TSTP Solution File: SEU294+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU294+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 07:28:44 EDT 2022
% Result : Theorem 0.18s 0.39s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU294+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.33 % Computer : n017.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sat Sep 3 11:05:09 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 0.18/0.39 % SZS status Theorem
% 0.18/0.39 % SZS output start Proof
% 0.18/0.39 tff(element_type, type, (
% 0.18/0.39 element: ( $i * $i ) > $o)).
% 0.18/0.39 tff(powerset_type, type, (
% 0.18/0.39 powerset: $i > $i)).
% 0.18/0.39 tff(tptp_fun_B_19_type, type, (
% 0.18/0.39 tptp_fun_B_19: $i)).
% 0.18/0.39 tff(tptp_fun_A_20_type, type, (
% 0.18/0.39 tptp_fun_A_20: $i)).
% 0.18/0.39 tff(subset_type, type, (
% 0.18/0.39 subset: ( $i * $i ) > $o)).
% 0.18/0.39 tff(finite_type, type, (
% 0.18/0.39 finite: $i > $o)).
% 0.18/0.39 tff(1,plain,
% 0.18/0.39 (^[A: $i, B: $i] : refl((element(A, powerset(B)) <=> subset(A, B)) <=> (element(A, powerset(B)) <=> subset(A, B)))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(2,plain,
% 0.18/0.39 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.39 tff(3,plain,
% 0.18/0.39 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(4,axiom,(![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t3_subset')).
% 0.18/0.39 tff(5,plain,
% 0.18/0.39 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.18/0.39 tff(6,plain,(
% 0.18/0.39 ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.18/0.39 inference(skolemize,[status(sab)],[5])).
% 0.18/0.39 tff(7,plain,
% 0.18/0.39 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.18/0.39 tff(8,plain,
% 0.18/0.39 ((~![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))) | (element(A!20, powerset(B!19)) <=> subset(A!20, B!19))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(9,plain,
% 0.18/0.39 (element(A!20, powerset(B!19)) <=> subset(A!20, B!19)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.18/0.39 tff(10,plain,
% 0.18/0.39 ((~![A: $i, B: $i] : (finite(A) | (~(subset(A, B) & finite(B))))) <=> (~![A: $i, B: $i] : (finite(A) | (~(subset(A, B) & finite(B)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(11,plain,
% 0.18/0.39 ((~![A: $i, B: $i] : ((subset(A, B) & finite(B)) => finite(A))) <=> (~![A: $i, B: $i] : (finite(A) | (~(subset(A, B) & finite(B)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(12,axiom,(~![A: $i, B: $i] : ((subset(A, B) & finite(B)) => finite(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t13_finset_1')).
% 0.18/0.39 tff(13,plain,
% 0.18/0.39 (~![A: $i, B: $i] : (finite(A) | (~(subset(A, B) & finite(B))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.18/0.39 tff(14,plain,
% 0.18/0.39 (~![A: $i, B: $i] : (finite(A) | (~(subset(A, B) & finite(B))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.18/0.39 tff(15,plain,
% 0.18/0.39 (~![A: $i, B: $i] : (finite(A) | (~(subset(A, B) & finite(B))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.18/0.39 tff(16,plain,
% 0.18/0.39 (~![A: $i, B: $i] : (finite(A) | (~(subset(A, B) & finite(B))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.18/0.39 tff(17,plain,
% 0.18/0.39 (~![A: $i, B: $i] : (finite(A) | (~(subset(A, B) & finite(B))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[16, 10])).
% 0.18/0.39 tff(18,plain,
% 0.18/0.39 (~![A: $i, B: $i] : (finite(A) | (~(subset(A, B) & finite(B))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.18/0.39 tff(19,plain,
% 0.18/0.39 (~![A: $i, B: $i] : (finite(A) | (~(subset(A, B) & finite(B))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[18, 10])).
% 0.18/0.39 tff(20,plain,(
% 0.18/0.39 ~(finite(A!20) | (~(subset(A!20, B!19) & finite(B!19))))),
% 0.18/0.39 inference(skolemize,[status(sab)],[19])).
% 0.18/0.39 tff(21,plain,
% 0.18/0.39 (subset(A!20, B!19) & finite(B!19)),
% 0.18/0.39 inference(or_elim,[status(thm)],[20])).
% 0.18/0.39 tff(22,plain,
% 0.18/0.39 (subset(A!20, B!19)),
% 0.18/0.39 inference(and_elim,[status(thm)],[21])).
% 0.18/0.39 tff(23,plain,
% 0.18/0.39 ((~(element(A!20, powerset(B!19)) <=> subset(A!20, B!19))) | element(A!20, powerset(B!19)) | (~subset(A!20, B!19))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(24,plain,
% 0.18/0.39 ((~(element(A!20, powerset(B!19)) <=> subset(A!20, B!19))) | element(A!20, powerset(B!19))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.18/0.39 tff(25,plain,
% 0.18/0.39 (element(A!20, powerset(B!19))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[24, 9])).
% 0.18/0.39 tff(26,plain,
% 0.18/0.39 (finite(B!19)),
% 0.18/0.39 inference(and_elim,[status(thm)],[21])).
% 0.18/0.39 tff(27,plain,
% 0.18/0.39 (^[A: $i] : refl(((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A))))) <=> ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(28,plain,
% 0.18/0.39 (![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A))))) <=> ![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[27])).
% 0.18/0.39 tff(29,plain,
% 0.18/0.39 (^[A: $i] : rewrite(((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A))))) <=> ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(30,plain,
% 0.18/0.39 (![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A))))) <=> ![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[29])).
% 0.18/0.39 tff(31,plain,
% 0.18/0.39 (![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A))))) <=> ![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.18/0.39 inference(transitivity,[status(thm)],[30, 28])).
% 0.18/0.39 tff(32,plain,
% 0.18/0.39 (![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A))))) <=> ![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(33,plain,
% 0.18/0.39 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((element(B, powerset(A)) => finite(B)) <=> (finite(B) | (~element(B, powerset(A)))))), (![B: $i] : (element(B, powerset(A)) => finite(B)) <=> ![B: $i] : (finite(B) | (~element(B, powerset(A)))))), ((finite(A) => ![B: $i] : (element(B, powerset(A)) => finite(B))) <=> (finite(A) => ![B: $i] : (finite(B) | (~element(B, powerset(A))))))), rewrite((finite(A) => ![B: $i] : (finite(B) | (~element(B, powerset(A))))) <=> ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))), ((finite(A) => ![B: $i] : (element(B, powerset(A)) => finite(B))) <=> ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(34,plain,
% 0.18/0.39 (![A: $i] : (finite(A) => ![B: $i] : (element(B, powerset(A)) => finite(B))) <=> ![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[33])).
% 0.18/0.39 tff(35,axiom,(![A: $i] : (finite(A) => ![B: $i] : (element(B, powerset(A)) => finite(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cc2_finset_1')).
% 0.18/0.39 tff(36,plain,
% 0.18/0.39 (![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.18/0.39 tff(37,plain,
% 0.18/0.39 (![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.18/0.39 tff(38,plain,(
% 0.18/0.39 ![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.18/0.39 inference(skolemize,[status(sab)],[37])).
% 0.18/0.39 tff(39,plain,
% 0.18/0.39 (![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.18/0.39 tff(40,plain,
% 0.18/0.39 (((~![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))) | ((~finite(B!19)) | ![B: $i] : (finite(B) | (~element(B, powerset(B!19)))))) <=> ((~![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))) | (~finite(B!19)) | ![B: $i] : (finite(B) | (~element(B, powerset(B!19)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(41,plain,
% 0.18/0.39 ((~![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))) | ((~finite(B!19)) | ![B: $i] : (finite(B) | (~element(B, powerset(B!19)))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(42,plain,
% 0.18/0.39 ((~![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))) | (~finite(B!19)) | ![B: $i] : (finite(B) | (~element(B, powerset(B!19))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.18/0.39 tff(43,plain,
% 0.18/0.39 (![B: $i] : (finite(B) | (~element(B, powerset(B!19))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[42, 39, 26])).
% 0.18/0.40 tff(44,plain,
% 0.18/0.40 (~finite(A!20)),
% 0.18/0.40 inference(or_elim,[status(thm)],[20])).
% 0.18/0.40 tff(45,plain,
% 0.18/0.40 (((~![B: $i] : (finite(B) | (~element(B, powerset(B!19))))) | (finite(A!20) | (~element(A!20, powerset(B!19))))) <=> ((~![B: $i] : (finite(B) | (~element(B, powerset(B!19))))) | finite(A!20) | (~element(A!20, powerset(B!19))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(46,plain,
% 0.18/0.40 ((~![B: $i] : (finite(B) | (~element(B, powerset(B!19))))) | (finite(A!20) | (~element(A!20, powerset(B!19))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(47,plain,
% 0.18/0.40 ((~![B: $i] : (finite(B) | (~element(B, powerset(B!19))))) | finite(A!20) | (~element(A!20, powerset(B!19)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.18/0.40 tff(48,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[47, 44, 43, 25])).
% 0.18/0.40 % SZS output end Proof
%------------------------------------------------------------------------------