TSTP Solution File: SEU219+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU219+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 07:28:15 EDT 2022
% Result : Theorem 0.18s 0.40s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU219+3 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 10:31:14 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.18/0.34 Usage: tptp [options] [-file:]file
% 0.18/0.34 -h, -? prints this message.
% 0.18/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.18/0.34 -m, -model generate model.
% 0.18/0.34 -p, -proof generate proof.
% 0.18/0.34 -c, -core generate unsat core of named formulas.
% 0.18/0.34 -st, -statistics display statistics.
% 0.18/0.34 -t:timeout set timeout (in second).
% 0.18/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.18/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.18/0.34 -<param>:<value> configuration parameter and value.
% 0.18/0.34 -o:<output-file> file to place output in.
% 0.18/0.40 % SZS status Theorem
% 0.18/0.40 % SZS output start Proof
% 0.18/0.40 tff(relation_dom_type, type, (
% 0.18/0.40 relation_dom: $i > $i)).
% 0.18/0.40 tff(function_inverse_type, type, (
% 0.18/0.40 function_inverse: $i > $i)).
% 0.18/0.40 tff(tptp_fun_A_11_type, type, (
% 0.18/0.40 tptp_fun_A_11: $i)).
% 0.18/0.40 tff(relation_rng_type, type, (
% 0.18/0.40 relation_rng: $i > $i)).
% 0.18/0.40 tff(relation_inverse_type, type, (
% 0.18/0.40 relation_inverse: $i > $i)).
% 0.18/0.40 tff(function_type, type, (
% 0.18/0.40 function: $i > $o)).
% 0.18/0.40 tff(relation_type, type, (
% 0.18/0.40 relation: $i > $o)).
% 0.18/0.40 tff(one_to_one_type, type, (
% 0.18/0.40 one_to_one: $i > $o)).
% 0.18/0.40 tff(1,plain,
% 0.18/0.40 ((~(((relation_rng(A!11) = relation_dom(function_inverse(A!11))) & (relation_dom(A!11) = relation_rng(function_inverse(A!11)))) | (~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)))) | (~one_to_one(A!11)) | (~(relation(A!11) & function(A!11)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(2,plain,
% 0.18/0.40 ((~![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~one_to_one(A)) | (~(relation(A) & function(A))))) <=> (~![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~one_to_one(A)) | (~(relation(A) & function(A)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(3,plain,
% 0.18/0.40 ((~![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)))) | (~one_to_one(A)) | (~(relation(A) & function(A)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(4,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')).
% 0.18/0.40 tff(5,plain,
% 0.18/0.40 (~![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~one_to_one(A)) | (~(relation(A) & function(A))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.18/0.40 tff(6,plain,
% 0.18/0.40 (~![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~one_to_one(A)) | (~(relation(A) & function(A))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.18/0.40 tff(7,plain,
% 0.18/0.40 (~![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~one_to_one(A)) | (~(relation(A) & function(A))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.18/0.40 tff(8,plain,
% 0.18/0.40 (~![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~one_to_one(A)) | (~(relation(A) & function(A))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.18/0.40 tff(9,plain,
% 0.18/0.40 (~![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~one_to_one(A)) | (~(relation(A) & function(A))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.18/0.40 tff(10,plain,
% 0.18/0.40 (~![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~one_to_one(A)) | (~(relation(A) & function(A))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.18/0.40 tff(11,plain,
% 0.18/0.40 (~![A: $i] : (((relation_rng(A) = relation_dom(function_inverse(A))) & (relation_dom(A) = relation_rng(function_inverse(A)))) | (~one_to_one(A)) | (~(relation(A) & function(A))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.18/0.40 tff(12,plain,(
% 0.18/0.40 ~(((relation_rng(A!11) = relation_dom(function_inverse(A!11))) & (relation_dom(A!11) = relation_rng(function_inverse(A!11)))) | (~one_to_one(A!11)) | (~(relation(A!11) & function(A!11))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[11])).
% 0.18/0.40 tff(13,plain,
% 0.18/0.40 (~(((relation_rng(A!11) = relation_dom(function_inverse(A!11))) & (relation_dom(A!11) = relation_rng(function_inverse(A!11)))) | (~one_to_one(A!11)) | (~(relation(A!11) & function(A!11))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[12, 1])).
% 0.18/0.40 tff(14,plain,
% 0.18/0.40 (relation(A!11) & function(A!11)),
% 0.18/0.40 inference(or_elim,[status(thm)],[13])).
% 0.18/0.40 tff(15,plain,
% 0.18/0.40 (function(A!11)),
% 0.18/0.40 inference(and_elim,[status(thm)],[14])).
% 0.18/0.40 tff(16,plain,
% 0.18/0.40 (relation(A!11)),
% 0.18/0.40 inference(and_elim,[status(thm)],[14])).
% 0.18/0.40 tff(17,plain,
% 0.18/0.40 (one_to_one(A!11)),
% 0.18/0.40 inference(or_elim,[status(thm)],[13])).
% 0.18/0.40 tff(18,plain,
% 0.18/0.40 (^[A: $i] : refl(((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A))) <=> ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(19,plain,
% 0.18/0.40 (![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A))) <=> ![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[18])).
% 0.18/0.40 tff(20,plain,
% 0.18/0.40 (^[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))))), (((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~(relation(A) & function(A)))) <=> ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | ((~relation(A)) | (~function(A)))))), rewrite(((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | ((~relation(A)) | (~function(A)))) <=> ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))), (((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~(relation(A) & function(A)))) <=> ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(21,plain,
% 0.18/0.40 (![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~(relation(A) & function(A)))) <=> ![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[20])).
% 0.18/0.40 tff(22,plain,
% 0.18/0.40 (![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~(relation(A) & function(A)))) <=> ![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~(relation(A) & function(A))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(23,plain,
% 0.18/0.40 (^[A: $i] : trans(monotonicity(rewrite((one_to_one(A) => (function_inverse(A) = relation_inverse(A))) <=> ((~one_to_one(A)) | (function_inverse(A) = relation_inverse(A)))), (((relation(A) & function(A)) => (one_to_one(A) => (function_inverse(A) = relation_inverse(A)))) <=> ((relation(A) & function(A)) => ((~one_to_one(A)) | (function_inverse(A) = relation_inverse(A)))))), rewrite(((relation(A) & function(A)) => ((~one_to_one(A)) | (function_inverse(A) = relation_inverse(A)))) <=> ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~(relation(A) & function(A))))), (((relation(A) & function(A)) => (one_to_one(A) => (function_inverse(A) = relation_inverse(A)))) <=> ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~(relation(A) & function(A))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(24,plain,
% 0.18/0.40 (![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => (function_inverse(A) = relation_inverse(A)))) <=> ![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~(relation(A) & function(A))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[23])).
% 0.18/0.40 tff(25,axiom,(![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => (function_inverse(A) = relation_inverse(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d9_funct_1')).
% 0.18/0.40 tff(26,plain,
% 0.18/0.40 (![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~(relation(A) & function(A))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.18/0.40 tff(27,plain,
% 0.18/0.40 (![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~(relation(A) & function(A))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.18/0.40 tff(28,plain,(
% 0.18/0.40 ![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~(relation(A) & function(A))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[27])).
% 0.18/0.40 tff(29,plain,
% 0.18/0.40 (![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.18/0.40 tff(30,plain,
% 0.18/0.40 (![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[29, 19])).
% 0.18/0.40 tff(31,plain,
% 0.18/0.40 (((~![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))) | ((~one_to_one(A!11)) | (function_inverse(A!11) = relation_inverse(A!11)) | (~relation(A!11)) | (~function(A!11)))) <=> ((~![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))) | (~one_to_one(A!11)) | (function_inverse(A!11) = relation_inverse(A!11)) | (~relation(A!11)) | (~function(A!11)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(32,plain,
% 0.18/0.40 (((function_inverse(A!11) = relation_inverse(A!11)) | (~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11))) <=> ((~one_to_one(A!11)) | (function_inverse(A!11) = relation_inverse(A!11)) | (~relation(A!11)) | (~function(A!11)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(33,plain,
% 0.18/0.40 (((~![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))) | ((function_inverse(A!11) = relation_inverse(A!11)) | (~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)))) <=> ((~![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))) | ((~one_to_one(A!11)) | (function_inverse(A!11) = relation_inverse(A!11)) | (~relation(A!11)) | (~function(A!11))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[32])).
% 0.18/0.40 tff(34,plain,
% 0.18/0.40 (((~![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))) | ((function_inverse(A!11) = relation_inverse(A!11)) | (~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)))) <=> ((~![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))) | (~one_to_one(A!11)) | (function_inverse(A!11) = relation_inverse(A!11)) | (~relation(A!11)) | (~function(A!11)))),
% 0.18/0.40 inference(transitivity,[status(thm)],[33, 31])).
% 0.18/0.40 tff(35,plain,
% 0.18/0.40 ((~![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))) | ((function_inverse(A!11) = relation_inverse(A!11)) | (~one_to_one(A!11)) | (~relation(A!11)) | (~function(A!11)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(36,plain,
% 0.18/0.40 ((~![A: $i] : ((function_inverse(A) = relation_inverse(A)) | (~one_to_one(A)) | (~relation(A)) | (~function(A)))) | (~one_to_one(A!11)) | (function_inverse(A!11) = relation_inverse(A!11)) | (~relation(A!11)) | (~function(A!11))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.18/0.40 tff(37,plain,
% 0.18/0.40 (function_inverse(A!11) = relation_inverse(A!11)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[36, 30, 17, 16, 15])).
% 0.18/0.40 tff(38,plain,
% 0.18/0.40 (relation_dom(function_inverse(A!11)) = relation_dom(relation_inverse(A!11))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[37])).
% 0.18/0.40 tff(39,plain,
% 0.18/0.40 (relation_dom(relation_inverse(A!11)) = relation_dom(function_inverse(A!11))),
% 0.18/0.40 inference(symmetry,[status(thm)],[38])).
% 0.18/0.40 tff(40,plain,
% 0.18/0.40 (^[A: $i] : refl(((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A))))))) <=> ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A))))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(41,plain,
% 0.18/0.40 (![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A))))))) <=> ![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[40])).
% 0.18/0.40 tff(42,plain,
% 0.18/0.40 (^[A: $i] : rewrite(((~relation(A)) | ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A))))) <=> ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A))))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(43,plain,
% 0.18/0.40 (![A: $i] : ((~relation(A)) | ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A))))) <=> ![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[42])).
% 0.18/0.40 tff(44,plain,
% 0.18/0.40 (![A: $i] : ((~relation(A)) | ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A))))) <=> ![A: $i] : ((~relation(A)) | ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(45,plain,
% 0.18/0.40 (^[A: $i] : rewrite((relation(A) => ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A))))) <=> ((~relation(A)) | ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(46,plain,
% 0.18/0.40 (![A: $i] : (relation(A) => ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A))))) <=> ![A: $i] : ((~relation(A)) | ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A)))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[45])).
% 0.18/0.40 tff(47,axiom,(![A: $i] : (relation(A) => ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t37_relat_1')).
% 0.18/0.40 tff(48,plain,
% 0.18/0.40 (![A: $i] : ((~relation(A)) | ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.18/0.40 tff(49,plain,
% 0.18/0.40 (![A: $i] : ((~relation(A)) | ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.18/0.40 tff(50,plain,(
% 0.18/0.40 ![A: $i] : ((~relation(A)) | ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A)))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[49])).
% 0.18/0.40 tff(51,plain,
% 0.18/0.40 (![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.18/0.40 tff(52,plain,
% 0.18/0.40 (![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[51, 41])).
% 0.18/0.40 tff(53,plain,
% 0.18/0.40 (((~![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))) | ((~relation(A!11)) | (~((~(relation_rng(A!11) = relation_dom(relation_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(relation_inverse(A!11)))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))) | (~relation(A!11)) | (~((~(relation_rng(A!11) = relation_dom(relation_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(relation_inverse(A!11)))))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(54,plain,
% 0.18/0.40 ((~![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))) | ((~relation(A!11)) | (~((~(relation_rng(A!11) = relation_dom(relation_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(relation_inverse(A!11)))))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(55,plain,
% 0.18/0.40 ((~![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))) | (~relation(A!11)) | (~((~(relation_rng(A!11) = relation_dom(relation_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(relation_inverse(A!11))))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.18/0.40 tff(56,plain,
% 0.18/0.40 (~((~(relation_rng(A!11) = relation_dom(relation_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(relation_inverse(A!11)))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[55, 52, 16])).
% 0.18/0.40 tff(57,plain,
% 0.18/0.40 (((~(relation_rng(A!11) = relation_dom(relation_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(relation_inverse(A!11))))) | (relation_rng(A!11) = relation_dom(relation_inverse(A!11)))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(58,plain,
% 0.18/0.40 (relation_rng(A!11) = relation_dom(relation_inverse(A!11))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.18/0.40 tff(59,plain,
% 0.18/0.40 (relation_rng(A!11) = relation_dom(function_inverse(A!11))),
% 0.18/0.40 inference(transitivity,[status(thm)],[58, 39])).
% 0.18/0.40 tff(60,plain,
% 0.18/0.40 (relation_rng(function_inverse(A!11)) = relation_rng(relation_inverse(A!11))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[37])).
% 0.18/0.40 tff(61,plain,
% 0.18/0.40 (relation_rng(relation_inverse(A!11)) = relation_rng(function_inverse(A!11))),
% 0.18/0.40 inference(symmetry,[status(thm)],[60])).
% 0.18/0.40 tff(62,plain,
% 0.18/0.40 (((~(relation_rng(A!11) = relation_dom(relation_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(relation_inverse(A!11))))) | (relation_dom(A!11) = relation_rng(relation_inverse(A!11)))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(63,plain,
% 0.18/0.40 (relation_dom(A!11) = relation_rng(relation_inverse(A!11))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[62, 56])).
% 0.18/0.40 tff(64,plain,
% 0.18/0.40 (relation_dom(A!11) = relation_rng(function_inverse(A!11))),
% 0.18/0.40 inference(transitivity,[status(thm)],[63, 61])).
% 0.18/0.40 tff(65,plain,
% 0.18/0.40 ((~(~((~(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)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(66,plain,
% 0.18/0.40 (((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)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11))))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(67,plain,
% 0.18/0.40 ((~((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)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11)))))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[66])).
% 0.18/0.40 tff(68,plain,
% 0.18/0.40 ((~((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)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11)))))),
% 0.18/0.40 inference(transitivity,[status(thm)],[67, 65])).
% 0.18/0.40 tff(69,plain,
% 0.18/0.40 (~((relation_rng(A!11) = relation_dom(function_inverse(A!11))) & (relation_dom(A!11) = relation_rng(function_inverse(A!11))))),
% 0.18/0.40 inference(or_elim,[status(thm)],[13])).
% 0.18/0.40 tff(70,plain,
% 0.18/0.40 ((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.18/0.41 tff(71,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[70, 64, 59])).
% 0.18/0.41 % SZS output end Proof
%------------------------------------------------------------------------------