TSTP Solution File: SEU303+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU303+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU303+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 11:46:32 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(finite_type, type, (
% 0.19/0.39 finite: $i > $o)).
% 0.19/0.39 tff(relation_image_type, type, (
% 0.19/0.39 relation_image: ( $i * $i ) > $i)).
% 0.19/0.39 tff(relation_dom_type, type, (
% 0.19/0.39 relation_dom: $i > $i)).
% 0.19/0.39 tff(tptp_fun_A_1_type, type, (
% 0.19/0.39 tptp_fun_A_1: $i)).
% 0.19/0.39 tff(relation_rng_type, type, (
% 0.19/0.39 relation_rng: $i > $i)).
% 0.19/0.39 tff(relation_type, type, (
% 0.19/0.39 relation: $i > $o)).
% 0.19/0.39 tff(function_type, type, (
% 0.19/0.39 function: $i > $o)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 ((~(finite(relation_rng(A!1)) | (~(relation(A!1) & function(A!1))) | (~finite(relation_dom(A!1))))) <=> (~(finite(relation_rng(A!1)) | (~(relation(A!1) & function(A!1))) | (~finite(relation_dom(A!1)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 ((~![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)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 ((~![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)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(4,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')).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (~![A: $i] : (finite(relation_rng(A)) | (~(relation(A) & function(A))) | (~finite(relation_dom(A))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 (~![A: $i] : (finite(relation_rng(A)) | (~(relation(A) & function(A))) | (~finite(relation_dom(A))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (~![A: $i] : (finite(relation_rng(A)) | (~(relation(A) & function(A))) | (~finite(relation_dom(A))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 (~![A: $i] : (finite(relation_rng(A)) | (~(relation(A) & function(A))) | (~finite(relation_dom(A))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (~![A: $i] : (finite(relation_rng(A)) | (~(relation(A) & function(A))) | (~finite(relation_dom(A))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (~![A: $i] : (finite(relation_rng(A)) | (~(relation(A) & function(A))) | (~finite(relation_dom(A))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 (~![A: $i] : (finite(relation_rng(A)) | (~(relation(A) & function(A))) | (~finite(relation_dom(A))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.19/0.39 tff(12,plain,(
% 0.19/0.39 ~(finite(relation_rng(A!1)) | (~(relation(A!1) & function(A!1))) | (~finite(relation_dom(A!1))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[11])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (~(finite(relation_rng(A!1)) | (~(relation(A!1) & function(A!1))) | (~finite(relation_dom(A!1))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[12, 1])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (relation(A!1) & function(A!1)),
% 0.19/0.39 inference(or_elim,[status(thm)],[13])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (relation(A!1)),
% 0.19/0.39 inference(and_elim,[status(thm)],[14])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (^[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))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (^[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))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.39 tff(21,axiom,(![A: $i] : (relation(A) => (relation_image(A, relation_dom(A)) = relation_rng(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t146_relat_1')).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.19/0.39 tff(24,plain,(
% 0.19/0.39 ![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[23])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (((~![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))) | ((~relation(A!1)) | (relation_image(A!1, relation_dom(A!1)) = relation_rng(A!1)))) <=> ((~![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))) | (~relation(A!1)) | (relation_image(A!1, relation_dom(A!1)) = relation_rng(A!1)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 ((~![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))) | ((~relation(A!1)) | (relation_image(A!1, relation_dom(A!1)) = relation_rng(A!1)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 ((~![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))) | (~relation(A!1)) | (relation_image(A!1, relation_dom(A!1)) = relation_rng(A!1))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (relation_image(A!1, relation_dom(A!1)) = relation_rng(A!1)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[28, 25, 15])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (finite(relation_image(A!1, relation_dom(A!1))) <=> finite(relation_rng(A!1))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[29])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (finite(relation_rng(A!1)) <=> finite(relation_image(A!1, relation_dom(A!1)))),
% 0.19/0.39 inference(symmetry,[status(thm)],[30])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 ((~finite(relation_rng(A!1))) <=> (~finite(relation_image(A!1, relation_dom(A!1))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[31])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (~finite(relation_rng(A!1))),
% 0.19/0.39 inference(or_elim,[status(thm)],[13])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 (~finite(relation_image(A!1, relation_dom(A!1)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 (finite(relation_dom(A!1))),
% 0.19/0.39 inference(or_elim,[status(thm)],[13])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (function(A!1)),
% 0.19/0.39 inference(and_elim,[status(thm)],[14])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (^[A: $i, B: $i] : refl((finite(relation_image(A, B)) | (~relation(A)) | (~function(A)) | (~finite(B))) <=> (finite(relation_image(A, B)) | (~relation(A)) | (~function(A)) | (~finite(B))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (![A: $i, B: $i] : (finite(relation_image(A, B)) | (~relation(A)) | (~function(A)) | (~finite(B))) <=> ![A: $i, B: $i] : (finite(relation_image(A, B)) | (~relation(A)) | (~function(A)) | (~finite(B)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[37])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & function(A) & finite(B)) <=> (~((~relation(A)) | (~function(A)) | (~finite(B))))), ((~(relation(A) & function(A) & finite(B))) <=> (~(~((~relation(A)) | (~function(A)) | (~finite(B))))))), rewrite((~(~((~relation(A)) | (~function(A)) | (~finite(B))))) <=> ((~relation(A)) | (~function(A)) | (~finite(B)))), ((~(relation(A) & function(A) & finite(B))) <=> ((~relation(A)) | (~function(A)) | (~finite(B))))), ((finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B)))) <=> (finite(relation_image(A, B)) | ((~relation(A)) | (~function(A)) | (~finite(B)))))), rewrite((finite(relation_image(A, B)) | ((~relation(A)) | (~function(A)) | (~finite(B)))) <=> (finite(relation_image(A, B)) | (~relation(A)) | (~function(A)) | (~finite(B)))), ((finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B)))) <=> (finite(relation_image(A, B)) | (~relation(A)) | (~function(A)) | (~finite(B)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (![A: $i, B: $i] : (finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B)))) <=> ![A: $i, B: $i] : (finite(relation_image(A, B)) | (~relation(A)) | (~function(A)) | (~finite(B)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[39])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (![A: $i, B: $i] : (finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B)))) <=> ![A: $i, B: $i] : (finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((relation(A) & function(A)) & finite(B)) <=> (relation(A) & function(A) & finite(B))), ((((relation(A) & function(A)) & finite(B)) => finite(relation_image(A, B))) <=> ((relation(A) & function(A) & finite(B)) => finite(relation_image(A, B))))), rewrite(((relation(A) & function(A) & finite(B)) => finite(relation_image(A, B))) <=> (finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B))))), ((((relation(A) & function(A)) & finite(B)) => finite(relation_image(A, B))) <=> (finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 (![A: $i, B: $i] : (((relation(A) & function(A)) & finite(B)) => finite(relation_image(A, B))) <=> ![A: $i, B: $i] : (finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[42])).
% 0.19/0.39 tff(44,axiom,(![A: $i, B: $i] : (((relation(A) & function(A)) & finite(B)) => finite(relation_image(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc13_finset_1')).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 (![A: $i, B: $i] : (finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 (![A: $i, B: $i] : (finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.19/0.39 tff(47,plain,(
% 0.19/0.39 ![A: $i, B: $i] : (finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[46])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 (![A: $i, B: $i] : (finite(relation_image(A, B)) | (~relation(A)) | (~function(A)) | (~finite(B)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 (![A: $i, B: $i] : (finite(relation_image(A, B)) | (~relation(A)) | (~function(A)) | (~finite(B)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[48, 38])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 (((~![A: $i, B: $i] : (finite(relation_image(A, B)) | (~relation(A)) | (~function(A)) | (~finite(B)))) | ((~finite(relation_dom(A!1))) | (~relation(A!1)) | finite(relation_image(A!1, relation_dom(A!1))) | (~function(A!1)))) <=> ((~![A: $i, B: $i] : (finite(relation_image(A, B)) | (~relation(A)) | (~function(A)) | (~finite(B)))) | (~finite(relation_dom(A!1))) | (~relation(A!1)) | finite(relation_image(A!1, relation_dom(A!1))) | (~function(A!1)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 ((finite(relation_image(A!1, relation_dom(A!1))) | (~relation(A!1)) | (~function(A!1)) | (~finite(relation_dom(A!1)))) <=> ((~finite(relation_dom(A!1))) | (~relation(A!1)) | finite(relation_image(A!1, relation_dom(A!1))) | (~function(A!1)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 (((~![A: $i, B: $i] : (finite(relation_image(A, B)) | (~relation(A)) | (~function(A)) | (~finite(B)))) | (finite(relation_image(A!1, relation_dom(A!1))) | (~relation(A!1)) | (~function(A!1)) | (~finite(relation_dom(A!1))))) <=> ((~![A: $i, B: $i] : (finite(relation_image(A, B)) | (~relation(A)) | (~function(A)) | (~finite(B)))) | ((~finite(relation_dom(A!1))) | (~relation(A!1)) | finite(relation_image(A!1, relation_dom(A!1))) | (~function(A!1))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[51])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 (((~![A: $i, B: $i] : (finite(relation_image(A, B)) | (~relation(A)) | (~function(A)) | (~finite(B)))) | (finite(relation_image(A!1, relation_dom(A!1))) | (~relation(A!1)) | (~function(A!1)) | (~finite(relation_dom(A!1))))) <=> ((~![A: $i, B: $i] : (finite(relation_image(A, B)) | (~relation(A)) | (~function(A)) | (~finite(B)))) | (~finite(relation_dom(A!1))) | (~relation(A!1)) | finite(relation_image(A!1, relation_dom(A!1))) | (~function(A!1)))),
% 0.19/0.39 inference(transitivity,[status(thm)],[52, 50])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : (finite(relation_image(A, B)) | (~relation(A)) | (~function(A)) | (~finite(B)))) | (finite(relation_image(A!1, relation_dom(A!1))) | (~relation(A!1)) | (~function(A!1)) | (~finite(relation_dom(A!1))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : (finite(relation_image(A, B)) | (~relation(A)) | (~function(A)) | (~finite(B)))) | (~finite(relation_dom(A!1))) | (~relation(A!1)) | finite(relation_image(A!1, relation_dom(A!1))) | (~function(A!1))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 (finite(relation_image(A!1, relation_dom(A!1)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[55, 49, 15, 36, 35])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[56, 34])).
% 0.19/0.39 % SZS output end Proof
%------------------------------------------------------------------------------