TSTP Solution File: SEU026+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU026+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 07:27:19 EDT 2022
% Result : Theorem 1.81s 1.42s
% Output : Proof 1.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU026+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 09:11:18 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 1.81/1.42 % SZS status Theorem
% 1.81/1.42 % SZS output start Proof
% 1.81/1.42 tff(subset_type, type, (
% 1.81/1.42 subset: ( $i * $i ) > $o)).
% 1.81/1.42 tff(relation_dom_type, type, (
% 1.81/1.42 relation_dom: $i > $i)).
% 1.81/1.42 tff(tptp_fun_A_11_type, type, (
% 1.81/1.42 tptp_fun_A_11: $i)).
% 1.81/1.42 tff(relation_rng_type, type, (
% 1.81/1.42 relation_rng: $i > $i)).
% 1.81/1.42 tff(function_inverse_type, type, (
% 1.81/1.42 function_inverse: $i > $i)).
% 1.81/1.42 tff(one_to_one_type, type, (
% 1.81/1.42 one_to_one: $i > $o)).
% 1.81/1.42 tff(function_type, type, (
% 1.81/1.42 function: $i > $o)).
% 1.81/1.42 tff(relation_type, type, (
% 1.81/1.42 relation: $i > $o)).
% 1.81/1.42 tff(relation_composition_type, type, (
% 1.81/1.42 relation_composition: ( $i * $i ) > $i)).
% 1.81/1.42 tff(1,plain,
% 1.81/1.42 ((~(((relation_dom(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11)) & (relation_rng(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11))) | (~(relation(A!11) & function(A!11))) | (~one_to_one(A!11)))) <=> (~(((relation_dom(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11)) & (relation_rng(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11))) | (~(relation(A!11) & function(A!11))) | (~one_to_one(A!11))))),
% 1.81/1.42 inference(rewrite,[status(thm)],[])).
% 1.81/1.42 tff(2,plain,
% 1.81/1.42 ((~![A: $i] : (((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))) <=> (~![A: $i] : (((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation(A) & function(A))) | (~one_to_one(A))))),
% 1.81/1.42 inference(rewrite,[status(thm)],[])).
% 1.81/1.42 tff(3,plain,
% 1.81/1.42 ((~![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => ((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A)))))) <=> (~![A: $i] : (((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation(A) & function(A))) | (~one_to_one(A))))),
% 1.81/1.42 inference(rewrite,[status(thm)],[])).
% 1.81/1.42 tff(4,axiom,(~![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) => ((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t59_funct_1')).
% 1.81/1.42 tff(5,plain,
% 1.81/1.42 (~![A: $i] : (((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.81/1.42 tff(6,plain,
% 1.81/1.42 (~![A: $i] : (((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[5, 2])).
% 1.81/1.42 tff(7,plain,
% 1.81/1.42 (~![A: $i] : (((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.81/1.42 tff(8,plain,
% 1.81/1.42 (~![A: $i] : (((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[7, 2])).
% 1.81/1.42 tff(9,plain,
% 1.81/1.42 (~![A: $i] : (((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[8, 2])).
% 1.81/1.42 tff(10,plain,
% 1.81/1.42 (~![A: $i] : (((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[9, 2])).
% 1.81/1.42 tff(11,plain,
% 1.81/1.42 (~![A: $i] : (((relation_dom(relation_composition(function_inverse(A), A)) = relation_rng(A)) & (relation_rng(relation_composition(function_inverse(A), A)) = relation_rng(A))) | (~(relation(A) & function(A))) | (~one_to_one(A)))),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[10, 2])).
% 1.81/1.42 tff(12,plain,(
% 1.81/1.42 ~(((relation_dom(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11)) & (relation_rng(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11))) | (~(relation(A!11) & function(A!11))) | (~one_to_one(A!11)))),
% 1.81/1.42 inference(skolemize,[status(sab)],[11])).
% 1.81/1.42 tff(13,plain,
% 1.81/1.42 (~(((relation_dom(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11)) & (relation_rng(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11))) | (~(relation(A!11) & function(A!11))) | (~one_to_one(A!11)))),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[12, 1])).
% 1.81/1.42 tff(14,plain,
% 1.81/1.42 (one_to_one(A!11)),
% 1.81/1.42 inference(or_elim,[status(thm)],[13])).
% 1.81/1.42 tff(15,plain,
% 1.81/1.42 (relation(A!11) & function(A!11)),
% 1.81/1.42 inference(or_elim,[status(thm)],[13])).
% 1.81/1.42 tff(16,plain,
% 1.81/1.42 (function(A!11)),
% 1.81/1.42 inference(and_elim,[status(thm)],[15])).
% 1.81/1.42 tff(17,plain,
% 1.81/1.42 (relation(A!11)),
% 1.81/1.42 inference(and_elim,[status(thm)],[15])).
% 1.81/1.42 tff(18,plain,
% 1.81/1.42 (^[A: $i] : refl(((~relation(A)) | (~one_to_one(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A))))))) <=> ((~relation(A)) | (~one_to_one(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A))))))))),
% 1.81/1.42 inference(bind,[status(th)],[])).
% 1.81/1.42 tff(19,plain,
% 1.81/1.42 (![A: $i] : ((~relation(A)) | (~one_to_one(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A))))))) <=> ![A: $i] : ((~relation(A)) | (~one_to_one(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))),
% 1.81/1.42 inference(quant_intro,[status(thm)],[18])).
% 1.81/1.42 tff(20,plain,
% 1.81/1.42 (^[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))) <=> ((~relation(A)) | (~one_to_one(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))) <=> ((~relation(A)) | (~one_to_one(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))))),
% 1.81/1.42 inference(bind,[status(th)],[])).
% 1.81/1.42 tff(21,plain,
% 1.81/1.42 (![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(A)) | (~one_to_one(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))),
% 1.81/1.42 inference(quant_intro,[status(thm)],[20])).
% 1.81/1.42 tff(22,plain,
% 1.81/1.42 (![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)))),
% 1.81/1.42 inference(rewrite,[status(thm)],[])).
% 1.81/1.42 tff(23,plain,
% 1.81/1.42 (^[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)))))),
% 1.81/1.42 inference(bind,[status(th)],[])).
% 1.81/1.42 tff(24,plain,
% 1.81/1.42 (![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)))),
% 1.81/1.42 inference(quant_intro,[status(thm)],[23])).
% 1.81/1.42 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/sandbox2/benchmark/theBenchmark.p','t55_funct_1')).
% 1.81/1.42 tff(26,plain,
% 1.81/1.42 (![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)))),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[25, 24])).
% 1.81/1.42 tff(27,plain,
% 1.81/1.42 (![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)))),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[26, 22])).
% 1.81/1.42 tff(28,plain,(
% 1.81/1.42 ![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)))),
% 1.81/1.42 inference(skolemize,[status(sab)],[27])).
% 1.81/1.42 tff(29,plain,
% 1.81/1.42 (![A: $i] : ((~relation(A)) | (~one_to_one(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[28, 21])).
% 1.81/1.42 tff(30,plain,
% 1.81/1.42 (![A: $i] : ((~relation(A)) | (~one_to_one(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[29, 19])).
% 1.81/1.42 tff(31,plain,
% 1.81/1.42 (((~![A: $i] : ((~relation(A)) | (~one_to_one(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] : ((~relation(A)) | (~one_to_one(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)))))))),
% 1.81/1.42 inference(rewrite,[status(thm)],[])).
% 1.81/1.42 tff(32,plain,
% 1.81/1.42 (((~relation(A!11)) | (~one_to_one(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)) | (~((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11)))))))),
% 1.81/1.42 inference(rewrite,[status(thm)],[])).
% 1.81/1.42 tff(33,plain,
% 1.81/1.42 ((~((~(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))))))),
% 1.81/1.42 inference(rewrite,[status(thm)],[])).
% 1.81/1.42 tff(34,plain,
% 1.81/1.42 (((~relation(A!11)) | (~one_to_one(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))))))) <=> ((~relation(A!11)) | (~one_to_one(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)))))))),
% 1.81/1.42 inference(monotonicity,[status(thm)],[33])).
% 1.81/1.42 tff(35,plain,
% 1.81/1.42 (((~relation(A!11)) | (~one_to_one(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)) | (~((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11)))))))),
% 1.81/1.42 inference(transitivity,[status(thm)],[34, 32])).
% 1.81/1.42 tff(36,plain,
% 1.81/1.42 (((~![A: $i] : ((~relation(A)) | (~one_to_one(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))) | ((~relation(A!11)) | (~one_to_one(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] : ((~relation(A)) | (~one_to_one(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))))))))),
% 1.81/1.42 inference(monotonicity,[status(thm)],[35])).
% 1.81/1.42 tff(37,plain,
% 1.81/1.42 (((~![A: $i] : ((~relation(A)) | (~one_to_one(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))) | ((~relation(A!11)) | (~one_to_one(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] : ((~relation(A)) | (~one_to_one(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)))))))),
% 1.89/1.42 inference(transitivity,[status(thm)],[36, 31])).
% 1.89/1.42 tff(38,plain,
% 1.89/1.42 ((~![A: $i] : ((~relation(A)) | (~one_to_one(A)) | (~function(A)) | (~((~(relation_rng(A) = relation_dom(function_inverse(A)))) | (~(relation_dom(A) = relation_rng(function_inverse(A)))))))) | ((~relation(A!11)) | (~one_to_one(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)))))))),
% 1.89/1.42 inference(quant_inst,[status(thm)],[])).
% 1.89/1.42 tff(39,plain,
% 1.89/1.42 ((~![A: $i] : ((~relation(A)) | (~one_to_one(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))))))),
% 1.89/1.42 inference(modus_ponens,[status(thm)],[38, 37])).
% 1.89/1.42 tff(40,plain,
% 1.89/1.42 (~((~(relation_rng(A!11) = relation_dom(function_inverse(A!11)))) | (~(relation_dom(A!11) = relation_rng(function_inverse(A!11)))))),
% 1.89/1.42 inference(unit_resolution,[status(thm)],[39, 30, 17, 16, 14])).
% 1.89/1.42 tff(41,plain,
% 1.89/1.42 (((~(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)))),
% 1.89/1.42 inference(tautology,[status(thm)],[])).
% 1.89/1.42 tff(42,plain,
% 1.89/1.42 (relation_dom(A!11) = relation_rng(function_inverse(A!11))),
% 1.89/1.42 inference(unit_resolution,[status(thm)],[41, 40])).
% 1.89/1.42 tff(43,plain,
% 1.89/1.42 (relation_rng(function_inverse(A!11)) = relation_dom(A!11)),
% 1.89/1.42 inference(symmetry,[status(thm)],[42])).
% 1.89/1.42 tff(44,plain,
% 1.89/1.42 (subset(relation_rng(function_inverse(A!11)), relation_dom(A!11)) <=> subset(relation_dom(A!11), relation_rng(function_inverse(A!11)))),
% 1.89/1.42 inference(monotonicity,[status(thm)],[43, 42])).
% 1.89/1.42 tff(45,plain,
% 1.89/1.42 (subset(relation_dom(A!11), relation_rng(function_inverse(A!11))) <=> subset(relation_rng(function_inverse(A!11)), relation_dom(A!11))),
% 1.89/1.42 inference(symmetry,[status(thm)],[44])).
% 1.89/1.42 tff(46,plain,
% 1.89/1.42 (subset(relation_rng(function_inverse(A!11)), relation_rng(function_inverse(A!11))) <=> subset(relation_dom(A!11), relation_rng(function_inverse(A!11)))),
% 1.89/1.42 inference(monotonicity,[status(thm)],[43])).
% 1.89/1.42 tff(47,plain,
% 1.89/1.42 (subset(relation_dom(A!11), relation_rng(function_inverse(A!11))) <=> subset(relation_rng(function_inverse(A!11)), relation_rng(function_inverse(A!11)))),
% 1.89/1.42 inference(symmetry,[status(thm)],[46])).
% 1.89/1.42 tff(48,plain,
% 1.89/1.42 ((~subset(relation_dom(A!11), relation_rng(function_inverse(A!11)))) <=> (~subset(relation_rng(function_inverse(A!11)), relation_rng(function_inverse(A!11))))),
% 1.89/1.42 inference(monotonicity,[status(thm)],[47])).
% 1.89/1.42 tff(49,assumption,(~subset(relation_dom(A!11), relation_rng(function_inverse(A!11)))), introduced(assumption)).
% 1.89/1.42 tff(50,plain,
% 1.89/1.42 (~subset(relation_rng(function_inverse(A!11)), relation_rng(function_inverse(A!11)))),
% 1.89/1.42 inference(modus_ponens,[status(thm)],[49, 48])).
% 1.89/1.42 tff(51,plain,
% 1.89/1.42 (^[A: $i] : refl(subset(A, A) <=> subset(A, A))),
% 1.89/1.42 inference(bind,[status(th)],[])).
% 1.89/1.42 tff(52,plain,
% 1.89/1.42 (![A: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 1.89/1.42 inference(quant_intro,[status(thm)],[51])).
% 1.89/1.42 tff(53,plain,
% 1.89/1.42 (![A: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 1.89/1.42 inference(rewrite,[status(thm)],[])).
% 1.89/1.42 tff(54,plain,
% 1.89/1.42 (![A: $i, B: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 1.89/1.42 inference(elim_unused_vars,[status(thm)],[])).
% 1.89/1.42 tff(55,axiom,(![A: $i, B: $i] : subset(A, A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reflexivity_r1_tarski')).
% 1.89/1.42 tff(56,plain,
% 1.89/1.42 (![A: $i] : subset(A, A)),
% 1.89/1.42 inference(modus_ponens,[status(thm)],[55, 54])).
% 1.89/1.42 tff(57,plain,
% 1.89/1.42 (![A: $i] : subset(A, A)),
% 1.89/1.42 inference(modus_ponens,[status(thm)],[56, 53])).
% 1.89/1.42 tff(58,plain,(
% 1.89/1.42 ![A: $i] : subset(A, A)),
% 1.89/1.42 inference(skolemize,[status(sab)],[57])).
% 1.89/1.42 tff(59,plain,
% 1.89/1.42 (![A: $i] : subset(A, A)),
% 1.89/1.42 inference(modus_ponens,[status(thm)],[58, 52])).
% 1.89/1.42 tff(60,plain,
% 1.89/1.42 ((~![A: $i] : subset(A, A)) | subset(relation_rng(function_inverse(A!11)), relation_rng(function_inverse(A!11)))),
% 1.89/1.42 inference(quant_inst,[status(thm)],[])).
% 1.89/1.42 tff(61,plain,
% 1.89/1.42 (subset(relation_rng(function_inverse(A!11)), relation_rng(function_inverse(A!11)))),
% 1.89/1.42 inference(unit_resolution,[status(thm)],[60, 59])).
% 1.89/1.42 tff(62,plain,
% 1.89/1.42 ($false),
% 1.89/1.42 inference(unit_resolution,[status(thm)],[61, 50])).
% 1.89/1.42 tff(63,plain,(subset(relation_dom(A!11), relation_rng(function_inverse(A!11)))), inference(lemma,lemma(discharge,[]))).
% 1.89/1.42 tff(64,plain,
% 1.89/1.42 (subset(relation_rng(function_inverse(A!11)), relation_dom(A!11))),
% 1.89/1.42 inference(modus_ponens,[status(thm)],[63, 45])).
% 1.89/1.42 tff(65,plain,
% 1.89/1.42 (((~(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)))),
% 1.89/1.42 inference(tautology,[status(thm)],[])).
% 1.89/1.42 tff(66,plain,
% 1.89/1.42 (relation_rng(A!11) = relation_dom(function_inverse(A!11))),
% 1.89/1.42 inference(unit_resolution,[status(thm)],[65, 40])).
% 1.89/1.42 tff(67,plain,
% 1.89/1.42 (relation_dom(function_inverse(A!11)) = relation_rng(A!11)),
% 1.89/1.42 inference(symmetry,[status(thm)],[66])).
% 1.89/1.42 tff(68,plain,
% 1.89/1.42 ((relation_dom(relation_composition(function_inverse(A!11), A!11)) = relation_dom(function_inverse(A!11))) <=> (relation_dom(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11))),
% 1.89/1.42 inference(monotonicity,[status(thm)],[67])).
% 1.89/1.42 tff(69,plain,
% 1.89/1.42 ((relation_dom(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11)) <=> (relation_dom(relation_composition(function_inverse(A!11), A!11)) = relation_dom(function_inverse(A!11)))),
% 1.89/1.42 inference(symmetry,[status(thm)],[68])).
% 1.89/1.42 tff(70,plain,
% 1.89/1.42 ((~(relation_dom(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11))) <=> (~(relation_dom(relation_composition(function_inverse(A!11), A!11)) = relation_dom(function_inverse(A!11))))),
% 1.89/1.42 inference(monotonicity,[status(thm)],[69])).
% 1.89/1.42 tff(71,plain,
% 1.89/1.42 (^[A: $i] : refl(((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))) <=> ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))))),
% 1.89/1.42 inference(bind,[status(th)],[])).
% 1.89/1.42 tff(72,plain,
% 1.89/1.42 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 1.89/1.42 inference(quant_intro,[status(thm)],[71])).
% 1.89/1.42 tff(73,plain,
% 1.89/1.42 (^[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))))), rewrite((relation(function_inverse(A)) & function(function_inverse(A))) <=> (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))), (((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A)))) <=> (((~relation(A)) | (~function(A))) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))))), rewrite((((~relation(A)) | (~function(A))) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A)))))) <=> ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))), (((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A)))) <=> ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))))),
% 1.89/1.42 inference(bind,[status(th)],[])).
% 1.89/1.42 tff(74,plain,
% 1.89/1.42 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A)))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 1.89/1.42 inference(quant_intro,[status(thm)],[73])).
% 1.89/1.42 tff(75,plain,
% 1.89/1.42 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A)))) <=> ![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 1.89/1.42 inference(rewrite,[status(thm)],[])).
% 1.89/1.42 tff(76,plain,
% 1.89/1.42 (^[A: $i] : rewrite(((relation(A) & function(A)) => (relation(function_inverse(A)) & function(function_inverse(A)))) <=> ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A)))))),
% 1.89/1.42 inference(bind,[status(th)],[])).
% 1.89/1.42 tff(77,plain,
% 1.89/1.42 (![A: $i] : ((relation(A) & function(A)) => (relation(function_inverse(A)) & function(function_inverse(A)))) <=> ![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 1.89/1.42 inference(quant_intro,[status(thm)],[76])).
% 1.89/1.42 tff(78,axiom,(![A: $i] : ((relation(A) & function(A)) => (relation(function_inverse(A)) & function(function_inverse(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k2_funct_1')).
% 1.89/1.42 tff(79,plain,
% 1.89/1.42 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 1.89/1.42 inference(modus_ponens,[status(thm)],[78, 77])).
% 1.89/1.42 tff(80,plain,
% 1.89/1.42 (![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 1.89/1.42 inference(modus_ponens,[status(thm)],[79, 75])).
% 1.89/1.42 tff(81,plain,(
% 1.89/1.42 ![A: $i] : ((~(relation(A) & function(A))) | (relation(function_inverse(A)) & function(function_inverse(A))))),
% 1.89/1.42 inference(skolemize,[status(sab)],[80])).
% 1.89/1.42 tff(82,plain,
% 1.89/1.42 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 1.89/1.42 inference(modus_ponens,[status(thm)],[81, 74])).
% 1.89/1.42 tff(83,plain,
% 1.89/1.42 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~relation(function_inverse(A))) | (~function(function_inverse(A))))))),
% 1.89/1.42 inference(modus_ponens,[status(thm)],[82, 72])).
% 1.89/1.42 tff(84,plain,
% 1.89/1.42 (((~![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))))))),
% 1.89/1.42 inference(rewrite,[status(thm)],[])).
% 1.89/1.42 tff(85,plain,
% 1.89/1.42 ((~![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))))))),
% 1.89/1.42 inference(quant_inst,[status(thm)],[])).
% 1.89/1.42 tff(86,plain,
% 1.89/1.42 ((~![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)))))),
% 1.89/1.42 inference(modus_ponens,[status(thm)],[85, 84])).
% 1.89/1.42 tff(87,plain,
% 1.89/1.42 (~((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11))))),
% 1.89/1.42 inference(unit_resolution,[status(thm)],[86, 83, 17, 16])).
% 1.89/1.42 tff(88,plain,
% 1.89/1.42 (((~relation(function_inverse(A!11))) | (~function(function_inverse(A!11)))) | relation(function_inverse(A!11))),
% 1.89/1.42 inference(tautology,[status(thm)],[])).
% 1.89/1.42 tff(89,plain,
% 1.89/1.42 (relation(function_inverse(A!11))),
% 1.89/1.42 inference(unit_resolution,[status(thm)],[88, 87])).
% 1.89/1.42 tff(90,plain,
% 1.89/1.42 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : ((relation_rng(relation_composition(B, A)) = relation_rng(A)) | (~relation(B)) | (~subset(relation_dom(A), relation_rng(B))))) <=> ((~relation(A)) | ![B: $i] : ((relation_rng(relation_composition(B, A)) = relation_rng(A)) | (~relation(B)) | (~subset(relation_dom(A), relation_rng(B))))))),
% 1.89/1.42 inference(bind,[status(th)],[])).
% 1.89/1.42 tff(91,plain,
% 1.89/1.42 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_rng(relation_composition(B, A)) = relation_rng(A)) | (~relation(B)) | (~subset(relation_dom(A), relation_rng(B))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_rng(relation_composition(B, A)) = relation_rng(A)) | (~relation(B)) | (~subset(relation_dom(A), relation_rng(B)))))),
% 1.89/1.42 inference(quant_intro,[status(thm)],[90])).
% 1.89/1.42 tff(92,plain,
% 1.89/1.42 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : ((relation_rng(relation_composition(B, A)) = relation_rng(A)) | (~relation(B)) | (~subset(relation_dom(A), relation_rng(B))))) <=> ((~relation(A)) | ![B: $i] : ((relation_rng(relation_composition(B, A)) = relation_rng(A)) | (~relation(B)) | (~subset(relation_dom(A), relation_rng(B))))))),
% 1.89/1.42 inference(bind,[status(th)],[])).
% 1.89/1.42 tff(93,plain,
% 1.89/1.42 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_rng(relation_composition(B, A)) = relation_rng(A)) | (~relation(B)) | (~subset(relation_dom(A), relation_rng(B))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_rng(relation_composition(B, A)) = relation_rng(A)) | (~relation(B)) | (~subset(relation_dom(A), relation_rng(B)))))),
% 1.89/1.42 inference(quant_intro,[status(thm)],[92])).
% 1.89/1.42 tff(94,plain,
% 1.89/1.42 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_rng(relation_composition(B, A)) = relation_rng(A)) | (~relation(B)) | (~subset(relation_dom(A), relation_rng(B))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_rng(relation_composition(B, A)) = relation_rng(A)) | (~relation(B)) | (~subset(relation_dom(A), relation_rng(B)))))),
% 1.89/1.42 inference(transitivity,[status(thm)],[93, 91])).
% 1.89/1.42 tff(95,plain,
% 1.89/1.42 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_rng(relation_composition(B, A)) = relation_rng(A)) | (~relation(B)) | (~subset(relation_dom(A), relation_rng(B))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_rng(relation_composition(B, A)) = relation_rng(A)) | (~relation(B)) | (~subset(relation_dom(A), relation_rng(B)))))),
% 1.89/1.42 inference(rewrite,[status(thm)],[])).
% 1.89/1.42 tff(96,plain,
% 1.89/1.42 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((subset(relation_dom(A), relation_rng(B)) => (relation_rng(relation_composition(B, A)) = relation_rng(A))) <=> ((~subset(relation_dom(A), relation_rng(B))) | (relation_rng(relation_composition(B, A)) = relation_rng(A)))), ((relation(B) => (subset(relation_dom(A), relation_rng(B)) => (relation_rng(relation_composition(B, A)) = relation_rng(A)))) <=> (relation(B) => ((~subset(relation_dom(A), relation_rng(B))) | (relation_rng(relation_composition(B, A)) = relation_rng(A)))))), rewrite((relation(B) => ((~subset(relation_dom(A), relation_rng(B))) | (relation_rng(relation_composition(B, A)) = relation_rng(A)))) <=> ((relation_rng(relation_composition(B, A)) = relation_rng(A)) | (~relation(B)) | (~subset(relation_dom(A), relation_rng(B))))), ((relation(B) => (subset(relation_dom(A), relation_rng(B)) => (relation_rng(relation_composition(B, A)) = relation_rng(A)))) <=> ((relation_rng(relation_composition(B, A)) = relation_rng(A)) | (~relation(B)) | (~subset(relation_dom(A), relation_rng(B))))))), (![B: $i] : (relation(B) => (subset(relation_dom(A), relation_rng(B)) => (relation_rng(relation_composition(B, A)) = relation_rng(A)))) <=> ![B: $i] : ((relation_rng(relation_composition(B, A)) = relation_rng(A)) | (~relation(B)) | (~subset(relation_dom(A), relation_rng(B)))))), ((relation(A) => ![B: $i] : (relation(B) => (subset(relation_dom(A), relation_rng(B)) => (relation_rng(relation_composition(B, A)) = relation_rng(A))))) <=> (relation(A) => ![B: $i] : ((relation_rng(relation_composition(B, A)) = relation_rng(A)) | (~relation(B)) | (~subset(relation_dom(A), relation_rng(B))))))), rewrite((relation(A) => ![B: $i] : ((relation_rng(relation_composition(B, A)) = relation_rng(A)) | (~relation(B)) | (~subset(relation_dom(A), relation_rng(B))))) <=> ((~relation(A)) | ![B: $i] : ((relation_rng(relation_composition(B, A)) = relation_rng(A)) | (~relation(B)) | (~subset(relation_dom(A), relation_rng(B)))))), ((relation(A) => ![B: $i] : (relation(B) => (subset(relation_dom(A), relation_rng(B)) => (relation_rng(relation_composition(B, A)) = relation_rng(A))))) <=> ((~relation(A)) | ![B: $i] : ((relation_rng(relation_composition(B, A)) = relation_rng(A)) | (~relation(B)) | (~subset(relation_dom(A), relation_rng(B)))))))),
% 1.89/1.42 inference(bind,[status(th)],[])).
% 1.89/1.42 tff(97,plain,
% 1.89/1.42 (![A: $i] : (relation(A) => ![B: $i] : (relation(B) => (subset(relation_dom(A), relation_rng(B)) => (relation_rng(relation_composition(B, A)) = relation_rng(A))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_rng(relation_composition(B, A)) = relation_rng(A)) | (~relation(B)) | (~subset(relation_dom(A), relation_rng(B)))))),
% 1.89/1.42 inference(quant_intro,[status(thm)],[96])).
% 1.89/1.42 tff(98,axiom,(![A: $i] : (relation(A) => ![B: $i] : (relation(B) => (subset(relation_dom(A), relation_rng(B)) => (relation_rng(relation_composition(B, A)) = relation_rng(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t47_relat_1')).
% 1.89/1.42 tff(99,plain,
% 1.89/1.42 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_rng(relation_composition(B, A)) = relation_rng(A)) | (~relation(B)) | (~subset(relation_dom(A), relation_rng(B)))))),
% 1.89/1.42 inference(modus_ponens,[status(thm)],[98, 97])).
% 1.89/1.42 tff(100,plain,
% 1.89/1.42 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_rng(relation_composition(B, A)) = relation_rng(A)) | (~relation(B)) | (~subset(relation_dom(A), relation_rng(B)))))),
% 1.89/1.42 inference(modus_ponens,[status(thm)],[99, 95])).
% 1.89/1.42 tff(101,plain,(
% 1.89/1.42 ![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_rng(relation_composition(B, A)) = relation_rng(A)) | (~relation(B)) | (~subset(relation_dom(A), relation_rng(B)))))),
% 1.89/1.42 inference(skolemize,[status(sab)],[100])).
% 1.89/1.42 tff(102,plain,
% 1.89/1.42 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_rng(relation_composition(B, A)) = relation_rng(A)) | (~relation(B)) | (~subset(relation_dom(A), relation_rng(B)))))),
% 1.89/1.42 inference(modus_ponens,[status(thm)],[101, 94])).
% 1.89/1.42 tff(103,plain,
% 1.89/1.42 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_rng(relation_composition(B, A)) = relation_rng(A)) | (~relation(B)) | (~subset(relation_dom(A), relation_rng(B)))))) | ((~relation(A!11)) | ![B: $i] : ((~relation(B)) | (relation_rng(relation_composition(B, A!11)) = relation_rng(A!11)) | (~subset(relation_dom(A!11), relation_rng(B)))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_rng(relation_composition(B, A)) = relation_rng(A)) | (~relation(B)) | (~subset(relation_dom(A), relation_rng(B)))))) | (~relation(A!11)) | ![B: $i] : ((~relation(B)) | (relation_rng(relation_composition(B, A!11)) = relation_rng(A!11)) | (~subset(relation_dom(A!11), relation_rng(B)))))),
% 1.89/1.42 inference(rewrite,[status(thm)],[])).
% 1.89/1.42 tff(104,plain,
% 1.89/1.42 (((~relation(A!11)) | ![B: $i] : ((relation_rng(relation_composition(B, A!11)) = relation_rng(A!11)) | (~relation(B)) | (~subset(relation_dom(A!11), relation_rng(B))))) <=> ((~relation(A!11)) | ![B: $i] : ((~relation(B)) | (relation_rng(relation_composition(B, A!11)) = relation_rng(A!11)) | (~subset(relation_dom(A!11), relation_rng(B)))))),
% 1.89/1.42 inference(rewrite,[status(thm)],[])).
% 1.89/1.42 tff(105,plain,
% 1.89/1.42 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_rng(relation_composition(B, A)) = relation_rng(A)) | (~relation(B)) | (~subset(relation_dom(A), relation_rng(B)))))) | ((~relation(A!11)) | ![B: $i] : ((relation_rng(relation_composition(B, A!11)) = relation_rng(A!11)) | (~relation(B)) | (~subset(relation_dom(A!11), relation_rng(B)))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_rng(relation_composition(B, A)) = relation_rng(A)) | (~relation(B)) | (~subset(relation_dom(A), relation_rng(B)))))) | ((~relation(A!11)) | ![B: $i] : ((~relation(B)) | (relation_rng(relation_composition(B, A!11)) = relation_rng(A!11)) | (~subset(relation_dom(A!11), relation_rng(B))))))),
% 1.89/1.42 inference(monotonicity,[status(thm)],[104])).
% 1.89/1.42 tff(106,plain,
% 1.89/1.42 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_rng(relation_composition(B, A)) = relation_rng(A)) | (~relation(B)) | (~subset(relation_dom(A), relation_rng(B)))))) | ((~relation(A!11)) | ![B: $i] : ((relation_rng(relation_composition(B, A!11)) = relation_rng(A!11)) | (~relation(B)) | (~subset(relation_dom(A!11), relation_rng(B)))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_rng(relation_composition(B, A)) = relation_rng(A)) | (~relation(B)) | (~subset(relation_dom(A), relation_rng(B)))))) | (~relation(A!11)) | ![B: $i] : ((~relation(B)) | (relation_rng(relation_composition(B, A!11)) = relation_rng(A!11)) | (~subset(relation_dom(A!11), relation_rng(B)))))),
% 1.89/1.42 inference(transitivity,[status(thm)],[105, 103])).
% 1.89/1.42 tff(107,plain,
% 1.89/1.42 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_rng(relation_composition(B, A)) = relation_rng(A)) | (~relation(B)) | (~subset(relation_dom(A), relation_rng(B)))))) | ((~relation(A!11)) | ![B: $i] : ((relation_rng(relation_composition(B, A!11)) = relation_rng(A!11)) | (~relation(B)) | (~subset(relation_dom(A!11), relation_rng(B)))))),
% 1.89/1.42 inference(quant_inst,[status(thm)],[])).
% 1.89/1.42 tff(108,plain,
% 1.89/1.42 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_rng(relation_composition(B, A)) = relation_rng(A)) | (~relation(B)) | (~subset(relation_dom(A), relation_rng(B)))))) | (~relation(A!11)) | ![B: $i] : ((~relation(B)) | (relation_rng(relation_composition(B, A!11)) = relation_rng(A!11)) | (~subset(relation_dom(A!11), relation_rng(B))))),
% 1.89/1.42 inference(modus_ponens,[status(thm)],[107, 106])).
% 1.89/1.42 tff(109,plain,
% 1.89/1.42 (![B: $i] : ((~relation(B)) | (relation_rng(relation_composition(B, A!11)) = relation_rng(A!11)) | (~subset(relation_dom(A!11), relation_rng(B))))),
% 1.89/1.42 inference(unit_resolution,[status(thm)],[108, 102, 17])).
% 1.89/1.42 tff(110,plain,
% 1.89/1.42 (((~![B: $i] : ((~relation(B)) | (relation_rng(relation_composition(B, A!11)) = relation_rng(A!11)) | (~subset(relation_dom(A!11), relation_rng(B))))) | ((relation_rng(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11)) | (~relation(function_inverse(A!11))) | (~subset(relation_dom(A!11), relation_rng(function_inverse(A!11)))))) <=> ((~![B: $i] : ((~relation(B)) | (relation_rng(relation_composition(B, A!11)) = relation_rng(A!11)) | (~subset(relation_dom(A!11), relation_rng(B))))) | (relation_rng(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11)) | (~relation(function_inverse(A!11))) | (~subset(relation_dom(A!11), relation_rng(function_inverse(A!11)))))),
% 1.89/1.42 inference(rewrite,[status(thm)],[])).
% 1.89/1.42 tff(111,plain,
% 1.89/1.42 (((~relation(function_inverse(A!11))) | (relation_rng(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11)) | (~subset(relation_dom(A!11), relation_rng(function_inverse(A!11))))) <=> ((relation_rng(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11)) | (~relation(function_inverse(A!11))) | (~subset(relation_dom(A!11), relation_rng(function_inverse(A!11)))))),
% 1.89/1.42 inference(rewrite,[status(thm)],[])).
% 1.89/1.42 tff(112,plain,
% 1.89/1.42 (((~![B: $i] : ((~relation(B)) | (relation_rng(relation_composition(B, A!11)) = relation_rng(A!11)) | (~subset(relation_dom(A!11), relation_rng(B))))) | ((~relation(function_inverse(A!11))) | (relation_rng(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11)) | (~subset(relation_dom(A!11), relation_rng(function_inverse(A!11)))))) <=> ((~![B: $i] : ((~relation(B)) | (relation_rng(relation_composition(B, A!11)) = relation_rng(A!11)) | (~subset(relation_dom(A!11), relation_rng(B))))) | ((relation_rng(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11)) | (~relation(function_inverse(A!11))) | (~subset(relation_dom(A!11), relation_rng(function_inverse(A!11))))))),
% 1.89/1.42 inference(monotonicity,[status(thm)],[111])).
% 1.89/1.42 tff(113,plain,
% 1.89/1.42 (((~![B: $i] : ((~relation(B)) | (relation_rng(relation_composition(B, A!11)) = relation_rng(A!11)) | (~subset(relation_dom(A!11), relation_rng(B))))) | ((~relation(function_inverse(A!11))) | (relation_rng(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11)) | (~subset(relation_dom(A!11), relation_rng(function_inverse(A!11)))))) <=> ((~![B: $i] : ((~relation(B)) | (relation_rng(relation_composition(B, A!11)) = relation_rng(A!11)) | (~subset(relation_dom(A!11), relation_rng(B))))) | (relation_rng(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11)) | (~relation(function_inverse(A!11))) | (~subset(relation_dom(A!11), relation_rng(function_inverse(A!11)))))),
% 1.89/1.43 inference(transitivity,[status(thm)],[112, 110])).
% 1.89/1.43 tff(114,plain,
% 1.89/1.43 ((~![B: $i] : ((~relation(B)) | (relation_rng(relation_composition(B, A!11)) = relation_rng(A!11)) | (~subset(relation_dom(A!11), relation_rng(B))))) | ((~relation(function_inverse(A!11))) | (relation_rng(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11)) | (~subset(relation_dom(A!11), relation_rng(function_inverse(A!11)))))),
% 1.89/1.43 inference(quant_inst,[status(thm)],[])).
% 1.89/1.43 tff(115,plain,
% 1.89/1.43 ((~![B: $i] : ((~relation(B)) | (relation_rng(relation_composition(B, A!11)) = relation_rng(A!11)) | (~subset(relation_dom(A!11), relation_rng(B))))) | (relation_rng(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11)) | (~relation(function_inverse(A!11))) | (~subset(relation_dom(A!11), relation_rng(function_inverse(A!11))))),
% 1.89/1.43 inference(modus_ponens,[status(thm)],[114, 113])).
% 1.89/1.43 tff(116,plain,
% 1.89/1.43 ((relation_rng(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11)) | (~subset(relation_dom(A!11), relation_rng(function_inverse(A!11))))),
% 1.89/1.43 inference(unit_resolution,[status(thm)],[115, 109, 89])).
% 1.89/1.43 tff(117,plain,
% 1.89/1.43 (relation_rng(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11)),
% 1.89/1.43 inference(unit_resolution,[status(thm)],[116, 63])).
% 1.89/1.43 tff(118,plain,
% 1.89/1.43 ((~(~((~(relation_dom(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11))) | (~(relation_rng(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11)))))) <=> ((~(relation_dom(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11))) | (~(relation_rng(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11))))),
% 1.89/1.43 inference(rewrite,[status(thm)],[])).
% 1.89/1.43 tff(119,plain,
% 1.89/1.43 (((relation_dom(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11)) & (relation_rng(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11))) <=> (~((~(relation_dom(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11))) | (~(relation_rng(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11)))))),
% 1.89/1.43 inference(rewrite,[status(thm)],[])).
% 1.89/1.43 tff(120,plain,
% 1.89/1.43 ((~((relation_dom(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11)) & (relation_rng(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11)))) <=> (~(~((~(relation_dom(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11))) | (~(relation_rng(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11))))))),
% 1.89/1.43 inference(monotonicity,[status(thm)],[119])).
% 1.89/1.43 tff(121,plain,
% 1.89/1.43 ((~((relation_dom(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11)) & (relation_rng(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11)))) <=> ((~(relation_dom(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11))) | (~(relation_rng(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11))))),
% 1.89/1.43 inference(transitivity,[status(thm)],[120, 118])).
% 1.89/1.43 tff(122,plain,
% 1.89/1.43 (~((relation_dom(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11)) & (relation_rng(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11)))),
% 1.89/1.43 inference(or_elim,[status(thm)],[13])).
% 1.89/1.43 tff(123,plain,
% 1.89/1.43 ((~(relation_dom(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11))) | (~(relation_rng(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11)))),
% 1.89/1.43 inference(modus_ponens,[status(thm)],[122, 121])).
% 1.89/1.43 tff(124,plain,
% 1.89/1.43 (~(relation_dom(relation_composition(function_inverse(A!11), A!11)) = relation_rng(A!11))),
% 1.89/1.43 inference(unit_resolution,[status(thm)],[123, 117])).
% 1.89/1.43 tff(125,plain,
% 1.89/1.43 (~(relation_dom(relation_composition(function_inverse(A!11), A!11)) = relation_dom(function_inverse(A!11)))),
% 1.89/1.43 inference(modus_ponens,[status(thm)],[124, 70])).
% 1.89/1.43 tff(126,plain,
% 1.89/1.43 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))) <=> ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))))),
% 1.89/1.43 inference(bind,[status(th)],[])).
% 1.89/1.43 tff(127,plain,
% 1.89/1.43 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 1.89/1.43 inference(quant_intro,[status(thm)],[126])).
% 1.89/1.43 tff(128,plain,
% 1.89/1.43 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))) <=> ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))))),
% 1.89/1.43 inference(bind,[status(th)],[])).
% 1.89/1.43 tff(129,plain,
% 1.89/1.43 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 1.89/1.43 inference(quant_intro,[status(thm)],[128])).
% 1.89/1.43 tff(130,plain,
% 1.89/1.43 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 1.89/1.43 inference(transitivity,[status(thm)],[129, 127])).
% 1.89/1.43 tff(131,plain,
% 1.89/1.43 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 1.89/1.43 inference(rewrite,[status(thm)],[])).
% 1.89/1.43 tff(132,plain,
% 1.89/1.43 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((subset(relation_rng(A), relation_dom(B)) => (relation_dom(relation_composition(A, B)) = relation_dom(A))) <=> ((~subset(relation_rng(A), relation_dom(B))) | (relation_dom(relation_composition(A, B)) = relation_dom(A)))), ((relation(B) => (subset(relation_rng(A), relation_dom(B)) => (relation_dom(relation_composition(A, B)) = relation_dom(A)))) <=> (relation(B) => ((~subset(relation_rng(A), relation_dom(B))) | (relation_dom(relation_composition(A, B)) = relation_dom(A)))))), rewrite((relation(B) => ((~subset(relation_rng(A), relation_dom(B))) | (relation_dom(relation_composition(A, B)) = relation_dom(A)))) <=> ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))), ((relation(B) => (subset(relation_rng(A), relation_dom(B)) => (relation_dom(relation_composition(A, B)) = relation_dom(A)))) <=> ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))))), (![B: $i] : (relation(B) => (subset(relation_rng(A), relation_dom(B)) => (relation_dom(relation_composition(A, B)) = relation_dom(A)))) <=> ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))), ((relation(A) => ![B: $i] : (relation(B) => (subset(relation_rng(A), relation_dom(B)) => (relation_dom(relation_composition(A, B)) = relation_dom(A))))) <=> (relation(A) => ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))))), rewrite((relation(A) => ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))) <=> ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))), ((relation(A) => ![B: $i] : (relation(B) => (subset(relation_rng(A), relation_dom(B)) => (relation_dom(relation_composition(A, B)) = relation_dom(A))))) <=> ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))))),
% 1.89/1.43 inference(bind,[status(th)],[])).
% 1.89/1.43 tff(133,plain,
% 1.89/1.43 (![A: $i] : (relation(A) => ![B: $i] : (relation(B) => (subset(relation_rng(A), relation_dom(B)) => (relation_dom(relation_composition(A, B)) = relation_dom(A))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 1.89/1.43 inference(quant_intro,[status(thm)],[132])).
% 1.89/1.43 tff(134,axiom,(![A: $i] : (relation(A) => ![B: $i] : (relation(B) => (subset(relation_rng(A), relation_dom(B)) => (relation_dom(relation_composition(A, B)) = relation_dom(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t46_relat_1')).
% 1.89/1.43 tff(135,plain,
% 1.89/1.43 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 1.89/1.43 inference(modus_ponens,[status(thm)],[134, 133])).
% 1.89/1.43 tff(136,plain,
% 1.89/1.43 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 1.89/1.43 inference(modus_ponens,[status(thm)],[135, 131])).
% 1.89/1.43 tff(137,plain,(
% 1.89/1.43 ![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 1.89/1.43 inference(skolemize,[status(sab)],[136])).
% 1.89/1.43 tff(138,plain,
% 1.89/1.43 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 1.89/1.43 inference(modus_ponens,[status(thm)],[137, 130])).
% 1.89/1.43 tff(139,plain,
% 1.89/1.43 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))) | ((~relation(function_inverse(A!11))) | ![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(function_inverse(A!11), B)) = relation_dom(function_inverse(A!11))) | (~subset(relation_rng(function_inverse(A!11)), relation_dom(B)))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))) | (~relation(function_inverse(A!11))) | ![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(function_inverse(A!11), B)) = relation_dom(function_inverse(A!11))) | (~subset(relation_rng(function_inverse(A!11)), relation_dom(B)))))),
% 1.89/1.43 inference(rewrite,[status(thm)],[])).
% 1.89/1.43 tff(140,plain,
% 1.89/1.43 (((~relation(function_inverse(A!11))) | ![B: $i] : ((relation_dom(relation_composition(function_inverse(A!11), B)) = relation_dom(function_inverse(A!11))) | (~subset(relation_rng(function_inverse(A!11)), relation_dom(B))) | (~relation(B)))) <=> ((~relation(function_inverse(A!11))) | ![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(function_inverse(A!11), B)) = relation_dom(function_inverse(A!11))) | (~subset(relation_rng(function_inverse(A!11)), relation_dom(B)))))),
% 1.89/1.43 inference(rewrite,[status(thm)],[])).
% 1.89/1.43 tff(141,plain,
% 1.89/1.43 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))) | ((~relation(function_inverse(A!11))) | ![B: $i] : ((relation_dom(relation_composition(function_inverse(A!11), B)) = relation_dom(function_inverse(A!11))) | (~subset(relation_rng(function_inverse(A!11)), relation_dom(B))) | (~relation(B))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))) | ((~relation(function_inverse(A!11))) | ![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(function_inverse(A!11), B)) = relation_dom(function_inverse(A!11))) | (~subset(relation_rng(function_inverse(A!11)), relation_dom(B))))))),
% 1.89/1.43 inference(monotonicity,[status(thm)],[140])).
% 1.89/1.43 tff(142,plain,
% 1.89/1.43 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))) | ((~relation(function_inverse(A!11))) | ![B: $i] : ((relation_dom(relation_composition(function_inverse(A!11), B)) = relation_dom(function_inverse(A!11))) | (~subset(relation_rng(function_inverse(A!11)), relation_dom(B))) | (~relation(B))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))) | (~relation(function_inverse(A!11))) | ![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(function_inverse(A!11), B)) = relation_dom(function_inverse(A!11))) | (~subset(relation_rng(function_inverse(A!11)), relation_dom(B)))))),
% 1.89/1.43 inference(transitivity,[status(thm)],[141, 139])).
% 1.89/1.43 tff(143,plain,
% 1.89/1.43 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))) | ((~relation(function_inverse(A!11))) | ![B: $i] : ((relation_dom(relation_composition(function_inverse(A!11), B)) = relation_dom(function_inverse(A!11))) | (~subset(relation_rng(function_inverse(A!11)), relation_dom(B))) | (~relation(B))))),
% 1.89/1.43 inference(quant_inst,[status(thm)],[])).
% 1.89/1.43 tff(144,plain,
% 1.89/1.43 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))) | (~relation(function_inverse(A!11))) | ![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(function_inverse(A!11), B)) = relation_dom(function_inverse(A!11))) | (~subset(relation_rng(function_inverse(A!11)), relation_dom(B))))),
% 1.89/1.43 inference(modus_ponens,[status(thm)],[143, 142])).
% 1.89/1.43 tff(145,plain,
% 1.89/1.43 ((~relation(function_inverse(A!11))) | ![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(function_inverse(A!11), B)) = relation_dom(function_inverse(A!11))) | (~subset(relation_rng(function_inverse(A!11)), relation_dom(B))))),
% 1.89/1.43 inference(unit_resolution,[status(thm)],[144, 138])).
% 1.89/1.43 tff(146,plain,
% 1.89/1.43 (![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(function_inverse(A!11), B)) = relation_dom(function_inverse(A!11))) | (~subset(relation_rng(function_inverse(A!11)), relation_dom(B))))),
% 1.89/1.43 inference(unit_resolution,[status(thm)],[145, 89])).
% 1.89/1.43 tff(147,plain,
% 1.89/1.43 (((~![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(function_inverse(A!11), B)) = relation_dom(function_inverse(A!11))) | (~subset(relation_rng(function_inverse(A!11)), relation_dom(B))))) | ((~relation(A!11)) | (relation_dom(relation_composition(function_inverse(A!11), A!11)) = relation_dom(function_inverse(A!11))) | (~subset(relation_rng(function_inverse(A!11)), relation_dom(A!11))))) <=> ((~![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(function_inverse(A!11), B)) = relation_dom(function_inverse(A!11))) | (~subset(relation_rng(function_inverse(A!11)), relation_dom(B))))) | (~relation(A!11)) | (relation_dom(relation_composition(function_inverse(A!11), A!11)) = relation_dom(function_inverse(A!11))) | (~subset(relation_rng(function_inverse(A!11)), relation_dom(A!11))))),
% 1.89/1.43 inference(rewrite,[status(thm)],[])).
% 1.89/1.43 tff(148,plain,
% 1.89/1.43 ((~![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(function_inverse(A!11), B)) = relation_dom(function_inverse(A!11))) | (~subset(relation_rng(function_inverse(A!11)), relation_dom(B))))) | ((~relation(A!11)) | (relation_dom(relation_composition(function_inverse(A!11), A!11)) = relation_dom(function_inverse(A!11))) | (~subset(relation_rng(function_inverse(A!11)), relation_dom(A!11))))),
% 1.89/1.43 inference(quant_inst,[status(thm)],[])).
% 1.89/1.43 tff(149,plain,
% 1.89/1.43 ((~![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(function_inverse(A!11), B)) = relation_dom(function_inverse(A!11))) | (~subset(relation_rng(function_inverse(A!11)), relation_dom(B))))) | (~relation(A!11)) | (relation_dom(relation_composition(function_inverse(A!11), A!11)) = relation_dom(function_inverse(A!11))) | (~subset(relation_rng(function_inverse(A!11)), relation_dom(A!11)))),
% 1.89/1.43 inference(modus_ponens,[status(thm)],[148, 147])).
% 1.89/1.43 tff(150,plain,
% 1.89/1.43 ((relation_dom(relation_composition(function_inverse(A!11), A!11)) = relation_dom(function_inverse(A!11))) | (~subset(relation_rng(function_inverse(A!11)), relation_dom(A!11)))),
% 1.89/1.43 inference(unit_resolution,[status(thm)],[149, 17, 146])).
% 1.89/1.43 tff(151,plain,
% 1.89/1.43 ($false),
% 1.89/1.43 inference(unit_resolution,[status(thm)],[150, 125, 64])).
% 1.89/1.43 % SZS output end Proof
%------------------------------------------------------------------------------