%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW469+1 : TPTP v9.0.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:37:04 AM UTC 2025
% Result : Theorem 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWW469+1 : TPTP v9.0.0. Released v5.3.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 11:46:54 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 % SZS output start Proof
% 0.12/0.36 tff(tptp_fun_T_1_type, type, (
% 0.12/0.36 tptp_fun_T_1: $i)).
% 0.12/0.36 tff(tptp_fun_S_2_type, type, (
% 0.12/0.36 tptp_fun_S_2: $i)).
% 0.12/0.36 tff(tptp_fun_T_3_type, type, (
% 0.12/0.36 tptp_fun_T_3: $i)).
% 0.12/0.36 tff(is_state_type, type, (
% 0.12/0.36 is_state: $i > $o)).
% 0.12/0.36 tff(hoare_165779456gleton_type, type, (
% 0.12/0.36 hoare_165779456gleton: $o)).
% 0.12/0.36 tff(1,plain,
% 0.12/0.36 ((T!3 = T!1) <=> (T!1 = T!3)),
% 0.12/0.36 inference(commutativity,[status(thm)],[])).
% 0.12/0.36 tff(2,plain,
% 0.12/0.36 (^[S: $i] : refl(((~is_state(S)) | (S = T!3)) <=> ((~is_state(S)) | (S = T!3)))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(3,plain,
% 0.12/0.36 (![S: $i] : ((~is_state(S)) | (S = T!3)) <=> ![S: $i] : ((~is_state(S)) | (S = T!3))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.36 tff(4,plain,
% 0.12/0.36 ((is_state(T!3) & ![S: $i] : ((~is_state(S)) | (S = T!3))) <=> (is_state(T!3) & ![S: $i] : ((~is_state(S)) | (S = T!3)))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(5,plain,
% 0.12/0.36 ((~![T: $i] : ((~is_state(T)) | (~![S: $i] : ((~is_state(S)) | (S = T))))) <=> (~![T: $i] : ((~is_state(T)) | (~![S: $i] : ((~is_state(S)) | (S = T)))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(6,plain,
% 0.12/0.36 ((~![T: $i] : (is_state(T) => (~![S: $i] : (is_state(S) => (S = T))))) <=> (~![T: $i] : ((~is_state(T)) | (~![S: $i] : ((~is_state(S)) | (S = T)))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(7,axiom,(~![T: $i] : (is_state(T) => (~![S: $i] : (is_state(S) => (S = T))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj_1')).
% 0.12/0.36 tff(8,plain,
% 0.12/0.36 (~![T: $i] : ((~is_state(T)) | (~![S: $i] : ((~is_state(S)) | (S = T))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.12/0.36 tff(9,plain,
% 0.12/0.36 (~![T: $i] : ((~is_state(T)) | (~![S: $i] : ((~is_state(S)) | (S = T))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.12/0.36 tff(10,plain,
% 0.12/0.36 (~![T: $i] : ((~is_state(T)) | (~![S: $i] : ((~is_state(S)) | (S = T))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.12/0.36 tff(11,plain,
% 0.12/0.36 (~![T: $i] : ((~is_state(T)) | (~![S: $i] : ((~is_state(S)) | (S = T))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.12/0.36 tff(12,plain,
% 0.12/0.36 (is_state(T!3) & ![S: $i] : ((~is_state(S)) | (S = T!3))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.12/0.36 tff(13,plain,
% 0.12/0.36 (![S: $i] : ((~is_state(S)) | (S = T!3))),
% 0.12/0.36 inference(and_elim,[status(thm)],[12])).
% 0.12/0.36 tff(14,plain,
% 0.12/0.36 (![S: $i] : ((~is_state(S)) | (S = T!3))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[13, 3])).
% 0.12/0.36 tff(15,plain,
% 0.12/0.36 (hoare_165779456gleton <=> hoare_165779456gleton),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(16,axiom,(hoare_165779456gleton), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj_0')).
% 0.12/0.36 tff(17,plain,
% 0.12/0.36 (hoare_165779456gleton),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.12/0.36 tff(18,plain,
% 0.12/0.36 (((~hoare_165779456gleton) | (is_state(S!2) & is_state(T!1) & (~(S!2 = T!1)))) <=> ((~hoare_165779456gleton) | (~((~is_state(S!2)) | (~is_state(T!1)) | (S!2 = T!1))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(19,plain,
% 0.12/0.36 ((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)))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(20,plain,
% 0.12/0.36 ((((~hoare_165779456gleton) | (is_state(S!2) & is_state(T!1) & (~(S!2 = T!1)))) & (hoare_165779456gleton | ![S: $i, T: $i] : (~(is_state(S) & is_state(T) & (~(S = T)))))) <=> (((~hoare_165779456gleton) | (is_state(S!2) & is_state(T!1) & (~(S!2 = T!1)))) & (hoare_165779456gleton | ![S: $i, T: $i] : (~(is_state(S) & is_state(T) & (~(S = T))))))),
% 0.12/0.36 inference(monotonicity,[status(thm)],[19])).
% 0.12/0.36 tff(21,plain,
% 0.12/0.36 ((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))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(22,plain,
% 0.12/0.36 ((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))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(23,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')).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 (hoare_165779456gleton <=> ?[S: $i, T: $i] : (is_state(S) & is_state(T) & (~(S = T)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (hoare_165779456gleton <=> ?[S: $i, T: $i] : (is_state(S) & is_state(T) & (~(S = T)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 (hoare_165779456gleton <=> ?[S: $i, T: $i] : (is_state(S) & is_state(T) & (~(S = T)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 (hoare_165779456gleton <=> ?[S: $i, T: $i] : (is_state(S) & is_state(T) & (~(S = T)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.12/0.37 tff(28,plain,(
% 0.12/0.37 ((~hoare_165779456gleton) | (is_state(S!2) & is_state(T!1) & (~(S!2 = T!1)))) & (hoare_165779456gleton | ![S: $i, T: $i] : (~(is_state(S) & is_state(T) & (~(S = T)))))),
% 0.12/0.37 inference(skolemize,[status(sab)],[27])).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 (((~hoare_165779456gleton) | (is_state(S!2) & is_state(T!1) & (~(S!2 = T!1)))) & (hoare_165779456gleton | ![S: $i, T: $i] : (~(is_state(S) & is_state(T) & (~(S = T)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[28, 20])).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 ((~hoare_165779456gleton) | (is_state(S!2) & is_state(T!1) & (~(S!2 = T!1)))),
% 0.12/0.37 inference(and_elim,[status(thm)],[29])).
% 0.12/0.37 tff(31,plain,
% 0.12/0.37 ((~hoare_165779456gleton) | (~((~is_state(S!2)) | (~is_state(T!1)) | (S!2 = T!1)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[30, 18])).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 (~((~is_state(S!2)) | (~is_state(T!1)) | (S!2 = T!1))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[31, 17])).
% 0.12/0.37 tff(33,plain,
% 0.12/0.37 (((~is_state(S!2)) | (~is_state(T!1)) | (S!2 = T!1)) | is_state(S!2)),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(34,plain,
% 0.12/0.37 (is_state(S!2)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.12/0.37 tff(35,plain,
% 0.12/0.37 (((~![S: $i] : ((~is_state(S)) | (S = T!3))) | ((~is_state(S!2)) | (S!2 = T!3))) <=> ((~![S: $i] : ((~is_state(S)) | (S = T!3))) | (~is_state(S!2)) | (S!2 = T!3))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(36,plain,
% 0.12/0.37 ((~![S: $i] : ((~is_state(S)) | (S = T!3))) | ((~is_state(S!2)) | (S!2 = T!3))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(37,plain,
% 0.12/0.37 ((~![S: $i] : ((~is_state(S)) | (S = T!3))) | (~is_state(S!2)) | (S!2 = T!3)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.12/0.37 tff(38,plain,
% 0.12/0.37 (S!2 = T!3),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[37, 34, 14])).
% 0.12/0.37 tff(39,plain,
% 0.12/0.37 ((S!2 = T!1) <=> (T!3 = T!1)),
% 0.12/0.37 inference(monotonicity,[status(thm)],[38])).
% 0.12/0.37 tff(40,plain,
% 0.12/0.37 ((S!2 = T!1) <=> (T!1 = T!3)),
% 0.12/0.37 inference(transitivity,[status(thm)],[39, 1])).
% 0.12/0.37 tff(41,plain,
% 0.12/0.37 ((T!1 = T!3) <=> (S!2 = T!1)),
% 0.12/0.37 inference(symmetry,[status(thm)],[40])).
% 0.12/0.37 tff(42,plain,
% 0.12/0.37 (((~is_state(S!2)) | (~is_state(T!1)) | (S!2 = T!1)) | is_state(T!1)),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(43,plain,
% 0.12/0.37 (is_state(T!1)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[42, 32])).
% 0.12/0.37 tff(44,plain,
% 0.12/0.37 (((~![S: $i] : ((~is_state(S)) | (S = T!3))) | ((~is_state(T!1)) | (T!1 = T!3))) <=> ((~![S: $i] : ((~is_state(S)) | (S = T!3))) | (~is_state(T!1)) | (T!1 = T!3))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(45,plain,
% 0.12/0.37 ((~![S: $i] : ((~is_state(S)) | (S = T!3))) | ((~is_state(T!1)) | (T!1 = T!3))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(46,plain,
% 0.12/0.37 ((~![S: $i] : ((~is_state(S)) | (S = T!3))) | (~is_state(T!1)) | (T!1 = T!3)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.12/0.37 tff(47,plain,
% 0.12/0.37 (T!1 = T!3),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[46, 43, 14])).
% 0.12/0.37 tff(48,plain,
% 0.12/0.37 (S!2 = T!1),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[47, 41])).
% 0.12/0.37 tff(49,plain,
% 0.12/0.37 (((~is_state(S!2)) | (~is_state(T!1)) | (S!2 = T!1)) | (~(S!2 = T!1))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(50,plain,
% 0.12/0.37 (~(S!2 = T!1)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[49, 32])).
% 0.12/0.37 tff(51,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[50, 48])).
% 0.12/0.37 % SZS output end Proof
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------