TSTP Solution File: SET978+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET978+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 05:08:48 EDT 2022
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET978+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n011.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 08:46:43 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.
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(disjoint_type, type, (
% 0.19/0.38 disjoint: ( $i * $i ) > $o)).
% 0.19/0.38 tff(singleton_type, type, (
% 0.19/0.38 singleton: $i > $i)).
% 0.19/0.38 tff(tptp_fun_B_4_type, type, (
% 0.19/0.38 tptp_fun_B_4: $i)).
% 0.19/0.38 tff(tptp_fun_A_5_type, type, (
% 0.19/0.38 tptp_fun_A_5: $i)).
% 0.19/0.38 tff(tptp_fun_D_2_type, type, (
% 0.19/0.38 tptp_fun_D_2: $i)).
% 0.19/0.38 tff(tptp_fun_C_3_type, type, (
% 0.19/0.38 tptp_fun_C_3: $i)).
% 0.19/0.38 tff(cartesian_product2_type, type, (
% 0.19/0.38 cartesian_product2: ( $i * $i ) > $i)).
% 0.19/0.38 tff(1,assumption,(~disjoint(singleton(A!5), singleton(B!4))), introduced(assumption)).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 (^[A: $i, B: $i] : refl(((A = B) | disjoint(singleton(A), singleton(B))) <=> ((A = B) | disjoint(singleton(A), singleton(B))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(3,plain,
% 0.19/0.38 (![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B))) <=> ![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.38 tff(4,plain,
% 0.19/0.38 (![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B))) <=> ![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 (^[A: $i, B: $i] : rewrite(((~(A = B)) => disjoint(singleton(A), singleton(B))) <=> ((A = B) | disjoint(singleton(A), singleton(B))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(6,plain,
% 0.19/0.38 (![A: $i, B: $i] : ((~(A = B)) => disjoint(singleton(A), singleton(B))) <=> ![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[5])).
% 0.19/0.38 tff(7,axiom,(![A: $i, B: $i] : ((~(A = B)) => disjoint(singleton(A), singleton(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t17_zfmisc_1')).
% 0.19/0.38 tff(8,plain,
% 0.19/0.38 (![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.19/0.38 tff(9,plain,
% 0.19/0.38 (![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.19/0.38 tff(10,plain,(
% 0.19/0.38 ![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[9])).
% 0.19/0.38 tff(11,plain,
% 0.19/0.38 (![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 ((~![A: $i, B: $i, C: $i, D: $i] : ((A = B) | (disjoint(cartesian_product2(singleton(A), C), cartesian_product2(singleton(B), D)) & disjoint(cartesian_product2(C, singleton(A)), cartesian_product2(D, singleton(B)))))) <=> (~![A: $i, B: $i, C: $i, D: $i] : ((A = B) | (disjoint(cartesian_product2(singleton(A), C), cartesian_product2(singleton(B), D)) & disjoint(cartesian_product2(C, singleton(A)), cartesian_product2(D, singleton(B))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 ((~![A: $i, B: $i, C: $i, D: $i] : ((~(A = B)) => (disjoint(cartesian_product2(singleton(A), C), cartesian_product2(singleton(B), D)) & disjoint(cartesian_product2(C, singleton(A)), cartesian_product2(D, singleton(B)))))) <=> (~![A: $i, B: $i, C: $i, D: $i] : ((A = B) | (disjoint(cartesian_product2(singleton(A), C), cartesian_product2(singleton(B), D)) & disjoint(cartesian_product2(C, singleton(A)), cartesian_product2(D, singleton(B))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(14,axiom,(~![A: $i, B: $i, C: $i, D: $i] : ((~(A = B)) => (disjoint(cartesian_product2(singleton(A), C), cartesian_product2(singleton(B), D)) & disjoint(cartesian_product2(C, singleton(A)), cartesian_product2(D, singleton(B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t131_zfmisc_1')).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 (~![A: $i, B: $i, C: $i, D: $i] : ((A = B) | (disjoint(cartesian_product2(singleton(A), C), cartesian_product2(singleton(B), D)) & disjoint(cartesian_product2(C, singleton(A)), cartesian_product2(D, singleton(B)))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 (~![A: $i, B: $i, C: $i, D: $i] : ((A = B) | (disjoint(cartesian_product2(singleton(A), C), cartesian_product2(singleton(B), D)) & disjoint(cartesian_product2(C, singleton(A)), cartesian_product2(D, singleton(B)))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (~![A: $i, B: $i, C: $i, D: $i] : ((A = B) | (disjoint(cartesian_product2(singleton(A), C), cartesian_product2(singleton(B), D)) & disjoint(cartesian_product2(C, singleton(A)), cartesian_product2(D, singleton(B)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 (~![A: $i, B: $i, C: $i, D: $i] : ((A = B) | (disjoint(cartesian_product2(singleton(A), C), cartesian_product2(singleton(B), D)) & disjoint(cartesian_product2(C, singleton(A)), cartesian_product2(D, singleton(B)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (~![A: $i, B: $i, C: $i, D: $i] : ((A = B) | (disjoint(cartesian_product2(singleton(A), C), cartesian_product2(singleton(B), D)) & disjoint(cartesian_product2(C, singleton(A)), cartesian_product2(D, singleton(B)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[18, 12])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (~![A: $i, B: $i, C: $i, D: $i] : ((A = B) | (disjoint(cartesian_product2(singleton(A), C), cartesian_product2(singleton(B), D)) & disjoint(cartesian_product2(C, singleton(A)), cartesian_product2(D, singleton(B)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (~![A: $i, B: $i, C: $i, D: $i] : ((A = B) | (disjoint(cartesian_product2(singleton(A), C), cartesian_product2(singleton(B), D)) & disjoint(cartesian_product2(C, singleton(A)), cartesian_product2(D, singleton(B)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[20, 12])).
% 0.19/0.39 tff(22,plain,(
% 0.19/0.39 ~((A!5 = B!4) | (disjoint(cartesian_product2(singleton(A!5), C!3), cartesian_product2(singleton(B!4), D!2)) & disjoint(cartesian_product2(C!3, singleton(A!5)), cartesian_product2(D!2, singleton(B!4)))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[21])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (~(A!5 = B!4)),
% 0.19/0.39 inference(or_elim,[status(thm)],[22])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (((~![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B)))) | ((A!5 = B!4) | disjoint(singleton(A!5), singleton(B!4)))) <=> ((~![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B)))) | (A!5 = B!4) | disjoint(singleton(A!5), singleton(B!4)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B)))) | ((A!5 = B!4) | disjoint(singleton(A!5), singleton(B!4)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : ((A = B) | disjoint(singleton(A), singleton(B)))) | (A!5 = B!4) | disjoint(singleton(A!5), singleton(B!4))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[26, 23, 11, 1])).
% 0.19/0.39 tff(28,plain,(disjoint(singleton(A!5), singleton(B!4))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 ((disjoint(C!3, D!2) | disjoint(singleton(A!5), singleton(B!4))) | (~disjoint(singleton(A!5), singleton(B!4)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (disjoint(C!3, D!2) | disjoint(singleton(A!5), singleton(B!4))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.19/0.39 tff(31,assumption,(~disjoint(cartesian_product2(singleton(A!5), C!3), cartesian_product2(singleton(B!4), D!2))), introduced(assumption)).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (^[A: $i, B: $i, C: $i, D: $i] : refl(((~(disjoint(C, D) | disjoint(A, B))) | disjoint(cartesian_product2(A, C), cartesian_product2(B, D))) <=> ((~(disjoint(C, D) | disjoint(A, B))) | disjoint(cartesian_product2(A, C), cartesian_product2(B, D))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i, D: $i] : ((~(disjoint(C, D) | disjoint(A, B))) | disjoint(cartesian_product2(A, C), cartesian_product2(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(disjoint(C, D) | disjoint(A, B))) | disjoint(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i, D: $i] : ((~(disjoint(C, D) | disjoint(A, B))) | disjoint(cartesian_product2(A, C), cartesian_product2(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(disjoint(C, D) | disjoint(A, B))) | disjoint(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(rewrite((disjoint(A, B) | disjoint(C, D)) <=> (disjoint(C, D) | disjoint(A, B))), (((disjoint(A, B) | disjoint(C, D)) => disjoint(cartesian_product2(A, C), cartesian_product2(B, D))) <=> ((disjoint(C, D) | disjoint(A, B)) => disjoint(cartesian_product2(A, C), cartesian_product2(B, D))))), rewrite(((disjoint(C, D) | disjoint(A, B)) => disjoint(cartesian_product2(A, C), cartesian_product2(B, D))) <=> ((~(disjoint(C, D) | disjoint(A, B))) | disjoint(cartesian_product2(A, C), cartesian_product2(B, D)))), (((disjoint(A, B) | disjoint(C, D)) => disjoint(cartesian_product2(A, C), cartesian_product2(B, D))) <=> ((~(disjoint(C, D) | disjoint(A, B))) | disjoint(cartesian_product2(A, C), cartesian_product2(B, D)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i, D: $i] : ((disjoint(A, B) | disjoint(C, D)) => disjoint(cartesian_product2(A, C), cartesian_product2(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(disjoint(C, D) | disjoint(A, B))) | disjoint(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[35])).
% 0.19/0.39 tff(37,axiom,(![A: $i, B: $i, C: $i, D: $i] : ((disjoint(A, B) | disjoint(C, D)) => disjoint(cartesian_product2(A, C), cartesian_product2(B, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t127_zfmisc_1')).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i, D: $i] : ((~(disjoint(C, D) | disjoint(A, B))) | disjoint(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i, D: $i] : ((~(disjoint(C, D) | disjoint(A, B))) | disjoint(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.19/0.39 tff(40,plain,(
% 0.19/0.39 ![A: $i, B: $i, C: $i, D: $i] : ((~(disjoint(C, D) | disjoint(A, B))) | disjoint(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[39])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i, D: $i] : ((~(disjoint(C, D) | disjoint(A, B))) | disjoint(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (((~![A: $i, B: $i, C: $i, D: $i] : ((~(disjoint(C, D) | disjoint(A, B))) | disjoint(cartesian_product2(A, C), cartesian_product2(B, D)))) | ((~(disjoint(C!3, D!2) | disjoint(singleton(A!5), singleton(B!4)))) | disjoint(cartesian_product2(singleton(A!5), C!3), cartesian_product2(singleton(B!4), D!2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~(disjoint(C, D) | disjoint(A, B))) | disjoint(cartesian_product2(A, C), cartesian_product2(B, D)))) | (~(disjoint(C!3, D!2) | disjoint(singleton(A!5), singleton(B!4)))) | disjoint(cartesian_product2(singleton(A!5), C!3), cartesian_product2(singleton(B!4), D!2)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 ((~![A: $i, B: $i, C: $i, D: $i] : ((~(disjoint(C, D) | disjoint(A, B))) | disjoint(cartesian_product2(A, C), cartesian_product2(B, D)))) | ((~(disjoint(C!3, D!2) | disjoint(singleton(A!5), singleton(B!4)))) | disjoint(cartesian_product2(singleton(A!5), C!3), cartesian_product2(singleton(B!4), D!2)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 ((~![A: $i, B: $i, C: $i, D: $i] : ((~(disjoint(C, D) | disjoint(A, B))) | disjoint(cartesian_product2(A, C), cartesian_product2(B, D)))) | (~(disjoint(C!3, D!2) | disjoint(singleton(A!5), singleton(B!4)))) | disjoint(cartesian_product2(singleton(A!5), C!3), cartesian_product2(singleton(B!4), D!2))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[44, 41, 31, 30])).
% 0.19/0.39 tff(46,plain,(disjoint(cartesian_product2(singleton(A!5), C!3), cartesian_product2(singleton(B!4), D!2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 ((~(~((~disjoint(cartesian_product2(singleton(A!5), C!3), cartesian_product2(singleton(B!4), D!2))) | (~disjoint(cartesian_product2(C!3, singleton(A!5)), cartesian_product2(D!2, singleton(B!4))))))) <=> ((~disjoint(cartesian_product2(singleton(A!5), C!3), cartesian_product2(singleton(B!4), D!2))) | (~disjoint(cartesian_product2(C!3, singleton(A!5)), cartesian_product2(D!2, singleton(B!4)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 ((disjoint(cartesian_product2(singleton(A!5), C!3), cartesian_product2(singleton(B!4), D!2)) & disjoint(cartesian_product2(C!3, singleton(A!5)), cartesian_product2(D!2, singleton(B!4)))) <=> (~((~disjoint(cartesian_product2(singleton(A!5), C!3), cartesian_product2(singleton(B!4), D!2))) | (~disjoint(cartesian_product2(C!3, singleton(A!5)), cartesian_product2(D!2, singleton(B!4))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 ((~(disjoint(cartesian_product2(singleton(A!5), C!3), cartesian_product2(singleton(B!4), D!2)) & disjoint(cartesian_product2(C!3, singleton(A!5)), cartesian_product2(D!2, singleton(B!4))))) <=> (~(~((~disjoint(cartesian_product2(singleton(A!5), C!3), cartesian_product2(singleton(B!4), D!2))) | (~disjoint(cartesian_product2(C!3, singleton(A!5)), cartesian_product2(D!2, singleton(B!4)))))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[48])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 ((~(disjoint(cartesian_product2(singleton(A!5), C!3), cartesian_product2(singleton(B!4), D!2)) & disjoint(cartesian_product2(C!3, singleton(A!5)), cartesian_product2(D!2, singleton(B!4))))) <=> ((~disjoint(cartesian_product2(singleton(A!5), C!3), cartesian_product2(singleton(B!4), D!2))) | (~disjoint(cartesian_product2(C!3, singleton(A!5)), cartesian_product2(D!2, singleton(B!4)))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[49, 47])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 (~(disjoint(cartesian_product2(singleton(A!5), C!3), cartesian_product2(singleton(B!4), D!2)) & disjoint(cartesian_product2(C!3, singleton(A!5)), cartesian_product2(D!2, singleton(B!4))))),
% 0.19/0.39 inference(or_elim,[status(thm)],[22])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 ((~disjoint(cartesian_product2(singleton(A!5), C!3), cartesian_product2(singleton(B!4), D!2))) | (~disjoint(cartesian_product2(C!3, singleton(A!5)), cartesian_product2(D!2, singleton(B!4))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 (~disjoint(cartesian_product2(C!3, singleton(A!5)), cartesian_product2(D!2, singleton(B!4)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[52, 46])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 (((~![A: $i, B: $i, C: $i, D: $i] : ((~(disjoint(C, D) | disjoint(A, B))) | disjoint(cartesian_product2(A, C), cartesian_product2(B, D)))) | ((~(disjoint(C!3, D!2) | disjoint(singleton(A!5), singleton(B!4)))) | disjoint(cartesian_product2(C!3, singleton(A!5)), cartesian_product2(D!2, singleton(B!4))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~(disjoint(C, D) | disjoint(A, B))) | disjoint(cartesian_product2(A, C), cartesian_product2(B, D)))) | (~(disjoint(C!3, D!2) | disjoint(singleton(A!5), singleton(B!4)))) | disjoint(cartesian_product2(C!3, singleton(A!5)), cartesian_product2(D!2, singleton(B!4))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 (((~(disjoint(singleton(A!5), singleton(B!4)) | disjoint(C!3, D!2))) | disjoint(cartesian_product2(C!3, singleton(A!5)), cartesian_product2(D!2, singleton(B!4)))) <=> ((~(disjoint(C!3, D!2) | disjoint(singleton(A!5), singleton(B!4)))) | disjoint(cartesian_product2(C!3, singleton(A!5)), cartesian_product2(D!2, singleton(B!4))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 (((~![A: $i, B: $i, C: $i, D: $i] : ((~(disjoint(C, D) | disjoint(A, B))) | disjoint(cartesian_product2(A, C), cartesian_product2(B, D)))) | ((~(disjoint(singleton(A!5), singleton(B!4)) | disjoint(C!3, D!2))) | disjoint(cartesian_product2(C!3, singleton(A!5)), cartesian_product2(D!2, singleton(B!4))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~(disjoint(C, D) | disjoint(A, B))) | disjoint(cartesian_product2(A, C), cartesian_product2(B, D)))) | ((~(disjoint(C!3, D!2) | disjoint(singleton(A!5), singleton(B!4)))) | disjoint(cartesian_product2(C!3, singleton(A!5)), cartesian_product2(D!2, singleton(B!4)))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[55])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 (((~![A: $i, B: $i, C: $i, D: $i] : ((~(disjoint(C, D) | disjoint(A, B))) | disjoint(cartesian_product2(A, C), cartesian_product2(B, D)))) | ((~(disjoint(singleton(A!5), singleton(B!4)) | disjoint(C!3, D!2))) | disjoint(cartesian_product2(C!3, singleton(A!5)), cartesian_product2(D!2, singleton(B!4))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~(disjoint(C, D) | disjoint(A, B))) | disjoint(cartesian_product2(A, C), cartesian_product2(B, D)))) | (~(disjoint(C!3, D!2) | disjoint(singleton(A!5), singleton(B!4)))) | disjoint(cartesian_product2(C!3, singleton(A!5)), cartesian_product2(D!2, singleton(B!4))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[56, 54])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 ((~![A: $i, B: $i, C: $i, D: $i] : ((~(disjoint(C, D) | disjoint(A, B))) | disjoint(cartesian_product2(A, C), cartesian_product2(B, D)))) | ((~(disjoint(singleton(A!5), singleton(B!4)) | disjoint(C!3, D!2))) | disjoint(cartesian_product2(C!3, singleton(A!5)), cartesian_product2(D!2, singleton(B!4))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 ((~![A: $i, B: $i, C: $i, D: $i] : ((~(disjoint(C, D) | disjoint(A, B))) | disjoint(cartesian_product2(A, C), cartesian_product2(B, D)))) | (~(disjoint(C!3, D!2) | disjoint(singleton(A!5), singleton(B!4)))) | disjoint(cartesian_product2(C!3, singleton(A!5)), cartesian_product2(D!2, singleton(B!4)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[59, 41, 53, 30])).
% 0.19/0.39 % SZS output end Proof
%------------------------------------------------------------------------------