TSTP Solution File: SEU303+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU303+2 : TPTP v8.1.0. Released v3.3.0.
% 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 07:28:47 EDT 2022
% Result : Theorem 203.41s 128.30s
% Output : Proof 203.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU303+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n025.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Sep 3 11:58:18 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 203.41/128.30 % SZS status Theorem
% 203.41/128.30 % SZS output start Proof
% 203.41/128.30 tff(finite_type, type, (
% 203.41/128.30 finite: $i > $o)).
% 203.41/128.30 tff(relation_rng_type, type, (
% 203.41/128.30 relation_rng: $i > $i)).
% 203.41/128.30 tff(relation_inverse_type, type, (
% 203.41/128.30 relation_inverse: $i > $i)).
% 203.41/128.30 tff(tptp_fun_A_272_type, type, (
% 203.41/128.30 tptp_fun_A_272: $i)).
% 203.41/128.30 tff(relation_dom_type, type, (
% 203.41/128.30 relation_dom: $i > $i)).
% 203.41/128.30 tff(relation_type, type, (
% 203.41/128.30 relation: $i > $o)).
% 203.41/128.30 tff(function_type, type, (
% 203.41/128.30 function: $i > $o)).
% 203.41/128.30 tff(relation_image_type, type, (
% 203.41/128.30 relation_image: ( $i * $i ) > $i)).
% 203.41/128.30 tff(1,plain,
% 203.41/128.30 (^[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))))))))),
% 203.41/128.30 inference(bind,[status(th)],[])).
% 203.41/128.30 tff(2,plain,
% 203.41/128.30 (![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)))))))),
% 203.41/128.30 inference(quant_intro,[status(thm)],[1])).
% 203.41/128.30 tff(3,plain,
% 203.41/128.30 (^[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))))))))),
% 203.41/128.30 inference(bind,[status(th)],[])).
% 203.41/128.30 tff(4,plain,
% 203.41/128.30 (![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)))))))),
% 203.41/128.30 inference(quant_intro,[status(thm)],[3])).
% 203.41/128.30 tff(5,plain,
% 203.41/128.30 (![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)))))),
% 203.41/128.30 inference(rewrite,[status(thm)],[])).
% 203.41/128.30 tff(6,plain,
% 203.41/128.30 (^[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))))))),
% 203.41/128.30 inference(bind,[status(th)],[])).
% 203.41/128.30 tff(7,plain,
% 203.41/128.30 (![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)))))),
% 203.41/128.30 inference(quant_intro,[status(thm)],[6])).
% 203.41/128.30 tff(8,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')).
% 203.41/128.30 tff(9,plain,
% 203.41/128.30 (![A: $i] : ((~relation(A)) | ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A)))))),
% 203.41/128.30 inference(modus_ponens,[status(thm)],[8, 7])).
% 203.41/128.30 tff(10,plain,
% 203.41/128.30 (![A: $i] : ((~relation(A)) | ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A)))))),
% 203.41/128.30 inference(modus_ponens,[status(thm)],[9, 5])).
% 203.41/128.30 tff(11,plain,(
% 203.41/128.30 ![A: $i] : ((~relation(A)) | ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A)))))),
% 203.41/128.30 inference(skolemize,[status(sab)],[10])).
% 203.41/128.30 tff(12,plain,
% 203.41/128.30 (![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))),
% 203.41/128.30 inference(modus_ponens,[status(thm)],[11, 4])).
% 203.41/128.30 tff(13,plain,
% 203.41/128.30 (![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))),
% 203.41/128.30 inference(modus_ponens,[status(thm)],[12, 2])).
% 203.41/128.30 tff(14,plain,
% 203.41/128.30 ((~(finite(relation_rng(A!272)) | (~(relation(A!272) & function(A!272))) | (~finite(relation_dom(A!272))))) <=> (~(finite(relation_rng(A!272)) | (~(relation(A!272) & function(A!272))) | (~finite(relation_dom(A!272)))))),
% 203.41/128.30 inference(rewrite,[status(thm)],[])).
% 203.41/128.30 tff(15,plain,
% 203.41/128.30 ((~![A: $i] : (finite(relation_rng(A)) | (~(relation(A) & function(A))) | (~finite(relation_dom(A))))) <=> (~![A: $i] : (finite(relation_rng(A)) | (~(relation(A) & function(A))) | (~finite(relation_dom(A)))))),
% 203.41/128.30 inference(rewrite,[status(thm)],[])).
% 203.41/128.30 tff(16,plain,
% 203.41/128.30 ((~![A: $i] : ((relation(A) & function(A)) => (finite(relation_dom(A)) => finite(relation_rng(A))))) <=> (~![A: $i] : (finite(relation_rng(A)) | (~(relation(A) & function(A))) | (~finite(relation_dom(A)))))),
% 203.41/128.30 inference(rewrite,[status(thm)],[])).
% 203.41/128.30 tff(17,axiom,(~![A: $i] : ((relation(A) & function(A)) => (finite(relation_dom(A)) => finite(relation_rng(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t26_finset_1')).
% 203.41/128.30 tff(18,plain,
% 203.41/128.30 (~![A: $i] : (finite(relation_rng(A)) | (~(relation(A) & function(A))) | (~finite(relation_dom(A))))),
% 203.41/128.30 inference(modus_ponens,[status(thm)],[17, 16])).
% 203.41/128.30 tff(19,plain,
% 203.41/128.30 (~![A: $i] : (finite(relation_rng(A)) | (~(relation(A) & function(A))) | (~finite(relation_dom(A))))),
% 203.41/128.30 inference(modus_ponens,[status(thm)],[18, 15])).
% 203.41/128.30 tff(20,plain,
% 203.41/128.30 (~![A: $i] : (finite(relation_rng(A)) | (~(relation(A) & function(A))) | (~finite(relation_dom(A))))),
% 203.41/128.30 inference(modus_ponens,[status(thm)],[19, 15])).
% 203.41/128.30 tff(21,plain,
% 203.41/128.30 (~![A: $i] : (finite(relation_rng(A)) | (~(relation(A) & function(A))) | (~finite(relation_dom(A))))),
% 203.41/128.30 inference(modus_ponens,[status(thm)],[20, 15])).
% 203.41/128.30 tff(22,plain,
% 203.41/128.30 (~![A: $i] : (finite(relation_rng(A)) | (~(relation(A) & function(A))) | (~finite(relation_dom(A))))),
% 203.41/128.30 inference(modus_ponens,[status(thm)],[21, 15])).
% 203.41/128.30 tff(23,plain,
% 203.41/128.30 (~![A: $i] : (finite(relation_rng(A)) | (~(relation(A) & function(A))) | (~finite(relation_dom(A))))),
% 203.41/128.30 inference(modus_ponens,[status(thm)],[22, 15])).
% 203.41/128.30 tff(24,plain,
% 203.41/128.30 (~![A: $i] : (finite(relation_rng(A)) | (~(relation(A) & function(A))) | (~finite(relation_dom(A))))),
% 203.41/128.30 inference(modus_ponens,[status(thm)],[23, 15])).
% 203.41/128.30 tff(25,plain,(
% 203.41/128.30 ~(finite(relation_rng(A!272)) | (~(relation(A!272) & function(A!272))) | (~finite(relation_dom(A!272))))),
% 203.41/128.30 inference(skolemize,[status(sab)],[24])).
% 203.41/128.30 tff(26,plain,
% 203.41/128.30 (~(finite(relation_rng(A!272)) | (~(relation(A!272) & function(A!272))) | (~finite(relation_dom(A!272))))),
% 203.41/128.30 inference(modus_ponens,[status(thm)],[25, 14])).
% 203.41/128.30 tff(27,plain,
% 203.41/128.30 (relation(A!272) & function(A!272)),
% 203.41/128.30 inference(or_elim,[status(thm)],[26])).
% 203.41/128.30 tff(28,plain,
% 203.41/128.30 (relation(A!272)),
% 203.41/128.30 inference(and_elim,[status(thm)],[27])).
% 203.41/128.30 tff(29,plain,
% 203.41/128.30 (((~![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))) | ((~relation(A!272)) | (~((~(relation_rng(A!272) = relation_dom(relation_inverse(A!272)))) | (~(relation_dom(A!272) = relation_rng(relation_inverse(A!272)))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))) | (~relation(A!272)) | (~((~(relation_rng(A!272) = relation_dom(relation_inverse(A!272)))) | (~(relation_dom(A!272) = relation_rng(relation_inverse(A!272)))))))),
% 203.41/128.30 inference(rewrite,[status(thm)],[])).
% 203.41/128.30 tff(30,plain,
% 203.41/128.30 ((~![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))) | ((~relation(A!272)) | (~((~(relation_rng(A!272) = relation_dom(relation_inverse(A!272)))) | (~(relation_dom(A!272) = relation_rng(relation_inverse(A!272)))))))),
% 203.41/128.30 inference(quant_inst,[status(thm)],[])).
% 203.41/128.30 tff(31,plain,
% 203.41/128.30 ((~![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))) | (~relation(A!272)) | (~((~(relation_rng(A!272) = relation_dom(relation_inverse(A!272)))) | (~(relation_dom(A!272) = relation_rng(relation_inverse(A!272))))))),
% 203.41/128.31 inference(modus_ponens,[status(thm)],[30, 29])).
% 203.41/128.31 tff(32,plain,
% 203.41/128.31 (~((~(relation_rng(A!272) = relation_dom(relation_inverse(A!272)))) | (~(relation_dom(A!272) = relation_rng(relation_inverse(A!272)))))),
% 203.41/128.31 inference(unit_resolution,[status(thm)],[31, 28, 13])).
% 203.41/128.31 tff(33,plain,
% 203.41/128.31 (((~(relation_rng(A!272) = relation_dom(relation_inverse(A!272)))) | (~(relation_dom(A!272) = relation_rng(relation_inverse(A!272))))) | (relation_dom(A!272) = relation_rng(relation_inverse(A!272)))),
% 203.41/128.31 inference(tautology,[status(thm)],[])).
% 203.41/128.31 tff(34,plain,
% 203.41/128.31 (relation_dom(A!272) = relation_rng(relation_inverse(A!272))),
% 203.41/128.31 inference(unit_resolution,[status(thm)],[33, 32])).
% 203.41/128.31 tff(35,plain,
% 203.41/128.31 (relation_rng(relation_inverse(A!272)) = relation_dom(A!272)),
% 203.41/128.31 inference(symmetry,[status(thm)],[34])).
% 203.41/128.31 tff(36,plain,
% 203.41/128.31 (finite(relation_rng(relation_inverse(A!272))) <=> finite(relation_dom(A!272))),
% 203.41/128.31 inference(monotonicity,[status(thm)],[35])).
% 203.41/128.31 tff(37,plain,
% 203.41/128.31 (finite(relation_dom(A!272)) <=> finite(relation_rng(relation_inverse(A!272)))),
% 203.41/128.31 inference(symmetry,[status(thm)],[36])).
% 203.41/128.31 tff(38,plain,
% 203.41/128.31 (finite(relation_dom(A!272))),
% 203.41/128.31 inference(or_elim,[status(thm)],[26])).
% 203.41/128.31 tff(39,plain,
% 203.41/128.31 (finite(relation_rng(relation_inverse(A!272)))),
% 203.41/128.31 inference(modus_ponens,[status(thm)],[38, 37])).
% 203.41/128.31 tff(40,plain,
% 203.41/128.31 (^[A: $i] : refl(((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A))) <=> ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A))))),
% 203.41/128.31 inference(bind,[status(th)],[])).
% 203.41/128.31 tff(41,plain,
% 203.41/128.31 (![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A))) <=> ![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))),
% 203.41/128.31 inference(quant_intro,[status(thm)],[40])).
% 203.41/128.31 tff(42,plain,
% 203.41/128.31 (![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A))) <=> ![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))),
% 203.41/128.31 inference(rewrite,[status(thm)],[])).
% 203.41/128.31 tff(43,plain,
% 203.41/128.31 (^[A: $i] : rewrite((relation(A) => (relation_image(A, relation_dom(A)) = relation_rng(A))) <=> ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A))))),
% 203.41/128.31 inference(bind,[status(th)],[])).
% 203.41/128.31 tff(44,plain,
% 203.41/128.31 (![A: $i] : (relation(A) => (relation_image(A, relation_dom(A)) = relation_rng(A))) <=> ![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))),
% 203.41/128.31 inference(quant_intro,[status(thm)],[43])).
% 203.41/128.31 tff(45,axiom,(![A: $i] : (relation(A) => (relation_image(A, relation_dom(A)) = relation_rng(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t146_relat_1')).
% 203.41/128.31 tff(46,plain,
% 203.41/128.31 (![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))),
% 203.41/128.31 inference(modus_ponens,[status(thm)],[45, 44])).
% 203.41/128.31 tff(47,plain,
% 203.41/128.31 (![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))),
% 203.41/128.31 inference(modus_ponens,[status(thm)],[46, 42])).
% 203.41/128.31 tff(48,plain,(
% 203.41/128.31 ![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))),
% 203.41/128.31 inference(skolemize,[status(sab)],[47])).
% 203.41/128.31 tff(49,plain,
% 203.41/128.31 (![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))),
% 203.41/128.31 inference(modus_ponens,[status(thm)],[48, 41])).
% 203.41/128.31 tff(50,plain,
% 203.41/128.31 (((~![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))) | ((~relation(A!272)) | (relation_image(A!272, relation_dom(A!272)) = relation_rng(A!272)))) <=> ((~![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))) | (~relation(A!272)) | (relation_image(A!272, relation_dom(A!272)) = relation_rng(A!272)))),
% 203.41/128.31 inference(rewrite,[status(thm)],[])).
% 203.41/128.31 tff(51,plain,
% 203.41/128.31 ((~![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))) | ((~relation(A!272)) | (relation_image(A!272, relation_dom(A!272)) = relation_rng(A!272)))),
% 203.41/128.31 inference(quant_inst,[status(thm)],[])).
% 203.41/128.31 tff(52,plain,
% 203.41/128.31 ((~![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))) | (~relation(A!272)) | (relation_image(A!272, relation_dom(A!272)) = relation_rng(A!272))),
% 203.41/128.31 inference(modus_ponens,[status(thm)],[51, 50])).
% 203.41/128.31 tff(53,plain,
% 203.41/128.31 (relation_image(A!272, relation_dom(A!272)) = relation_rng(A!272)),
% 203.41/128.31 inference(unit_resolution,[status(thm)],[52, 49, 28])).
% 203.41/128.31 tff(54,plain,
% 203.41/128.31 (relation_image(A!272, relation_rng(relation_inverse(A!272))) = relation_image(A!272, relation_dom(A!272))),
% 203.41/128.31 inference(monotonicity,[status(thm)],[35])).
% 203.41/128.31 tff(55,plain,
% 203.41/128.31 (relation_image(A!272, relation_rng(relation_inverse(A!272))) = relation_rng(A!272)),
% 203.41/128.31 inference(transitivity,[status(thm)],[54, 53])).
% 203.41/128.31 tff(56,plain,
% 203.41/128.31 (finite(relation_image(A!272, relation_rng(relation_inverse(A!272)))) <=> finite(relation_rng(A!272))),
% 203.41/128.31 inference(monotonicity,[status(thm)],[55])).
% 203.41/128.31 tff(57,plain,
% 203.41/128.31 (finite(relation_rng(A!272)) <=> finite(relation_image(A!272, relation_rng(relation_inverse(A!272))))),
% 203.41/128.31 inference(symmetry,[status(thm)],[56])).
% 203.41/128.31 tff(58,plain,
% 203.41/128.31 ((~finite(relation_rng(A!272))) <=> (~finite(relation_image(A!272, relation_rng(relation_inverse(A!272)))))),
% 203.41/128.31 inference(monotonicity,[status(thm)],[57])).
% 203.41/128.31 tff(59,plain,
% 203.41/128.31 (~finite(relation_rng(A!272))),
% 203.41/128.31 inference(or_elim,[status(thm)],[26])).
% 203.41/128.31 tff(60,plain,
% 203.41/128.31 (~finite(relation_image(A!272, relation_rng(relation_inverse(A!272))))),
% 203.41/128.31 inference(modus_ponens,[status(thm)],[59, 58])).
% 203.41/128.31 tff(61,plain,
% 203.41/128.31 (function(A!272)),
% 203.41/128.31 inference(and_elim,[status(thm)],[27])).
% 203.41/128.31 tff(62,plain,
% 203.41/128.31 (^[A: $i, B: $i] : refl((finite(relation_image(B, A)) | (~relation(B)) | (~finite(A)) | (~function(B))) <=> (finite(relation_image(B, A)) | (~relation(B)) | (~finite(A)) | (~function(B))))),
% 203.41/128.31 inference(bind,[status(th)],[])).
% 203.41/128.31 tff(63,plain,
% 203.41/128.31 (![A: $i, B: $i] : (finite(relation_image(B, A)) | (~relation(B)) | (~finite(A)) | (~function(B))) <=> ![A: $i, B: $i] : (finite(relation_image(B, A)) | (~relation(B)) | (~finite(A)) | (~function(B)))),
% 203.41/128.31 inference(quant_intro,[status(thm)],[62])).
% 203.41/128.31 tff(64,plain,
% 203.41/128.31 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B))))), ((~(relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B))))))), rewrite((~(~((~relation(B)) | (~function(B))))) <=> ((~relation(B)) | (~function(B)))), ((~(relation(B) & function(B))) <=> ((~relation(B)) | (~function(B))))), ((finite(relation_image(B, A)) | (~(relation(B) & function(B))) | (~finite(A))) <=> (finite(relation_image(B, A)) | ((~relation(B)) | (~function(B))) | (~finite(A))))), rewrite((finite(relation_image(B, A)) | ((~relation(B)) | (~function(B))) | (~finite(A))) <=> (finite(relation_image(B, A)) | (~relation(B)) | (~finite(A)) | (~function(B)))), ((finite(relation_image(B, A)) | (~(relation(B) & function(B))) | (~finite(A))) <=> (finite(relation_image(B, A)) | (~relation(B)) | (~finite(A)) | (~function(B)))))),
% 203.41/128.31 inference(bind,[status(th)],[])).
% 203.41/128.31 tff(65,plain,
% 203.41/128.31 (![A: $i, B: $i] : (finite(relation_image(B, A)) | (~(relation(B) & function(B))) | (~finite(A))) <=> ![A: $i, B: $i] : (finite(relation_image(B, A)) | (~relation(B)) | (~finite(A)) | (~function(B)))),
% 203.41/128.31 inference(quant_intro,[status(thm)],[64])).
% 203.41/128.31 tff(66,plain,
% 203.41/128.31 (![A: $i, B: $i] : (finite(relation_image(B, A)) | (~(relation(B) & function(B))) | (~finite(A))) <=> ![A: $i, B: $i] : (finite(relation_image(B, A)) | (~(relation(B) & function(B))) | (~finite(A)))),
% 203.41/128.31 inference(rewrite,[status(thm)],[])).
% 203.41/128.31 tff(67,plain,
% 203.41/128.31 (^[A: $i, B: $i] : trans(monotonicity(rewrite((finite(A) => finite(relation_image(B, A))) <=> (finite(relation_image(B, A)) | (~finite(A)))), (((relation(B) & function(B)) => (finite(A) => finite(relation_image(B, A)))) <=> ((relation(B) & function(B)) => (finite(relation_image(B, A)) | (~finite(A)))))), rewrite(((relation(B) & function(B)) => (finite(relation_image(B, A)) | (~finite(A)))) <=> (finite(relation_image(B, A)) | (~(relation(B) & function(B))) | (~finite(A)))), (((relation(B) & function(B)) => (finite(A) => finite(relation_image(B, A)))) <=> (finite(relation_image(B, A)) | (~(relation(B) & function(B))) | (~finite(A)))))),
% 203.46/128.31 inference(bind,[status(th)],[])).
% 203.46/128.31 tff(68,plain,
% 203.46/128.31 (![A: $i, B: $i] : ((relation(B) & function(B)) => (finite(A) => finite(relation_image(B, A)))) <=> ![A: $i, B: $i] : (finite(relation_image(B, A)) | (~(relation(B) & function(B))) | (~finite(A)))),
% 203.46/128.31 inference(quant_intro,[status(thm)],[67])).
% 203.46/128.31 tff(69,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => (finite(A) => finite(relation_image(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t17_finset_1')).
% 203.46/128.31 tff(70,plain,
% 203.46/128.31 (![A: $i, B: $i] : (finite(relation_image(B, A)) | (~(relation(B) & function(B))) | (~finite(A)))),
% 203.46/128.31 inference(modus_ponens,[status(thm)],[69, 68])).
% 203.46/128.31 tff(71,plain,
% 203.46/128.31 (![A: $i, B: $i] : (finite(relation_image(B, A)) | (~(relation(B) & function(B))) | (~finite(A)))),
% 203.46/128.31 inference(modus_ponens,[status(thm)],[70, 66])).
% 203.46/128.31 tff(72,plain,(
% 203.46/128.31 ![A: $i, B: $i] : (finite(relation_image(B, A)) | (~(relation(B) & function(B))) | (~finite(A)))),
% 203.46/128.31 inference(skolemize,[status(sab)],[71])).
% 203.46/128.31 tff(73,plain,
% 203.46/128.31 (![A: $i, B: $i] : (finite(relation_image(B, A)) | (~relation(B)) | (~finite(A)) | (~function(B)))),
% 203.46/128.31 inference(modus_ponens,[status(thm)],[72, 65])).
% 203.46/128.31 tff(74,plain,
% 203.46/128.31 (![A: $i, B: $i] : (finite(relation_image(B, A)) | (~relation(B)) | (~finite(A)) | (~function(B)))),
% 203.46/128.31 inference(modus_ponens,[status(thm)],[73, 63])).
% 203.46/128.31 tff(75,plain,
% 203.46/128.31 (((~![A: $i, B: $i] : (finite(relation_image(B, A)) | (~relation(B)) | (~finite(A)) | (~function(B)))) | ((~relation(A!272)) | (~function(A!272)) | finite(relation_image(A!272, relation_rng(relation_inverse(A!272)))) | (~finite(relation_rng(relation_inverse(A!272)))))) <=> ((~![A: $i, B: $i] : (finite(relation_image(B, A)) | (~relation(B)) | (~finite(A)) | (~function(B)))) | (~relation(A!272)) | (~function(A!272)) | finite(relation_image(A!272, relation_rng(relation_inverse(A!272)))) | (~finite(relation_rng(relation_inverse(A!272)))))),
% 203.46/128.31 inference(rewrite,[status(thm)],[])).
% 203.46/128.31 tff(76,plain,
% 203.46/128.31 ((finite(relation_image(A!272, relation_rng(relation_inverse(A!272)))) | (~relation(A!272)) | (~finite(relation_rng(relation_inverse(A!272)))) | (~function(A!272))) <=> ((~relation(A!272)) | (~function(A!272)) | finite(relation_image(A!272, relation_rng(relation_inverse(A!272)))) | (~finite(relation_rng(relation_inverse(A!272)))))),
% 203.46/128.31 inference(rewrite,[status(thm)],[])).
% 203.46/128.31 tff(77,plain,
% 203.46/128.31 (((~![A: $i, B: $i] : (finite(relation_image(B, A)) | (~relation(B)) | (~finite(A)) | (~function(B)))) | (finite(relation_image(A!272, relation_rng(relation_inverse(A!272)))) | (~relation(A!272)) | (~finite(relation_rng(relation_inverse(A!272)))) | (~function(A!272)))) <=> ((~![A: $i, B: $i] : (finite(relation_image(B, A)) | (~relation(B)) | (~finite(A)) | (~function(B)))) | ((~relation(A!272)) | (~function(A!272)) | finite(relation_image(A!272, relation_rng(relation_inverse(A!272)))) | (~finite(relation_rng(relation_inverse(A!272))))))),
% 203.46/128.31 inference(monotonicity,[status(thm)],[76])).
% 203.46/128.31 tff(78,plain,
% 203.46/128.31 (((~![A: $i, B: $i] : (finite(relation_image(B, A)) | (~relation(B)) | (~finite(A)) | (~function(B)))) | (finite(relation_image(A!272, relation_rng(relation_inverse(A!272)))) | (~relation(A!272)) | (~finite(relation_rng(relation_inverse(A!272)))) | (~function(A!272)))) <=> ((~![A: $i, B: $i] : (finite(relation_image(B, A)) | (~relation(B)) | (~finite(A)) | (~function(B)))) | (~relation(A!272)) | (~function(A!272)) | finite(relation_image(A!272, relation_rng(relation_inverse(A!272)))) | (~finite(relation_rng(relation_inverse(A!272)))))),
% 203.46/128.31 inference(transitivity,[status(thm)],[77, 75])).
% 203.46/128.31 tff(79,plain,
% 203.46/128.31 ((~![A: $i, B: $i] : (finite(relation_image(B, A)) | (~relation(B)) | (~finite(A)) | (~function(B)))) | (finite(relation_image(A!272, relation_rng(relation_inverse(A!272)))) | (~relation(A!272)) | (~finite(relation_rng(relation_inverse(A!272)))) | (~function(A!272)))),
% 203.58/128.43 inference(quant_inst,[status(thm)],[])).
% 203.58/128.43 tff(80,plain,
% 203.58/128.43 ((~![A: $i, B: $i] : (finite(relation_image(B, A)) | (~relation(B)) | (~finite(A)) | (~function(B)))) | (~relation(A!272)) | (~function(A!272)) | finite(relation_image(A!272, relation_rng(relation_inverse(A!272)))) | (~finite(relation_rng(relation_inverse(A!272))))),
% 203.58/128.43 inference(modus_ponens,[status(thm)],[79, 78])).
% 203.58/128.43 tff(81,plain,
% 203.58/128.43 (finite(relation_image(A!272, relation_rng(relation_inverse(A!272)))) | (~finite(relation_rng(relation_inverse(A!272))))),
% 203.58/128.43 inference(unit_resolution,[status(thm)],[80, 74, 28, 61])).
% 203.58/128.43 tff(82,plain,
% 203.58/128.43 ($false),
% 203.58/128.43 inference(unit_resolution,[status(thm)],[81, 60, 39])).
% 203.58/128.43 % SZS output end Proof
%------------------------------------------------------------------------------