TSTP Solution File: SET063+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET063+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 05:05:17 EDT 2022
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET063+3 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 01:56:48 EDT 2022
% 0.12/0.34 % 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.
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(subset_type, type, (
% 0.12/0.39 subset: ( $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_B_2_type, type, (
% 0.12/0.39 tptp_fun_B_2: $i)).
% 0.12/0.39 tff(empty_set_type, type, (
% 0.12/0.39 empty_set: $i)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 (^[B: $i, C: $i] : refl(((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))) <=> ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))) <=> ![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (^[B: $i, C: $i] : rewrite(((B = C) <=> (subset(B, C) & subset(C, B))) <=> ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B))) <=> ![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B))) <=> ![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(6,axiom,(![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','equal_defn')).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.12/0.39 tff(8,plain,(
% 0.12/0.39 ![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[7])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 ((~![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))) | ((B!2 = empty_set) <=> (~((~subset(B!2, empty_set)) | (~subset(empty_set, B!2)))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 ((B!2 = empty_set) <=> (~((~subset(B!2, empty_set)) | (~subset(empty_set, B!2))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 ((~![B: $i] : ((~subset(B, empty_set)) | (B = empty_set))) <=> (~![B: $i] : ((~subset(B, empty_set)) | (B = empty_set)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 ((~![B: $i] : (subset(B, empty_set) => (B = empty_set))) <=> (~![B: $i] : ((~subset(B, empty_set)) | (B = empty_set)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(15,axiom,(~![B: $i] : (subset(B, empty_set) => (B = empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_subset_of_empty_set_is_empty_set')).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (~![B: $i] : ((~subset(B, empty_set)) | (B = empty_set))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 (~![B: $i] : ((~subset(B, empty_set)) | (B = empty_set))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (~![B: $i] : ((~subset(B, empty_set)) | (B = empty_set))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (~![B: $i] : ((~subset(B, empty_set)) | (B = empty_set))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (~![B: $i] : ((~subset(B, empty_set)) | (B = empty_set))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[19, 13])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 (~![B: $i] : ((~subset(B, empty_set)) | (B = empty_set))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (~![B: $i] : ((~subset(B, empty_set)) | (B = empty_set))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[21, 13])).
% 0.12/0.39 tff(23,plain,(
% 0.12/0.39 ~((~subset(B!2, empty_set)) | (B!2 = empty_set))),
% 0.12/0.39 inference(skolemize,[status(sab)],[22])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (~(B!2 = empty_set)),
% 0.12/0.39 inference(or_elim,[status(thm)],[23])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 ((~((B!2 = empty_set) <=> (~((~subset(B!2, empty_set)) | (~subset(empty_set, B!2)))))) | (B!2 = empty_set) | ((~subset(B!2, empty_set)) | (~subset(empty_set, B!2)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 ((~((B!2 = empty_set) <=> (~((~subset(B!2, empty_set)) | (~subset(empty_set, B!2)))))) | ((~subset(B!2, empty_set)) | (~subset(empty_set, B!2)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 ((~subset(B!2, empty_set)) | (~subset(empty_set, B!2))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[26, 12])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 (subset(B!2, empty_set)),
% 0.12/0.39 inference(or_elim,[status(thm)],[23])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 ((~((~subset(B!2, empty_set)) | (~subset(empty_set, B!2)))) | (~subset(B!2, empty_set)) | (~subset(empty_set, B!2))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 ((~((~subset(B!2, empty_set)) | (~subset(empty_set, B!2)))) | (~subset(empty_set, B!2))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 (~subset(empty_set, B!2)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[30, 27])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 (^[B: $i] : refl(subset(empty_set, B) <=> subset(empty_set, B))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 (![B: $i] : subset(empty_set, B) <=> ![B: $i] : subset(empty_set, B)),
% 0.12/0.39 inference(quant_intro,[status(thm)],[32])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 (![B: $i] : subset(empty_set, B) <=> ![B: $i] : subset(empty_set, B)),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(35,axiom,(![B: $i] : subset(empty_set, B)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','empty_set_subset')).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 (![B: $i] : subset(empty_set, B)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.12/0.39 tff(37,plain,(
% 0.12/0.39 ![B: $i] : subset(empty_set, B)),
% 0.12/0.39 inference(skolemize,[status(sab)],[36])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 (![B: $i] : subset(empty_set, B)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 ((~![B: $i] : subset(empty_set, B)) | subset(empty_set, B!2)),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(40,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[39, 38, 31])).
% 0.12/0.39 % SZS output end Proof
%------------------------------------------------------------------------------