%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO146+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:05:40 AM UTC 2025
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO146+1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.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 : Thu Jun 19 14:33:53 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(once_type, type, (
% 0.20/0.41 once: $i > $o)).
% 0.20/0.41 tff(at_the_same_time_type, type, (
% 0.20/0.41 at_the_same_time: ( $i * $i ) > $i)).
% 0.20/0.41 tff(at_type, type, (
% 0.20/0.41 at: ( $i * $i ) > $i)).
% 0.20/0.41 tff(tptp_fun_P_23_type, type, (
% 0.20/0.41 tptp_fun_P_23: $i)).
% 0.20/0.41 tff(tptp_fun_X_25_type, type, (
% 0.20/0.41 tptp_fun_X_25: $i)).
% 0.20/0.41 tff(tptp_fun_Y_24_type, type, (
% 0.20/0.41 tptp_fun_Y_24: $i)).
% 0.20/0.41 tff(connect_type, type, (
% 0.20/0.41 connect: ( $i * $i * $i ) > $o)).
% 0.20/0.41 tff(1,assumption,(~connect(Y!24, X!25, P!23)), introduced(assumption)).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 (^[X: $i, Y: $i, P: $i] : refl((connect(X, Y, P) <=> once(at_the_same_time(at(X, P), at(Y, P)))) <=> (connect(X, Y, P) <=> once(at_the_same_time(at(X, P), at(Y, P)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 (![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> once(at_the_same_time(at(X, P), at(Y, P)))) <=> ![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> once(at_the_same_time(at(X, P), at(Y, P))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.41 tff(4,plain,
% 0.20/0.41 (![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> once(at_the_same_time(at(X, P), at(Y, P)))) <=> ![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> once(at_the_same_time(at(X, P), at(Y, P))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(5,axiom,(![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> once(at_the_same_time(at(X, P), at(Y, P))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004+3.ax','connect_defn')).
% 0.20/0.41 tff(6,plain,
% 0.20/0.41 (![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> once(at_the_same_time(at(X, P), at(Y, P))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.41 tff(7,plain,(
% 0.20/0.41 ![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> once(at_the_same_time(at(X, P), at(Y, P))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[6])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 (![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> once(at_the_same_time(at(X, P), at(Y, P))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 ((~![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> once(at_the_same_time(at(X, P), at(Y, P))))) | (connect(Y!24, X!25, P!23) <=> once(at_the_same_time(at(Y!24, P!23), at(X!25, P!23))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 (connect(Y!24, X!25, P!23) <=> once(at_the_same_time(at(Y!24, P!23), at(X!25, P!23)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.20/0.41 tff(11,plain,
% 0.20/0.41 ((~(connect(Y!24, X!25, P!23) <=> once(at_the_same_time(at(Y!24, P!23), at(X!25, P!23))))) | connect(Y!24, X!25, P!23) | (~once(at_the_same_time(at(Y!24, P!23), at(X!25, P!23))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(12,plain,
% 0.20/0.41 (connect(Y!24, X!25, P!23) | (~once(at_the_same_time(at(Y!24, P!23), at(X!25, P!23))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.20/0.41 tff(13,plain,
% 0.20/0.41 (~once(at_the_same_time(at(Y!24, P!23), at(X!25, P!23)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[12, 1])).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 ((~(connect(X!25, Y!24, P!23) <=> connect(Y!24, X!25, P!23))) <=> (~(connect(X!25, Y!24, P!23) <=> connect(Y!24, X!25, P!23)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 ((~![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> connect(Y, X, P))) <=> (~![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> connect(Y, X, P)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(16,axiom,(~![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> connect(Y, X, P))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t12')).
% 0.20/0.41 tff(17,plain,
% 0.20/0.41 (~![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> connect(Y, X, P))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.41 tff(18,plain,
% 0.20/0.41 (~![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> connect(Y, X, P))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[17, 15])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 (~![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> connect(Y, X, P))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[18, 15])).
% 0.20/0.41 tff(20,plain,
% 0.20/0.41 (~![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> connect(Y, X, P))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.20/0.41 tff(21,plain,(
% 0.20/0.41 ~(connect(X!25, Y!24, P!23) <=> connect(Y!24, X!25, P!23))),
% 0.20/0.41 inference(skolemize,[status(sab)],[20])).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 (~(connect(X!25, Y!24, P!23) <=> connect(Y!24, X!25, P!23))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 ((connect(X!25, Y!24, P!23) <=> connect(Y!24, X!25, P!23)) | connect(X!25, Y!24, P!23) | connect(Y!24, X!25, P!23)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 (connect(X!25, Y!24, P!23) | connect(Y!24, X!25, P!23)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 (connect(X!25, Y!24, P!23)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[24, 1])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 ((~![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> once(at_the_same_time(at(X, P), at(Y, P))))) | (connect(X!25, Y!24, P!23) <=> once(at_the_same_time(at(X!25, P!23), at(Y!24, P!23))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 (connect(X!25, Y!24, P!23) <=> once(at_the_same_time(at(X!25, P!23), at(Y!24, P!23)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[26, 8])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 ((~(connect(X!25, Y!24, P!23) <=> once(at_the_same_time(at(X!25, P!23), at(Y!24, P!23))))) | (~connect(X!25, Y!24, P!23)) | once(at_the_same_time(at(X!25, P!23), at(Y!24, P!23)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 ((~connect(X!25, Y!24, P!23)) | once(at_the_same_time(at(X!25, P!23), at(Y!24, P!23)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 (once(at_the_same_time(at(X!25, P!23), at(Y!24, P!23)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[29, 25])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 (^[A: $i, B: $i] : refl((once(at_the_same_time(A, B)) <=> once(at_the_same_time(B, A))) <=> (once(at_the_same_time(A, B)) <=> once(at_the_same_time(B, A))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 (![A: $i, B: $i] : (once(at_the_same_time(A, B)) <=> once(at_the_same_time(B, A))) <=> ![A: $i, B: $i] : (once(at_the_same_time(A, B)) <=> once(at_the_same_time(B, A)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 (![A: $i, B: $i] : (once(at_the_same_time(A, B)) <=> once(at_the_same_time(B, A))) <=> ![A: $i, B: $i] : (once(at_the_same_time(A, B)) <=> once(at_the_same_time(B, A)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(34,axiom,(![A: $i, B: $i] : (once(at_the_same_time(A, B)) <=> once(at_the_same_time(B, A)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004+3.ax','symmetry_of_at_the_same_time')).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (![A: $i, B: $i] : (once(at_the_same_time(A, B)) <=> once(at_the_same_time(B, A)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.41 tff(36,plain,(
% 0.20/0.41 ![A: $i, B: $i] : (once(at_the_same_time(A, B)) <=> once(at_the_same_time(B, A)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[35])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 (![A: $i, B: $i] : (once(at_the_same_time(A, B)) <=> once(at_the_same_time(B, A)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 ((~![A: $i, B: $i] : (once(at_the_same_time(A, B)) <=> once(at_the_same_time(B, A)))) | (once(at_the_same_time(at(X!25, P!23), at(Y!24, P!23))) <=> once(at_the_same_time(at(Y!24, P!23), at(X!25, P!23))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (once(at_the_same_time(at(X!25, P!23), at(Y!24, P!23))) <=> once(at_the_same_time(at(Y!24, P!23), at(X!25, P!23)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 ((~(once(at_the_same_time(at(X!25, P!23), at(Y!24, P!23))) <=> once(at_the_same_time(at(Y!24, P!23), at(X!25, P!23))))) | (~once(at_the_same_time(at(X!25, P!23), at(Y!24, P!23)))) | once(at_the_same_time(at(Y!24, P!23), at(X!25, P!23)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 ((~once(at_the_same_time(at(X!25, P!23), at(Y!24, P!23)))) | once(at_the_same_time(at(Y!24, P!23), at(X!25, P!23)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[41, 30, 13])).
% 0.20/0.41 tff(43,plain,(connect(Y!24, X!25, P!23)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 ((~(connect(Y!24, X!25, P!23) <=> once(at_the_same_time(at(Y!24, P!23), at(X!25, P!23))))) | (~connect(Y!24, X!25, P!23)) | once(at_the_same_time(at(Y!24, P!23), at(X!25, P!23)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 ((~connect(Y!24, X!25, P!23)) | once(at_the_same_time(at(Y!24, P!23), at(X!25, P!23)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[44, 10])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 (once(at_the_same_time(at(Y!24, P!23), at(X!25, P!23)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[45, 43])).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 ((connect(X!25, Y!24, P!23) <=> connect(Y!24, X!25, P!23)) | (~connect(X!25, Y!24, P!23)) | (~connect(Y!24, X!25, P!23))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 ((~connect(X!25, Y!24, P!23)) | (~connect(Y!24, X!25, P!23))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[47, 22])).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 (~connect(X!25, Y!24, P!23)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[48, 43])).
% 0.20/0.42 tff(50,plain,
% 0.20/0.42 ((~(connect(X!25, Y!24, P!23) <=> once(at_the_same_time(at(X!25, P!23), at(Y!24, P!23))))) | connect(X!25, Y!24, P!23) | (~once(at_the_same_time(at(X!25, P!23), at(Y!24, P!23))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 (connect(X!25, Y!24, P!23) | (~once(at_the_same_time(at(X!25, P!23), at(Y!24, P!23))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[50, 27])).
% 0.20/0.42 tff(52,plain,
% 0.20/0.42 (~once(at_the_same_time(at(X!25, P!23), at(Y!24, P!23)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[51, 49])).
% 0.20/0.42 tff(53,plain,
% 0.20/0.42 ((~(once(at_the_same_time(at(X!25, P!23), at(Y!24, P!23))) <=> once(at_the_same_time(at(Y!24, P!23), at(X!25, P!23))))) | once(at_the_same_time(at(X!25, P!23), at(Y!24, P!23))) | (~once(at_the_same_time(at(Y!24, P!23), at(X!25, P!23))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(54,plain,
% 0.20/0.42 (once(at_the_same_time(at(X!25, P!23), at(Y!24, P!23))) | (~once(at_the_same_time(at(Y!24, P!23), at(X!25, P!23))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[53, 39])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[54, 52, 46])).
% 0.20/0.42 % SZS output end Proof
% 0.20/0.42 % E exiting
%------------------------------------------------------------------------------