TSTP Solution File: SET926+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET926+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 05:08:39 EDT 2022
% Result : Theorem 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET926+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n015.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Sep 3 08:46:40 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(in_type, type, (
% 0.21/0.39 in: ( $i * $i ) > $o)).
% 0.21/0.39 tff(tptp_fun_B_2_type, type, (
% 0.21/0.39 tptp_fun_B_2: $i)).
% 0.21/0.39 tff(tptp_fun_A_3_type, type, (
% 0.21/0.39 tptp_fun_A_3: $i)).
% 0.21/0.39 tff(empty_set_type, type, (
% 0.21/0.39 empty_set: $i)).
% 0.21/0.39 tff(set_difference_type, type, (
% 0.21/0.39 set_difference: ( $i * $i ) > $i)).
% 0.21/0.39 tff(singleton_type, type, (
% 0.21/0.39 singleton: $i > $i)).
% 0.21/0.39 tff(1,plain,
% 0.21/0.39 (^[A: $i, B: $i] : refl(((set_difference(singleton(A), B) = empty_set) <=> in(A, B)) <=> ((set_difference(singleton(A), B) = empty_set) <=> in(A, B)))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 (![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) <=> in(A, B)) <=> ![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) <=> in(A, B))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.39 tff(3,plain,
% 0.21/0.39 (![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) <=> in(A, B)) <=> ![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) <=> in(A, B))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(4,axiom,(![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) <=> in(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l36_zfmisc_1')).
% 0.21/0.39 tff(5,plain,
% 0.21/0.39 (![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) <=> in(A, B))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.39 tff(6,plain,(
% 0.21/0.39 ![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) <=> in(A, B))),
% 0.21/0.39 inference(skolemize,[status(sab)],[5])).
% 0.21/0.39 tff(7,plain,
% 0.21/0.39 (![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) <=> in(A, B))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.39 tff(8,plain,
% 0.21/0.39 ((~![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) <=> in(A, B))) | ((set_difference(singleton(A!3), B!2) = empty_set) <=> in(A!3, B!2))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(9,plain,
% 0.21/0.39 ((set_difference(singleton(A!3), B!2) = empty_set) <=> in(A!3, B!2)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.39 tff(10,plain,
% 0.21/0.39 (^[A: $i, B: $i] : refl(((set_difference(singleton(A), B) = singleton(A)) <=> (~in(A, B))) <=> ((set_difference(singleton(A), B) = singleton(A)) <=> (~in(A, B))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(11,plain,
% 0.21/0.39 (![A: $i, B: $i] : ((set_difference(singleton(A), B) = singleton(A)) <=> (~in(A, B))) <=> ![A: $i, B: $i] : ((set_difference(singleton(A), B) = singleton(A)) <=> (~in(A, B)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.39 tff(12,plain,
% 0.21/0.39 (![A: $i, B: $i] : ((set_difference(singleton(A), B) = singleton(A)) <=> (~in(A, B))) <=> ![A: $i, B: $i] : ((set_difference(singleton(A), B) = singleton(A)) <=> (~in(A, B)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(13,axiom,(![A: $i, B: $i] : ((set_difference(singleton(A), B) = singleton(A)) <=> (~in(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l34_zfmisc_1')).
% 0.21/0.39 tff(14,plain,
% 0.21/0.39 (![A: $i, B: $i] : ((set_difference(singleton(A), B) = singleton(A)) <=> (~in(A, B)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.21/0.39 tff(15,plain,(
% 0.21/0.39 ![A: $i, B: $i] : ((set_difference(singleton(A), B) = singleton(A)) <=> (~in(A, B)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[14])).
% 0.21/0.39 tff(16,plain,
% 0.21/0.39 (![A: $i, B: $i] : ((set_difference(singleton(A), B) = singleton(A)) <=> (~in(A, B)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.21/0.39 tff(17,plain,
% 0.21/0.39 ((~![A: $i, B: $i] : ((set_difference(singleton(A), B) = singleton(A)) <=> (~in(A, B)))) | ((set_difference(singleton(A!3), B!2) = singleton(A!3)) <=> (~in(A!3, B!2)))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(18,plain,
% 0.21/0.39 ((set_difference(singleton(A!3), B!2) = singleton(A!3)) <=> (~in(A!3, B!2))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.21/0.39 tff(19,plain,
% 0.21/0.39 ((~![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) | (set_difference(singleton(A), B) = singleton(A)))) <=> (~![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) | (set_difference(singleton(A), B) = singleton(A))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(20,axiom,(~![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) | (set_difference(singleton(A), B) = singleton(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t69_zfmisc_1')).
% 0.21/0.40 tff(21,plain,
% 0.21/0.40 (~![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) | (set_difference(singleton(A), B) = singleton(A)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.21/0.40 tff(22,plain,
% 0.21/0.40 (~![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) | (set_difference(singleton(A), B) = singleton(A)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[21, 19])).
% 0.21/0.40 tff(23,plain,
% 0.21/0.40 (~![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) | (set_difference(singleton(A), B) = singleton(A)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[22, 19])).
% 0.21/0.40 tff(24,plain,
% 0.21/0.40 (~![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) | (set_difference(singleton(A), B) = singleton(A)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.21/0.40 tff(25,plain,
% 0.21/0.40 (~![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) | (set_difference(singleton(A), B) = singleton(A)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[24, 19])).
% 0.21/0.40 tff(26,plain,
% 0.21/0.40 (~![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) | (set_difference(singleton(A), B) = singleton(A)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[25, 19])).
% 0.21/0.40 tff(27,plain,
% 0.21/0.40 (~![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) | (set_difference(singleton(A), B) = singleton(A)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.21/0.40 tff(28,plain,(
% 0.21/0.40 ~((set_difference(singleton(A!3), B!2) = empty_set) | (set_difference(singleton(A!3), B!2) = singleton(A!3)))),
% 0.21/0.40 inference(skolemize,[status(sab)],[27])).
% 0.21/0.40 tff(29,plain,
% 0.21/0.40 (~(set_difference(singleton(A!3), B!2) = singleton(A!3))),
% 0.21/0.40 inference(or_elim,[status(thm)],[28])).
% 0.21/0.40 tff(30,plain,
% 0.21/0.40 ((~((set_difference(singleton(A!3), B!2) = singleton(A!3)) <=> (~in(A!3, B!2)))) | (set_difference(singleton(A!3), B!2) = singleton(A!3)) | in(A!3, B!2)),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(31,plain,
% 0.21/0.40 ((~((set_difference(singleton(A!3), B!2) = singleton(A!3)) <=> (~in(A!3, B!2)))) | in(A!3, B!2)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.21/0.40 tff(32,plain,
% 0.21/0.40 (in(A!3, B!2)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[31, 18])).
% 0.21/0.40 tff(33,plain,
% 0.21/0.40 (~(set_difference(singleton(A!3), B!2) = empty_set)),
% 0.21/0.40 inference(or_elim,[status(thm)],[28])).
% 0.21/0.40 tff(34,plain,
% 0.21/0.40 ((~((set_difference(singleton(A!3), B!2) = empty_set) <=> in(A!3, B!2))) | (set_difference(singleton(A!3), B!2) = empty_set) | (~in(A!3, B!2))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(35,plain,
% 0.21/0.40 ((~((set_difference(singleton(A!3), B!2) = empty_set) <=> in(A!3, B!2))) | (~in(A!3, B!2))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.21/0.40 tff(36,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[35, 32, 9])).
% 0.21/0.40 % SZS output end Proof
%------------------------------------------------------------------------------