TSTP Solution File: SWW469+5 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW469+5 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 : Thu Sep 29 20:58:48 EDT 2022
% Result : Theorem 0.21s 0.44s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW469+5 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n018.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 : Sun Sep 4 17:37:46 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.
% 0.21/0.44 % SZS status Theorem
% 0.21/0.44 % SZS output start Proof
% 0.21/0.44 tff(ti_type, type, (
% 0.21/0.44 ti: ( $i * $i ) > $i)).
% 0.21/0.44 tff(tptp_fun_T_0_type, type, (
% 0.21/0.44 tptp_fun_T_0: $i)).
% 0.21/0.44 tff(state_type, type, (
% 0.21/0.44 state: $i)).
% 0.21/0.44 tff(tptp_fun_S_1_type, type, (
% 0.21/0.44 tptp_fun_S_1: $i)).
% 0.21/0.44 tff(tptp_fun_T_11_type, type, (
% 0.21/0.44 tptp_fun_T_11: $i)).
% 0.21/0.44 tff(hBOOL_type, type, (
% 0.21/0.44 hBOOL: $i > $o)).
% 0.21/0.44 tff(hoare_1883395792gleton_type, type, (
% 0.21/0.44 hoare_1883395792gleton: $i)).
% 0.21/0.44 tff(1,plain,
% 0.21/0.44 ((ti(state, T!11) = ti(state, T!0)) <=> (ti(state, T!0) = ti(state, T!11))),
% 0.21/0.44 inference(commutativity,[status(thm)],[])).
% 0.21/0.44 tff(2,plain,
% 0.21/0.44 (^[S: $i] : refl((ti(state, S) = ti(state, T!11)) <=> (ti(state, S) = ti(state, T!11)))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(3,plain,
% 0.21/0.44 (![S: $i] : (ti(state, S) = ti(state, T!11)) <=> ![S: $i] : (ti(state, S) = ti(state, T!11))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.44 tff(4,plain,
% 0.21/0.44 ((~![T: $i] : (~![S: $i] : (ti(state, S) = ti(state, T)))) <=> (~![T: $i] : (~![S: $i] : (ti(state, S) = ti(state, T))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(5,axiom,(~![T: $i] : (~![S: $i] : (ti(state, S) = ti(state, T)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj_1')).
% 0.21/0.44 tff(6,plain,
% 0.21/0.44 (~![T: $i] : (~![S: $i] : (ti(state, S) = ti(state, T)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.21/0.44 tff(7,plain,
% 0.21/0.44 (~![T: $i] : (~![S: $i] : (ti(state, S) = ti(state, T)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[6, 4])).
% 0.21/0.44 tff(8,plain,
% 0.21/0.44 (~![T: $i] : (~![S: $i] : (ti(state, S) = ti(state, T)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[7, 4])).
% 0.21/0.44 tff(9,plain,
% 0.21/0.44 (~![T: $i] : (~![S: $i] : (ti(state, S) = ti(state, T)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.21/0.44 tff(10,plain,
% 0.21/0.44 (~![T: $i] : (~![S: $i] : (ti(state, S) = ti(state, T)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[9, 4])).
% 0.21/0.44 tff(11,plain,
% 0.21/0.44 (~![T: $i] : (~![S: $i] : (ti(state, S) = ti(state, T)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.21/0.44 tff(12,plain,
% 0.21/0.44 (~![T: $i] : (~![S: $i] : (ti(state, S) = ti(state, T)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.21/0.45 tff(13,plain,
% 0.21/0.45 (~![T: $i] : (~![S: $i] : (ti(state, S) = ti(state, T)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[12, 4])).
% 0.21/0.45 tff(14,plain,(
% 0.21/0.45 $oeq((~(~![S: $i] : (ti(state, S) = ti(state, T!11)))), ![S: $i] : (ti(state, S) = ti(state, T!11)))),
% 0.21/0.45 inference(transitivity,[status(sab)],[13])).
% 0.21/0.45 tff(15,plain,
% 0.21/0.45 (![S: $i] : (ti(state, S) = ti(state, T!11))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[14, 3])).
% 0.21/0.45 tff(16,plain,
% 0.21/0.45 ((~![S: $i] : (ti(state, S) = ti(state, T!11))) | (ti(state, S!1) = ti(state, T!11))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(17,plain,
% 0.21/0.45 (ti(state, S!1) = ti(state, T!11)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.21/0.45 tff(18,plain,
% 0.21/0.45 ((ti(state, S!1) = ti(state, T!0)) <=> (ti(state, T!11) = ti(state, T!0))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[17])).
% 0.21/0.45 tff(19,plain,
% 0.21/0.45 ((ti(state, S!1) = ti(state, T!0)) <=> (ti(state, T!0) = ti(state, T!11))),
% 0.21/0.45 inference(transitivity,[status(thm)],[18, 1])).
% 0.21/0.45 tff(20,plain,
% 0.21/0.45 ((ti(state, T!0) = ti(state, T!11)) <=> (ti(state, S!1) = ti(state, T!0))),
% 0.21/0.45 inference(symmetry,[status(thm)],[19])).
% 0.21/0.45 tff(21,plain,
% 0.21/0.45 ((~![S: $i] : (ti(state, S) = ti(state, T!11))) | (ti(state, T!0) = ti(state, T!11))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(22,plain,
% 0.21/0.45 (ti(state, T!0) = ti(state, T!11)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[21, 15])).
% 0.21/0.45 tff(23,plain,
% 0.21/0.45 (ti(state, S!1) = ti(state, T!0)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[22, 20])).
% 0.21/0.45 tff(24,plain,
% 0.21/0.45 (?[S: $i, T: $i] : (~(ti(state, S) = ti(state, T))) <=> ?[S: $i, T: $i] : (~(ti(state, S) = ti(state, T)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(25,plain,
% 0.21/0.45 (($true <=> ?[S: $i, T: $i] : (~(ti(state, S) = ti(state, T)))) <=> ?[S: $i, T: $i] : (~(ti(state, S) = ti(state, T)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(26,axiom,(hBOOL(hoare_1883395792gleton)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj_0')).
% 0.21/0.45 tff(27,plain,
% 0.21/0.45 (hBOOL(hoare_1883395792gleton) <=> $true),
% 0.21/0.45 inference(iff_true,[status(thm)],[26])).
% 0.21/0.45 tff(28,plain,
% 0.21/0.45 ((hBOOL(hoare_1883395792gleton) <=> ?[S: $i, T: $i] : (~(ti(state, S) = ti(state, T)))) <=> ($true <=> ?[S: $i, T: $i] : (~(ti(state, S) = ti(state, T))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[27])).
% 0.21/0.45 tff(29,plain,
% 0.21/0.45 ((hBOOL(hoare_1883395792gleton) <=> ?[S: $i, T: $i] : (~(ti(state, S) = ti(state, T)))) <=> ?[S: $i, T: $i] : (~(ti(state, S) = ti(state, T)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[28, 25])).
% 0.21/0.45 tff(30,plain,
% 0.21/0.45 ((hBOOL(hoare_1883395792gleton) <=> ?[S: $i, T: $i] : (~(ti(state, S) = ti(state, T)))) <=> (hBOOL(hoare_1883395792gleton) <=> ?[S: $i, T: $i] : (~(ti(state, S) = ti(state, T))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(31,axiom,(hBOOL(hoare_1883395792gleton) <=> ?[S: $i, T: $i] : (~(ti(state, S) = ti(state, T)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fact_0_state__not__singleton__def')).
% 0.21/0.45 tff(32,plain,
% 0.21/0.45 (hBOOL(hoare_1883395792gleton) <=> ?[S: $i, T: $i] : (~(ti(state, S) = ti(state, T)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.21/0.45 tff(33,plain,
% 0.21/0.45 (hBOOL(hoare_1883395792gleton) <=> ?[S: $i, T: $i] : (~(ti(state, S) = ti(state, T)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[32, 30])).
% 0.21/0.45 tff(34,plain,
% 0.21/0.45 (?[S: $i, T: $i] : (~(ti(state, S) = ti(state, T)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.21/0.45 tff(35,plain,
% 0.21/0.45 (?[S: $i, T: $i] : (~(ti(state, S) = ti(state, T)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[34, 24])).
% 0.21/0.45 tff(36,plain,(
% 0.21/0.45 ~(ti(state, S!1) = ti(state, T!0))),
% 0.21/0.45 inference(skolemize,[status(sab)],[35])).
% 0.21/0.45 tff(37,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[36, 23])).
% 0.21/0.45 % SZS output end Proof
%------------------------------------------------------------------------------