TSTP Solution File: SET639+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET639+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 05:07:28 EDT 2022
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SET639+3 : TPTP v8.1.0. Released v2.2.0.
% 0.09/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n026.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 07:19:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(empty_set_type, type, (
% 0.12/0.38 empty_set: $i)).
% 0.12/0.38 tff(tptp_fun_B_4_type, type, (
% 0.12/0.38 tptp_fun_B_4: $i)).
% 0.12/0.38 tff(intersection_type, type, (
% 0.12/0.38 intersection: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_C_3_type, type, (
% 0.12/0.38 tptp_fun_C_3: $i)).
% 0.12/0.38 tff(subset_type, type, (
% 0.12/0.38 subset: ( $i * $i ) > $o)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 ((~![B: $i, C: $i] : ((~(subset(B, C) & (intersection(C, B) = empty_set))) | (B = empty_set))) <=> (~![B: $i, C: $i] : ((~(subset(B, C) & (intersection(C, B) = empty_set))) | (B = empty_set)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 ((~![B: $i, C: $i] : ((subset(B, C) & (intersection(C, B) = empty_set)) => (B = empty_set))) <=> (~![B: $i, C: $i] : ((~(subset(B, C) & (intersection(C, B) = empty_set))) | (B = empty_set)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(3,axiom,(~![B: $i, C: $i] : ((subset(B, C) & (intersection(C, B) = empty_set)) => (B = empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_th121')).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (~![B: $i, C: $i] : ((~(subset(B, C) & (intersection(C, B) = empty_set))) | (B = empty_set))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (~![B: $i, C: $i] : ((~(subset(B, C) & (intersection(C, B) = empty_set))) | (B = empty_set))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (~![B: $i, C: $i] : ((~(subset(B, C) & (intersection(C, B) = empty_set))) | (B = empty_set))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (~![B: $i, C: $i] : ((~(subset(B, C) & (intersection(C, B) = empty_set))) | (B = empty_set))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (~![B: $i, C: $i] : ((~(subset(B, C) & (intersection(C, B) = empty_set))) | (B = empty_set))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (~![B: $i, C: $i] : ((~(subset(B, C) & (intersection(C, B) = empty_set))) | (B = empty_set))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (~![B: $i, C: $i] : ((~(subset(B, C) & (intersection(C, B) = empty_set))) | (B = empty_set))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.12/0.38 tff(11,plain,(
% 0.12/0.38 ~((~(subset(B!4, C!3) & (intersection(C!3, B!4) = empty_set))) | (B!4 = empty_set))),
% 0.12/0.38 inference(skolemize,[status(sab)],[10])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (subset(B!4, C!3) & (intersection(C!3, B!4) = empty_set)),
% 0.12/0.38 inference(or_elim,[status(thm)],[11])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (intersection(C!3, B!4) = empty_set),
% 0.12/0.38 inference(and_elim,[status(thm)],[12])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[14])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(17,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.12/0.38 tff(19,plain,(
% 0.12/0.38 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.12/0.38 inference(skolemize,[status(sab)],[18])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(B!4, C!3) = intersection(C!3, B!4))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (intersection(B!4, C!3) = intersection(C!3, B!4)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (subset(B!4, C!3)),
% 0.12/0.38 inference(and_elim,[status(thm)],[12])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (^[B: $i, C: $i] : refl(((~subset(B, C)) | (intersection(B, C) = B)) <=> ((~subset(B, C)) | (intersection(B, C) = B)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (![B: $i, C: $i] : ((~subset(B, C)) | (intersection(B, C) = B)) <=> ![B: $i, C: $i] : ((~subset(B, C)) | (intersection(B, C) = B))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[24])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (![B: $i, C: $i] : ((~subset(B, C)) | (intersection(B, C) = B)) <=> ![B: $i, C: $i] : ((~subset(B, C)) | (intersection(B, C) = B))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (^[B: $i, C: $i] : rewrite((subset(B, C) => (intersection(B, C) = B)) <=> ((~subset(B, C)) | (intersection(B, C) = B)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (![B: $i, C: $i] : (subset(B, C) => (intersection(B, C) = B)) <=> ![B: $i, C: $i] : ((~subset(B, C)) | (intersection(B, C) = B))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[27])).
% 0.12/0.38 tff(29,axiom,(![B: $i, C: $i] : (subset(B, C) => (intersection(B, C) = B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','subset_intersection')).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (![B: $i, C: $i] : ((~subset(B, C)) | (intersection(B, C) = B))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (![B: $i, C: $i] : ((~subset(B, C)) | (intersection(B, C) = B))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.12/0.38 tff(32,plain,(
% 0.12/0.38 ![B: $i, C: $i] : ((~subset(B, C)) | (intersection(B, C) = B))),
% 0.12/0.38 inference(skolemize,[status(sab)],[31])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (![B: $i, C: $i] : ((~subset(B, C)) | (intersection(B, C) = B))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (((~![B: $i, C: $i] : ((~subset(B, C)) | (intersection(B, C) = B))) | ((~subset(B!4, C!3)) | (intersection(B!4, C!3) = B!4))) <=> ((~![B: $i, C: $i] : ((~subset(B, C)) | (intersection(B, C) = B))) | (~subset(B!4, C!3)) | (intersection(B!4, C!3) = B!4))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 ((~![B: $i, C: $i] : ((~subset(B, C)) | (intersection(B, C) = B))) | ((~subset(B!4, C!3)) | (intersection(B!4, C!3) = B!4))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 ((~![B: $i, C: $i] : ((~subset(B, C)) | (intersection(B, C) = B))) | (~subset(B!4, C!3)) | (intersection(B!4, C!3) = B!4)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (intersection(B!4, C!3) = B!4),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[36, 33, 23])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (B!4 = intersection(B!4, C!3)),
% 0.12/0.38 inference(symmetry,[status(thm)],[37])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 (B!4 = empty_set),
% 0.12/0.38 inference(transitivity,[status(thm)],[38, 22, 13])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 (~(B!4 = empty_set)),
% 0.12/0.38 inference(or_elim,[status(thm)],[11])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.12/0.38 % SZS output end Proof
%------------------------------------------------------------------------------