse(A!12), A!12))) | (~((~((relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))) | (~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))) | (~((~(relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12)))) | (~((~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~![C: $i] : ((~in(C, relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), C) = C)))))))))),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[150, 149])).
% 1.95/1.47 tff(152,plain,
% 1.95/1.48 ($false),
% 1.95/1.48 inference(unit_resolution,[status(thm)],[151, 106, 148, 140, 133])).
% 1.95/1.48 tff(153,plain,(~((~((relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))) | (~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))) | (~((~(relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12)))) | (~((~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~![C: $i] : ((~in(C, relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), C) = C))))))))), inference(lemma,lemma(discharge,[]))).
% 1.95/1.48 tff(154,plain,
% 1.95/1.48 (((~((relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))) | (~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))) | (~((~(relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12)))) | (~((~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~![C: $i] : ((~in(C, relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), C) = C)))))))) | ((relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))) | (~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))),
% 1.95/1.48 inference(tautology,[status(thm)],[])).
% 1.95/1.48 tff(155,plain,
% 1.95/1.48 ((relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))) | (~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))),
% 1.95/1.48 inference(unit_resolution,[status(thm)],[154, 153])).
% 1.95/1.48 tff(156,assumption,(~((~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))), introduced(assumption)).
% 1.95/1.48 tff(157,plain,
% 1.95/1.48 (((~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))) | in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))),
% 1.95/1.48 inference(tautology,[status(thm)],[])).
% 1.95/1.48 tff(158,plain,
% 1.95/1.48 (in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))),
% 1.95/1.48 inference(unit_resolution,[status(thm)],[157, 156])).
% 1.95/1.48 tff(159,plain,
% 1.95/1.48 (^[A: $i, B: $i] : refl(((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B)))) <=> ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B)))))),
% 1.95/1.48 inference(bind,[status(th)],[])).
% 1.95/1.48 tff(160,plain,
% 1.95/1.48 (![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B)))) <=> ![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))),
% 1.95/1.48 inference(quant_intro,[status(thm)],[159])).
% 1.95/1.48 tff(161,plain,
% 1.95/1.48 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) <=> (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A)))))), trans(monotonicity(rewrite((relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B))))), ((~(relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B))))))), rewrite((~(~((~relation(B)) | (~function(B))))) <=> ((~relation(B)) | (~function(B)))), ((~(relation(B) & function(B))) <=> ((~relation(B)) | (~function(B))))), trans(monotonicity(rewrite((one_to_one(B) & in(A, relation_rng(B))) <=> (~((~one_to_one(B)) | (~in(A, relation_rng(B)))))), ((~(one_to_one(B) & in(A, relation_rng(B)))) <=> (~(~((~one_to_one(B)) | (~in(A, relation_rng(B)))))))), rewrite((~(~((~one_to_one(B)) | (~in(A, relation_rng(B)))))) <=> ((~one_to_one(B)) | (~in(A, relation_rng(B))))), ((~(one_to_one(B) & in(A, relation_rng(B)))) <=> ((~one_to_one(B)) | (~in(A, relation_rng(B)))))), ((((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B))))) <=> ((~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | ((~relation(B)) | (~function(B))) | ((~one_to_one(B)) | (~in(A, relation_rng(B))))))), rewrite(((~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | ((~relation(B)) | (~function(B))) | ((~one_to_one(B)) | (~in(A, relation_rng(B))))) <=> ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))), ((((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B))))) <=> ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))))),
% 1.95/1.48 inference(bind,[status(th)],[])).
% 1.95/1.48 tff(162,plain,
% 1.95/1.48 (![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B))))) <=> ![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))),
% 1.95/1.48 inference(quant_intro,[status(thm)],[161])).
% 1.95/1.48 tff(163,plain,
% 1.95/1.48 (![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B))))) <=> ![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))),
% 1.95/1.48 inference(rewrite,[status(thm)],[])).
% 1.95/1.48 tff(164,plain,
% 1.95/1.48 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((one_to_one(B) & in(A, relation_rng(B))) => ((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A)))) <=> ((~(one_to_one(B) & in(A, relation_rng(B)))) | ((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))))), (((relation(B) & function(B)) => ((one_to_one(B) & in(A, relation_rng(B))) => ((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))))) <=> ((relation(B) & function(B)) => ((~(one_to_one(B) & in(A, relation_rng(B)))) | ((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))))))), rewrite(((relation(B) & function(B)) => ((~(one_to_one(B) & in(A, relation_rng(B)))) | ((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))))) <=> (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))), (((relation(B) & function(B)) => ((one_to_one(B) & in(A, relation_rng(B))) => ((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))))) <=> (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))))),
% 1.95/1.48 inference(bind,[status(th)],[])).
% 1.95/1.48 tff(165,plain,
% 1.95/1.48 (![A: $i, B: $i] : ((relation(B) & function(B)) => ((one_to_one(B) & in(A, relation_rng(B))) => ((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))))) <=> ![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))),
% 1.95/1.48 inference(quant_intro,[status(thm)],[164])).
% 1.95/1.48 tff(166,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => ((one_to_one(B) & in(A, relation_rng(B))) => ((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t57_funct_1')).
% 1.95/1.48 tff(167,plain,
% 1.95/1.48 (![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))),
% 1.95/1.48 inference(modus_ponens,[status(thm)],[166, 165])).
% 1.95/1.48 tff(168,plain,
% 1.95/1.48 (![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))),
% 1.95/1.48 inference(modus_ponens,[status(thm)],[167, 163])).
% 1.95/1.48 tff(169,plain,(
% 1.95/1.48 ![A: $i, B: $i] : (((A = apply(B, apply(function_inverse(B), A))) & (A = apply(relation_composition(function_inverse(B), B), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_rng(B)))))),
% 1.95/1.48 inference(skolemize,[status(sab)],[168])).
% 1.95/1.48 tff(170,plain,
% 1.95/1.48 (![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))),
% 1.95/1.48 inference(modus_ponens,[status(thm)],[169, 162])).
% 1.95/1.48 tff(171,plain,
% 1.95/1.48 (![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))),
% 1.95/1.48 inference(modus_ponens,[status(thm)],[170, 160])).
% 1.95/1.48 tff(172,plain,
% 1.95/1.48 (((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))) | ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (~((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))))) <=> ((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))) | (~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (~((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))))),
% 1.95/1.48 inference(rewrite,[status(thm)],[])).
% 1.95/1.48 tff(173,plain,
% 1.95/1.48 (((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))) | (~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12)))) <=> ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (~((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))))),
% 1.95/1.48 inference(rewrite,[status(thm)],[])).
% 1.95/1.48 tff(174,plain,
% 1.95/1.48 ((~((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))) <=> (~((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))))),
% 1.95/1.48 inference(rewrite,[status(thm)],[])).
% 1.95/1.48 tff(175,plain,
% 1.95/1.48 (((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))) | (~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12)))) <=> ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))) | (~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))))),
% 1.95/1.48 inference(monotonicity,[status(thm)],[174])).
% 1.95/1.48 tff(176,plain,
% 1.95/1.48 (((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))) | (~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12)))) <=> ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (~((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))))),
% 1.95/1.48 inference(transitivity,[status(thm)],[175, 173])).
% 1.95/1.48 tff(177,plain,
% 1.95/1.48 (((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))) | ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))) | (~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))))) <=> ((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))) | ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (~((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))))))),
% 1.95/1.49 inference(monotonicity,[status(thm)],[176])).
% 1.95/1.49 tff(178,plain,
% 1.95/1.49 (((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))) | ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))) | (~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))))) <=> ((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))) | (~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (~((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))))),
% 1.95/1.49 inference(transitivity,[status(thm)],[177, 172])).
% 1.95/1.49 tff(179,plain,
% 1.95/1.49 ((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))) | ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))) | (~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))))),
% 1.95/1.49 inference(quant_inst,[status(thm)],[])).
% 1.95/1.49 tff(180,plain,
% 1.95/1.49 ((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(B, apply(function_inverse(B), A)))) | (~(A = apply(relation_composition(function_inverse(B), B), A))))) | (~in(A, relation_rng(B))))) | (~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (~((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))))),
% 1.95/1.49 inference(modus_ponens,[status(thm)],[179, 178])).
% 1.95/1.49 tff(181,plain,
% 1.95/1.49 (~((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))),
% 1.95/1.49 inference(unit_resolution,[status(thm)],[180, 171, 16, 15, 113, 158])).
% 1.95/1.49 tff(182,plain,
% 1.95/1.49 (((~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(A!12, apply(function_inverse(A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (~(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))) | (tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))),
% 1.95/1.49 inference(tautology,[status(thm)],[])).
% 1.95/1.49 tff(183,plain,
% 1.95/1.49 (tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)) = apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))),
% 1.95/1.49 inference(unit_resolution,[status(thm)],[182, 181])).
% 1.95/1.49 tff(184,plain,
% 1.95/1.49 (apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))),
% 1.95/1.49 inference(symmetry,[status(thm)],[183])).
% 1.95/1.49 tff(185,plain,
% 1.95/1.49 (((~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))) | (~(apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))),
% 1.95/1.49 inference(tautology,[status(thm)],[])).
% 1.95/1.49 tff(186,plain,
% 1.95/1.49 (~(apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))),
% 1.95/1.49 inference(unit_resolution,[status(thm)],[185, 156])).
% 1.95/1.49 tff(187,plain,
% 1.95/1.49 ($false),
% 1.95/1.49 inference(unit_resolution,[status(thm)],[186, 184])).
% 1.95/1.49 tff(188,plain,((~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))), inference(lemma,lemma(discharge,[]))).
% 1.95/1.49 tff(189,plain,
% 1.95/1.49 (^[A: $i] : refl(((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A)))))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A)))))))),
% 1.95/1.49 inference(bind,[status(th)],[])).
% 1.95/1.49 tff(190,plain,
% 1.95/1.49 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A)))))) <=> ![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))))),
% 1.95/1.49 inference(quant_intro,[status(thm)],[189])).
% 1.95/1.49 tff(191,plain,
% 1.95/1.49 (^[A: $i] : trans(monotonicity(rewrite(((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))) <=> (~((~(relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A)))))), 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))))), ((((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ((~((~(relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))) | ((~relation(A)) | (~function(A))) | (~one_to_one(A))))), rewrite(((~((~(relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))) | ((~relation(A)) | (~function(A))) | (~one_to_one(A))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))))), ((((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))))))),
% 1.95/1.49 inference(bind,[status(th)],[])).
% 1.95/1.49 tff(192,plain,
% 1.95/1.49 (![A: $i] : (((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))))),
% 1.95/1.49 inference(quant_intro,[status(thm)],[191])).
% 1.95/1.49 tff(193,plain,
% 1.95/1.49 (![A: $i] : (((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ![A: $i] : (((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 1.95/1.49 inference(rewrite,[status(thm)],[])).
% 1.95/1.49 tff(194,plain,
% 1.95/1.49 (^[A: $i] : trans(monotonicity(rewrite((one_to_one(A) => ((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A)))) <=> ((~one_to_one(A)) | ((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))), (((relation(A) & function(A)) => (one_to_one(A) => ((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))) <=> ((relation(A) & function(A)) => ((~one_to_one(A)) | ((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))))), rewrite(((relation(A) & function(A)) => ((~one_to_one(A)) | ((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))) <=> (((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))), (((relation(A) & function(A)) => (one_to_one(A) => ((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))) <=> (((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))))),
% 1.95/1.49 inference(bind,[status(th)],[])).
% 1.95/1.49 tff(195,plain,
% 1.95/1.49 (![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => ((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))) <=> ![A: $i] : (((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 1.95/1.49 inference(quant_intro,[status(thm)],[194])).
% 1.95/1.49 tff(196,axiom,(![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => ((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t59_funct_1')).
% 1.95/1.49 tff(197,plain,
% 1.95/1.49 (![A: $i] : (((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 1.95/1.49 inference(modus_ponens,[status(thm)],[196, 195])).
% 1.95/1.49 tff(198,plain,
% 1.95/1.49 (![A: $i] : (((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 1.95/1.49 inference(modus_ponens,[status(thm)],[197, 193])).
% 1.95/1.49 tff(199,plain,(
% 1.95/1.49 ![A: $i] : (((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 1.95/1.49 inference(skolemize,[status(sab)],[198])).
% 1.95/1.49 tff(200,plain,
% 1.95/1.49 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))))),
% 1.95/1.49 inference(modus_ponens,[status(thm)],[199, 192])).
% 1.95/1.49 tff(201,plain,
% 1.95/1.49 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))))),
% 1.95/1.49 inference(modus_ponens,[status(thm)],[200, 190])).
% 1.95/1.49 tff(202,plain,
% 1.95/1.49 (((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))))) | ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~(relation_rng(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))))))) <=> ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))))) | (~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~(relation_rng(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))))))),
% 1.95/1.49 inference(rewrite,[status(thm)],[])).
% 1.95/1.49 tff(203,plain,
% 1.95/1.49 ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))))) | ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~(relation_rng(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))))))),
% 1.95/1.49 inference(quant_inst,[status(thm)],[])).
% 1.95/1.49 tff(204,plain,
% 1.95/1.49 ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))))))) | (~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~(relation_rng(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12)))))),
% 1.95/1.49 inference(modus_ponens,[status(thm)],[203, 202])).
% 1.95/1.49 tff(205,plain,
% 1.95/1.49 (~((~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~(relation_rng(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))))),
% 1.95/1.49 inference(unit_resolution,[status(thm)],[204, 201, 16, 15, 113])).
% 1.95/1.49 tff(206,plain,
% 1.95/1.49 (((~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~(relation_rng(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12)))) | (relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))),
% 1.95/1.49 inference(tautology,[status(thm)],[])).
% 1.95/1.49 tff(207,plain,
% 1.95/1.49 (relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12)),
% 1.95/1.49 inference(unit_resolution,[status(thm)],[206, 205])).
% 1.95/1.49 tff(208,plain,
% 1.95/1.49 ((~((relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))) | (~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))) | (relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))) | (~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)))))),
% 1.95/1.49 inference(tautology,[status(thm)],[])).
% 1.95/1.49 tff(209,plain,
% 1.95/1.49 ((~((relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))) | (~(relation_dom(relation_composition(function_inverse(A!12), A!12)) = relation_rng(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12)), relation_rng(A!12))) | (apply(relation_composition(function_inverse(A!12), A!12), tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))) = tptp_fun_C_11(relation_composition(function_inverse(A!12), A!12), relation_rng(A!12))))))) | (relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12)))),
% 1.99/1.50 inference(unit_resolution,[status(thm)],[208, 207, 188])).
% 1.99/1.50 tff(210,plain,
% 1.99/1.50 (relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))),
% 1.99/1.50 inference(unit_resolution,[status(thm)],[209, 155])).
% 1.99/1.50 tff(211,plain,
% 1.99/1.50 ((~(~((~(relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12)))) | (~(relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))))))) <=> ((~(relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12)))) | (~(relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12)))))),
% 1.99/1.50 inference(rewrite,[status(thm)],[])).
% 1.99/1.50 tff(212,plain,
% 1.99/1.50 (((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) & (relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12)))) <=> (~((~(relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12)))) | (~(relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))))))),
% 1.99/1.50 inference(rewrite,[status(thm)],[])).
% 1.99/1.50 tff(213,plain,
% 1.99/1.50 ((~((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) & (relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))))) <=> (~(~((~(relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12)))) | (~(relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12)))))))),
% 1.99/1.50 inference(monotonicity,[status(thm)],[212])).
% 1.99/1.50 tff(214,plain,
% 1.99/1.50 ((~((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) & (relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))))) <=> ((~(relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12)))) | (~(relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12)))))),
% 1.99/1.50 inference(transitivity,[status(thm)],[213, 211])).
% 1.99/1.50 tff(215,plain,
% 1.99/1.50 (~((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) & (relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))))),
% 1.99/1.50 inference(or_elim,[status(thm)],[13])).
% 1.99/1.50 tff(216,plain,
% 1.99/1.50 ((~(relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12)))) | (~(relation_composition(function_inverse(A!12), A!12) = identity_relation(relation_rng(A!12))))),
% 1.99/1.50 inference(modus_ponens,[status(thm)],[215, 214])).
% 1.99/1.50 tff(217,plain,
% 1.99/1.50 (~(relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12)))),
% 1.99/1.50 inference(unit_resolution,[status(thm)],[216, 210])).
% 1.99/1.50 tff(218,plain,
% 1.99/1.50 ((~((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) | (~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))) | (relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) | (~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))),
% 1.99/1.50 inference(tautology,[status(thm)],[])).
% 1.99/1.50 tff(219,plain,
% 1.99/1.50 ((~((relation_composition(A!12, function_inverse(A!12)) = identity_relation(relation_dom(A!12))) | (~(relation_dom(relation_composition(A!12, function_inverse(A!12))) = relation_dom(A!12))) | (~((~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))) | (~((~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))),
% 1.99/1.50 inference(unit_resolution,[status(thm)],[218, 217, 132])).
% 1.99/1.50 tff(220,plain,
% 1.99/1.50 (~((~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))),
% 1.99/1.50 inference(unit_resolution,[status(thm)],[219, 112])).
% 1.99/1.50 tff(221,plain,
% 1.99/1.50 (((~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))) | in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))),
% 1.99/1.50 inference(tautology,[status(thm)],[])).
% 1.99/1.50 tff(222,plain,
% 1.99/1.50 (in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))),
% 1.99/1.50 inference(unit_resolution,[status(thm)],[221, 220])).
% 1.99/1.50 tff(223,plain,
% 1.99/1.50 (^[A: $i, B: $i] : refl(((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | (~in(A, relation_dom(B)))) <=> ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | (~in(A, relation_dom(B)))))),
% 1.99/1.50 inference(bind,[status(th)],[])).
% 1.99/1.50 tff(224,plain,
% 1.99/1.50 (![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | (~in(A, relation_dom(B)))) <=> ![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | (~in(A, relation_dom(B))))),
% 1.99/1.50 inference(quant_intro,[status(thm)],[223])).
% 1.99/1.50 tff(225,plain,
% 1.99/1.50 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))) <=> (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A)))))), trans(monotonicity(rewrite((relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B))))), ((~(relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B))))))), rewrite((~(~((~relation(B)) | (~function(B))))) <=> ((~relation(B)) | (~function(B)))), ((~(relation(B) & function(B))) <=> ((~relation(B)) | (~function(B))))), trans(monotonicity(rewrite((one_to_one(B) & in(A, relation_dom(B))) <=> (~((~one_to_one(B)) | (~in(A, relation_dom(B)))))), ((~(one_to_one(B) & in(A, relation_dom(B)))) <=> (~(~((~one_to_one(B)) | (~in(A, relation_dom(B)))))))), rewrite((~(~((~one_to_one(B)) | (~in(A, relation_dom(B)))))) <=> ((~one_to_one(B)) | (~in(A, relation_dom(B))))), ((~(one_to_one(B) & in(A, relation_dom(B)))) <=> ((~one_to_one(B)) | (~in(A, relation_dom(B)))))), ((((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_dom(B))))) <=> ((~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | ((~relation(B)) | (~function(B))) | ((~one_to_one(B)) | (~in(A, relation_dom(B))))))), rewrite(((~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | ((~relation(B)) | (~function(B))) | ((~one_to_one(B)) | (~in(A, relation_dom(B))))) <=> ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | (~in(A, relation_dom(B))))), ((((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_dom(B))))) <=> ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | (~in(A, relation_dom(B))))))),
% 1.99/1.50 inference(bind,[status(th)],[])).
% 1.99/1.50 tff(226,plain,
% 1.99/1.50 (![A: $i, B: $i] : (((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_dom(B))))) <=> ![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | (~in(A, relation_dom(B))))),
% 1.99/1.50 inference(quant_intro,[status(thm)],[225])).
% 1.99/1.50 tff(227,plain,
% 1.99/1.50 (![A: $i, B: $i] : (((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_dom(B))))) <=> ![A: $i, B: $i] : (((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_dom(B)))))),
% 1.99/1.50 inference(rewrite,[status(thm)],[])).
% 1.99/1.50 tff(228,plain,
% 1.99/1.50 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((one_to_one(B) & in(A, relation_dom(B))) => ((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A)))) <=> ((~(one_to_one(B) & in(A, relation_dom(B)))) | ((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))))), (((relation(B) & function(B)) => ((one_to_one(B) & in(A, relation_dom(B))) => ((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))))) <=> ((relation(B) & function(B)) => ((~(one_to_one(B) & in(A, relation_dom(B)))) | ((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))))))), rewrite(((relation(B) & function(B)) => ((~(one_to_one(B) & in(A, relation_dom(B)))) | ((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))))) <=> (((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_dom(B)))))), (((relation(B) & function(B)) => ((one_to_one(B) & in(A, relation_dom(B))) => ((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))))) <=> (((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_dom(B)))))))),
% 1.99/1.50 inference(bind,[status(th)],[])).
% 1.99/1.50 tff(229,plain,
% 1.99/1.50 (![A: $i, B: $i] : ((relation(B) & function(B)) => ((one_to_one(B) & in(A, relation_dom(B))) => ((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))))) <=> ![A: $i, B: $i] : (((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_dom(B)))))),
% 1.99/1.50 inference(quant_intro,[status(thm)],[228])).
% 1.99/1.50 tff(230,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => ((one_to_one(B) & in(A, relation_dom(B))) => ((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t56_funct_1')).
% 1.99/1.50 tff(231,plain,
% 1.99/1.50 (![A: $i, B: $i] : (((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_dom(B)))))),
% 1.99/1.50 inference(modus_ponens,[status(thm)],[230, 229])).
% 1.99/1.50 tff(232,plain,
% 1.99/1.50 (![A: $i, B: $i] : (((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_dom(B)))))),
% 1.99/1.50 inference(modus_ponens,[status(thm)],[231, 227])).
% 1.99/1.50 tff(233,plain,(
% 1.99/1.50 ![A: $i, B: $i] : (((A = apply(function_inverse(B), apply(B, A))) & (A = apply(relation_composition(B, function_inverse(B)), A))) | (~(relation(B) & function(B))) | (~(one_to_one(B) & in(A, relation_dom(B)))))),
% 1.99/1.50 inference(skolemize,[status(sab)],[232])).
% 1.99/1.50 tff(234,plain,
% 1.99/1.50 (![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | (~in(A, relation_dom(B))))),
% 1.99/1.50 inference(modus_ponens,[status(thm)],[233, 226])).
% 1.99/1.50 tff(235,plain,
% 1.99/1.50 (![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | (~in(A, relation_dom(B))))),
% 1.99/1.50 inference(modus_ponens,[status(thm)],[234, 224])).
% 1.99/1.50 tff(236,plain,
% 1.99/1.50 (((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | (~in(A, relation_dom(B))))) | ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (~((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))))) <=> ((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | (~in(A, relation_dom(B))))) | (~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (~((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))))),
% 1.99/1.50 inference(rewrite,[status(thm)],[])).
% 1.99/1.50 tff(237,plain,
% 1.99/1.50 (((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))) | (~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12)))) <=> ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (~((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))))),
% 1.99/1.50 inference(rewrite,[status(thm)],[])).
% 1.99/1.50 tff(238,plain,
% 1.99/1.50 ((~((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))) <=> (~((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))))),
% 1.99/1.50 inference(rewrite,[status(thm)],[])).
% 1.99/1.50 tff(239,plain,
% 1.99/1.50 (((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))) | (~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12)))) <=> ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))) | (~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))))),
% 1.99/1.50 inference(monotonicity,[status(thm)],[238])).
% 1.99/1.50 tff(240,plain,
% 1.99/1.51 (((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))) | (~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12)))) <=> ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (~((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))))),
% 1.99/1.51 inference(transitivity,[status(thm)],[239, 237])).
% 1.99/1.51 tff(241,plain,
% 1.99/1.51 (((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | (~in(A, relation_dom(B))))) | ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))) | (~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))))) <=> ((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | (~in(A, relation_dom(B))))) | ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (~((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))))))),
% 1.99/1.51 inference(monotonicity,[status(thm)],[240])).
% 1.99/1.51 tff(242,plain,
% 1.99/1.51 (((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | (~in(A, relation_dom(B))))) | ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))) | (~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))))) <=> ((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | (~in(A, relation_dom(B))))) | (~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (~((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))))),
% 1.99/1.51 inference(transitivity,[status(thm)],[241, 236])).
% 1.99/1.51 tff(243,plain,
% 1.99/1.51 ((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | (~in(A, relation_dom(B))))) | ((~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))) | (~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))))),
% 1.99/1.51 inference(quant_inst,[status(thm)],[])).
% 1.99/1.51 tff(244,plain,
% 1.99/1.51 ((~![A: $i, B: $i] : ((~one_to_one(B)) | (~relation(B)) | (~function(B)) | (~((~(A = apply(function_inverse(B), apply(B, A)))) | (~(A = apply(relation_composition(B, function_inverse(B)), A))))) | (~in(A, relation_dom(B))))) | (~one_to_one(A!12)) | (~relation(A!12)) | (~function(A!12)) | (~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (~((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))))),
% 1.99/1.51 inference(modus_ponens,[status(thm)],[243, 242])).
% 1.99/1.51 tff(245,plain,
% 1.99/1.51 (~((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))))),
% 1.99/1.51 inference(unit_resolution,[status(thm)],[244, 235, 16, 15, 113, 222])).
% 1.99/1.51 tff(246,plain,
% 1.99/1.51 (((~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(function_inverse(A!12), apply(A!12, tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (~(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))))) | (tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))),
% 1.99/1.52 inference(tautology,[status(thm)],[])).
% 1.99/1.52 tff(247,plain,
% 1.99/1.52 (tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)) = apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))),
% 1.99/1.52 inference(unit_resolution,[status(thm)],[246, 245])).
% 1.99/1.52 tff(248,plain,
% 1.99/1.52 (apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))),
% 1.99/1.52 inference(symmetry,[status(thm)],[247])).
% 1.99/1.52 tff(249,plain,
% 1.99/1.52 (((~in(tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)), relation_dom(A!12))) | (apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))) | (~(apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))))),
% 1.99/1.52 inference(tautology,[status(thm)],[])).
% 1.99/1.52 tff(250,plain,
% 1.99/1.52 (~(apply(relation_composition(A!12, function_inverse(A!12)), tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12))) = tptp_fun_C_11(relation_composition(A!12, function_inverse(A!12)), relation_dom(A!12)))),
% 1.99/1.52 inference(unit_resolution,[status(thm)],[249, 220])).
% 1.99/1.52 tff(251,plain,
% 1.99/1.52 ($false),
% 1.99/1.52 inference(unit_resolution,[status(thm)],[250, 248])).
% 1.99/1.52 % SZS output end Proof
%------------------------------------------------------------------------------