TSTP Solution File: SET971+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET971+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 05:08:47 EDT 2022
% Result : Theorem 0.17s 0.37s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET971+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.31 % Computer : n021.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Sat Sep 3 08:43:14 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.32 Usage: tptp [options] [-file:]file
% 0.12/0.32 -h, -? prints this message.
% 0.12/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.32 -m, -model generate model.
% 0.12/0.32 -p, -proof generate proof.
% 0.12/0.32 -c, -core generate unsat core of named formulas.
% 0.12/0.32 -st, -statistics display statistics.
% 0.12/0.32 -t:timeout set timeout (in second).
% 0.12/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.32 -<param>:<value> configuration parameter and value.
% 0.12/0.32 -o:<output-file> file to place output in.
% 0.17/0.37 % SZS status Theorem
% 0.17/0.37 % SZS output start Proof
% 0.17/0.37 tff(cartesian_product2_type, type, (
% 0.17/0.37 cartesian_product2: ( $i * $i ) > $i)).
% 0.17/0.37 tff(tptp_fun_C_3_type, type, (
% 0.17/0.37 tptp_fun_C_3: $i)).
% 0.17/0.37 tff(tptp_fun_A_5_type, type, (
% 0.17/0.37 tptp_fun_A_5: $i)).
% 0.17/0.37 tff(set_intersection2_type, type, (
% 0.17/0.37 set_intersection2: ( $i * $i ) > $i)).
% 0.17/0.37 tff(tptp_fun_B_4_type, type, (
% 0.17/0.37 tptp_fun_B_4: $i)).
% 0.17/0.37 tff(tptp_fun_D_2_type, type, (
% 0.17/0.37 tptp_fun_D_2: $i)).
% 0.17/0.37 tff(subset_type, type, (
% 0.17/0.37 subset: ( $i * $i ) > $o)).
% 0.17/0.37 tff(1,plain,
% 0.17/0.37 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 0.17/0.37 inference(bind,[status(th)],[])).
% 0.17/0.37 tff(2,plain,
% 0.17/0.37 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.17/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.17/0.37 tff(3,plain,
% 0.17/0.37 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(4,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 0.17/0.37 tff(5,plain,
% 0.17/0.37 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.17/0.37 tff(6,plain,(
% 0.17/0.37 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.17/0.37 inference(skolemize,[status(sab)],[5])).
% 0.17/0.37 tff(7,plain,
% 0.17/0.37 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.17/0.37 tff(8,plain,
% 0.17/0.37 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(D!2, C!3) = set_intersection2(C!3, D!2))),
% 0.17/0.37 inference(quant_inst,[status(thm)],[])).
% 0.17/0.37 tff(9,plain,
% 0.17/0.37 (set_intersection2(D!2, C!3) = set_intersection2(C!3, D!2)),
% 0.17/0.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.17/0.37 tff(10,plain,
% 0.17/0.37 (set_intersection2(C!3, D!2) = set_intersection2(D!2, C!3)),
% 0.17/0.37 inference(symmetry,[status(thm)],[9])).
% 0.17/0.37 tff(11,plain,
% 0.17/0.37 (^[A: $i, B: $i] : refl(((~subset(A, B)) | (set_intersection2(A, B) = A)) <=> ((~subset(A, B)) | (set_intersection2(A, B) = A)))),
% 0.17/0.37 inference(bind,[status(th)],[])).
% 0.17/0.37 tff(12,plain,
% 0.17/0.37 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.17/0.37 inference(quant_intro,[status(thm)],[11])).
% 0.17/0.37 tff(13,plain,
% 0.17/0.37 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(14,plain,
% 0.17/0.37 (^[A: $i, B: $i] : rewrite((subset(A, B) => (set_intersection2(A, B) = A)) <=> ((~subset(A, B)) | (set_intersection2(A, B) = A)))),
% 0.17/0.37 inference(bind,[status(th)],[])).
% 0.17/0.37 tff(15,plain,
% 0.17/0.37 (![A: $i, B: $i] : (subset(A, B) => (set_intersection2(A, B) = A)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.17/0.37 inference(quant_intro,[status(thm)],[14])).
% 0.17/0.37 tff(16,axiom,(![A: $i, B: $i] : (subset(A, B) => (set_intersection2(A, B) = A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t28_xboole_1')).
% 0.17/0.37 tff(17,plain,
% 0.17/0.37 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.17/0.37 tff(18,plain,
% 0.17/0.37 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.17/0.37 tff(19,plain,(
% 0.17/0.37 ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.17/0.37 inference(skolemize,[status(sab)],[18])).
% 0.17/0.37 tff(20,plain,
% 0.17/0.37 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.17/0.37 tff(21,plain,
% 0.17/0.37 ((~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | (set_intersection2(cartesian_product2(A, D), cartesian_product2(B, C)) = cartesian_product2(A, C)))) <=> (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | (set_intersection2(cartesian_product2(A, D), cartesian_product2(B, C)) = cartesian_product2(A, C))))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(22,plain,
% 0.17/0.37 ((~![A: $i, B: $i, C: $i, D: $i] : ((subset(A, B) & subset(C, D)) => (set_intersection2(cartesian_product2(A, D), cartesian_product2(B, C)) = cartesian_product2(A, C)))) <=> (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | (set_intersection2(cartesian_product2(A, D), cartesian_product2(B, C)) = cartesian_product2(A, C))))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(23,axiom,(~![A: $i, B: $i, C: $i, D: $i] : ((subset(A, B) & subset(C, D)) => (set_intersection2(cartesian_product2(A, D), cartesian_product2(B, C)) = cartesian_product2(A, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t124_zfmisc_1')).
% 0.17/0.37 tff(24,plain,
% 0.17/0.37 (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | (set_intersection2(cartesian_product2(A, D), cartesian_product2(B, C)) = cartesian_product2(A, C)))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.17/0.37 tff(25,plain,
% 0.17/0.37 (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | (set_intersection2(cartesian_product2(A, D), cartesian_product2(B, C)) = cartesian_product2(A, C)))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.17/0.37 tff(26,plain,
% 0.17/0.37 (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | (set_intersection2(cartesian_product2(A, D), cartesian_product2(B, C)) = cartesian_product2(A, C)))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.17/0.37 tff(27,plain,
% 0.17/0.37 (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | (set_intersection2(cartesian_product2(A, D), cartesian_product2(B, C)) = cartesian_product2(A, C)))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.17/0.37 tff(28,plain,
% 0.17/0.37 (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | (set_intersection2(cartesian_product2(A, D), cartesian_product2(B, C)) = cartesian_product2(A, C)))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[27, 21])).
% 0.17/0.37 tff(29,plain,
% 0.17/0.37 (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | (set_intersection2(cartesian_product2(A, D), cartesian_product2(B, C)) = cartesian_product2(A, C)))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.17/0.37 tff(30,plain,
% 0.17/0.37 (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | (set_intersection2(cartesian_product2(A, D), cartesian_product2(B, C)) = cartesian_product2(A, C)))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[29, 21])).
% 0.17/0.37 tff(31,plain,(
% 0.17/0.37 ~((~(subset(A!5, B!4) & subset(C!3, D!2))) | (set_intersection2(cartesian_product2(A!5, D!2), cartesian_product2(B!4, C!3)) = cartesian_product2(A!5, C!3)))),
% 0.17/0.37 inference(skolemize,[status(sab)],[30])).
% 0.17/0.37 tff(32,plain,
% 0.17/0.37 (subset(A!5, B!4) & subset(C!3, D!2)),
% 0.17/0.37 inference(or_elim,[status(thm)],[31])).
% 0.17/0.37 tff(33,plain,
% 0.17/0.37 (subset(C!3, D!2)),
% 0.17/0.37 inference(and_elim,[status(thm)],[32])).
% 0.17/0.37 tff(34,plain,
% 0.17/0.37 (((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | ((~subset(C!3, D!2)) | (set_intersection2(C!3, D!2) = C!3))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | (~subset(C!3, D!2)) | (set_intersection2(C!3, D!2) = C!3))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(35,plain,
% 0.17/0.37 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | ((~subset(C!3, D!2)) | (set_intersection2(C!3, D!2) = C!3))),
% 0.17/0.37 inference(quant_inst,[status(thm)],[])).
% 0.17/0.37 tff(36,plain,
% 0.17/0.37 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | (~subset(C!3, D!2)) | (set_intersection2(C!3, D!2) = C!3)),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.17/0.37 tff(37,plain,
% 0.17/0.37 (set_intersection2(C!3, D!2) = C!3),
% 0.17/0.37 inference(unit_resolution,[status(thm)],[36, 33, 20])).
% 0.17/0.37 tff(38,plain,
% 0.17/0.37 (C!3 = set_intersection2(C!3, D!2)),
% 0.17/0.37 inference(symmetry,[status(thm)],[37])).
% 0.17/0.37 tff(39,plain,
% 0.17/0.37 (C!3 = set_intersection2(D!2, C!3)),
% 0.17/0.37 inference(transitivity,[status(thm)],[38, 10])).
% 0.17/0.37 tff(40,plain,
% 0.17/0.37 (subset(A!5, B!4)),
% 0.17/0.37 inference(and_elim,[status(thm)],[32])).
% 0.17/0.37 tff(41,plain,
% 0.17/0.37 (((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | ((~subset(A!5, B!4)) | (set_intersection2(A!5, B!4) = A!5))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | (~subset(A!5, B!4)) | (set_intersection2(A!5, B!4) = A!5))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(42,plain,
% 0.17/0.37 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | ((~subset(A!5, B!4)) | (set_intersection2(A!5, B!4) = A!5))),
% 0.17/0.37 inference(quant_inst,[status(thm)],[])).
% 0.17/0.37 tff(43,plain,
% 0.17/0.37 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | (~subset(A!5, B!4)) | (set_intersection2(A!5, B!4) = A!5)),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.17/0.37 tff(44,plain,
% 0.17/0.37 (set_intersection2(A!5, B!4) = A!5),
% 0.17/0.37 inference(unit_resolution,[status(thm)],[43, 40, 20])).
% 0.17/0.37 tff(45,plain,
% 0.17/0.37 (A!5 = set_intersection2(A!5, B!4)),
% 0.17/0.37 inference(symmetry,[status(thm)],[44])).
% 0.17/0.37 tff(46,plain,
% 0.17/0.37 (cartesian_product2(A!5, C!3) = cartesian_product2(set_intersection2(A!5, B!4), set_intersection2(D!2, C!3))),
% 0.17/0.37 inference(monotonicity,[status(thm)],[45, 39])).
% 0.17/0.37 tff(47,plain,
% 0.17/0.37 (cartesian_product2(set_intersection2(A!5, B!4), set_intersection2(D!2, C!3)) = cartesian_product2(A!5, C!3)),
% 0.17/0.37 inference(symmetry,[status(thm)],[46])).
% 0.17/0.37 tff(48,plain,
% 0.17/0.37 (^[A: $i, B: $i, C: $i, D: $i] : refl((cartesian_product2(set_intersection2(A, B), set_intersection2(C, D)) = set_intersection2(cartesian_product2(A, C), cartesian_product2(B, D))) <=> (cartesian_product2(set_intersection2(A, B), set_intersection2(C, D)) = set_intersection2(cartesian_product2(A, C), cartesian_product2(B, D))))),
% 0.17/0.37 inference(bind,[status(th)],[])).
% 0.17/0.37 tff(49,plain,
% 0.17/0.37 (![A: $i, B: $i, C: $i, D: $i] : (cartesian_product2(set_intersection2(A, B), set_intersection2(C, D)) = set_intersection2(cartesian_product2(A, C), cartesian_product2(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (cartesian_product2(set_intersection2(A, B), set_intersection2(C, D)) = set_intersection2(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.17/0.37 inference(quant_intro,[status(thm)],[48])).
% 0.17/0.37 tff(50,plain,
% 0.17/0.37 (![A: $i, B: $i, C: $i, D: $i] : (cartesian_product2(set_intersection2(A, B), set_intersection2(C, D)) = set_intersection2(cartesian_product2(A, C), cartesian_product2(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (cartesian_product2(set_intersection2(A, B), set_intersection2(C, D)) = set_intersection2(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(51,axiom,(![A: $i, B: $i, C: $i, D: $i] : (cartesian_product2(set_intersection2(A, B), set_intersection2(C, D)) = set_intersection2(cartesian_product2(A, C), cartesian_product2(B, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t123_zfmisc_1')).
% 0.17/0.37 tff(52,plain,
% 0.17/0.37 (![A: $i, B: $i, C: $i, D: $i] : (cartesian_product2(set_intersection2(A, B), set_intersection2(C, D)) = set_intersection2(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.17/0.37 tff(53,plain,(
% 0.17/0.37 ![A: $i, B: $i, C: $i, D: $i] : (cartesian_product2(set_intersection2(A, B), set_intersection2(C, D)) = set_intersection2(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.17/0.37 inference(skolemize,[status(sab)],[52])).
% 0.17/0.37 tff(54,plain,
% 0.17/0.37 (![A: $i, B: $i, C: $i, D: $i] : (cartesian_product2(set_intersection2(A, B), set_intersection2(C, D)) = set_intersection2(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.17/0.37 tff(55,plain,
% 0.17/0.37 ((~![A: $i, B: $i, C: $i, D: $i] : (cartesian_product2(set_intersection2(A, B), set_intersection2(C, D)) = set_intersection2(cartesian_product2(A, C), cartesian_product2(B, D)))) | (cartesian_product2(set_intersection2(A!5, B!4), set_intersection2(D!2, C!3)) = set_intersection2(cartesian_product2(A!5, D!2), cartesian_product2(B!4, C!3)))),
% 0.17/0.37 inference(quant_inst,[status(thm)],[])).
% 0.17/0.37 tff(56,plain,
% 0.17/0.37 (cartesian_product2(set_intersection2(A!5, B!4), set_intersection2(D!2, C!3)) = set_intersection2(cartesian_product2(A!5, D!2), cartesian_product2(B!4, C!3))),
% 0.17/0.37 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.17/0.37 tff(57,plain,
% 0.17/0.37 (set_intersection2(cartesian_product2(A!5, D!2), cartesian_product2(B!4, C!3)) = cartesian_product2(set_intersection2(A!5, B!4), set_intersection2(D!2, C!3))),
% 0.17/0.37 inference(symmetry,[status(thm)],[56])).
% 0.17/0.37 tff(58,plain,
% 0.17/0.37 (set_intersection2(cartesian_product2(A!5, D!2), cartesian_product2(B!4, C!3)) = cartesian_product2(A!5, C!3)),
% 0.17/0.37 inference(transitivity,[status(thm)],[57, 47])).
% 0.17/0.37 tff(59,plain,
% 0.17/0.37 (~(set_intersection2(cartesian_product2(A!5, D!2), cartesian_product2(B!4, C!3)) = cartesian_product2(A!5, C!3))),
% 0.17/0.37 inference(or_elim,[status(thm)],[31])).
% 0.17/0.37 tff(60,plain,
% 0.17/0.37 ($false),
% 0.17/0.37 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.17/0.37 % SZS output end Proof
%------------------------------------------------------------------------------