TSTP Solution File: SET002+3 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET002+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 05:04:38 EDT 2022
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET002+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 00:58:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(subset_type, type, (
% 0.13/0.39 subset: ( $i * $i ) > $o)).
% 0.13/0.39 tff(tptp_fun_B_2_type, type, (
% 0.13/0.39 tptp_fun_B_2: $i)).
% 0.13/0.39 tff(union_type, type, (
% 0.13/0.39 union: ( $i * $i ) > $i)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 ((~![B: $i] : (union(B, B) = B)) <=> (~![B: $i] : (union(B, B) = B))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(2,axiom,(~![B: $i] : (union(B, B) = B)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_idempotency_of_union')).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (~![B: $i] : (union(B, B) = B)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (~![B: $i] : (union(B, B) = B)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[3, 1])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (~![B: $i] : (union(B, B) = B)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (~![B: $i] : (union(B, B) = B)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (~![B: $i] : (union(B, B) = B)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (~![B: $i] : (union(B, B) = B)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (~![B: $i] : (union(B, B) = B)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.13/0.39 tff(10,plain,(
% 0.13/0.39 ~(union(B!2, B!2) = B!2)),
% 0.13/0.39 inference(skolemize,[status(sab)],[9])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (^[B: $i, C: $i] : refl(((~subset(B, C)) | (union(B, C) = C)) <=> ((~subset(B, C)) | (union(B, C) = C)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C)) <=> ![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[11])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C)) <=> ![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (^[B: $i, C: $i] : rewrite((subset(B, C) => (union(B, C) = C)) <=> ((~subset(B, C)) | (union(B, C) = C)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (![B: $i, C: $i] : (subset(B, C) => (union(B, C) = C)) <=> ![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[14])).
% 0.13/0.39 tff(16,axiom,(![B: $i, C: $i] : (subset(B, C) => (union(B, C) = C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','subset_union')).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.13/0.39 tff(19,plain,(
% 0.13/0.39 ![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))),
% 0.13/0.39 inference(skolemize,[status(sab)],[18])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 (![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (((~![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))) | ((~subset(B!2, B!2)) | (union(B!2, B!2) = B!2))) <=> ((~![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))) | (~subset(B!2, B!2)) | (union(B!2, B!2) = B!2))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 ((~![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))) | ((~subset(B!2, B!2)) | (union(B!2, B!2) = B!2))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 ((~![B: $i, C: $i] : ((~subset(B, C)) | (union(B, C) = C))) | (~subset(B!2, B!2)) | (union(B!2, B!2) = B!2)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (~subset(B!2, B!2)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[23, 20, 10])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (^[B: $i] : refl(subset(B, B) <=> subset(B, B))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 (![B: $i] : subset(B, B) <=> ![B: $i] : subset(B, B)),
% 0.13/0.39 inference(quant_intro,[status(thm)],[25])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (![B: $i] : subset(B, B) <=> ![B: $i] : subset(B, B)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(28,axiom,(![B: $i] : subset(B, B)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reflexivity_of_subset')).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 (![B: $i] : subset(B, B)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.13/0.40 tff(30,plain,(
% 0.13/0.40 ![B: $i] : subset(B, B)),
% 0.13/0.40 inference(skolemize,[status(sab)],[29])).
% 0.13/0.40 tff(31,plain,
% 0.13/0.40 (![B: $i] : subset(B, B)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 ((~![B: $i] : subset(B, B)) | subset(B!2, B!2)),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(33,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[32, 31, 24])).
% 0.13/0.40 % SZS output end Proof
%------------------------------------------------------------------------------