TSTP Solution File: SEU032+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU032+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 07:27:20 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU032+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n016.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Sep 3 09:26:07 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(tptp_fun_A_11_type, type, (
% 0.20/0.40 tptp_fun_A_11: $i)).
% 0.20/0.40 tff(function_inverse_type, type, (
% 0.20/0.40 function_inverse: $i > $i)).
% 0.20/0.40 tff(identity_relation_type, type, (
% 0.20/0.40 identity_relation: $i > $i)).
% 0.20/0.40 tff(relation_dom_type, type, (
% 0.20/0.40 relation_dom: $i > $i)).
% 0.20/0.40 tff(relation_composition_type, type, (
% 0.20/0.40 relation_composition: ( $i * $i ) > $i)).
% 0.20/0.40 tff(relation_rng_type, type, (
% 0.20/0.40 relation_rng: $i > $i)).
% 0.20/0.40 tff(one_to_one_type, type, (
% 0.20/0.40 one_to_one: $i > $o)).
% 0.20/0.40 tff(function_type, type, (
% 0.20/0.40 function: $i > $o)).
% 0.20/0.40 tff(relation_type, type, (
% 0.20/0.40 relation: $i > $o)).
% 0.20/0.40 tff(1,plain,
% 0.20/0.40 ((~((function_inverse(function_inverse(A!11)) = A!11) | (~(relation(A!11) & function(A!11))) | (~one_to_one(A!11)))) <=> (~((function_inverse(function_inverse(A!11)) = A!11) | (~(relation(A!11) & function(A!11))) | (~one_to_one(A!11))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 ((~![A: $i] : ((function_inverse(function_inverse(A)) = A) | (~(relation(A) & function(A))) | (~one_to_one(A)))) <=> (~![A: $i] : ((function_inverse(function_inverse(A)) = A) | (~(relation(A) & function(A))) | (~one_to_one(A))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 ((~![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => (function_inverse(function_inverse(A)) = A)))) <=> (~![A: $i] : ((function_inverse(function_inverse(A)) = A) | (~(relation(A) & function(A))) | (~one_to_one(A))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(4,axiom,(~![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => (function_inverse(function_inverse(A)) = A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t65_funct_1')).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (~![A: $i] : ((function_inverse(function_inverse(A)) = A) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 (~![A: $i] : ((function_inverse(function_inverse(A)) = A) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 (~![A: $i] : ((function_inverse(function_inverse(A)) = A) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (~![A: $i] : ((function_inverse(function_inverse(A)) = A) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (~![A: $i] : ((function_inverse(function_inverse(A)) = A) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (~![A: $i] : ((function_inverse(function_inverse(A)) = A) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (~![A: $i] : ((function_inverse(function_inverse(A)) = A) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.20/0.40 tff(12,plain,(
% 0.20/0.40 ~((function_inverse(function_inverse(A!11)) = A!11) | (~(relation(A!11) & function(A!11))) | (~one_to_one(A!11)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[11])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (~((function_inverse(function_inverse(A!11)) = A!11) | (~(relation(A!11) & function(A!11))) | (~one_to_one(A!11)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[12, 1])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (one_to_one(A!11)),
% 0.20/0.40 inference(or_elim,[status(thm)],[13])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (relation(A!11) & function(A!11)),
% 0.20/0.40 inference(or_elim,[status(thm)],[13])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (function(A!11)),
% 0.20/0.40 inference(and_elim,[status(thm)],[15])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (relation(A!11)),
% 0.20/0.40 inference(and_elim,[status(thm)],[15])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (^[A: $i] : refl(((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A))))))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A))))))) <=> ![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 (^[A: $i] : trans(monotonicity(rewrite(((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) <=> (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(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_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ((~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))) | ((~relation(A)) | (~function(A))) | (~one_to_one(A))))), rewrite(((~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))) | ((~relation(A)) | (~function(A))) | (~one_to_one(A))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))), ((((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 (![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[20])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 (^[A: $i] : trans(monotonicity(rewrite((one_to_one(A) => ((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A))))) <=> ((~one_to_one(A)) | ((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))))), (((relation(A) & function(A)) => (one_to_one(A) => ((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))))) <=> ((relation(A) & function(A)) => ((~one_to_one(A)) | ((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))))))), rewrite(((relation(A) & function(A)) => ((~one_to_one(A)) | ((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))))) <=> (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))), (((relation(A) & function(A)) => (one_to_one(A) => ((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))))) <=> (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 (![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => ((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))))) <=> ![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[23])).
% 0.20/0.41 tff(25,axiom,(![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => ((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t55_funct_1')).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 (![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 (![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.20/0.41 tff(28,plain,(
% 0.20/0.41 ![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[27])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[29, 19])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 (((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))) | ((~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)) | (~((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11)))))))) <=> ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))) | (~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)) | (~((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11)))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))) | ((~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)) | (~((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11)))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))) | (~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)) | (~((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 (~((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11)))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[33, 30, 17, 16, 14])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11))))) | (relation_rng(A!11) = relation_dom(function_inverse(A!11)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 (relation_rng(A!11) = relation_dom(function_inverse(A!11))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 (identity_relation(relation_rng(A!11)) = identity_relation(relation_dom(function_inverse(A!11)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[36])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (^[A: $i] : refl(((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A))))))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(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] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 (^[A: $i] : trans(monotonicity(rewrite(((relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A))) & (relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))) <=> (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(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_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))) <=> ((~((~(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))))), rewrite(((~((~(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))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))), ((((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))) <=> ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 (![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] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[40])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 (^[A: $i] : trans(monotonicity(rewrite((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))))) <=> ((~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)))))), (((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)))))) <=> ((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)))))))), rewrite(((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)))))) <=> (((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)))), (((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)))))) <=> (((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)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[43])).
% 0.20/0.41 tff(45,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')).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.20/0.41 tff(48,plain,(
% 0.20/0.41 ![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)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[47])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 (![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[49, 39])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))) | ((~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)) | (~((~(relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11)))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_rng(A!11)))))))) <=> ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))) | (~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)) | (~((~(relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11)))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_rng(A!11)))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))) | ((~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)) | (~((~(relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11)))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_rng(A!11)))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 ((~![A: $i] : ((~one_to_one(A)) | (~relation(A)) | (~function(A)) | (~((~(relation_composition(A, function_inverse(A)) = identity_relation(relation_dom(A)))) | (~(relation_composition(function_inverse(A), A) = identity_relation(relation_rng(A)))))))) | (~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)) | (~((~(relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11)))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_rng(A!11))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 (~((~(relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11)))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_rng(A!11)))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[53, 50, 17, 16, 14])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 (((~(relation_composition(A!11, function_inverse(A!11)) = identity_relation(relation_dom(A!11)))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_rng(A!11))))) | (relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_rng(A!11)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(56,plain,
% 0.20/0.41 (relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_rng(A!11))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 (relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(function_inverse(A!11)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[56, 37])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 (((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11))))) | (relation_dom(A!11) = relation_rng(function_inverse(A!11)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 (relation_dom(A!11) = relation_rng(function_inverse(A!11))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[58, 34])).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 (relation_rng(function_inverse(A!11)) = relation_dom(A!11)),
% 0.20/0.41 inference(symmetry,[status(thm)],[59])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 (^[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)))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 (![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))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[61])).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & function(A)) <=> (~((~relation(A)) | (~function(A))))), ((~(relation(A) & function(A))) <=> (~(~((~relation(A)) | (~function(A))))))), rewrite((~(~((~relation(A)) | (~function(A))))) <=> ((~relation(A)) | (~function(A)))), ((~(relation(A) & function(A))) <=> ((~relation(A)) | (~function(A))))), 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))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(64,plain,
% 0.20/0.41 (![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))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[63])).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 (![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))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 (^[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)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 (![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))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[66])).
% 0.20/0.41 tff(68,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')).
% 0.20/0.41 tff(69,plain,
% 0.20/0.41 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.20/0.41 tff(71,plain,(
% 0.20/0.41 ![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[70])).
% 0.20/0.41 tff(72,plain,
% 0.20/0.41 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.20/0.41 tff(73,plain,
% 0.20/0.41 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[72, 62])).
% 0.20/0.41 tff(74,plain,
% 0.20/0.41 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~relation(A!11)) | (~function(A!11)) | (~((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | (~relation(A!11)) | (~function(A!11)) | (~((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(75,plain,
% 0.20/0.41 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | ((~relation(A!11)) | (~function(A!11)) | (~((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(76,plain,
% 0.20/0.41 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))) | (~relation(A!11)) | (~function(A!11)) | (~((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.20/0.41 tff(77,plain,
% 0.20/0.41 (~((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[76, 73, 17, 16])).
% 0.20/0.41 tff(78,plain,
% 0.20/0.41 (((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11)))) | relation(function_inverse(A!11))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(79,plain,
% 0.20/0.41 (relation(function_inverse(A!11))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.20/0.41 tff(80,plain,
% 0.20/0.41 (((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11)))) | function(function_inverse(A!11))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(81,plain,
% 0.20/0.41 (function(function_inverse(A!11))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[80, 77])).
% 0.20/0.41 tff(82,plain,
% 0.20/0.41 (^[A: $i] : refl(((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A)))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A)))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(83,plain,
% 0.20/0.41 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A)))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[82])).
% 0.20/0.41 tff(84,plain,
% 0.20/0.41 (^[A: $i] : rewrite(((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A)))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A)))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(85,plain,
% 0.20/0.41 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A)))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[84])).
% 0.20/0.41 tff(86,plain,
% 0.20/0.41 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A)))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[85, 83])).
% 0.20/0.41 tff(87,plain,
% 0.20/0.41 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & function(A)) <=> (~((~relation(A)) | (~function(A))))), ((~(relation(A) & function(A))) <=> (~(~((~relation(A)) | (~function(A))))))), rewrite((~(~((~relation(A)) | (~function(A))))) <=> ((~relation(A)) | (~function(A)))), ((~(relation(A) & function(A))) <=> ((~relation(A)) | (~function(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B))))), ((~(relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B))))))), rewrite((~(~((~relation(B)) | (~function(B))))) <=> ((~relation(B)) | (~function(B)))), ((~(relation(B) & function(B))) <=> ((~relation(B)) | (~function(B))))), trans(monotonicity(rewrite((one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))) <=> (~((~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))), ((~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A))))) <=> (~(~((~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))))), rewrite((~(~((~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))) <=> ((~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A)))))), ((~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A))))) <=> ((~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))), (((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))))) <=> ((B = function_inverse(A)) | ((~relation(B)) | (~function(B))) | ((~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A)))))))), rewrite(((B = function_inverse(A)) | ((~relation(B)) | (~function(B))) | ((~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A)))))) <=> ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A)))))), (((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))))) <=> ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A)))))))), (![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))))) <=> ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))), (((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A))))))) <=> (((~relation(A)) | (~function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A)))))))), rewrite((((~relation(A)) | (~function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A)))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))), (((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(88,plain,
% 0.20/0.41 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[87])).
% 0.20/0.41 tff(89,plain,
% 0.20/0.41 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A))))))) <=> ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(90,plain,
% 0.20/0.41 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((one_to_one(A) & (relation_rng(A) = relation_dom(B))) & (relation_composition(A, B) = identity_relation(relation_dom(A)))) <=> (one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A))))), ((((one_to_one(A) & (relation_rng(A) = relation_dom(B))) & (relation_composition(A, B) = identity_relation(relation_dom(A)))) => (B = function_inverse(A))) <=> ((one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))) => (B = function_inverse(A))))), rewrite(((one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))) => (B = function_inverse(A))) <=> ((~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A))))) | (B = function_inverse(A)))), ((((one_to_one(A) & (relation_rng(A) = relation_dom(B))) & (relation_composition(A, B) = identity_relation(relation_dom(A)))) => (B = function_inverse(A))) <=> ((~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A))))) | (B = function_inverse(A))))), (((relation(B) & function(B)) => (((one_to_one(A) & (relation_rng(A) = relation_dom(B))) & (relation_composition(A, B) = identity_relation(relation_dom(A)))) => (B = function_inverse(A)))) <=> ((relation(B) & function(B)) => ((~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A))))) | (B = function_inverse(A)))))), rewrite(((relation(B) & function(B)) => ((~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A))))) | (B = function_inverse(A)))) <=> ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A))))))), (((relation(B) & function(B)) => (((one_to_one(A) & (relation_rng(A) = relation_dom(B))) & (relation_composition(A, B) = identity_relation(relation_dom(A)))) => (B = function_inverse(A)))) <=> ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A))))))))), (![B: $i] : ((relation(B) & function(B)) => (((one_to_one(A) & (relation_rng(A) = relation_dom(B))) & (relation_composition(A, B) = identity_relation(relation_dom(A)))) => (B = function_inverse(A)))) <=> ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))))))), (((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => (((one_to_one(A) & (relation_rng(A) = relation_dom(B))) & (relation_composition(A, B) = identity_relation(relation_dom(A)))) => (B = function_inverse(A))))) <=> ((relation(A) & function(A)) => ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A))))))))), rewrite(((relation(A) & function(A)) => ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A))))))) <=> ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))))))), (((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => (((one_to_one(A) & (relation_rng(A) = relation_dom(B))) & (relation_composition(A, B) = identity_relation(relation_dom(A)))) => (B = function_inverse(A))))) <=> ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(91,plain,
% 0.20/0.42 (![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => (((one_to_one(A) & (relation_rng(A) = relation_dom(B))) & (relation_composition(A, B) = identity_relation(relation_dom(A)))) => (B = function_inverse(A))))) <=> ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[90])).
% 0.20/0.42 tff(92,axiom,(![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => (((one_to_one(A) & (relation_rng(A) = relation_dom(B))) & (relation_composition(A, B) = identity_relation(relation_dom(A)))) => (B = function_inverse(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t63_funct_1')).
% 0.20/0.42 tff(93,plain,
% 0.20/0.42 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.42 tff(94,plain,
% 0.20/0.42 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.20/0.42 tff(95,plain,(
% 0.20/0.42 ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = function_inverse(A)) | (~(relation(B) & function(B))) | (~(one_to_one(A) & (relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[94])).
% 0.20/0.42 tff(96,plain,
% 0.20/0.42 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.20/0.42 tff(97,plain,
% 0.20/0.42 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[96, 86])).
% 0.20/0.42 tff(98,plain,
% 0.20/0.42 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))) | ((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11)))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))) | (~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11)))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(99,plain,
% 0.20/0.42 (((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11))))))) <=> ((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11)))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(100,plain,
% 0.20/0.42 (^[B: $i] : rewrite(((B = function_inverse(function_inverse(A!11))) | (~relation(B)) | (~function(B)) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11)))))) <=> ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11)))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(101,plain,
% 0.20/0.42 (![B: $i] : ((B = function_inverse(function_inverse(A!11))) | (~relation(B)) | (~function(B)) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11)))))) <=> ![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[100])).
% 0.20/0.42 tff(102,plain,
% 0.20/0.42 (((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![B: $i] : ((B = function_inverse(function_inverse(A!11))) | (~relation(B)) | (~function(B)) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11))))))) <=> ((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11)))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[101])).
% 0.20/0.42 tff(103,plain,
% 0.20/0.42 (((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![B: $i] : ((B = function_inverse(function_inverse(A!11))) | (~relation(B)) | (~function(B)) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11))))))) <=> ((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11)))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[102, 99])).
% 0.20/0.42 tff(104,plain,
% 0.20/0.42 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))) | ((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![B: $i] : ((B = function_inverse(function_inverse(A!11))) | (~relation(B)) | (~function(B)) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11)))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))) | ((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11))))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[103])).
% 0.20/0.42 tff(105,plain,
% 0.20/0.42 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))) | ((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![B: $i] : ((B = function_inverse(function_inverse(A!11))) | (~relation(B)) | (~function(B)) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11)))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))) | (~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11)))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[104, 98])).
% 0.20/0.42 tff(106,plain,
% 0.20/0.42 ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))) | ((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![B: $i] : ((B = function_inverse(function_inverse(A!11))) | (~relation(B)) | (~function(B)) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11)))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(107,plain,
% 0.20/0.42 ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : ((B = function_inverse(A)) | (~relation(B)) | (~function(B)) | (~one_to_one(A)) | (~(relation_rng(A) = relation_dom(B))) | (~(relation_composition(A, B) = identity_relation(relation_dom(A))))))) | (~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.20/0.42 tff(108,plain,
% 0.20/0.42 ((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))) | ![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[107, 97])).
% 0.20/0.42 tff(109,plain,
% 0.20/0.42 (![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[108, 81, 79])).
% 0.20/0.42 tff(110,plain,
% 0.20/0.42 (^[A: $i] : refl((one_to_one(function_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A))) <=> (one_to_one(function_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(111,plain,
% 0.20/0.42 (![A: $i] : (one_to_one(function_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A))) <=> ![A: $i] : (one_to_one(function_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[110])).
% 0.20/0.42 tff(112,plain,
% 0.20/0.42 (^[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))))), ((one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> (one_to_one(function_inverse(A)) | ((~relation(A)) | (~function(A))) | (~one_to_one(A))))), rewrite((one_to_one(function_inverse(A)) | ((~relation(A)) | (~function(A))) | (~one_to_one(A))) <=> (one_to_one(function_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))), ((one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> (one_to_one(function_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(113,plain,
% 0.20/0.42 (![A: $i] : (one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ![A: $i] : (one_to_one(function_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[112])).
% 0.20/0.42 tff(114,plain,
% 0.20/0.42 (![A: $i] : (one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A))) <=> ![A: $i] : (one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(115,plain,
% 0.20/0.42 (^[A: $i] : trans(monotonicity(rewrite((one_to_one(A) => one_to_one(function_inverse(A))) <=> ((~one_to_one(A)) | one_to_one(function_inverse(A)))), (((relation(A) & function(A)) => (one_to_one(A) => one_to_one(function_inverse(A)))) <=> ((relation(A) & function(A)) => ((~one_to_one(A)) | one_to_one(function_inverse(A)))))), rewrite(((relation(A) & function(A)) => ((~one_to_one(A)) | one_to_one(function_inverse(A)))) <=> (one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A)))), (((relation(A) & function(A)) => (one_to_one(A) => one_to_one(function_inverse(A)))) <=> (one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(116,plain,
% 0.20/0.42 (![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => one_to_one(function_inverse(A)))) <=> ![A: $i] : (one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[115])).
% 0.20/0.42 tff(117,axiom,(![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => one_to_one(function_inverse(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t62_funct_1')).
% 0.20/0.42 tff(118,plain,
% 0.20/0.42 (![A: $i] : (one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.20/0.42 tff(119,plain,
% 0.20/0.42 (![A: $i] : (one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.20/0.42 tff(120,plain,(
% 0.20/0.42 ![A: $i] : (one_to_one(function_inverse(A)) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[119])).
% 0.20/0.42 tff(121,plain,
% 0.20/0.42 (![A: $i] : (one_to_one(function_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.20/0.42 tff(122,plain,
% 0.20/0.42 (![A: $i] : (one_to_one(function_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[121, 111])).
% 0.20/0.42 tff(123,plain,
% 0.20/0.42 (((~![A: $i] : (one_to_one(function_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))) | ((~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)) | one_to_one(function_inverse(A!11)))) <=> ((~![A: $i] : (one_to_one(function_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))) | (~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)) | one_to_one(function_inverse(A!11)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(124,plain,
% 0.20/0.42 ((one_to_one(function_inverse(A!11)) | (~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11))) <=> ((~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)) | one_to_one(function_inverse(A!11)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(125,plain,
% 0.20/0.42 (((~![A: $i] : (one_to_one(function_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))) | (one_to_one(function_inverse(A!11)) | (~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)))) <=> ((~![A: $i] : (one_to_one(function_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))) | ((~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)) | one_to_one(function_inverse(A!11))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[124])).
% 0.20/0.42 tff(126,plain,
% 0.20/0.42 (((~![A: $i] : (one_to_one(function_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))) | (one_to_one(function_inverse(A!11)) | (~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)))) <=> ((~![A: $i] : (one_to_one(function_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))) | (~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)) | one_to_one(function_inverse(A!11)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[125, 123])).
% 0.20/0.42 tff(127,plain,
% 0.20/0.42 ((~![A: $i] : (one_to_one(function_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))) | (one_to_one(function_inverse(A!11)) | (~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(128,plain,
% 0.20/0.42 ((~![A: $i] : (one_to_one(function_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))) | (~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)) | one_to_one(function_inverse(A!11))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.20/0.42 tff(129,plain,
% 0.20/0.42 (one_to_one(function_inverse(A!11))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[128, 122, 17, 16, 14])).
% 0.20/0.42 tff(130,plain,
% 0.20/0.42 (((~![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11))))))) | ((~relation(A!11)) | (~function(A!11)) | (~one_to_one(function_inverse(A!11))) | (A!11 = function_inverse(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(A!11))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(function_inverse(A!11))))))) <=> ((~![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11))))))) | (~relation(A!11)) | (~function(A!11)) | (~one_to_one(function_inverse(A!11))) | (A!11 = function_inverse(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(A!11))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(function_inverse(A!11))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(131,plain,
% 0.20/0.43 (((~relation(A!11)) | (~function(A!11)) | (A!11 = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(A!11))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(function_inverse(A!11)))))) <=> ((~relation(A!11)) | (~function(A!11)) | (~one_to_one(function_inverse(A!11))) | (A!11 = function_inverse(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(A!11))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(function_inverse(A!11))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(132,plain,
% 0.20/0.43 (((~![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11))))))) | ((~relation(A!11)) | (~function(A!11)) | (A!11 = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(A!11))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(function_inverse(A!11))))))) <=> ((~![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11))))))) | ((~relation(A!11)) | (~function(A!11)) | (~one_to_one(function_inverse(A!11))) | (A!11 = function_inverse(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(A!11))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(function_inverse(A!11)))))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[131])).
% 0.20/0.43 tff(133,plain,
% 0.20/0.43 (((~![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11))))))) | ((~relation(A!11)) | (~function(A!11)) | (A!11 = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(A!11))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(function_inverse(A!11))))))) <=> ((~![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11))))))) | (~relation(A!11)) | (~function(A!11)) | (~one_to_one(function_inverse(A!11))) | (A!11 = function_inverse(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(A!11))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(function_inverse(A!11))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[132, 130])).
% 0.20/0.43 tff(134,plain,
% 0.20/0.43 ((~![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11))))))) | ((~relation(A!11)) | (~function(A!11)) | (A!11 = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(A!11))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(function_inverse(A!11))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(135,plain,
% 0.20/0.43 ((~![B: $i] : ((~relation(B)) | (~function(B)) | (B = function_inverse(function_inverse(A!11))) | (~one_to_one(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(B))) | (~(relation_composition(function_inverse(A!11), B) = identity_relation(relation_dom(function_inverse(A!11))))))) | (~relation(A!11)) | (~function(A!11)) | (~one_to_one(function_inverse(A!11))) | (A!11 = function_inverse(function_inverse(A!11))) | (~(relation_rng(function_inverse(A!11)) = relation_dom(A!11))) | (~(relation_composition(function_inverse(A!11), A!11) = identity_relation(relation_dom(function_inverse(A!11)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.20/0.43 tff(136,plain,
% 0.20/0.43 (A!11 = function_inverse(function_inverse(A!11))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[135, 17, 16, 129, 109, 60, 57])).
% 0.20/0.43 tff(137,plain,
% 0.20/0.43 (function_inverse(function_inverse(A!11)) = A!11),
% 0.20/0.43 inference(symmetry,[status(thm)],[136])).
% 0.20/0.43 tff(138,plain,
% 0.20/0.43 (~(function_inverse(function_inverse(A!11)) = A!11)),
% 0.20/0.43 inference(or_elim,[status(thm)],[13])).
% 0.20/0.43 tff(139,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.20/0.43 % SZS output end Proof
%------------------------------------------------------------------------------