TSTP Solution File: SWW469+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW469+1 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 20:58:47 EDT 2022
% Result : Theorem 0.12s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW469+1 : TPTP v8.1.0. Released v5.3.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n014.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 17:33:14 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.12/0.40 % SZS status Theorem
% 0.12/0.40 % SZS output start Proof
% 0.12/0.40 tff(tptp_fun_T_0_type, type, (
% 0.12/0.40 tptp_fun_T_0: $i)).
% 0.12/0.40 tff(tptp_fun_S_1_type, type, (
% 0.12/0.40 tptp_fun_S_1: $i)).
% 0.12/0.40 tff(tptp_fun_T_2_type, type, (
% 0.12/0.40 tptp_fun_T_2: $i)).
% 0.12/0.40 tff(is_state_type, type, (
% 0.12/0.40 is_state: $i > $o)).
% 0.12/0.40 tff(hoare_165779456gleton_type, type, (
% 0.12/0.40 hoare_165779456gleton: $o)).
% 0.12/0.40 tff(1,plain,
% 0.12/0.40 ((T!2 = T!0) <=> (T!0 = T!2)),
% 0.12/0.40 inference(commutativity,[status(thm)],[])).
% 0.12/0.40 tff(2,plain,
% 0.12/0.40 (^[S: $i] : refl(((~is_state(S)) | (S = T!2)) <=> ((~is_state(S)) | (S = T!2)))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(3,plain,
% 0.12/0.40 (![S: $i] : ((~is_state(S)) | (S = T!2)) <=> ![S: $i] : ((~is_state(S)) | (S = T!2))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.40 tff(4,plain,
% 0.12/0.40 (((~(~is_state(T!2))) & ![S: $i] : ((~is_state(S)) | (S = T!2))) <=> (is_state(T!2) & ![S: $i] : ((~is_state(S)) | (S = T!2)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(5,plain,
% 0.12/0.40 ((~![T: $i] : ((~is_state(T)) | (~![S: $i] : ((~is_state(S)) | (S = T))))) <=> (~![T: $i] : ((~is_state(T)) | (~![S: $i] : ((~is_state(S)) | (S = T)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(6,plain,
% 0.12/0.40 ((~![T: $i] : (is_state(T) => (~![S: $i] : (is_state(S) => (S = T))))) <=> (~![T: $i] : ((~is_state(T)) | (~![S: $i] : ((~is_state(S)) | (S = T)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(7,axiom,(~![T: $i] : (is_state(T) => (~![S: $i] : (is_state(S) => (S = T))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj_1')).
% 0.12/0.40 tff(8,plain,
% 0.12/0.40 (~![T: $i] : ((~is_state(T)) | (~![S: $i] : ((~is_state(S)) | (S = T))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.12/0.40 tff(9,plain,
% 0.12/0.40 (~![T: $i] : ((~is_state(T)) | (~![S: $i] : ((~is_state(S)) | (S = T))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.12/0.40 tff(10,plain,
% 0.12/0.40 (~![T: $i] : ((~is_state(T)) | (~![S: $i] : ((~is_state(S)) | (S = T))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.12/0.40 tff(11,plain,
% 0.12/0.40 (~![T: $i] : ((~is_state(T)) | (~![S: $i] : ((~is_state(S)) | (S = T))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.12/0.40 tff(12,plain,
% 0.12/0.40 (~![T: $i] : ((~is_state(T)) | (~![S: $i] : ((~is_state(S)) | (S = T))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[11, 5])).
% 0.12/0.40 tff(13,plain,
% 0.12/0.40 (~![T: $i] : ((~is_state(T)) | (~![S: $i] : ((~is_state(S)) | (S = T))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.12/0.40 tff(14,plain,
% 0.12/0.40 (~![T: $i] : ((~is_state(T)) | (~![S: $i] : ((~is_state(S)) | (S = T))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[13, 5])).
% 0.12/0.40 tff(15,plain,
% 0.12/0.40 (~![T: $i] : ((~is_state(T)) | (~![S: $i] : ((~is_state(S)) | (S = T))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[14, 5])).
% 0.12/0.40 tff(16,plain,
% 0.12/0.40 (~![T: $i] : ((~is_state(T)) | (~![S: $i] : ((~is_state(S)) | (S = T))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.12/0.40 tff(17,plain,
% 0.12/0.40 (is_state(T!2) & ![S: $i] : ((~is_state(S)) | (S = T!2))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[16, 4])).
% 0.12/0.40 tff(18,plain,
% 0.12/0.40 (![S: $i] : ((~is_state(S)) | (S = T!2))),
% 0.12/0.40 inference(and_elim,[status(thm)],[17])).
% 0.12/0.40 tff(19,plain,
% 0.12/0.40 (![S: $i] : ((~is_state(S)) | (S = T!2))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[18, 3])).
% 0.12/0.40 tff(20,plain,
% 0.12/0.40 (?[S: $i, T: $i] : (is_state(S) & is_state(T) & (~(S = T))) <=> ?[S: $i, T: $i] : (is_state(S) & is_state(T) & (~(S = T)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(21,plain,
% 0.12/0.40 (($true <=> ?[S: $i, T: $i] : (is_state(S) & is_state(T) & (~(S = T)))) <=> ?[S: $i, T: $i] : (is_state(S) & is_state(T) & (~(S = T)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(22,axiom,(hoare_165779456gleton), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj_0')).
% 0.12/0.40 tff(23,plain,
% 0.12/0.40 (hoare_165779456gleton <=> $true),
% 0.12/0.40 inference(iff_true,[status(thm)],[22])).
% 0.12/0.40 tff(24,plain,
% 0.12/0.40 ((hoare_165779456gleton <=> ?[S: $i, T: $i] : (is_state(S) & is_state(T) & (~(S = T)))) <=> ($true <=> ?[S: $i, T: $i] : (is_state(S) & is_state(T) & (~(S = T))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[23])).
% 0.12/0.40 tff(25,plain,
% 0.12/0.40 ((hoare_165779456gleton <=> ?[S: $i, T: $i] : (is_state(S) & is_state(T) & (~(S = T)))) <=> ?[S: $i, T: $i] : (is_state(S) & is_state(T) & (~(S = T)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[24, 21])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 ((hoare_165779456gleton <=> ?[S: $i, T: $i] : (is_state(S) & is_state(T) & (~(S = T)))) <=> (hoare_165779456gleton <=> ?[S: $i, T: $i] : (is_state(S) & is_state(T) & (~(S = T))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 ((hoare_165779456gleton <=> ?[S: $i, T: $i] : ((is_state(S) & is_state(T)) & (~(S = T)))) <=> (hoare_165779456gleton <=> ?[S: $i, T: $i] : (is_state(S) & is_state(T) & (~(S = T))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(28,axiom,(hoare_165779456gleton <=> ?[S: $i, T: $i] : ((is_state(S) & is_state(T)) & (~(S = T)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_0_state__not__singleton__def')).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (hoare_165779456gleton <=> ?[S: $i, T: $i] : (is_state(S) & is_state(T) & (~(S = T)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 (hoare_165779456gleton <=> ?[S: $i, T: $i] : (is_state(S) & is_state(T) & (~(S = T)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 (?[S: $i, T: $i] : (is_state(S) & is_state(T) & (~(S = T)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[30, 25])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 (?[S: $i, T: $i] : (is_state(S) & is_state(T) & (~(S = T)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[31, 20])).
% 0.20/0.41 tff(33,plain,(
% 0.20/0.41 is_state(S!1) & is_state(T!0) & (~(S!1 = T!0))),
% 0.20/0.41 inference(skolemize,[status(sab)],[32])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 (is_state(S!1)),
% 0.20/0.41 inference(and_elim,[status(thm)],[33])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (((~![S: $i] : ((~is_state(S)) | (S = T!2))) | ((~is_state(S!1)) | (S!1 = T!2))) <=> ((~![S: $i] : ((~is_state(S)) | (S = T!2))) | (~is_state(S!1)) | (S!1 = T!2))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 ((~![S: $i] : ((~is_state(S)) | (S = T!2))) | ((~is_state(S!1)) | (S!1 = T!2))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 ((~![S: $i] : ((~is_state(S)) | (S = T!2))) | (~is_state(S!1)) | (S!1 = T!2)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (S!1 = T!2),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[37, 34, 19])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 ((S!1 = T!0) <=> (T!2 = T!0)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[38])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 ((S!1 = T!0) <=> (T!0 = T!2)),
% 0.20/0.41 inference(transitivity,[status(thm)],[39, 1])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 ((T!0 = T!2) <=> (S!1 = T!0)),
% 0.20/0.41 inference(symmetry,[status(thm)],[40])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 (is_state(T!0)),
% 0.20/0.41 inference(and_elim,[status(thm)],[33])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 (((~![S: $i] : ((~is_state(S)) | (S = T!2))) | ((~is_state(T!0)) | (T!0 = T!2))) <=> ((~![S: $i] : ((~is_state(S)) | (S = T!2))) | (~is_state(T!0)) | (T!0 = T!2))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 ((~![S: $i] : ((~is_state(S)) | (S = T!2))) | ((~is_state(T!0)) | (T!0 = T!2))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 ((~![S: $i] : ((~is_state(S)) | (S = T!2))) | (~is_state(T!0)) | (T!0 = T!2)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 (T!0 = T!2),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[45, 42, 19])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (S!1 = T!0),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[46, 41])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 (~(S!1 = T!0)),
% 0.20/0.41 inference(and_elim,[status(thm)],[33])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.20/0.41 % SZS output end Proof
%------------------------------------------------------------------------------