TSTP Solution File: SET019+4 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET019+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 05:04:52 EDT 2022
% Result : Theorem 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET019+4 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n028.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 01:23:53 EDT 2022
% 0.13/0.33 % 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.
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % SZS output start Proof
% 0.13/0.38 tff(subset_type, type, (
% 0.13/0.38 subset: ( $i * $i ) > $o)).
% 0.13/0.38 tff(tptp_fun_A_4_type, type, (
% 0.13/0.38 tptp_fun_A_4: $i)).
% 0.13/0.38 tff(tptp_fun_B_3_type, type, (
% 0.13/0.38 tptp_fun_B_3: $i)).
% 0.13/0.38 tff(equal_set_type, type, (
% 0.13/0.38 equal_set: ( $i * $i ) > $o)).
% 0.13/0.38 tff(1,plain,
% 0.13/0.38 ((~![A: $i, B: $i] : ((~(subset(A, B) & subset(B, A))) | equal_set(A, B))) <=> (~![A: $i, B: $i] : ((~(subset(A, B) & subset(B, A))) | equal_set(A, B)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(2,plain,
% 0.13/0.38 ((~![A: $i, B: $i] : ((subset(A, B) & subset(B, A)) => equal_set(A, B))) <=> (~![A: $i, B: $i] : ((~(subset(A, B) & subset(B, A))) | equal_set(A, B)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(3,axiom,(~![A: $i, B: $i] : ((subset(A, B) & subset(B, A)) => equal_set(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thI02')).
% 0.13/0.38 tff(4,plain,
% 0.13/0.38 (~![A: $i, B: $i] : ((~(subset(A, B) & subset(B, A))) | equal_set(A, B))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.13/0.38 tff(5,plain,
% 0.13/0.38 (~![A: $i, B: $i] : ((~(subset(A, B) & subset(B, A))) | equal_set(A, B))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.13/0.38 tff(6,plain,
% 0.13/0.38 (~![A: $i, B: $i] : ((~(subset(A, B) & subset(B, A))) | equal_set(A, B))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.13/0.38 tff(7,plain,
% 0.13/0.38 (~![A: $i, B: $i] : ((~(subset(A, B) & subset(B, A))) | equal_set(A, B))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.13/0.38 tff(8,plain,
% 0.13/0.38 (~![A: $i, B: $i] : ((~(subset(A, B) & subset(B, A))) | equal_set(A, B))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.13/0.38 tff(9,plain,
% 0.13/0.38 (~![A: $i, B: $i] : ((~(subset(A, B) & subset(B, A))) | equal_set(A, B))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.13/0.38 tff(10,plain,
% 0.13/0.38 (~![A: $i, B: $i] : ((~(subset(A, B) & subset(B, A))) | equal_set(A, B))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.13/0.38 tff(11,plain,(
% 0.13/0.38 ~((~(subset(A!4, B!3) & subset(B!3, A!4))) | equal_set(A!4, B!3))),
% 0.13/0.38 inference(skolemize,[status(sab)],[10])).
% 0.13/0.38 tff(12,plain,
% 0.13/0.38 (subset(A!4, B!3) & subset(B!3, A!4)),
% 0.13/0.38 inference(or_elim,[status(thm)],[11])).
% 0.13/0.38 tff(13,plain,
% 0.13/0.38 (subset(B!3, A!4)),
% 0.13/0.38 inference(and_elim,[status(thm)],[12])).
% 0.13/0.38 tff(14,plain,
% 0.13/0.38 (subset(A!4, B!3)),
% 0.13/0.38 inference(and_elim,[status(thm)],[12])).
% 0.13/0.38 tff(15,plain,
% 0.13/0.38 ((~((~subset(A!4, B!3)) | (~subset(B!3, A!4)))) | (~subset(A!4, B!3)) | (~subset(B!3, A!4))),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(16,plain,
% 0.13/0.38 (~((~subset(A!4, B!3)) | (~subset(B!3, A!4)))),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[15, 14, 13])).
% 0.13/0.38 tff(17,plain,
% 0.13/0.38 (~equal_set(A!4, B!3)),
% 0.13/0.38 inference(or_elim,[status(thm)],[11])).
% 0.13/0.38 tff(18,plain,
% 0.13/0.38 ((~(equal_set(A!4, B!3) <=> (~((~subset(A!4, B!3)) | (~subset(B!3, A!4)))))) | equal_set(A!4, B!3) | ((~subset(A!4, B!3)) | (~subset(B!3, A!4)))),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(19,plain,
% 0.13/0.38 (~(equal_set(A!4, B!3) <=> (~((~subset(A!4, B!3)) | (~subset(B!3, A!4)))))),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[18, 17, 16])).
% 0.13/0.38 tff(20,plain,
% 0.13/0.38 (^[A: $i, B: $i] : refl((equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(21,plain,
% 0.13/0.38 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[20])).
% 0.13/0.38 tff(22,plain,
% 0.13/0.38 (^[A: $i, B: $i] : rewrite((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(23,plain,
% 0.13/0.38 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[22])).
% 0.13/0.38 tff(24,plain,
% 0.13/0.38 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(25,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','equal_set')).
% 0.13/0.38 tff(26,plain,
% 0.13/0.38 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.13/0.38 tff(27,plain,(
% 0.13/0.38 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.13/0.38 inference(skolemize,[status(sab)],[26])).
% 0.13/0.38 tff(28,plain,
% 0.13/0.38 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.13/0.38 tff(29,plain,
% 0.13/0.38 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.13/0.38 tff(30,plain,
% 0.13/0.38 ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(A!4, B!3) <=> (~((~subset(A!4, B!3)) | (~subset(B!3, A!4)))))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(31,plain,
% 0.13/0.38 ($false),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[30, 29, 19])).
% 0.13/0.38 % SZS output end Proof
%------------------------------------------------------------------------------