TSTP Solution File: SET917+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET917+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 05:08:37 EDT 2022
% Result : Theorem 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET917+1 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n018.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Sep 3 08:36:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % SZS output start Proof
% 0.13/0.38 tff(singleton_type, type, (
% 0.13/0.38 singleton: $i > $i)).
% 0.13/0.38 tff(tptp_fun_A_3_type, type, (
% 0.13/0.38 tptp_fun_A_3: $i)).
% 0.13/0.38 tff(set_intersection2_type, type, (
% 0.13/0.38 set_intersection2: ( $i * $i ) > $i)).
% 0.13/0.38 tff(tptp_fun_B_2_type, type, (
% 0.13/0.38 tptp_fun_B_2: $i)).
% 0.13/0.38 tff(in_type, type, (
% 0.13/0.38 in: ( $i * $i ) > $o)).
% 0.13/0.38 tff(disjoint_type, type, (
% 0.13/0.38 disjoint: ( $i * $i ) > $o)).
% 0.13/0.38 tff(1,plain,
% 0.13/0.38 ((~![A: $i, B: $i] : (disjoint(singleton(A), B) | (set_intersection2(singleton(A), B) = singleton(A)))) <=> (~![A: $i, B: $i] : (disjoint(singleton(A), B) | (set_intersection2(singleton(A), B) = singleton(A))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(2,axiom,(~![A: $i, B: $i] : (disjoint(singleton(A), B) | (set_intersection2(singleton(A), B) = singleton(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t58_zfmisc_1')).
% 0.13/0.38 tff(3,plain,
% 0.13/0.38 (~![A: $i, B: $i] : (disjoint(singleton(A), B) | (set_intersection2(singleton(A), B) = singleton(A)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.13/0.38 tff(4,plain,
% 0.13/0.38 (~![A: $i, B: $i] : (disjoint(singleton(A), B) | (set_intersection2(singleton(A), B) = singleton(A)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[3, 1])).
% 0.13/0.38 tff(5,plain,
% 0.13/0.38 (~![A: $i, B: $i] : (disjoint(singleton(A), B) | (set_intersection2(singleton(A), B) = singleton(A)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.13/0.38 tff(6,plain,
% 0.13/0.38 (~![A: $i, B: $i] : (disjoint(singleton(A), B) | (set_intersection2(singleton(A), B) = singleton(A)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.13/0.38 tff(7,plain,
% 0.13/0.38 (~![A: $i, B: $i] : (disjoint(singleton(A), B) | (set_intersection2(singleton(A), B) = singleton(A)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.13/0.38 tff(8,plain,
% 0.13/0.38 (~![A: $i, B: $i] : (disjoint(singleton(A), B) | (set_intersection2(singleton(A), B) = singleton(A)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.13/0.38 tff(9,plain,
% 0.13/0.38 (~![A: $i, B: $i] : (disjoint(singleton(A), B) | (set_intersection2(singleton(A), B) = singleton(A)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.13/0.38 tff(10,plain,(
% 0.13/0.38 ~(disjoint(singleton(A!3), B!2) | (set_intersection2(singleton(A!3), B!2) = singleton(A!3)))),
% 0.13/0.38 inference(skolemize,[status(sab)],[9])).
% 0.13/0.38 tff(11,plain,
% 0.13/0.38 (~disjoint(singleton(A!3), B!2)),
% 0.13/0.38 inference(or_elim,[status(thm)],[10])).
% 0.13/0.38 tff(12,plain,
% 0.13/0.38 (^[A: $i, B: $i] : refl((in(A, B) | disjoint(singleton(A), B)) <=> (in(A, B) | disjoint(singleton(A), B)))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(13,plain,
% 0.13/0.38 (![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B)) <=> ![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.13/0.38 tff(14,plain,
% 0.13/0.38 (![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B)) <=> ![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(15,plain,
% 0.13/0.38 (^[A: $i, B: $i] : rewrite(((~in(A, B)) => disjoint(singleton(A), B)) <=> (in(A, B) | disjoint(singleton(A), B)))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(16,plain,
% 0.13/0.38 (![A: $i, B: $i] : ((~in(A, B)) => disjoint(singleton(A), B)) <=> ![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.13/0.38 tff(17,axiom,(![A: $i, B: $i] : ((~in(A, B)) => disjoint(singleton(A), B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l28_zfmisc_1')).
% 0.13/0.38 tff(18,plain,
% 0.13/0.38 (![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.13/0.38 tff(19,plain,
% 0.13/0.38 (![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.13/0.38 tff(20,plain,(
% 0.13/0.38 ![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 0.13/0.38 inference(skolemize,[status(sab)],[19])).
% 0.13/0.38 tff(21,plain,
% 0.13/0.38 (![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.13/0.38 tff(22,plain,
% 0.13/0.38 (((~![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))) | (in(A!3, B!2) | disjoint(singleton(A!3), B!2))) <=> ((~![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))) | in(A!3, B!2) | disjoint(singleton(A!3), B!2))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(23,plain,
% 0.13/0.38 ((~![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))) | (in(A!3, B!2) | disjoint(singleton(A!3), B!2))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(24,plain,
% 0.13/0.38 ((~![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))) | in(A!3, B!2) | disjoint(singleton(A!3), B!2)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.13/0.38 tff(25,plain,
% 0.13/0.38 (in(A!3, B!2)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[24, 21, 11])).
% 0.13/0.38 tff(26,plain,
% 0.13/0.38 (^[A: $i, B: $i] : refl(((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A))) <=> ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(27,plain,
% 0.13/0.38 (![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A))) <=> ![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A)))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[26])).
% 0.13/0.38 tff(28,plain,
% 0.13/0.38 (![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A))) <=> ![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(29,plain,
% 0.13/0.38 (^[A: $i, B: $i] : rewrite((in(A, B) => (set_intersection2(B, singleton(A)) = singleton(A))) <=> ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(30,plain,
% 0.13/0.38 (![A: $i, B: $i] : (in(A, B) => (set_intersection2(B, singleton(A)) = singleton(A))) <=> ![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A)))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[29])).
% 0.13/0.38 tff(31,axiom,(![A: $i, B: $i] : (in(A, B) => (set_intersection2(B, singleton(A)) = singleton(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l32_zfmisc_1')).
% 0.13/0.38 tff(32,plain,
% 0.13/0.38 (![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.13/0.38 tff(33,plain,
% 0.13/0.38 (![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.13/0.38 tff(34,plain,(
% 0.13/0.38 ![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A)))),
% 0.13/0.38 inference(skolemize,[status(sab)],[33])).
% 0.13/0.38 tff(35,plain,
% 0.13/0.38 (![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.13/0.38 tff(36,plain,
% 0.13/0.38 (((~![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A)))) | ((~in(A!3, B!2)) | (set_intersection2(B!2, singleton(A!3)) = singleton(A!3)))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A)))) | (~in(A!3, B!2)) | (set_intersection2(B!2, singleton(A!3)) = singleton(A!3)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(37,plain,
% 0.13/0.38 ((~![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A)))) | ((~in(A!3, B!2)) | (set_intersection2(B!2, singleton(A!3)) = singleton(A!3)))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(38,plain,
% 0.13/0.38 ((~![A: $i, B: $i] : ((~in(A, B)) | (set_intersection2(B, singleton(A)) = singleton(A)))) | (~in(A!3, B!2)) | (set_intersection2(B!2, singleton(A!3)) = singleton(A!3))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.13/0.38 tff(39,plain,
% 0.13/0.38 (set_intersection2(B!2, singleton(A!3)) = singleton(A!3)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[38, 35, 25])).
% 0.13/0.38 tff(40,plain,
% 0.13/0.38 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(41,plain,
% 0.13/0.38 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[40])).
% 0.13/0.38 tff(42,plain,
% 0.13/0.38 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(43,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 0.13/0.39 tff(44,plain,
% 0.13/0.39 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.13/0.39 tff(45,plain,(
% 0.13/0.39 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.13/0.39 inference(skolemize,[status(sab)],[44])).
% 0.13/0.39 tff(46,plain,
% 0.13/0.39 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.13/0.39 tff(47,plain,
% 0.13/0.39 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(singleton(A!3), B!2) = set_intersection2(B!2, singleton(A!3)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(48,plain,
% 0.13/0.39 (set_intersection2(singleton(A!3), B!2) = set_intersection2(B!2, singleton(A!3))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.13/0.39 tff(49,plain,
% 0.13/0.39 (set_intersection2(singleton(A!3), B!2) = singleton(A!3)),
% 0.13/0.39 inference(transitivity,[status(thm)],[48, 39])).
% 0.13/0.39 tff(50,plain,
% 0.13/0.39 (~(set_intersection2(singleton(A!3), B!2) = singleton(A!3))),
% 0.13/0.39 inference(or_elim,[status(thm)],[10])).
% 0.13/0.39 tff(51,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.13/0.39 % SZS output end Proof
%------------------------------------------------------------------------------