TSTP Solution File: SET987+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET987+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 05:08:49 EDT 2022
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SET987+1 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n026.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 09:05:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(tptp_fun_B_2_type, type, (
% 0.20/0.38 tptp_fun_B_2: $i)).
% 0.20/0.38 tff(set_difference_type, type, (
% 0.20/0.38 set_difference: ( $i * $i ) > $i)).
% 0.20/0.38 tff(singleton_type, type, (
% 0.20/0.38 singleton: $i > $i)).
% 0.20/0.38 tff(tptp_fun_A_3_type, type, (
% 0.20/0.38 tptp_fun_A_3: $i)).
% 0.20/0.38 tff(set_union2_type, type, (
% 0.20/0.38 set_union2: ( $i * $i ) > $i)).
% 0.20/0.38 tff(in_type, type, (
% 0.20/0.38 in: ( $i * $i ) > $o)).
% 0.20/0.38 tff(1,plain,
% 0.20/0.38 (^[A: $i, B: $i] : refl((set_difference(set_union2(A, B), B) = set_difference(A, B)) <=> (set_difference(set_union2(A, B), B) = set_difference(A, B)))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B)) <=> ![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B)) <=> ![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(4,axiom,(![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t40_xboole_1')).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 (![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.38 tff(6,plain,(
% 0.20/0.38 ![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 0.20/0.38 inference(skolemize,[status(sab)],[5])).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 ((~![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))) | (set_difference(set_union2(B!2, singleton(A!3)), singleton(A!3)) = set_difference(B!2, singleton(A!3)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 (set_difference(set_union2(B!2, singleton(A!3)), singleton(A!3)) = set_difference(B!2, singleton(A!3))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 ((set_difference(set_union2(B!2, singleton(A!3)), singleton(A!3)) = B!2) <=> (set_difference(B!2, singleton(A!3)) = B!2)),
% 0.20/0.38 inference(monotonicity,[status(thm)],[9])).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 ((set_difference(B!2, singleton(A!3)) = B!2) <=> (set_difference(set_union2(B!2, singleton(A!3)), singleton(A!3)) = B!2)),
% 0.20/0.38 inference(symmetry,[status(thm)],[10])).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 (^[A: $i, B: $i] : refl(((set_difference(A, singleton(B)) = A) <=> (~in(B, A))) <=> ((set_difference(A, singleton(B)) = A) <=> (~in(B, A))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (![A: $i, B: $i] : ((set_difference(A, singleton(B)) = A) <=> (~in(B, A))) <=> ![A: $i, B: $i] : ((set_difference(A, singleton(B)) = A) <=> (~in(B, A)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 (![A: $i, B: $i] : ((set_difference(A, singleton(B)) = A) <=> (~in(B, A))) <=> ![A: $i, B: $i] : ((set_difference(A, singleton(B)) = A) <=> (~in(B, A)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(15,axiom,(![A: $i, B: $i] : ((set_difference(A, singleton(B)) = A) <=> (~in(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t65_zfmisc_1')).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (![A: $i, B: $i] : ((set_difference(A, singleton(B)) = A) <=> (~in(B, A)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.38 tff(17,plain,(
% 0.20/0.38 ![A: $i, B: $i] : ((set_difference(A, singleton(B)) = A) <=> (~in(B, A)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[16])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 (![A: $i, B: $i] : ((set_difference(A, singleton(B)) = A) <=> (~in(B, A)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 ((~![A: $i, B: $i] : ((set_difference(A, singleton(B)) = A) <=> (~in(B, A)))) | ((set_difference(B!2, singleton(A!3)) = B!2) <=> (~in(A!3, B!2)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 ((set_difference(B!2, singleton(A!3)) = B!2) <=> (~in(A!3, B!2))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 ((~![A: $i, B: $i] : (in(A, B) | (set_difference(set_union2(B, singleton(A)), singleton(A)) = B))) <=> (~![A: $i, B: $i] : (in(A, B) | (set_difference(set_union2(B, singleton(A)), singleton(A)) = B)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : ((~in(A, B)) => (set_difference(set_union2(B, singleton(A)), singleton(A)) = B))) <=> (~![A: $i, B: $i] : (in(A, B) | (set_difference(set_union2(B, singleton(A)), singleton(A)) = B)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(23,axiom,(~![A: $i, B: $i] : ((~in(A, B)) => (set_difference(set_union2(B, singleton(A)), singleton(A)) = B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t141_zfmisc_1')).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 (~![A: $i, B: $i] : (in(A, B) | (set_difference(set_union2(B, singleton(A)), singleton(A)) = B))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 (~![A: $i, B: $i] : (in(A, B) | (set_difference(set_union2(B, singleton(A)), singleton(A)) = B))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 (~![A: $i, B: $i] : (in(A, B) | (set_difference(set_union2(B, singleton(A)), singleton(A)) = B))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 (~![A: $i, B: $i] : (in(A, B) | (set_difference(set_union2(B, singleton(A)), singleton(A)) = B))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 (~![A: $i, B: $i] : (in(A, B) | (set_difference(set_union2(B, singleton(A)), singleton(A)) = B))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[27, 21])).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 (~![A: $i, B: $i] : (in(A, B) | (set_difference(set_union2(B, singleton(A)), singleton(A)) = B))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 (~![A: $i, B: $i] : (in(A, B) | (set_difference(set_union2(B, singleton(A)), singleton(A)) = B))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[29, 21])).
% 0.20/0.39 tff(31,plain,(
% 0.20/0.39 ~(in(A!3, B!2) | (set_difference(set_union2(B!2, singleton(A!3)), singleton(A!3)) = B!2))),
% 0.20/0.39 inference(skolemize,[status(sab)],[30])).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 (~in(A!3, B!2)),
% 0.20/0.39 inference(or_elim,[status(thm)],[31])).
% 0.20/0.39 tff(33,plain,
% 0.20/0.39 ((~((set_difference(B!2, singleton(A!3)) = B!2) <=> (~in(A!3, B!2)))) | (set_difference(B!2, singleton(A!3)) = B!2) | in(A!3, B!2)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(34,plain,
% 0.20/0.39 ((~((set_difference(B!2, singleton(A!3)) = B!2) <=> (~in(A!3, B!2)))) | (set_difference(B!2, singleton(A!3)) = B!2)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 (set_difference(B!2, singleton(A!3)) = B!2),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[34, 20])).
% 0.20/0.39 tff(36,plain,
% 0.20/0.39 (set_difference(set_union2(B!2, singleton(A!3)), singleton(A!3)) = B!2),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[35, 11])).
% 0.20/0.39 tff(37,plain,
% 0.20/0.39 (~(set_difference(set_union2(B!2, singleton(A!3)), singleton(A!3)) = B!2)),
% 0.20/0.39 inference(or_elim,[status(thm)],[31])).
% 0.20/0.39 tff(38,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.20/0.39 % SZS output end Proof
%------------------------------------------------------------------------------