%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW469+5 : TPTP v9.0.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWW469+5 : TPTP v9.0.0. Released v5.3.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n005.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 : Fri Jun 20 11:46:50 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 tff(ti_type, type, (
% 0.20/0.42 ti: ( $i * $i ) > $i)).
% 0.20/0.42 tff(tptp_fun_T_0_type, type, (
% 0.20/0.42 tptp_fun_T_0: $i)).
% 0.20/0.42 tff(state_type, type, (
% 0.20/0.42 state: $i)).
% 0.20/0.42 tff(tptp_fun_S_1_type, type, (
% 0.20/0.42 tptp_fun_S_1: $i)).
% 0.20/0.42 tff(tptp_fun_T_11_type, type, (
% 0.20/0.42 tptp_fun_T_11: $i)).
% 0.20/0.42 tff(hBOOL_type, type, (
% 0.20/0.42 hBOOL: $i > $o)).
% 0.20/0.42 tff(hoare_1883395792gleton_type, type, (
% 0.20/0.42 hoare_1883395792gleton: $i)).
% 0.20/0.42 tff(1,plain,
% 0.20/0.42 ((ti(state, T!11) = ti(state, T!0)) <=> (ti(state, T!0) = ti(state, T!11))),
% 0.20/0.42 inference(commutativity,[status(thm)],[])).
% 0.20/0.42 tff(2,plain,
% 0.20/0.42 (^[S: $i] : refl((ti(state, S) = ti(state, T!11)) <=> (ti(state, S) = ti(state, T!11)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(3,plain,
% 0.20/0.42 (![S: $i] : (ti(state, S) = ti(state, T!11)) <=> ![S: $i] : (ti(state, S) = ti(state, T!11))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.42 tff(4,plain,
% 0.20/0.42 ((~![T: $i] : (~![S: $i] : (ti(state, S) = ti(state, T)))) <=> (~![T: $i] : (~![S: $i] : (ti(state, S) = ti(state, T))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(5,axiom,(~![T: $i] : (~![S: $i] : (ti(state, S) = ti(state, T)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj_1')).
% 0.20/0.42 tff(6,plain,
% 0.20/0.42 (~![T: $i] : (~![S: $i] : (ti(state, S) = ti(state, T)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.42 tff(7,plain,
% 0.20/0.42 (~![T: $i] : (~![S: $i] : (ti(state, S) = ti(state, T)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[6, 4])).
% 0.20/0.42 tff(8,plain,
% 0.20/0.42 (~![T: $i] : (~![S: $i] : (ti(state, S) = ti(state, T)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[7, 4])).
% 0.20/0.42 tff(9,plain,
% 0.20/0.42 (~![T: $i] : (~![S: $i] : (ti(state, S) = ti(state, T)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.20/0.42 tff(10,plain,(
% 0.20/0.42 $oeq((~(~![S: $i] : (ti(state, S) = ti(state, T!11)))), ![S: $i] : (ti(state, S) = ti(state, T!11)))),
% 0.20/0.42 inference(transitivity,[status(sab)],[9])).
% 0.20/0.42 tff(11,plain,
% 0.20/0.42 (![S: $i] : (ti(state, S) = ti(state, T!11))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.20/0.42 tff(12,plain,
% 0.20/0.42 ((~![S: $i] : (ti(state, S) = ti(state, T!11))) | (ti(state, S!1) = ti(state, T!11))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 (ti(state, S!1) = ti(state, T!11)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 ((ti(state, S!1) = ti(state, T!0)) <=> (ti(state, T!11) = ti(state, T!0))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[13])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 ((ti(state, S!1) = ti(state, T!0)) <=> (ti(state, T!0) = ti(state, T!11))),
% 0.20/0.42 inference(transitivity,[status(thm)],[14, 1])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 ((ti(state, T!0) = ti(state, T!11)) <=> (ti(state, S!1) = ti(state, T!0))),
% 0.20/0.42 inference(symmetry,[status(thm)],[15])).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 ((~![S: $i] : (ti(state, S) = ti(state, T!11))) | (ti(state, T!0) = ti(state, T!11))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 (ti(state, T!0) = ti(state, T!11)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[17, 11])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 (ti(state, S!1) = ti(state, T!0)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[18, 16])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (hBOOL(hoare_1883395792gleton) <=> hBOOL(hoare_1883395792gleton)),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(21,axiom,(hBOOL(hoare_1883395792gleton)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj_0')).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 (hBOOL(hoare_1883395792gleton)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 ((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)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 ((((~hBOOL(hoare_1883395792gleton)) | (~(ti(state, S!1) = ti(state, T!0)))) & (hBOOL(hoare_1883395792gleton) | ![S: $i, T: $i] : (ti(state, S) = ti(state, T)))) <=> (((~hBOOL(hoare_1883395792gleton)) | (~(ti(state, S!1) = ti(state, T!0)))) & (hBOOL(hoare_1883395792gleton) | ![S: $i, T: $i] : (ti(state, S) = ti(state, T))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[23])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 ((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))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(26,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')).
% 0.20/0.44 tff(27,plain,
% 0.20/0.44 (hBOOL(hoare_1883395792gleton) <=> ?[S: $i, T: $i] : (~(ti(state, S) = ti(state, T)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.44 tff(28,plain,
% 0.20/0.44 (hBOOL(hoare_1883395792gleton) <=> ?[S: $i, T: $i] : (~(ti(state, S) = ti(state, T)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[27, 25])).
% 0.20/0.44 tff(29,plain,
% 0.20/0.44 (hBOOL(hoare_1883395792gleton) <=> ?[S: $i, T: $i] : (~(ti(state, S) = ti(state, T)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[28, 25])).
% 0.20/0.44 tff(30,plain,
% 0.20/0.44 (hBOOL(hoare_1883395792gleton) <=> ?[S: $i, T: $i] : (~(ti(state, S) = ti(state, T)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.20/0.44 tff(31,plain,(
% 0.20/0.44 ((~hBOOL(hoare_1883395792gleton)) | (~(ti(state, S!1) = ti(state, T!0)))) & (hBOOL(hoare_1883395792gleton) | ![S: $i, T: $i] : (ti(state, S) = ti(state, T)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[30])).
% 0.20/0.44 tff(32,plain,
% 0.20/0.44 (((~hBOOL(hoare_1883395792gleton)) | (~(ti(state, S!1) = ti(state, T!0)))) & (hBOOL(hoare_1883395792gleton) | ![S: $i, T: $i] : (ti(state, S) = ti(state, T)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.20/0.44 tff(33,plain,
% 0.20/0.44 ((~hBOOL(hoare_1883395792gleton)) | (~(ti(state, S!1) = ti(state, T!0)))),
% 0.20/0.44 inference(and_elim,[status(thm)],[32])).
% 0.20/0.44 tff(34,plain,
% 0.20/0.44 (~(ti(state, S!1) = ti(state, T!0))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[33, 22])).
% 0.20/0.44 tff(35,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[34, 19])).
% 0.20/0.44 % SZS output end Proof
% 0.20/0.44 % E exiting
%------------------------------------------------------------------------------