TSTP Solution File: SET923+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET923+1 : TPTP v8.1.0. Released v3.2.0.
% 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 05:08:38 EDT 2022
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET923+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 08:34:45 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(singleton_type, type, (
% 0.12/0.38 singleton: $i > $i)).
% 0.12/0.38 tff(tptp_fun_B_2_type, type, (
% 0.12/0.38 tptp_fun_B_2: $i)).
% 0.12/0.38 tff(tptp_fun_A_3_type, type, (
% 0.12/0.38 tptp_fun_A_3: $i)).
% 0.12/0.38 tff(empty_set_type, type, (
% 0.12/0.38 empty_set: $i)).
% 0.12/0.38 tff(subset_type, type, (
% 0.12/0.38 subset: ( $i * $i ) > $o)).
% 0.12/0.38 tff(set_difference_type, type, (
% 0.12/0.38 set_difference: ( $i * $i ) > $i)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 ((~(~((set_difference(A!3, singleton(B!2)) = empty_set) & (~(A!3 = empty_set)) & (~(A!3 = singleton(B!2)))))) <=> ((set_difference(A!3, singleton(B!2)) = empty_set) & (~(A!3 = empty_set)) & (~(A!3 = singleton(B!2))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 ((~![A: $i, B: $i] : (~((set_difference(A, singleton(B)) = empty_set) & (~(A = empty_set)) & (~(A = singleton(B)))))) <=> (~![A: $i, B: $i] : (~((set_difference(A, singleton(B)) = empty_set) & (~(A = empty_set)) & (~(A = singleton(B))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 ((~![A: $i, B: $i] : (~(((set_difference(A, singleton(B)) = empty_set) & (~(A = empty_set))) & (~(A = singleton(B)))))) <=> (~![A: $i, B: $i] : (~((set_difference(A, singleton(B)) = empty_set) & (~(A = empty_set)) & (~(A = singleton(B))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(4,axiom,(~![A: $i, B: $i] : (~(((set_difference(A, singleton(B)) = empty_set) & (~(A = empty_set))) & (~(A = singleton(B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t66_zfmisc_1')).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (~![A: $i, B: $i] : (~((set_difference(A, singleton(B)) = empty_set) & (~(A = empty_set)) & (~(A = singleton(B)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (~![A: $i, B: $i] : (~((set_difference(A, singleton(B)) = empty_set) & (~(A = empty_set)) & (~(A = singleton(B)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (~![A: $i, B: $i] : (~((set_difference(A, singleton(B)) = empty_set) & (~(A = empty_set)) & (~(A = singleton(B)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (~![A: $i, B: $i] : (~((set_difference(A, singleton(B)) = empty_set) & (~(A = empty_set)) & (~(A = singleton(B)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (~![A: $i, B: $i] : (~((set_difference(A, singleton(B)) = empty_set) & (~(A = empty_set)) & (~(A = singleton(B)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (~![A: $i, B: $i] : (~((set_difference(A, singleton(B)) = empty_set) & (~(A = empty_set)) & (~(A = singleton(B)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (~![A: $i, B: $i] : (~((set_difference(A, singleton(B)) = empty_set) & (~(A = empty_set)) & (~(A = singleton(B)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.12/0.38 tff(12,plain,(
% 0.12/0.38 ~(~((set_difference(A!3, singleton(B!2)) = empty_set) & (~(A!3 = empty_set)) & (~(A!3 = singleton(B!2)))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[11])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 ((set_difference(A!3, singleton(B!2)) = empty_set) & (~(A!3 = empty_set)) & (~(A!3 = singleton(B!2)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[12, 1])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (~(A!3 = singleton(B!2))),
% 0.12/0.38 inference(and_elim,[status(thm)],[13])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (~(A!3 = empty_set)),
% 0.12/0.38 inference(and_elim,[status(thm)],[13])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 ((~((A!3 = empty_set) | (A!3 = singleton(B!2)))) | (A!3 = empty_set) | (A!3 = singleton(B!2))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (~((A!3 = empty_set) | (A!3 = singleton(B!2)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[16, 15, 14])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (^[A: $i, B: $i] : refl(((set_difference(A, B) = empty_set) <=> subset(A, B)) <=> ((set_difference(A, B) = empty_set) <=> subset(A, B)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B)) <=> ![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[18])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B)) <=> ![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(21,axiom,(![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t37_xboole_1')).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.12/0.38 tff(23,plain,(
% 0.12/0.38 ![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.12/0.38 inference(skolemize,[status(sab)],[22])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 ((~![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))) | ((set_difference(A!3, singleton(B!2)) = empty_set) <=> subset(A!3, singleton(B!2)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 ((set_difference(A!3, singleton(B!2)) = empty_set) <=> subset(A!3, singleton(B!2))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (set_difference(A!3, singleton(B!2)) = empty_set),
% 0.12/0.38 inference(and_elim,[status(thm)],[13])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 ((~((set_difference(A!3, singleton(B!2)) = empty_set) <=> subset(A!3, singleton(B!2)))) | (~(set_difference(A!3, singleton(B!2)) = empty_set)) | subset(A!3, singleton(B!2))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 ((~((set_difference(A!3, singleton(B!2)) = empty_set) <=> subset(A!3, singleton(B!2)))) | subset(A!3, singleton(B!2))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (subset(A!3, singleton(B!2))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[29, 26])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 ((~(subset(A!3, singleton(B!2)) <=> ((A!3 = empty_set) | (A!3 = singleton(B!2))))) | (~subset(A!3, singleton(B!2))) | ((A!3 = empty_set) | (A!3 = singleton(B!2)))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (~(subset(A!3, singleton(B!2)) <=> ((A!3 = empty_set) | (A!3 = singleton(B!2))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[31, 30, 17])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (^[A: $i, B: $i] : refl((subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B)))) <=> (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B)))) <=> ![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[33])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 (![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B)))) <=> ![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(36,axiom,(![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l4_zfmisc_1')).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.12/0.38 tff(38,plain,(
% 0.12/0.38 ![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[37])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 (![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 ((~![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))) | (subset(A!3, singleton(B!2)) <=> ((A!3 = empty_set) | (A!3 = singleton(B!2))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[40, 39, 32])).
% 0.12/0.38 % SZS output end Proof
%------------------------------------------------------------------------------