TSTP Solution File: SET366+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET366+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 05:06:35 EDT 2022
% Result : Theorem 0.16s 0.59s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.32 % Problem : SET366+4 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.33 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.16/0.54 % Computer : n014.cluster.edu
% 0.16/0.54 % Model : x86_64 x86_64
% 0.16/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.54 % Memory : 8042.1875MB
% 0.16/0.54 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.54 % CPULimit : 300
% 0.16/0.54 % WCLimit : 300
% 0.16/0.54 % DateTime : Sat Sep 3 04:50:16 EDT 2022
% 0.16/0.54 % CPUTime :
% 0.16/0.54 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.16/0.54 Usage: tptp [options] [-file:]file
% 0.16/0.54 -h, -? prints this message.
% 0.16/0.54 -smt2 print SMT-LIB2 benchmark.
% 0.16/0.54 -m, -model generate model.
% 0.16/0.54 -p, -proof generate proof.
% 0.16/0.54 -c, -core generate unsat core of named formulas.
% 0.16/0.54 -st, -statistics display statistics.
% 0.16/0.54 -t:timeout set timeout (in second).
% 0.16/0.54 -smt2status display status in smt2 format instead of SZS.
% 0.16/0.54 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.16/0.54 -<param>:<value> configuration parameter and value.
% 0.16/0.54 -o:<output-file> file to place output in.
% 0.16/0.59 % SZS status Theorem
% 0.16/0.59 % SZS output start Proof
% 0.16/0.59 tff(member_type, type, (
% 0.16/0.59 member: ( $i * $i ) > $o)).
% 0.16/0.59 tff(empty_set_type, type, (
% 0.16/0.59 empty_set: $i)).
% 0.16/0.59 tff(tptp_fun_X_0_type, type, (
% 0.16/0.59 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.16/0.59 tff(tptp_fun_A_3_type, type, (
% 0.16/0.59 tptp_fun_A_3: $i)).
% 0.16/0.59 tff(subset_type, type, (
% 0.16/0.59 subset: ( $i * $i ) > $o)).
% 0.16/0.59 tff(power_set_type, type, (
% 0.16/0.59 power_set: $i > $i)).
% 0.16/0.59 tff(1,plain,
% 0.16/0.59 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.16/0.59 inference(bind,[status(th)],[])).
% 0.16/0.59 tff(2,plain,
% 0.16/0.59 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.16/0.59 inference(quant_intro,[status(thm)],[1])).
% 0.16/0.59 tff(3,plain,
% 0.16/0.59 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.16/0.59 inference(bind,[status(th)],[])).
% 0.16/0.59 tff(4,plain,
% 0.16/0.59 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.16/0.59 inference(quant_intro,[status(thm)],[3])).
% 0.16/0.59 tff(5,plain,
% 0.16/0.59 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.16/0.59 inference(transitivity,[status(thm)],[4, 2])).
% 0.16/0.59 tff(6,plain,
% 0.16/0.59 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.16/0.59 inference(bind,[status(th)],[])).
% 0.16/0.59 tff(7,plain,
% 0.16/0.59 (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.16/0.59 inference(quant_intro,[status(thm)],[6])).
% 0.16/0.59 tff(8,plain,
% 0.16/0.59 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.16/0.59 inference(rewrite,[status(thm)],[])).
% 0.16/0.59 tff(9,plain,
% 0.16/0.59 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.16/0.59 inference(bind,[status(th)],[])).
% 0.16/0.59 tff(10,plain,
% 0.16/0.59 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.16/0.59 inference(quant_intro,[status(thm)],[9])).
% 0.16/0.59 tff(11,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','subset')).
% 0.16/0.59 tff(12,plain,
% 0.16/0.59 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.16/0.59 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.16/0.59 tff(13,plain,
% 0.16/0.59 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.16/0.59 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.16/0.59 tff(14,plain,(
% 0.16/0.59 ![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 0.16/0.59 inference(skolemize,[status(sab)],[13])).
% 0.16/0.59 tff(15,plain,
% 0.16/0.59 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.16/0.59 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.16/0.59 tff(16,plain,
% 0.16/0.59 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.16/0.59 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.16/0.59 tff(17,plain,
% 0.16/0.59 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(empty_set, A!3)) | ![X: $i] : ((~member(X, empty_set)) | member(X, A!3)))) | (~(subset(empty_set, A!3) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3)))))))),
% 0.16/0.59 inference(quant_inst,[status(thm)],[])).
% 0.16/0.59 tff(18,plain,
% 0.16/0.59 (~((~((~subset(empty_set, A!3)) | ![X: $i] : ((~member(X, empty_set)) | member(X, A!3)))) | (~(subset(empty_set, A!3) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3))))))),
% 0.16/0.59 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.16/0.59 tff(19,plain,
% 0.16/0.59 (((~((~subset(empty_set, A!3)) | ![X: $i] : ((~member(X, empty_set)) | member(X, A!3)))) | (~(subset(empty_set, A!3) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3)))))) | (subset(empty_set, A!3) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3))))),
% 0.16/0.59 inference(tautology,[status(thm)],[])).
% 0.16/0.59 tff(20,plain,
% 0.16/0.59 (subset(empty_set, A!3) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3)))),
% 0.16/0.59 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.16/0.59 tff(21,plain,
% 0.16/0.59 (^[X: $i, A: $i] : refl((member(X, power_set(A)) <=> subset(X, A)) <=> (member(X, power_set(A)) <=> subset(X, A)))),
% 0.16/0.59 inference(bind,[status(th)],[])).
% 0.16/0.59 tff(22,plain,
% 0.16/0.59 (![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A)) <=> ![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 0.16/0.59 inference(quant_intro,[status(thm)],[21])).
% 0.16/0.59 tff(23,plain,
% 0.16/0.59 (![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A)) <=> ![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 0.16/0.59 inference(rewrite,[status(thm)],[])).
% 0.16/0.59 tff(24,axiom,(![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','power_set')).
% 0.16/0.59 tff(25,plain,
% 0.16/0.59 (![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 0.16/0.59 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.16/0.59 tff(26,plain,(
% 0.16/0.59 ![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 0.16/0.59 inference(skolemize,[status(sab)],[25])).
% 0.16/0.59 tff(27,plain,
% 0.16/0.59 (![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 0.16/0.59 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.16/0.59 tff(28,plain,
% 0.16/0.59 ((~![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))) | (member(empty_set, power_set(A!3)) <=> subset(empty_set, A!3))),
% 0.16/0.59 inference(quant_inst,[status(thm)],[])).
% 0.16/0.59 tff(29,plain,
% 0.16/0.59 (member(empty_set, power_set(A!3)) <=> subset(empty_set, A!3)),
% 0.16/0.59 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.16/0.59 tff(30,plain,
% 0.16/0.59 ((~![A: $i] : member(empty_set, power_set(A))) <=> (~![A: $i] : member(empty_set, power_set(A)))),
% 0.16/0.59 inference(rewrite,[status(thm)],[])).
% 0.16/0.59 tff(31,axiom,(~![A: $i] : member(empty_set, power_set(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thI47')).
% 0.16/0.59 tff(32,plain,
% 0.16/0.59 (~![A: $i] : member(empty_set, power_set(A))),
% 0.16/0.59 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.16/0.59 tff(33,plain,
% 0.16/0.59 (~![A: $i] : member(empty_set, power_set(A))),
% 0.16/0.59 inference(modus_ponens,[status(thm)],[32, 30])).
% 0.16/0.59 tff(34,plain,
% 0.16/0.59 (~![A: $i] : member(empty_set, power_set(A))),
% 0.16/0.59 inference(modus_ponens,[status(thm)],[33, 30])).
% 0.16/0.59 tff(35,plain,
% 0.16/0.59 (~![A: $i] : member(empty_set, power_set(A))),
% 0.16/0.59 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.16/0.59 tff(36,plain,
% 0.16/0.59 (~![A: $i] : member(empty_set, power_set(A))),
% 0.16/0.59 inference(modus_ponens,[status(thm)],[35, 30])).
% 0.16/0.59 tff(37,plain,
% 0.16/0.59 (~![A: $i] : member(empty_set, power_set(A))),
% 0.16/0.59 inference(modus_ponens,[status(thm)],[36, 30])).
% 0.16/0.59 tff(38,plain,
% 0.16/0.59 (~![A: $i] : member(empty_set, power_set(A))),
% 0.16/0.59 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.16/0.59 tff(39,plain,(
% 0.16/0.59 ~member(empty_set, power_set(A!3))),
% 0.16/0.59 inference(skolemize,[status(sab)],[38])).
% 0.16/0.59 tff(40,plain,
% 0.16/0.59 ((~(member(empty_set, power_set(A!3)) <=> subset(empty_set, A!3))) | member(empty_set, power_set(A!3)) | (~subset(empty_set, A!3))),
% 0.16/0.59 inference(tautology,[status(thm)],[])).
% 0.16/0.59 tff(41,plain,
% 0.16/0.59 ((~(member(empty_set, power_set(A!3)) <=> subset(empty_set, A!3))) | (~subset(empty_set, A!3))),
% 0.16/0.59 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.16/0.59 tff(42,plain,
% 0.16/0.59 (~subset(empty_set, A!3)),
% 0.16/0.59 inference(unit_resolution,[status(thm)],[41, 29])).
% 0.16/0.59 tff(43,plain,
% 0.16/0.59 ((~(subset(empty_set, A!3) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3))))) | subset(empty_set, A!3) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3)))),
% 0.16/0.59 inference(tautology,[status(thm)],[])).
% 0.16/0.59 tff(44,plain,
% 0.16/0.59 ((~(subset(empty_set, A!3) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3))))) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3)))),
% 0.16/0.59 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.16/0.59 tff(45,plain,
% 0.16/0.59 (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3))),
% 0.16/0.59 inference(unit_resolution,[status(thm)],[44, 20])).
% 0.16/0.59 tff(46,plain,
% 0.16/0.59 (((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3)) | member(tptp_fun_X_0(A!3, empty_set), empty_set)),
% 0.16/0.59 inference(tautology,[status(thm)],[])).
% 0.16/0.59 tff(47,plain,
% 0.16/0.59 (member(tptp_fun_X_0(A!3, empty_set), empty_set)),
% 0.16/0.59 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.16/0.59 tff(48,plain,
% 0.16/0.59 (^[X: $i] : refl((~member(X, empty_set)) <=> (~member(X, empty_set)))),
% 0.16/0.59 inference(bind,[status(th)],[])).
% 0.16/0.59 tff(49,plain,
% 0.16/0.59 (![X: $i] : (~member(X, empty_set)) <=> ![X: $i] : (~member(X, empty_set))),
% 0.16/0.59 inference(quant_intro,[status(thm)],[48])).
% 0.16/0.59 tff(50,plain,
% 0.16/0.59 (![X: $i] : (~member(X, empty_set)) <=> ![X: $i] : (~member(X, empty_set))),
% 0.16/0.59 inference(rewrite,[status(thm)],[])).
% 0.16/0.59 tff(51,axiom,(![X: $i] : (~member(X, empty_set))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','empty_set')).
% 0.16/0.59 tff(52,plain,
% 0.16/0.59 (![X: $i] : (~member(X, empty_set))),
% 0.16/0.59 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.16/0.59 tff(53,plain,(
% 0.16/0.59 ![X: $i] : (~member(X, empty_set))),
% 0.16/0.59 inference(skolemize,[status(sab)],[52])).
% 0.16/0.59 tff(54,plain,
% 0.16/0.59 (![X: $i] : (~member(X, empty_set))),
% 0.16/0.59 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.16/0.59 tff(55,plain,
% 0.16/0.59 ((~![X: $i] : (~member(X, empty_set))) | (~member(tptp_fun_X_0(A!3, empty_set), empty_set))),
% 0.16/0.59 inference(quant_inst,[status(thm)],[])).
% 0.16/0.59 tff(56,plain,
% 0.16/0.59 ($false),
% 0.16/0.59 inference(unit_resolution,[status(thm)],[55, 54, 47])).
% 0.16/0.59 % SZS output end Proof
%------------------------------------------------------------------------------