TSTP Solution File: SET984+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET984+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 0.10s 0.29s
% Output : Proof 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SET984+1 : TPTP v8.1.0. Released v3.2.0.
% 0.00/0.08 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.07/0.26 % Computer : n007.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Sat Sep 3 08:35:49 EDT 2022
% 0.07/0.26 % CPUTime :
% 0.07/0.26 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.07/0.26 Usage: tptp [options] [-file:]file
% 0.07/0.26 -h, -? prints this message.
% 0.07/0.26 -smt2 print SMT-LIB2 benchmark.
% 0.07/0.26 -m, -model generate model.
% 0.07/0.26 -p, -proof generate proof.
% 0.07/0.26 -c, -core generate unsat core of named formulas.
% 0.07/0.26 -st, -statistics display statistics.
% 0.07/0.26 -t:timeout set timeout (in second).
% 0.07/0.26 -smt2status display status in smt2 format instead of SZS.
% 0.07/0.26 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.07/0.26 -<param>:<value> configuration parameter and value.
% 0.07/0.26 -o:<output-file> file to place output in.
% 0.10/0.29 % SZS status Theorem
% 0.10/0.29 % SZS output start Proof
% 0.10/0.29 tff(subset_type, type, (
% 0.10/0.29 subset: ( $i * $i ) > $o)).
% 0.10/0.29 tff(tptp_fun_D_2_type, type, (
% 0.10/0.29 tptp_fun_D_2: $i)).
% 0.10/0.29 tff(tptp_fun_B_4_type, type, (
% 0.10/0.29 tptp_fun_B_4: $i)).
% 0.10/0.29 tff(set_intersection2_type, type, (
% 0.10/0.29 set_intersection2: ( $i * $i ) > $i)).
% 0.10/0.29 tff(tptp_fun_C_3_type, type, (
% 0.10/0.29 tptp_fun_C_3: $i)).
% 0.10/0.29 tff(tptp_fun_A_5_type, type, (
% 0.10/0.29 tptp_fun_A_5: $i)).
% 0.10/0.29 tff(cartesian_product2_type, type, (
% 0.10/0.29 cartesian_product2: ( $i * $i ) > $i)).
% 0.10/0.29 tff(empty_set_type, type, (
% 0.10/0.29 empty_set: $i)).
% 0.10/0.29 tff(1,plain,
% 0.10/0.29 (^[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))))),
% 0.10/0.29 inference(bind,[status(th)],[])).
% 0.10/0.29 tff(2,plain,
% 0.10/0.29 (![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)))),
% 0.10/0.29 inference(quant_intro,[status(thm)],[1])).
% 0.10/0.29 tff(3,plain,
% 0.10/0.29 (![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)))),
% 0.10/0.29 inference(rewrite,[status(thm)],[])).
% 0.10/0.29 tff(4,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/sandbox/benchmark/theBenchmark.p','t123_zfmisc_1')).
% 0.10/0.29 tff(5,plain,
% 0.10/0.29 (![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)))),
% 0.10/0.29 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.10/0.29 tff(6,plain,(
% 0.10/0.29 ![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)))),
% 0.10/0.29 inference(skolemize,[status(sab)],[5])).
% 0.10/0.29 tff(7,plain,
% 0.10/0.29 (![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)))),
% 0.10/0.29 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.10/0.29 tff(8,plain,
% 0.10/0.29 ((~![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, C!3), set_intersection2(B!4, D!2)) = set_intersection2(cartesian_product2(A!5, B!4), cartesian_product2(C!3, D!2)))),
% 0.10/0.29 inference(quant_inst,[status(thm)],[])).
% 0.10/0.29 tff(9,plain,
% 0.10/0.29 (cartesian_product2(set_intersection2(A!5, C!3), set_intersection2(B!4, D!2)) = set_intersection2(cartesian_product2(A!5, B!4), cartesian_product2(C!3, D!2))),
% 0.10/0.29 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.10/0.29 tff(10,plain,
% 0.10/0.29 (set_intersection2(cartesian_product2(A!5, B!4), cartesian_product2(C!3, D!2)) = cartesian_product2(set_intersection2(A!5, C!3), set_intersection2(B!4, D!2))),
% 0.10/0.29 inference(symmetry,[status(thm)],[9])).
% 0.10/0.29 tff(11,plain,
% 0.10/0.29 (^[A: $i, B: $i] : refl(((~subset(A, B)) | (set_intersection2(A, B) = A)) <=> ((~subset(A, B)) | (set_intersection2(A, B) = A)))),
% 0.10/0.29 inference(bind,[status(th)],[])).
% 0.10/0.29 tff(12,plain,
% 0.10/0.29 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.10/0.29 inference(quant_intro,[status(thm)],[11])).
% 0.10/0.29 tff(13,plain,
% 0.10/0.29 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.10/0.29 inference(rewrite,[status(thm)],[])).
% 0.10/0.29 tff(14,plain,
% 0.10/0.29 (^[A: $i, B: $i] : rewrite((subset(A, B) => (set_intersection2(A, B) = A)) <=> ((~subset(A, B)) | (set_intersection2(A, B) = A)))),
% 0.10/0.29 inference(bind,[status(th)],[])).
% 0.10/0.29 tff(15,plain,
% 0.10/0.29 (![A: $i, B: $i] : (subset(A, B) => (set_intersection2(A, B) = A)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.10/0.29 inference(quant_intro,[status(thm)],[14])).
% 0.10/0.29 tff(16,axiom,(![A: $i, B: $i] : (subset(A, B) => (set_intersection2(A, B) = A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t28_xboole_1')).
% 0.10/0.29 tff(17,plain,
% 0.10/0.29 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.10/0.29 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.10/0.29 tff(18,plain,
% 0.10/0.29 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.10/0.29 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.10/0.29 tff(19,plain,(
% 0.10/0.29 ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.10/0.29 inference(skolemize,[status(sab)],[18])).
% 0.10/0.29 tff(20,plain,
% 0.10/0.29 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.10/0.29 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.10/0.29 tff(21,plain,
% 0.10/0.29 ((~((subset(A!5, C!3) & subset(B!4, D!2)) | (cartesian_product2(A!5, B!4) = empty_set) | (~subset(cartesian_product2(A!5, B!4), cartesian_product2(C!3, D!2))))) <=> (~((subset(A!5, C!3) & subset(B!4, D!2)) | (cartesian_product2(A!5, B!4) = empty_set) | (~subset(cartesian_product2(A!5, B!4), cartesian_product2(C!3, D!2)))))),
% 0.10/0.29 inference(rewrite,[status(thm)],[])).
% 0.10/0.29 tff(22,plain,
% 0.10/0.29 ((~![A: $i, B: $i, C: $i, D: $i] : ((subset(A, C) & subset(B, D)) | (cartesian_product2(A, B) = empty_set) | (~subset(cartesian_product2(A, B), cartesian_product2(C, D))))) <=> (~![A: $i, B: $i, C: $i, D: $i] : ((subset(A, C) & subset(B, D)) | (cartesian_product2(A, B) = empty_set) | (~subset(cartesian_product2(A, B), cartesian_product2(C, D)))))),
% 0.10/0.29 inference(rewrite,[status(thm)],[])).
% 0.10/0.29 tff(23,plain,
% 0.10/0.29 ((~![A: $i, B: $i, C: $i, D: $i] : (subset(cartesian_product2(A, B), cartesian_product2(C, D)) => ((cartesian_product2(A, B) = empty_set) | (subset(A, C) & subset(B, D))))) <=> (~![A: $i, B: $i, C: $i, D: $i] : ((subset(A, C) & subset(B, D)) | (cartesian_product2(A, B) = empty_set) | (~subset(cartesian_product2(A, B), cartesian_product2(C, D)))))),
% 0.10/0.29 inference(rewrite,[status(thm)],[])).
% 0.10/0.29 tff(24,axiom,(~![A: $i, B: $i, C: $i, D: $i] : (subset(cartesian_product2(A, B), cartesian_product2(C, D)) => ((cartesian_product2(A, B) = empty_set) | (subset(A, C) & subset(B, D))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t138_zfmisc_1')).
% 0.10/0.29 tff(25,plain,
% 0.10/0.29 (~![A: $i, B: $i, C: $i, D: $i] : ((subset(A, C) & subset(B, D)) | (cartesian_product2(A, B) = empty_set) | (~subset(cartesian_product2(A, B), cartesian_product2(C, D))))),
% 0.10/0.29 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.10/0.29 tff(26,plain,
% 0.10/0.29 (~![A: $i, B: $i, C: $i, D: $i] : ((subset(A, C) & subset(B, D)) | (cartesian_product2(A, B) = empty_set) | (~subset(cartesian_product2(A, B), cartesian_product2(C, D))))),
% 0.10/0.29 inference(modus_ponens,[status(thm)],[25, 22])).
% 0.10/0.29 tff(27,plain,
% 0.10/0.29 (~![A: $i, B: $i, C: $i, D: $i] : ((subset(A, C) & subset(B, D)) | (cartesian_product2(A, B) = empty_set) | (~subset(cartesian_product2(A, B), cartesian_product2(C, D))))),
% 0.10/0.29 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.10/0.29 tff(28,plain,
% 0.10/0.29 (~![A: $i, B: $i, C: $i, D: $i] : ((subset(A, C) & subset(B, D)) | (cartesian_product2(A, B) = empty_set) | (~subset(cartesian_product2(A, B), cartesian_product2(C, D))))),
% 0.10/0.29 inference(modus_ponens,[status(thm)],[27, 22])).
% 0.10/0.29 tff(29,plain,
% 0.10/0.29 (~![A: $i, B: $i, C: $i, D: $i] : ((subset(A, C) & subset(B, D)) | (cartesian_product2(A, B) = empty_set) | (~subset(cartesian_product2(A, B), cartesian_product2(C, D))))),
% 0.10/0.29 inference(modus_ponens,[status(thm)],[28, 22])).
% 0.10/0.29 tff(30,plain,
% 0.10/0.29 (~![A: $i, B: $i, C: $i, D: $i] : ((subset(A, C) & subset(B, D)) | (cartesian_product2(A, B) = empty_set) | (~subset(cartesian_product2(A, B), cartesian_product2(C, D))))),
% 0.10/0.29 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.10/0.29 tff(31,plain,
% 0.10/0.29 (~![A: $i, B: $i, C: $i, D: $i] : ((subset(A, C) & subset(B, D)) | (cartesian_product2(A, B) = empty_set) | (~subset(cartesian_product2(A, B), cartesian_product2(C, D))))),
% 0.10/0.29 inference(modus_ponens,[status(thm)],[30, 22])).
% 0.10/0.29 tff(32,plain,(
% 0.10/0.29 ~((subset(A!5, C!3) & subset(B!4, D!2)) | (cartesian_product2(A!5, B!4) = empty_set) | (~subset(cartesian_product2(A!5, B!4), cartesian_product2(C!3, D!2))))),
% 0.10/0.29 inference(skolemize,[status(sab)],[31])).
% 0.10/0.29 tff(33,plain,
% 0.10/0.29 (~((subset(A!5, C!3) & subset(B!4, D!2)) | (cartesian_product2(A!5, B!4) = empty_set) | (~subset(cartesian_product2(A!5, B!4), cartesian_product2(C!3, D!2))))),
% 0.10/0.29 inference(modus_ponens,[status(thm)],[32, 21])).
% 0.10/0.29 tff(34,plain,
% 0.10/0.29 (subset(cartesian_product2(A!5, B!4), cartesian_product2(C!3, D!2))),
% 0.10/0.29 inference(or_elim,[status(thm)],[33])).
% 0.10/0.29 tff(35,plain,
% 0.10/0.29 (((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | ((~subset(cartesian_product2(A!5, B!4), cartesian_product2(C!3, D!2))) | (set_intersection2(cartesian_product2(A!5, B!4), cartesian_product2(C!3, D!2)) = cartesian_product2(A!5, B!4)))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | (~subset(cartesian_product2(A!5, B!4), cartesian_product2(C!3, D!2))) | (set_intersection2(cartesian_product2(A!5, B!4), cartesian_product2(C!3, D!2)) = cartesian_product2(A!5, B!4)))),
% 0.10/0.29 inference(rewrite,[status(thm)],[])).
% 0.10/0.29 tff(36,plain,
% 0.10/0.29 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | ((~subset(cartesian_product2(A!5, B!4), cartesian_product2(C!3, D!2))) | (set_intersection2(cartesian_product2(A!5, B!4), cartesian_product2(C!3, D!2)) = cartesian_product2(A!5, B!4)))),
% 0.10/0.29 inference(quant_inst,[status(thm)],[])).
% 0.10/0.29 tff(37,plain,
% 0.10/0.29 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | (~subset(cartesian_product2(A!5, B!4), cartesian_product2(C!3, D!2))) | (set_intersection2(cartesian_product2(A!5, B!4), cartesian_product2(C!3, D!2)) = cartesian_product2(A!5, B!4))),
% 0.10/0.29 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.10/0.29 tff(38,plain,
% 0.10/0.29 (set_intersection2(cartesian_product2(A!5, B!4), cartesian_product2(C!3, D!2)) = cartesian_product2(A!5, B!4)),
% 0.10/0.29 inference(unit_resolution,[status(thm)],[37, 34, 20])).
% 0.10/0.29 tff(39,plain,
% 0.10/0.29 (cartesian_product2(A!5, B!4) = set_intersection2(cartesian_product2(A!5, B!4), cartesian_product2(C!3, D!2))),
% 0.10/0.29 inference(symmetry,[status(thm)],[38])).
% 0.10/0.29 tff(40,plain,
% 0.10/0.29 (cartesian_product2(A!5, B!4) = cartesian_product2(set_intersection2(A!5, C!3), set_intersection2(B!4, D!2))),
% 0.10/0.29 inference(transitivity,[status(thm)],[39, 10])).
% 0.10/0.29 tff(41,plain,
% 0.10/0.29 (^[A: $i, B: $i] : refl(((cartesian_product2(A, B) = empty_set) <=> ((B = empty_set) | (A = empty_set))) <=> ((cartesian_product2(A, B) = empty_set) <=> ((B = empty_set) | (A = empty_set))))),
% 0.10/0.29 inference(bind,[status(th)],[])).
% 0.10/0.29 tff(42,plain,
% 0.10/0.29 (![A: $i, B: $i] : ((cartesian_product2(A, B) = empty_set) <=> ((B = empty_set) | (A = empty_set))) <=> ![A: $i, B: $i] : ((cartesian_product2(A, B) = empty_set) <=> ((B = empty_set) | (A = empty_set)))),
% 0.10/0.29 inference(quant_intro,[status(thm)],[41])).
% 0.10/0.29 tff(43,plain,
% 0.10/0.29 (![A: $i, B: $i] : ((cartesian_product2(A, B) = empty_set) <=> ((B = empty_set) | (A = empty_set))) <=> ![A: $i, B: $i] : ((cartesian_product2(A, B) = empty_set) <=> ((B = empty_set) | (A = empty_set)))),
% 0.10/0.29 inference(rewrite,[status(thm)],[])).
% 0.10/0.29 tff(44,plain,
% 0.10/0.29 (^[A: $i, B: $i] : rewrite(((cartesian_product2(A, B) = empty_set) <=> ((A = empty_set) | (B = empty_set))) <=> ((cartesian_product2(A, B) = empty_set) <=> ((B = empty_set) | (A = empty_set))))),
% 0.10/0.29 inference(bind,[status(th)],[])).
% 0.10/0.29 tff(45,plain,
% 0.10/0.29 (![A: $i, B: $i] : ((cartesian_product2(A, B) = empty_set) <=> ((A = empty_set) | (B = empty_set))) <=> ![A: $i, B: $i] : ((cartesian_product2(A, B) = empty_set) <=> ((B = empty_set) | (A = empty_set)))),
% 0.10/0.29 inference(quant_intro,[status(thm)],[44])).
% 0.10/0.29 tff(46,axiom,(![A: $i, B: $i] : ((cartesian_product2(A, B) = empty_set) <=> ((A = empty_set) | (B = empty_set)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t113_zfmisc_1')).
% 0.10/0.29 tff(47,plain,
% 0.10/0.29 (![A: $i, B: $i] : ((cartesian_product2(A, B) = empty_set) <=> ((B = empty_set) | (A = empty_set)))),
% 0.10/0.29 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.10/0.29 tff(48,plain,
% 0.10/0.29 (![A: $i, B: $i] : ((cartesian_product2(A, B) = empty_set) <=> ((B = empty_set) | (A = empty_set)))),
% 0.10/0.29 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.10/0.29 tff(49,plain,(
% 0.10/0.29 ![A: $i, B: $i] : ((cartesian_product2(A, B) = empty_set) <=> ((B = empty_set) | (A = empty_set)))),
% 0.10/0.29 inference(skolemize,[status(sab)],[48])).
% 0.10/0.29 tff(50,plain,
% 0.10/0.29 (![A: $i, B: $i] : ((cartesian_product2(A, B) = empty_set) <=> ((B = empty_set) | (A = empty_set)))),
% 0.10/0.29 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.10/0.29 tff(51,plain,
% 0.10/0.29 ((~![A: $i, B: $i] : ((cartesian_product2(A, B) = empty_set) <=> ((B = empty_set) | (A = empty_set)))) | ((cartesian_product2(A!5, B!4) = empty_set) <=> ((B!4 = empty_set) | (A!5 = empty_set)))),
% 0.10/0.29 inference(quant_inst,[status(thm)],[])).
% 0.10/0.29 tff(52,plain,
% 0.10/0.29 ((cartesian_product2(A!5, B!4) = empty_set) <=> ((B!4 = empty_set) | (A!5 = empty_set))),
% 0.10/0.29 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.10/0.29 tff(53,plain,
% 0.10/0.29 (~(cartesian_product2(A!5, B!4) = empty_set)),
% 0.10/0.29 inference(or_elim,[status(thm)],[33])).
% 0.10/0.29 tff(54,plain,
% 0.10/0.29 ((~((cartesian_product2(A!5, B!4) = empty_set) <=> ((B!4 = empty_set) | (A!5 = empty_set)))) | (cartesian_product2(A!5, B!4) = empty_set) | (~((B!4 = empty_set) | (A!5 = empty_set)))),
% 0.10/0.29 inference(tautology,[status(thm)],[])).
% 0.10/0.29 tff(55,plain,
% 0.10/0.29 ((~((cartesian_product2(A!5, B!4) = empty_set) <=> ((B!4 = empty_set) | (A!5 = empty_set)))) | (~((B!4 = empty_set) | (A!5 = empty_set)))),
% 0.10/0.29 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.10/0.29 tff(56,plain,
% 0.10/0.29 (~((B!4 = empty_set) | (A!5 = empty_set))),
% 0.10/0.29 inference(unit_resolution,[status(thm)],[55, 52])).
% 0.10/0.29 tff(57,plain,
% 0.10/0.29 (((B!4 = empty_set) | (A!5 = empty_set)) | (~(A!5 = empty_set))),
% 0.10/0.29 inference(tautology,[status(thm)],[])).
% 0.10/0.29 tff(58,plain,
% 0.10/0.29 (~(A!5 = empty_set)),
% 0.10/0.29 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.10/0.29 tff(59,plain,
% 0.10/0.29 (((B!4 = empty_set) | (A!5 = empty_set)) | (~(B!4 = empty_set))),
% 0.10/0.29 inference(tautology,[status(thm)],[])).
% 0.10/0.29 tff(60,plain,
% 0.10/0.29 (~(B!4 = empty_set)),
% 0.10/0.29 inference(unit_resolution,[status(thm)],[59, 56])).
% 0.10/0.29 tff(61,plain,
% 0.10/0.29 (^[A: $i, B: $i, C: $i, D: $i] : refl(((B = empty_set) | (A = empty_set) | (~(cartesian_product2(A, B) = cartesian_product2(C, D))) | (~((~(A = C)) | (~(B = D))))) <=> ((B = empty_set) | (A = empty_set) | (~(cartesian_product2(A, B) = cartesian_product2(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 0.10/0.29 inference(bind,[status(th)],[])).
% 0.10/0.29 tff(62,plain,
% 0.10/0.29 (![A: $i, B: $i, C: $i, D: $i] : ((B = empty_set) | (A = empty_set) | (~(cartesian_product2(A, B) = cartesian_product2(C, D))) | (~((~(A = C)) | (~(B = D))))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((B = empty_set) | (A = empty_set) | (~(cartesian_product2(A, B) = cartesian_product2(C, D))) | (~((~(A = C)) | (~(B = D)))))),
% 0.10/0.29 inference(quant_intro,[status(thm)],[61])).
% 0.10/0.29 tff(63,plain,
% 0.10/0.29 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(rewrite(((A = C) & (B = D)) <=> (~((~(A = C)) | (~(B = D))))), ((((A = C) & (B = D)) | (B = empty_set) | (A = empty_set) | (~(cartesian_product2(A, B) = cartesian_product2(C, D)))) <=> ((~((~(A = C)) | (~(B = D)))) | (B = empty_set) | (A = empty_set) | (~(cartesian_product2(A, B) = cartesian_product2(C, D)))))), rewrite(((~((~(A = C)) | (~(B = D)))) | (B = empty_set) | (A = empty_set) | (~(cartesian_product2(A, B) = cartesian_product2(C, D)))) <=> ((B = empty_set) | (A = empty_set) | (~(cartesian_product2(A, B) = cartesian_product2(C, D))) | (~((~(A = C)) | (~(B = D)))))), ((((A = C) & (B = D)) | (B = empty_set) | (A = empty_set) | (~(cartesian_product2(A, B) = cartesian_product2(C, D)))) <=> ((B = empty_set) | (A = empty_set) | (~(cartesian_product2(A, B) = cartesian_product2(C, D))) | (~((~(A = C)) | (~(B = D)))))))),
% 0.10/0.29 inference(bind,[status(th)],[])).
% 0.10/0.29 tff(64,plain,
% 0.10/0.29 (![A: $i, B: $i, C: $i, D: $i] : (((A = C) & (B = D)) | (B = empty_set) | (A = empty_set) | (~(cartesian_product2(A, B) = cartesian_product2(C, D)))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((B = empty_set) | (A = empty_set) | (~(cartesian_product2(A, B) = cartesian_product2(C, D))) | (~((~(A = C)) | (~(B = D)))))),
% 0.10/0.29 inference(quant_intro,[status(thm)],[63])).
% 0.10/0.29 tff(65,plain,
% 0.10/0.29 (![A: $i, B: $i, C: $i, D: $i] : (((A = C) & (B = D)) | (B = empty_set) | (A = empty_set) | (~(cartesian_product2(A, B) = cartesian_product2(C, D)))) <=> ![A: $i, B: $i, C: $i, D: $i] : (((A = C) & (B = D)) | (B = empty_set) | (A = empty_set) | (~(cartesian_product2(A, B) = cartesian_product2(C, D))))),
% 0.10/0.29 inference(rewrite,[status(thm)],[])).
% 0.10/0.29 tff(66,plain,
% 0.10/0.29 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite(((A = empty_set) | (B = empty_set)) <=> ((B = empty_set) | (A = empty_set))), ((((A = empty_set) | (B = empty_set)) | ((A = C) & (B = D))) <=> (((B = empty_set) | (A = empty_set)) | ((A = C) & (B = D))))), rewrite((((B = empty_set) | (A = empty_set)) | ((A = C) & (B = D))) <=> (((A = C) & (B = D)) | (B = empty_set) | (A = empty_set))), ((((A = empty_set) | (B = empty_set)) | ((A = C) & (B = D))) <=> (((A = C) & (B = D)) | (B = empty_set) | (A = empty_set)))), (((cartesian_product2(A, B) = cartesian_product2(C, D)) => (((A = empty_set) | (B = empty_set)) | ((A = C) & (B = D)))) <=> ((cartesian_product2(A, B) = cartesian_product2(C, D)) => (((A = C) & (B = D)) | (B = empty_set) | (A = empty_set))))), rewrite(((cartesian_product2(A, B) = cartesian_product2(C, D)) => (((A = C) & (B = D)) | (B = empty_set) | (A = empty_set))) <=> (((A = C) & (B = D)) | (B = empty_set) | (A = empty_set) | (~(cartesian_product2(A, B) = cartesian_product2(C, D))))), (((cartesian_product2(A, B) = cartesian_product2(C, D)) => (((A = empty_set) | (B = empty_set)) | ((A = C) & (B = D)))) <=> (((A = C) & (B = D)) | (B = empty_set) | (A = empty_set) | (~(cartesian_product2(A, B) = cartesian_product2(C, D))))))),
% 0.10/0.29 inference(bind,[status(th)],[])).
% 0.10/0.29 tff(67,plain,
% 0.10/0.29 (![A: $i, B: $i, C: $i, D: $i] : ((cartesian_product2(A, B) = cartesian_product2(C, D)) => (((A = empty_set) | (B = empty_set)) | ((A = C) & (B = D)))) <=> ![A: $i, B: $i, C: $i, D: $i] : (((A = C) & (B = D)) | (B = empty_set) | (A = empty_set) | (~(cartesian_product2(A, B) = cartesian_product2(C, D))))),
% 0.10/0.29 inference(quant_intro,[status(thm)],[66])).
% 0.10/0.29 tff(68,axiom,(![A: $i, B: $i, C: $i, D: $i] : ((cartesian_product2(A, B) = cartesian_product2(C, D)) => (((A = empty_set) | (B = empty_set)) | ((A = C) & (B = D))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t134_zfmisc_1')).
% 0.10/0.29 tff(69,plain,
% 0.10/0.29 (![A: $i, B: $i, C: $i, D: $i] : (((A = C) & (B = D)) | (B = empty_set) | (A = empty_set) | (~(cartesian_product2(A, B) = cartesian_product2(C, D))))),
% 0.10/0.29 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.10/0.29 tff(70,plain,
% 0.10/0.29 (![A: $i, B: $i, C: $i, D: $i] : (((A = C) & (B = D)) | (B = empty_set) | (A = empty_set) | (~(cartesian_product2(A, B) = cartesian_product2(C, D))))),
% 0.10/0.29 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.10/0.29 tff(71,plain,(
% 0.10/0.29 ![A: $i, B: $i, C: $i, D: $i] : (((A = C) & (B = D)) | (B = empty_set) | (A = empty_set) | (~(cartesian_product2(A, B) = cartesian_product2(C, D))))),
% 0.10/0.29 inference(skolemize,[status(sab)],[70])).
% 0.10/0.29 tff(72,plain,
% 0.10/0.29 (![A: $i, B: $i, C: $i, D: $i] : ((B = empty_set) | (A = empty_set) | (~(cartesian_product2(A, B) = cartesian_product2(C, D))) | (~((~(A = C)) | (~(B = D)))))),
% 0.10/0.29 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.10/0.29 tff(73,plain,
% 0.10/0.29 (![A: $i, B: $i, C: $i, D: $i] : ((B = empty_set) | (A = empty_set) | (~(cartesian_product2(A, B) = cartesian_product2(C, D))) | (~((~(A = C)) | (~(B = D)))))),
% 0.10/0.29 inference(modus_ponens,[status(thm)],[72, 62])).
% 0.10/0.29 tff(74,plain,
% 0.10/0.29 (((~![A: $i, B: $i, C: $i, D: $i] : ((B = empty_set) | (A = empty_set) | (~(cartesian_product2(A, B) = cartesian_product2(C, D))) | (~((~(A = C)) | (~(B = D)))))) | ((B!4 = empty_set) | (A!5 = empty_set) | (~(cartesian_product2(A!5, B!4) = cartesian_product2(set_intersection2(A!5, C!3), set_intersection2(B!4, D!2)))) | (~((~(A!5 = set_intersection2(A!5, C!3))) | (~(B!4 = set_intersection2(B!4, D!2))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((B = empty_set) | (A = empty_set) | (~(cartesian_product2(A, B) = cartesian_product2(C, D))) | (~((~(A = C)) | (~(B = D)))))) | (B!4 = empty_set) | (A!5 = empty_set) | (~(cartesian_product2(A!5, B!4) = cartesian_product2(set_intersection2(A!5, C!3), set_intersection2(B!4, D!2)))) | (~((~(A!5 = set_intersection2(A!5, C!3))) | (~(B!4 = set_intersection2(B!4, D!2))))))),
% 0.10/0.30 inference(rewrite,[status(thm)],[])).
% 0.10/0.30 tff(75,plain,
% 0.10/0.30 ((~![A: $i, B: $i, C: $i, D: $i] : ((B = empty_set) | (A = empty_set) | (~(cartesian_product2(A, B) = cartesian_product2(C, D))) | (~((~(A = C)) | (~(B = D)))))) | ((B!4 = empty_set) | (A!5 = empty_set) | (~(cartesian_product2(A!5, B!4) = cartesian_product2(set_intersection2(A!5, C!3), set_intersection2(B!4, D!2)))) | (~((~(A!5 = set_intersection2(A!5, C!3))) | (~(B!4 = set_intersection2(B!4, D!2))))))),
% 0.10/0.30 inference(quant_inst,[status(thm)],[])).
% 0.10/0.30 tff(76,plain,
% 0.10/0.30 ((~![A: $i, B: $i, C: $i, D: $i] : ((B = empty_set) | (A = empty_set) | (~(cartesian_product2(A, B) = cartesian_product2(C, D))) | (~((~(A = C)) | (~(B = D)))))) | (B!4 = empty_set) | (A!5 = empty_set) | (~(cartesian_product2(A!5, B!4) = cartesian_product2(set_intersection2(A!5, C!3), set_intersection2(B!4, D!2)))) | (~((~(A!5 = set_intersection2(A!5, C!3))) | (~(B!4 = set_intersection2(B!4, D!2)))))),
% 0.10/0.30 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.10/0.30 tff(77,plain,
% 0.10/0.30 (~((~(A!5 = set_intersection2(A!5, C!3))) | (~(B!4 = set_intersection2(B!4, D!2))))),
% 0.10/0.30 inference(unit_resolution,[status(thm)],[76, 73, 60, 58, 40])).
% 0.10/0.30 tff(78,plain,
% 0.10/0.30 (((~(A!5 = set_intersection2(A!5, C!3))) | (~(B!4 = set_intersection2(B!4, D!2)))) | (B!4 = set_intersection2(B!4, D!2))),
% 0.10/0.30 inference(tautology,[status(thm)],[])).
% 0.10/0.30 tff(79,plain,
% 0.10/0.30 (B!4 = set_intersection2(B!4, D!2)),
% 0.10/0.30 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.10/0.30 tff(80,plain,
% 0.10/0.30 (set_intersection2(B!4, D!2) = B!4),
% 0.10/0.30 inference(symmetry,[status(thm)],[79])).
% 0.10/0.30 tff(81,plain,
% 0.10/0.30 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 0.10/0.30 inference(bind,[status(th)],[])).
% 0.10/0.30 tff(82,plain,
% 0.10/0.30 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.10/0.30 inference(quant_intro,[status(thm)],[81])).
% 0.10/0.30 tff(83,plain,
% 0.10/0.30 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.10/0.30 inference(rewrite,[status(thm)],[])).
% 0.10/0.30 tff(84,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 0.10/0.30 tff(85,plain,
% 0.10/0.30 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.10/0.30 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.10/0.30 tff(86,plain,(
% 0.10/0.30 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.10/0.30 inference(skolemize,[status(sab)],[85])).
% 0.10/0.30 tff(87,plain,
% 0.10/0.30 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.10/0.30 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.10/0.30 tff(88,plain,
% 0.10/0.30 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(B!4, D!2) = set_intersection2(D!2, B!4))),
% 0.10/0.30 inference(quant_inst,[status(thm)],[])).
% 0.10/0.30 tff(89,plain,
% 0.10/0.30 (set_intersection2(B!4, D!2) = set_intersection2(D!2, B!4)),
% 0.10/0.30 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.10/0.30 tff(90,plain,
% 0.10/0.30 (set_intersection2(D!2, B!4) = set_intersection2(B!4, D!2)),
% 0.10/0.30 inference(symmetry,[status(thm)],[89])).
% 0.10/0.30 tff(91,plain,
% 0.10/0.30 (set_intersection2(D!2, set_intersection2(B!4, D!2)) = set_intersection2(D!2, B!4)),
% 0.10/0.30 inference(monotonicity,[status(thm)],[80])).
% 0.10/0.30 tff(92,plain,
% 0.10/0.30 (set_intersection2(D!2, set_intersection2(D!2, B!4)) = set_intersection2(D!2, set_intersection2(B!4, D!2))),
% 0.10/0.30 inference(monotonicity,[status(thm)],[90])).
% 0.10/0.30 tff(93,plain,
% 0.10/0.30 (set_intersection2(D!2, set_intersection2(D!2, B!4)) = B!4),
% 0.10/0.30 inference(transitivity,[status(thm)],[92, 91, 90, 80])).
% 0.10/0.30 tff(94,plain,
% 0.10/0.30 (subset(set_intersection2(D!2, set_intersection2(D!2, B!4)), D!2) <=> subset(B!4, D!2)),
% 0.10/0.30 inference(monotonicity,[status(thm)],[93])).
% 0.10/0.30 tff(95,plain,
% 0.10/0.30 (^[A: $i, B: $i] : refl(subset(set_intersection2(A, B), A) <=> subset(set_intersection2(A, B), A))),
% 0.10/0.30 inference(bind,[status(th)],[])).
% 0.10/0.30 tff(96,plain,
% 0.10/0.30 (![A: $i, B: $i] : subset(set_intersection2(A, B), A) <=> ![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 0.10/0.30 inference(quant_intro,[status(thm)],[95])).
% 0.10/0.30 tff(97,plain,
% 0.10/0.30 (![A: $i, B: $i] : subset(set_intersection2(A, B), A) <=> ![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 0.10/0.30 inference(rewrite,[status(thm)],[])).
% 0.10/0.30 tff(98,axiom,(![A: $i, B: $i] : subset(set_intersection2(A, B), A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t17_xboole_1')).
% 0.10/0.30 tff(99,plain,
% 0.10/0.30 (![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 0.10/0.30 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.10/0.30 tff(100,plain,(
% 0.10/0.30 ![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 0.10/0.30 inference(skolemize,[status(sab)],[99])).
% 0.10/0.30 tff(101,plain,
% 0.10/0.30 (![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 0.10/0.30 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.10/0.30 tff(102,plain,
% 0.10/0.30 ((~![A: $i, B: $i] : subset(set_intersection2(A, B), A)) | subset(set_intersection2(D!2, set_intersection2(D!2, B!4)), D!2)),
% 0.10/0.30 inference(quant_inst,[status(thm)],[])).
% 0.10/0.30 tff(103,plain,
% 0.10/0.30 (subset(set_intersection2(D!2, set_intersection2(D!2, B!4)), D!2)),
% 0.10/0.30 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.10/0.30 tff(104,plain,
% 0.10/0.30 (subset(B!4, D!2)),
% 0.10/0.30 inference(modus_ponens,[status(thm)],[103, 94])).
% 0.10/0.30 tff(105,plain,
% 0.10/0.30 (((~(A!5 = set_intersection2(A!5, C!3))) | (~(B!4 = set_intersection2(B!4, D!2)))) | (A!5 = set_intersection2(A!5, C!3))),
% 0.10/0.30 inference(tautology,[status(thm)],[])).
% 0.10/0.30 tff(106,plain,
% 0.10/0.30 (A!5 = set_intersection2(A!5, C!3)),
% 0.10/0.30 inference(unit_resolution,[status(thm)],[105, 77])).
% 0.10/0.30 tff(107,plain,
% 0.10/0.30 (set_intersection2(A!5, C!3) = A!5),
% 0.10/0.30 inference(symmetry,[status(thm)],[106])).
% 0.10/0.30 tff(108,plain,
% 0.10/0.30 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(A!5, C!3) = set_intersection2(C!3, A!5))),
% 0.10/0.30 inference(quant_inst,[status(thm)],[])).
% 0.10/0.30 tff(109,plain,
% 0.10/0.30 (set_intersection2(A!5, C!3) = set_intersection2(C!3, A!5)),
% 0.10/0.30 inference(unit_resolution,[status(thm)],[108, 87])).
% 0.10/0.30 tff(110,plain,
% 0.10/0.30 (set_intersection2(C!3, A!5) = set_intersection2(A!5, C!3)),
% 0.10/0.30 inference(symmetry,[status(thm)],[109])).
% 0.10/0.30 tff(111,plain,
% 0.10/0.30 (set_intersection2(C!3, set_intersection2(A!5, C!3)) = set_intersection2(C!3, A!5)),
% 0.10/0.30 inference(monotonicity,[status(thm)],[107])).
% 0.10/0.30 tff(112,plain,
% 0.10/0.30 (set_intersection2(C!3, set_intersection2(C!3, A!5)) = set_intersection2(C!3, set_intersection2(A!5, C!3))),
% 0.10/0.30 inference(monotonicity,[status(thm)],[110])).
% 0.10/0.30 tff(113,plain,
% 0.10/0.30 (set_intersection2(C!3, set_intersection2(C!3, A!5)) = A!5),
% 0.10/0.30 inference(transitivity,[status(thm)],[112, 111, 110, 107])).
% 0.10/0.30 tff(114,plain,
% 0.10/0.30 (subset(set_intersection2(C!3, set_intersection2(C!3, A!5)), C!3) <=> subset(A!5, C!3)),
% 0.10/0.30 inference(monotonicity,[status(thm)],[113])).
% 0.10/0.30 tff(115,plain,
% 0.10/0.30 ((~![A: $i, B: $i] : subset(set_intersection2(A, B), A)) | subset(set_intersection2(C!3, set_intersection2(C!3, A!5)), C!3)),
% 0.10/0.30 inference(quant_inst,[status(thm)],[])).
% 0.10/0.30 tff(116,plain,
% 0.10/0.30 (subset(set_intersection2(C!3, set_intersection2(C!3, A!5)), C!3)),
% 0.10/0.30 inference(unit_resolution,[status(thm)],[115, 101])).
% 0.10/0.30 tff(117,plain,
% 0.10/0.30 (subset(A!5, C!3)),
% 0.10/0.30 inference(modus_ponens,[status(thm)],[116, 114])).
% 0.10/0.30 tff(118,plain,
% 0.10/0.30 ((~(~((~subset(A!5, C!3)) | (~subset(B!4, D!2))))) <=> ((~subset(A!5, C!3)) | (~subset(B!4, D!2)))),
% 0.10/0.30 inference(rewrite,[status(thm)],[])).
% 0.10/0.30 tff(119,plain,
% 0.10/0.30 ((subset(A!5, C!3) & subset(B!4, D!2)) <=> (~((~subset(A!5, C!3)) | (~subset(B!4, D!2))))),
% 0.10/0.30 inference(rewrite,[status(thm)],[])).
% 0.10/0.30 tff(120,plain,
% 0.10/0.30 ((~(subset(A!5, C!3) & subset(B!4, D!2))) <=> (~(~((~subset(A!5, C!3)) | (~subset(B!4, D!2)))))),
% 0.10/0.30 inference(monotonicity,[status(thm)],[119])).
% 0.10/0.30 tff(121,plain,
% 0.10/0.30 ((~(subset(A!5, C!3) & subset(B!4, D!2))) <=> ((~subset(A!5, C!3)) | (~subset(B!4, D!2)))),
% 0.10/0.30 inference(transitivity,[status(thm)],[120, 118])).
% 0.10/0.30 tff(122,plain,
% 0.10/0.30 (~(subset(A!5, C!3) & subset(B!4, D!2))),
% 0.10/0.30 inference(or_elim,[status(thm)],[33])).
% 0.10/0.30 tff(123,plain,
% 0.10/0.30 ((~subset(A!5, C!3)) | (~subset(B!4, D!2))),
% 0.10/0.30 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.10/0.30 tff(124,plain,
% 0.10/0.30 ($false),
% 0.10/0.30 inference(unit_resolution,[status(thm)],[123, 117, 104])).
% 0.10/0.30 % SZS output end Proof
%------------------------------------------------------------------------------