TSTP Solution File: SET583+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET583+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 05:07:07 EDT 2022
% Result : Theorem 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET583+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 : n019.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 06:51:05 EDT 2022
% 0.13/0.35 % 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.
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(subset_type, type, (
% 0.21/0.39 subset: ( $i * $i ) > $o)).
% 0.21/0.39 tff(tptp_fun_B_2_type, type, (
% 0.21/0.39 tptp_fun_B_2: $i)).
% 0.21/0.39 tff(tptp_fun_C_1_type, type, (
% 0.21/0.39 tptp_fun_C_1: $i)).
% 0.21/0.39 tff(1,plain,
% 0.21/0.39 ((~![B: $i, C: $i] : ((~(subset(B, C) & subset(C, B))) | (B = C))) <=> (~![B: $i, C: $i] : ((~(subset(B, C) & subset(C, B))) | (B = C)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 ((~![B: $i, C: $i] : ((subset(B, C) & subset(C, B)) => (B = C))) <=> (~![B: $i, C: $i] : ((~(subset(B, C) & subset(C, B))) | (B = C)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(3,axiom,(~![B: $i, C: $i] : ((subset(B, C) & subset(C, B)) => (B = C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_extensionality')).
% 0.21/0.39 tff(4,plain,
% 0.21/0.39 (~![B: $i, C: $i] : ((~(subset(B, C) & subset(C, B))) | (B = C))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.21/0.39 tff(5,plain,
% 0.21/0.39 (~![B: $i, C: $i] : ((~(subset(B, C) & subset(C, B))) | (B = C))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.21/0.39 tff(6,plain,
% 0.21/0.39 (~![B: $i, C: $i] : ((~(subset(B, C) & subset(C, B))) | (B = C))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.21/0.39 tff(7,plain,
% 0.21/0.39 (~![B: $i, C: $i] : ((~(subset(B, C) & subset(C, B))) | (B = C))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.21/0.39 tff(8,plain,
% 0.21/0.39 (~![B: $i, C: $i] : ((~(subset(B, C) & subset(C, B))) | (B = C))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.21/0.39 tff(9,plain,
% 0.21/0.39 (~![B: $i, C: $i] : ((~(subset(B, C) & subset(C, B))) | (B = C))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.21/0.39 tff(10,plain,
% 0.21/0.39 (~![B: $i, C: $i] : ((~(subset(B, C) & subset(C, B))) | (B = C))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.21/0.39 tff(11,plain,(
% 0.21/0.39 ~((~(subset(B!2, C!1) & subset(C!1, B!2))) | (B!2 = C!1))),
% 0.21/0.39 inference(skolemize,[status(sab)],[10])).
% 0.21/0.39 tff(12,plain,
% 0.21/0.39 (subset(B!2, C!1) & subset(C!1, B!2)),
% 0.21/0.39 inference(or_elim,[status(thm)],[11])).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 (subset(C!1, B!2)),
% 0.21/0.39 inference(and_elim,[status(thm)],[12])).
% 0.21/0.39 tff(14,plain,
% 0.21/0.39 (subset(B!2, C!1)),
% 0.21/0.39 inference(and_elim,[status(thm)],[12])).
% 0.21/0.39 tff(15,plain,
% 0.21/0.39 ((~((~subset(B!2, C!1)) | (~subset(C!1, B!2)))) | (~subset(B!2, C!1)) | (~subset(C!1, B!2))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(16,plain,
% 0.21/0.39 (~((~subset(B!2, C!1)) | (~subset(C!1, B!2)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[15, 14, 13])).
% 0.21/0.39 tff(17,plain,
% 0.21/0.39 (~(B!2 = C!1)),
% 0.21/0.39 inference(or_elim,[status(thm)],[11])).
% 0.21/0.39 tff(18,plain,
% 0.21/0.39 ((~((B!2 = C!1) <=> (~((~subset(B!2, C!1)) | (~subset(C!1, B!2)))))) | (B!2 = C!1) | ((~subset(B!2, C!1)) | (~subset(C!1, B!2)))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(19,plain,
% 0.21/0.39 (~((B!2 = C!1) <=> (~((~subset(B!2, C!1)) | (~subset(C!1, B!2)))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[18, 17, 16])).
% 0.21/0.39 tff(20,plain,
% 0.21/0.39 (^[B: $i, C: $i] : refl(((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))) <=> ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(21,plain,
% 0.21/0.39 (![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))) <=> ![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[20])).
% 0.21/0.39 tff(22,plain,
% 0.21/0.39 (^[B: $i, C: $i] : rewrite(((B = C) <=> (subset(B, C) & subset(C, B))) <=> ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(23,plain,
% 0.21/0.39 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B))) <=> ![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.21/0.39 tff(24,plain,
% 0.21/0.39 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B))) <=> ![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(25,axiom,(![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','equal_defn')).
% 0.21/0.39 tff(26,plain,
% 0.21/0.39 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.21/0.39 tff(27,plain,(
% 0.21/0.40 ![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.21/0.40 inference(skolemize,[status(sab)],[26])).
% 0.21/0.40 tff(28,plain,
% 0.21/0.40 (![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.21/0.40 tff(29,plain,
% 0.21/0.40 (![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.21/0.40 tff(30,plain,
% 0.21/0.40 ((~![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))) | ((B!2 = C!1) <=> (~((~subset(B!2, C!1)) | (~subset(C!1, B!2)))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(31,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[30, 29, 19])).
% 0.21/0.40 % SZS output end Proof
%------------------------------------------------------------------------------