TSTP Solution File: SEV421_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEV421_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 08:12:32 EDT 2022
% Result : Theorem 0.15s 0.35s
% Output : Proof 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEV421_1 : TPTP v8.1.0. Released v5.0.0.
% 0.00/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.30 % Computer : n006.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Sat Sep 3 18:48:38 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.09/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.31 Usage: tptp [options] [-file:]file
% 0.09/0.31 -h, -? prints this message.
% 0.09/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.31 -m, -model generate model.
% 0.09/0.31 -p, -proof generate proof.
% 0.09/0.31 -c, -core generate unsat core of named formulas.
% 0.09/0.31 -st, -statistics display statistics.
% 0.09/0.31 -t:timeout set timeout (in second).
% 0.09/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.31 -<param>:<value> configuration parameter and value.
% 0.09/0.31 -o:<output-file> file to place output in.
% 0.15/0.35 % SZS status Theorem
% 0.15/0.35 % SZS output start Proof
% 0.15/0.35 tff(cardinality_type, type, (
% 0.15/0.35 cardinality: set > $int)).
% 0.15/0.35 tff(tptp_fun_C_3_type, type, (
% 0.15/0.35 tptp_fun_C_3: set)).
% 0.15/0.35 tff(tptp_fun_Size_2_type, type, (
% 0.15/0.35 tptp_fun_Size_2: $int)).
% 0.15/0.35 tff(member_type, type, (
% 0.15/0.35 member: ( element * set ) > $o)).
% 0.15/0.35 tff(tptp_fun_X_4_type, type, (
% 0.15/0.35 tptp_fun_X_4: element)).
% 0.15/0.35 tff(empty_set_type, type, (
% 0.15/0.35 empty_set: set)).
% 0.15/0.35 tff(1,plain,
% 0.15/0.35 ((~((~((~member(X!4, C!3)) & ($sum(cardinality(C!3), $product(-1, Size!2)) = 0))) | ((Size!2 = 0) <=> (C!3 = empty_set)))) <=> (~((~((~member(X!4, C!3)) & ($sum(Size!2, $product(-1, cardinality(C!3))) = 0))) | ((Size!2 = 0) <=> (C!3 = empty_set))))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(2,plain,
% 0.15/0.35 ((~![X: element, C: set, Size: $int] : ((~((~member(X, C)) & ($sum(cardinality(C), $product(-1, Size)) = 0))) | ((Size = 0) <=> (C = empty_set)))) <=> (~![X: element, C: set, Size: $int] : ((~((~member(X, C)) & ($sum(cardinality(C), $product(-1, Size)) = 0))) | ((Size = 0) <=> (C = empty_set))))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(3,plain,
% 0.15/0.35 ((~![X: element, C: set, Size: $int] : ((~((~member(X, C)) & ($sum(Size, $product(-1, cardinality(C))) = 0))) | ((Size = 0) <=> (C = empty_set)))) <=> (~![X: element, C: set, Size: $int] : ((~((~member(X, C)) & ($sum(cardinality(C), $product(-1, Size)) = 0))) | ((Size = 0) <=> (C = empty_set))))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(4,plain,
% 0.15/0.35 ((~![X: element, C: set, Size: $int] : ((~((~member(X, C)) & (Size = cardinality(C)))) | ((Size = 0) <=> (C = empty_set)))) <=> (~![X: element, C: set, Size: $int] : ((~((~member(X, C)) & ($sum(Size, $product(-1, cardinality(C))) = 0))) | ((Size = 0) <=> (C = empty_set))))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(5,plain,
% 0.15/0.35 ((~![X: element, C: set, Size: $int] : ((~((~member(X, C)) & (Size = cardinality(C)))) | ((Size = 0) <=> (C = empty_set)))) <=> (~![X: element, C: set, Size: $int] : ((~((~member(X, C)) & (Size = cardinality(C)))) | ((Size = 0) <=> (C = empty_set))))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(6,plain,
% 0.15/0.35 ((~![X: element, C: set, Size: $int] : (((~member(X, C)) & (Size = cardinality(C))) => ((Size = 0) <=> (C = empty_set)))) <=> (~![X: element, C: set, Size: $int] : ((~((~member(X, C)) & (Size = cardinality(C)))) | ((Size = 0) <=> (C = empty_set))))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(7,axiom,(~![X: element, C: set, Size: $int] : (((~member(X, C)) & (Size = cardinality(C))) => ((Size = 0) <=> (C = empty_set)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','vc1')).
% 0.15/0.35 tff(8,plain,
% 0.15/0.35 (~![X: element, C: set, Size: $int] : ((~((~member(X, C)) & (Size = cardinality(C)))) | ((Size = 0) <=> (C = empty_set)))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.15/0.35 tff(9,plain,
% 0.15/0.35 (~![X: element, C: set, Size: $int] : ((~((~member(X, C)) & (Size = cardinality(C)))) | ((Size = 0) <=> (C = empty_set)))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.15/0.35 tff(10,plain,
% 0.15/0.35 (~![X: element, C: set, Size: $int] : ((~((~member(X, C)) & (Size = cardinality(C)))) | ((Size = 0) <=> (C = empty_set)))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.15/0.35 tff(11,plain,
% 0.15/0.35 (~![X: element, C: set, Size: $int] : ((~((~member(X, C)) & (Size = cardinality(C)))) | ((Size = 0) <=> (C = empty_set)))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.15/0.35 tff(12,plain,
% 0.15/0.35 (~![X: element, C: set, Size: $int] : ((~((~member(X, C)) & ($sum(Size, $product(-1, cardinality(C))) = 0))) | ((Size = 0) <=> (C = empty_set)))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.15/0.35 tff(13,plain,
% 0.15/0.35 (~![X: element, C: set, Size: $int] : ((~((~member(X, C)) & ($sum(cardinality(C), $product(-1, Size)) = 0))) | ((Size = 0) <=> (C = empty_set)))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[12, 3])).
% 0.15/0.35 tff(14,plain,
% 0.15/0.35 (~![X: element, C: set, Size: $int] : ((~((~member(X, C)) & ($sum(cardinality(C), $product(-1, Size)) = 0))) | ((Size = 0) <=> (C = empty_set)))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[13, 2])).
% 0.15/0.35 tff(15,plain,
% 0.15/0.35 (~![X: element, C: set, Size: $int] : ((~((~member(X, C)) & ($sum(cardinality(C), $product(-1, Size)) = 0))) | ((Size = 0) <=> (C = empty_set)))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[14, 2])).
% 0.15/0.35 tff(16,plain,(
% 0.15/0.35 ~((~((~member(X!4, C!3)) & ($sum(cardinality(C!3), $product(-1, Size!2)) = 0))) | ((Size!2 = 0) <=> (C!3 = empty_set)))),
% 0.15/0.35 inference(skolemize,[status(sab)],[15])).
% 0.15/0.35 tff(17,plain,
% 0.15/0.35 (~((~((~member(X!4, C!3)) & ($sum(Size!2, $product(-1, cardinality(C!3))) = 0))) | ((Size!2 = 0) <=> (C!3 = empty_set)))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[16, 1])).
% 0.15/0.35 tff(18,plain,
% 0.15/0.35 ((~member(X!4, C!3)) & ($sum(Size!2, $product(-1, cardinality(C!3))) = 0)),
% 0.15/0.35 inference(or_elim,[status(thm)],[17])).
% 0.15/0.35 tff(19,plain,
% 0.15/0.35 ($sum(Size!2, $product(-1, cardinality(C!3))) = 0),
% 0.15/0.35 inference(and_elim,[status(thm)],[18])).
% 0.15/0.35 tff(20,plain,
% 0.15/0.35 ((~($sum(Size!2, $product(-1, cardinality(C!3))) = 0)) | $lesseq($sum(Size!2, $product(-1, cardinality(C!3))), 0)),
% 0.15/0.35 inference(theory_lemma,[status(thm)],[])).
% 0.15/0.35 tff(21,plain,
% 0.15/0.35 ($lesseq($sum(Size!2, $product(-1, cardinality(C!3))), 0)),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.15/0.35 tff(22,plain,
% 0.15/0.35 ((~($sum(Size!2, $product(-1, cardinality(C!3))) = 0)) | $greatereq($sum(Size!2, $product(-1, cardinality(C!3))), 0)),
% 0.15/0.35 inference(theory_lemma,[status(thm)],[])).
% 0.15/0.35 tff(23,plain,
% 0.15/0.35 ($greatereq($sum(Size!2, $product(-1, cardinality(C!3))), 0)),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[22, 19])).
% 0.15/0.35 tff(24,plain,
% 0.15/0.35 (Size!2 = cardinality(C!3)),
% 0.15/0.35 inference(theory_lemma,[status(thm)],[23, 21])).
% 0.15/0.35 tff(25,plain,
% 0.15/0.35 ((Size!2 = 0) <=> (cardinality(C!3) = 0)),
% 0.15/0.35 inference(monotonicity,[status(thm)],[24])).
% 0.15/0.35 tff(26,plain,
% 0.15/0.35 ((~(Size!2 = 0)) <=> (~(cardinality(C!3) = 0))),
% 0.15/0.35 inference(monotonicity,[status(thm)],[25])).
% 0.15/0.35 tff(27,assumption,(~(C!3 = empty_set)), introduced(assumption)).
% 0.15/0.35 tff(28,plain,
% 0.15/0.35 ((~((Size!2 = 0) <=> (C!3 = empty_set))) <=> ((~(Size!2 = 0)) <=> (C!3 = empty_set))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(29,plain,
% 0.15/0.35 (~((Size!2 = 0) <=> (C!3 = empty_set))),
% 0.15/0.35 inference(or_elim,[status(thm)],[17])).
% 0.15/0.35 tff(30,plain,
% 0.15/0.35 ((~(Size!2 = 0)) <=> (C!3 = empty_set)),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.15/0.35 tff(31,plain,
% 0.15/0.35 ((Size!2 = 0) | (C!3 = empty_set) | (~((~(Size!2 = 0)) <=> (C!3 = empty_set)))),
% 0.15/0.35 inference(tautology,[status(thm)],[])).
% 0.15/0.35 tff(32,plain,
% 0.15/0.35 ((Size!2 = 0) | (C!3 = empty_set)),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.15/0.35 tff(33,plain,
% 0.15/0.35 (Size!2 = 0),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[32, 27])).
% 0.15/0.35 tff(34,plain,
% 0.15/0.35 (cardinality(C!3) = 0),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[33, 25])).
% 0.15/0.35 tff(35,plain,
% 0.15/0.35 (^[S: set] : refl(((cardinality(S) = 0) <=> (S = empty_set)) <=> ((cardinality(S) = 0) <=> (S = empty_set)))),
% 0.15/0.35 inference(bind,[status(th)],[])).
% 0.15/0.35 tff(36,plain,
% 0.15/0.35 (![S: set] : ((cardinality(S) = 0) <=> (S = empty_set)) <=> ![S: set] : ((cardinality(S) = 0) <=> (S = empty_set))),
% 0.15/0.35 inference(quant_intro,[status(thm)],[35])).
% 0.15/0.35 tff(37,plain,
% 0.15/0.35 (![S: set] : ((cardinality(S) = 0) <=> (S = empty_set)) <=> ![S: set] : ((cardinality(S) = 0) <=> (S = empty_set))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(38,axiom,(![S: set] : ((cardinality(S) = 0) <=> (S = empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cardinality_empty_set')).
% 0.15/0.35 tff(39,plain,
% 0.15/0.35 (![S: set] : ((cardinality(S) = 0) <=> (S = empty_set))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.15/0.35 tff(40,plain,(
% 0.15/0.35 ![S: set] : ((cardinality(S) = 0) <=> (S = empty_set))),
% 0.15/0.35 inference(skolemize,[status(sab)],[39])).
% 0.15/0.35 tff(41,plain,
% 0.15/0.35 (![S: set] : ((cardinality(S) = 0) <=> (S = empty_set))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.15/0.35 tff(42,plain,
% 0.15/0.35 ((~![S: set] : ((cardinality(S) = 0) <=> (S = empty_set))) | ((cardinality(C!3) = 0) <=> (C!3 = empty_set))),
% 0.15/0.35 inference(quant_inst,[status(thm)],[])).
% 0.15/0.35 tff(43,plain,
% 0.15/0.35 ((cardinality(C!3) = 0) <=> (C!3 = empty_set)),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.15/0.35 tff(44,plain,
% 0.15/0.35 ((~((cardinality(C!3) = 0) <=> (C!3 = empty_set))) | (~(cardinality(C!3) = 0)) | (C!3 = empty_set)),
% 0.15/0.35 inference(tautology,[status(thm)],[])).
% 0.15/0.36 tff(45,plain,
% 0.15/0.36 ((~(cardinality(C!3) = 0)) | (C!3 = empty_set)),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.15/0.36 tff(46,plain,
% 0.15/0.36 (~(cardinality(C!3) = 0)),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[45, 27])).
% 0.15/0.36 tff(47,plain,
% 0.15/0.36 ($false),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[46, 34])).
% 0.15/0.36 tff(48,plain,(C!3 = empty_set), inference(lemma,lemma(discharge,[]))).
% 0.15/0.36 tff(49,plain,
% 0.15/0.36 ((~(Size!2 = 0)) | (~(C!3 = empty_set)) | (~((~(Size!2 = 0)) <=> (C!3 = empty_set)))),
% 0.15/0.36 inference(tautology,[status(thm)],[])).
% 0.15/0.36 tff(50,plain,
% 0.15/0.36 ((~(Size!2 = 0)) | (~(C!3 = empty_set))),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[49, 30])).
% 0.15/0.36 tff(51,plain,
% 0.15/0.36 (~(Size!2 = 0)),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[50, 48])).
% 0.15/0.36 tff(52,plain,
% 0.15/0.36 (~(cardinality(C!3) = 0)),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[51, 26])).
% 0.15/0.36 tff(53,plain,
% 0.15/0.36 ((~((cardinality(C!3) = 0) <=> (C!3 = empty_set))) | (cardinality(C!3) = 0) | (~(C!3 = empty_set))),
% 0.15/0.36 inference(tautology,[status(thm)],[])).
% 0.15/0.36 tff(54,plain,
% 0.15/0.36 ((cardinality(C!3) = 0) | (~(C!3 = empty_set))),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[53, 43])).
% 0.15/0.36 tff(55,plain,
% 0.15/0.36 (cardinality(C!3) = 0),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[54, 48])).
% 0.15/0.36 tff(56,plain,
% 0.15/0.36 ($false),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[55, 52])).
% 0.15/0.36 % SZS output end Proof
%------------------------------------------------------------------------------