TSTP Solution File: SEU167+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU167+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 07:27:57 EDT 2022
% Result : Theorem 0.19s 0.47s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEU167+3 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n022.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 09:51:54 EDT 2022
% 0.12/0.33 % 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.
% 0.19/0.47 % SZS status Theorem
% 0.19/0.47 % SZS output start Proof
% 0.19/0.47 tff(subset_type, type, (
% 0.19/0.47 subset: ( $i * $i ) > $o)).
% 0.19/0.47 tff(cartesian_product2_type, type, (
% 0.19/0.47 cartesian_product2: ( $i * $i ) > $i)).
% 0.19/0.47 tff(tptp_fun_C_3_type, type, (
% 0.19/0.47 tptp_fun_C_3: $i)).
% 0.19/0.47 tff(tptp_fun_B_4_type, type, (
% 0.19/0.47 tptp_fun_B_4: $i)).
% 0.19/0.47 tff(tptp_fun_A_5_type, type, (
% 0.19/0.47 tptp_fun_A_5: $i)).
% 0.19/0.47 tff(tptp_fun_D_2_type, type, (
% 0.19/0.47 tptp_fun_D_2: $i)).
% 0.19/0.47 tff(1,plain,
% 0.19/0.47 ((~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D)))) <=> (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(2,plain,
% 0.19/0.47 ((~![A: $i, B: $i, C: $i, D: $i] : ((subset(A, B) & subset(C, D)) => subset(cartesian_product2(A, C), cartesian_product2(B, D)))) <=> (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(3,axiom,(~![A: $i, B: $i, C: $i, D: $i] : ((subset(A, B) & subset(C, D)) => subset(cartesian_product2(A, C), cartesian_product2(B, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t119_zfmisc_1')).
% 0.19/0.47 tff(4,plain,
% 0.19/0.47 (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.47 tff(5,plain,
% 0.19/0.47 (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.19/0.47 tff(6,plain,
% 0.19/0.47 (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.19/0.47 tff(7,plain,
% 0.19/0.47 (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.19/0.47 tff(8,plain,
% 0.19/0.47 (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.19/0.47 tff(9,plain,
% 0.19/0.47 (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.19/0.47 tff(10,plain,
% 0.19/0.47 (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.19/0.47 tff(11,plain,(
% 0.19/0.47 ~((~(subset(A!5, B!4) & subset(C!3, D!2))) | subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, D!2)))),
% 0.19/0.47 inference(skolemize,[status(sab)],[10])).
% 0.19/0.47 tff(12,plain,
% 0.19/0.47 (subset(A!5, B!4) & subset(C!3, D!2)),
% 0.19/0.47 inference(or_elim,[status(thm)],[11])).
% 0.19/0.47 tff(13,plain,
% 0.19/0.47 (subset(A!5, B!4)),
% 0.19/0.47 inference(and_elim,[status(thm)],[12])).
% 0.19/0.47 tff(14,plain,
% 0.19/0.47 (^[A: $i, B: $i, C: $i] : refl(((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B)))))) <=> ((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B)))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(15,plain,
% 0.19/0.47 (![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B)))))) <=> ![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.47 tff(16,plain,
% 0.19/0.47 (^[A: $i, B: $i, C: $i] : rewrite(((~subset(A, B)) | (subset(cartesian_product2(A, C), cartesian_product2(B, C)) & subset(cartesian_product2(C, A), cartesian_product2(C, B)))) <=> ((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B)))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(17,plain,
% 0.19/0.47 (![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (subset(cartesian_product2(A, C), cartesian_product2(B, C)) & subset(cartesian_product2(C, A), cartesian_product2(C, B)))) <=> ![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.47 tff(18,plain,
% 0.19/0.47 (![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (subset(cartesian_product2(A, C), cartesian_product2(B, C)) & subset(cartesian_product2(C, A), cartesian_product2(C, B)))) <=> ![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (subset(cartesian_product2(A, C), cartesian_product2(B, C)) & subset(cartesian_product2(C, A), cartesian_product2(C, B))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(19,plain,
% 0.19/0.47 (^[A: $i, B: $i, C: $i] : rewrite((subset(A, B) => (subset(cartesian_product2(A, C), cartesian_product2(B, C)) & subset(cartesian_product2(C, A), cartesian_product2(C, B)))) <=> ((~subset(A, B)) | (subset(cartesian_product2(A, C), cartesian_product2(B, C)) & subset(cartesian_product2(C, A), cartesian_product2(C, B)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(20,plain,
% 0.19/0.47 (![A: $i, B: $i, C: $i] : (subset(A, B) => (subset(cartesian_product2(A, C), cartesian_product2(B, C)) & subset(cartesian_product2(C, A), cartesian_product2(C, B)))) <=> ![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (subset(cartesian_product2(A, C), cartesian_product2(B, C)) & subset(cartesian_product2(C, A), cartesian_product2(C, B))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.47 tff(21,axiom,(![A: $i, B: $i, C: $i] : (subset(A, B) => (subset(cartesian_product2(A, C), cartesian_product2(B, C)) & subset(cartesian_product2(C, A), cartesian_product2(C, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t118_zfmisc_1')).
% 0.19/0.47 tff(22,plain,
% 0.19/0.47 (![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (subset(cartesian_product2(A, C), cartesian_product2(B, C)) & subset(cartesian_product2(C, A), cartesian_product2(C, B))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.47 tff(23,plain,
% 0.19/0.47 (![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (subset(cartesian_product2(A, C), cartesian_product2(B, C)) & subset(cartesian_product2(C, A), cartesian_product2(C, B))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.19/0.47 tff(24,plain,(
% 0.19/0.47 ![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (subset(cartesian_product2(A, C), cartesian_product2(B, C)) & subset(cartesian_product2(C, A), cartesian_product2(C, B))))),
% 0.19/0.47 inference(skolemize,[status(sab)],[23])).
% 0.19/0.47 tff(25,plain,
% 0.19/0.47 (![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.19/0.47 tff(26,plain,
% 0.19/0.47 (![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[25, 15])).
% 0.19/0.47 tff(27,plain,
% 0.19/0.47 (((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B))))))) | ((~subset(A!5, B!4)) | (~((~subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, C!3))) | (~subset(cartesian_product2(C!3, A!5), cartesian_product2(C!3, B!4))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B))))))) | (~subset(A!5, B!4)) | (~((~subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, C!3))) | (~subset(cartesian_product2(C!3, A!5), cartesian_product2(C!3, B!4))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(28,plain,
% 0.19/0.47 ((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B))))))) | ((~subset(A!5, B!4)) | (~((~subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, C!3))) | (~subset(cartesian_product2(C!3, A!5), cartesian_product2(C!3, B!4))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(29,plain,
% 0.19/0.48 ((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B))))))) | (~subset(A!5, B!4)) | (~((~subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, C!3))) | (~subset(cartesian_product2(C!3, A!5), cartesian_product2(C!3, B!4)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.48 tff(30,plain,
% 0.19/0.48 (~((~subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, C!3))) | (~subset(cartesian_product2(C!3, A!5), cartesian_product2(C!3, B!4))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[29, 26, 13])).
% 0.19/0.48 tff(31,plain,
% 0.19/0.48 (((~subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, C!3))) | (~subset(cartesian_product2(C!3, A!5), cartesian_product2(C!3, B!4)))) | subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, C!3))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(32,plain,
% 0.19/0.48 (subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, C!3))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.19/0.48 tff(33,plain,
% 0.19/0.48 (subset(C!3, D!2)),
% 0.19/0.48 inference(and_elim,[status(thm)],[12])).
% 0.19/0.48 tff(34,plain,
% 0.19/0.48 (((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B))))))) | ((~subset(C!3, D!2)) | (~((~subset(cartesian_product2(B!4, C!3), cartesian_product2(B!4, D!2))) | (~subset(cartesian_product2(C!3, B!4), cartesian_product2(D!2, B!4))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B))))))) | (~subset(C!3, D!2)) | (~((~subset(cartesian_product2(B!4, C!3), cartesian_product2(B!4, D!2))) | (~subset(cartesian_product2(C!3, B!4), cartesian_product2(D!2, B!4))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(35,plain,
% 0.19/0.48 (((~subset(C!3, D!2)) | (~((~subset(cartesian_product2(C!3, B!4), cartesian_product2(D!2, B!4))) | (~subset(cartesian_product2(B!4, C!3), cartesian_product2(B!4, D!2)))))) <=> ((~subset(C!3, D!2)) | (~((~subset(cartesian_product2(B!4, C!3), cartesian_product2(B!4, D!2))) | (~subset(cartesian_product2(C!3, B!4), cartesian_product2(D!2, B!4))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(36,plain,
% 0.19/0.48 (((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B))))))) | ((~subset(C!3, D!2)) | (~((~subset(cartesian_product2(C!3, B!4), cartesian_product2(D!2, B!4))) | (~subset(cartesian_product2(B!4, C!3), cartesian_product2(B!4, D!2))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B))))))) | ((~subset(C!3, D!2)) | (~((~subset(cartesian_product2(B!4, C!3), cartesian_product2(B!4, D!2))) | (~subset(cartesian_product2(C!3, B!4), cartesian_product2(D!2, B!4)))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[35])).
% 0.19/0.48 tff(37,plain,
% 0.19/0.48 (((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B))))))) | ((~subset(C!3, D!2)) | (~((~subset(cartesian_product2(C!3, B!4), cartesian_product2(D!2, B!4))) | (~subset(cartesian_product2(B!4, C!3), cartesian_product2(B!4, D!2))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B))))))) | (~subset(C!3, D!2)) | (~((~subset(cartesian_product2(B!4, C!3), cartesian_product2(B!4, D!2))) | (~subset(cartesian_product2(C!3, B!4), cartesian_product2(D!2, B!4))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[36, 34])).
% 0.19/0.48 tff(38,plain,
% 0.19/0.48 ((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B))))))) | ((~subset(C!3, D!2)) | (~((~subset(cartesian_product2(C!3, B!4), cartesian_product2(D!2, B!4))) | (~subset(cartesian_product2(B!4, C!3), cartesian_product2(B!4, D!2))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(39,plain,
% 0.19/0.48 ((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B))))))) | (~subset(C!3, D!2)) | (~((~subset(cartesian_product2(B!4, C!3), cartesian_product2(B!4, D!2))) | (~subset(cartesian_product2(C!3, B!4), cartesian_product2(D!2, B!4)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.48 tff(40,plain,
% 0.19/0.48 (~((~subset(cartesian_product2(B!4, C!3), cartesian_product2(B!4, D!2))) | (~subset(cartesian_product2(C!3, B!4), cartesian_product2(D!2, B!4))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[39, 26, 33])).
% 0.19/0.48 tff(41,plain,
% 0.19/0.48 (((~subset(cartesian_product2(B!4, C!3), cartesian_product2(B!4, D!2))) | (~subset(cartesian_product2(C!3, B!4), cartesian_product2(D!2, B!4)))) | subset(cartesian_product2(B!4, C!3), cartesian_product2(B!4, D!2))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(42,plain,
% 0.19/0.48 (subset(cartesian_product2(B!4, C!3), cartesian_product2(B!4, D!2))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.19/0.48 tff(43,plain,
% 0.19/0.48 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C))) <=> ![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(44,plain,
% 0.19/0.48 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((subset(A, B) & subset(B, C)) <=> (~((~subset(A, B)) | (~subset(B, C))))), ((~(subset(A, B) & subset(B, C))) <=> (~(~((~subset(A, B)) | (~subset(B, C))))))), rewrite((~(~((~subset(A, B)) | (~subset(B, C))))) <=> ((~subset(A, B)) | (~subset(B, C)))), ((~(subset(A, B) & subset(B, C))) <=> ((~subset(A, B)) | (~subset(B, C))))), (((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> (((~subset(A, B)) | (~subset(B, C))) | subset(A, C)))), rewrite((((~subset(A, B)) | (~subset(B, C))) | subset(A, C)) <=> (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))), (((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(45,plain,
% 0.19/0.48 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> ![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[44])).
% 0.19/0.48 tff(46,plain,
% 0.19/0.48 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(47,plain,
% 0.19/0.48 (^[A: $i, B: $i, C: $i] : rewrite(((subset(A, B) & subset(B, C)) => subset(A, C)) <=> ((~(subset(A, B) & subset(B, C))) | subset(A, C)))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(48,plain,
% 0.19/0.48 (![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(B, C)) => subset(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.48 tff(49,axiom,(![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(B, C)) => subset(A, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t1_xboole_1')).
% 0.19/0.48 tff(50,plain,
% 0.19/0.48 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.48 tff(51,plain,
% 0.19/0.48 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.19/0.48 tff(52,plain,(
% 0.19/0.48 ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.19/0.48 inference(skolemize,[status(sab)],[51])).
% 0.19/0.48 tff(53,plain,
% 0.19/0.48 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.19/0.48 tff(54,plain,
% 0.19/0.48 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[53, 43])).
% 0.19/0.48 tff(55,plain,
% 0.19/0.48 (~subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, D!2))),
% 0.19/0.48 inference(or_elim,[status(thm)],[11])).
% 0.19/0.48 tff(56,plain,
% 0.19/0.48 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | (subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, D!2)) | (~subset(cartesian_product2(B!4, C!3), cartesian_product2(B!4, D!2))) | (~subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, C!3))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, D!2)) | (~subset(cartesian_product2(B!4, C!3), cartesian_product2(B!4, D!2))) | (~subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, C!3))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(57,plain,
% 0.19/0.48 ((subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, D!2)) | (~subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, C!3))) | (~subset(cartesian_product2(B!4, C!3), cartesian_product2(B!4, D!2)))) <=> (subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, D!2)) | (~subset(cartesian_product2(B!4, C!3), cartesian_product2(B!4, D!2))) | (~subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, C!3))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(58,plain,
% 0.19/0.48 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | (subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, D!2)) | (~subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, C!3))) | (~subset(cartesian_product2(B!4, C!3), cartesian_product2(B!4, D!2))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | (subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, D!2)) | (~subset(cartesian_product2(B!4, C!3), cartesian_product2(B!4, D!2))) | (~subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, C!3)))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[57])).
% 0.19/0.48 tff(59,plain,
% 0.19/0.48 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | (subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, D!2)) | (~subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, C!3))) | (~subset(cartesian_product2(B!4, C!3), cartesian_product2(B!4, D!2))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, D!2)) | (~subset(cartesian_product2(B!4, C!3), cartesian_product2(B!4, D!2))) | (~subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, C!3))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[58, 56])).
% 0.19/0.48 tff(60,plain,
% 0.19/0.48 ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | (subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, D!2)) | (~subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, C!3))) | (~subset(cartesian_product2(B!4, C!3), cartesian_product2(B!4, D!2))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(61,plain,
% 0.19/0.48 ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, D!2)) | (~subset(cartesian_product2(B!4, C!3), cartesian_product2(B!4, D!2))) | (~subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, C!3)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.48 tff(62,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[61, 55, 54, 42, 32])).
% 0.19/0.48 % SZS output end Proof
%------------------------------------------------------------------------------