%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO147+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:05:41 AM UTC 2025
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO147+1 : TPTP v9.0.0. Released v2.4.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.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 14:33:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(incident_o_type, type, (
% 0.19/0.38 incident_o: ( $i * $i ) > $o)).
% 0.19/0.38 tff(trajectory_of_type, type, (
% 0.19/0.38 trajectory_of: $i > $i)).
% 0.19/0.38 tff(tptp_fun_Y_23_type, type, (
% 0.19/0.38 tptp_fun_Y_23: $i)).
% 0.19/0.38 tff(tptp_fun_P_25_type, type, (
% 0.19/0.38 tptp_fun_P_25: $i)).
% 0.19/0.38 tff(once_type, type, (
% 0.19/0.38 once: $i > $o)).
% 0.19/0.38 tff(at_type, type, (
% 0.19/0.38 at: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_X_24_type, type, (
% 0.19/0.38 tptp_fun_X_24: $i)).
% 0.19/0.38 tff(at_the_same_time_type, type, (
% 0.19/0.38 at_the_same_time: ( $i * $i ) > $i)).
% 0.19/0.38 tff(connect_type, type, (
% 0.19/0.38 connect: ( $i * $i * $i ) > $o)).
% 0.19/0.38 tff(1,plain,
% 0.19/0.38 (^[X: $i, P: $i] : refl((once(at(X, P)) <=> incident_o(P, trajectory_of(X))) <=> (once(at(X, P)) <=> incident_o(P, trajectory_of(X))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 (![X: $i, P: $i] : (once(at(X, P)) <=> incident_o(P, trajectory_of(X))) <=> ![X: $i, P: $i] : (once(at(X, P)) <=> incident_o(P, trajectory_of(X)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.38 tff(3,plain,
% 0.19/0.38 (![X: $i, P: $i] : (once(at(X, P)) <=> incident_o(P, trajectory_of(X))) <=> ![X: $i, P: $i] : (once(at(X, P)) <=> incident_o(P, trajectory_of(X)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(4,axiom,(![X: $i, P: $i] : (once(at(X, P)) <=> incident_o(P, trajectory_of(X)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004+3.ax','at_on_trajectory')).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 (![X: $i, P: $i] : (once(at(X, P)) <=> incident_o(P, trajectory_of(X)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.38 tff(6,plain,(
% 0.19/0.38 ![X: $i, P: $i] : (once(at(X, P)) <=> incident_o(P, trajectory_of(X)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[5])).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 (![X: $i, P: $i] : (once(at(X, P)) <=> incident_o(P, trajectory_of(X)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.38 tff(8,plain,
% 0.19/0.38 ((~![X: $i, P: $i] : (once(at(X, P)) <=> incident_o(P, trajectory_of(X)))) | (once(at(Y!23, P!25)) <=> incident_o(P!25, trajectory_of(Y!23)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(9,plain,
% 0.19/0.38 (once(at(Y!23, P!25)) <=> incident_o(P!25, trajectory_of(Y!23))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 (^[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)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(11,plain,
% 0.19/0.38 (![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))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (![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))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(13,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')).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 (![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> once(at_the_same_time(at(X, P), at(Y, P))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.38 tff(15,plain,(
% 0.19/0.38 ![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> once(at_the_same_time(at(X, P), at(Y, P))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[14])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 (![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> once(at_the_same_time(at(X, P), at(Y, P))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.19/0.38 tff(17,plain,
% 0.19/0.38 ((~![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> once(at_the_same_time(at(X, P), at(Y, P))))) | (connect(X!24, Y!23, P!25) <=> once(at_the_same_time(at(X!24, P!25), at(Y!23, P!25))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 (connect(X!24, Y!23, P!25) <=> once(at_the_same_time(at(X!24, P!25), at(Y!23, P!25)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 ((~![P: $i, X: $i, Y: $i] : ((~connect(X, Y, P)) | (incident_o(P, trajectory_of(X)) & incident_o(P, trajectory_of(Y))))) <=> (~![P: $i, X: $i, Y: $i] : ((~connect(X, Y, P)) | (incident_o(P, trajectory_of(X)) & incident_o(P, trajectory_of(Y)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(20,plain,
% 0.19/0.38 ((~![P: $i, X: $i, Y: $i] : (connect(X, Y, P) => (incident_o(P, trajectory_of(X)) & incident_o(P, trajectory_of(Y))))) <=> (~![P: $i, X: $i, Y: $i] : ((~connect(X, Y, P)) | (incident_o(P, trajectory_of(X)) & incident_o(P, trajectory_of(Y)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(21,axiom,(~![P: $i, X: $i, Y: $i] : (connect(X, Y, P) => (incident_o(P, trajectory_of(X)) & incident_o(P, trajectory_of(Y))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t13')).
% 0.19/0.38 tff(22,plain,
% 0.19/0.38 (~![P: $i, X: $i, Y: $i] : ((~connect(X, Y, P)) | (incident_o(P, trajectory_of(X)) & incident_o(P, trajectory_of(Y))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.38 tff(23,plain,
% 0.19/0.38 (~![P: $i, X: $i, Y: $i] : ((~connect(X, Y, P)) | (incident_o(P, trajectory_of(X)) & incident_o(P, trajectory_of(Y))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[22, 19])).
% 0.19/0.38 tff(24,plain,
% 0.19/0.38 (~![P: $i, X: $i, Y: $i] : ((~connect(X, Y, P)) | (incident_o(P, trajectory_of(X)) & incident_o(P, trajectory_of(Y))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.19/0.38 tff(25,plain,
% 0.19/0.38 (~![P: $i, X: $i, Y: $i] : ((~connect(X, Y, P)) | (incident_o(P, trajectory_of(X)) & incident_o(P, trajectory_of(Y))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[24, 19])).
% 0.19/0.38 tff(26,plain,(
% 0.19/0.38 ~((~connect(X!24, Y!23, P!25)) | (incident_o(P!25, trajectory_of(X!24)) & incident_o(P!25, trajectory_of(Y!23))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[25])).
% 0.19/0.38 tff(27,plain,
% 0.19/0.38 (connect(X!24, Y!23, P!25)),
% 0.19/0.38 inference(or_elim,[status(thm)],[26])).
% 0.19/0.38 tff(28,plain,
% 0.19/0.38 ((~(connect(X!24, Y!23, P!25) <=> once(at_the_same_time(at(X!24, P!25), at(Y!23, P!25))))) | (~connect(X!24, Y!23, P!25)) | once(at_the_same_time(at(X!24, P!25), at(Y!23, P!25)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(29,plain,
% 0.19/0.38 ((~(connect(X!24, Y!23, P!25) <=> once(at_the_same_time(at(X!24, P!25), at(Y!23, P!25))))) | once(at_the_same_time(at(X!24, P!25), at(Y!23, P!25)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.19/0.38 tff(30,plain,
% 0.19/0.38 (once(at_the_same_time(at(X!24, P!25), at(Y!23, P!25)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[29, 18])).
% 0.19/0.38 tff(31,plain,
% 0.19/0.38 (^[A: $i, B: $i] : refl(((~once(at_the_same_time(A, B))) | (~((~once(B)) | (~once(A))))) <=> ((~once(at_the_same_time(A, B))) | (~((~once(B)) | (~once(A))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(32,plain,
% 0.19/0.38 (![A: $i, B: $i] : ((~once(at_the_same_time(A, B))) | (~((~once(B)) | (~once(A))))) <=> ![A: $i, B: $i] : ((~once(at_the_same_time(A, B))) | (~((~once(B)) | (~once(A)))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[31])).
% 0.19/0.38 tff(33,plain,
% 0.19/0.38 (^[A: $i, B: $i] : rewrite(((~once(at_the_same_time(A, B))) | (once(A) & once(B))) <=> ((~once(at_the_same_time(A, B))) | (~((~once(B)) | (~once(A))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(34,plain,
% 0.19/0.38 (![A: $i, B: $i] : ((~once(at_the_same_time(A, B))) | (once(A) & once(B))) <=> ![A: $i, B: $i] : ((~once(at_the_same_time(A, B))) | (~((~once(B)) | (~once(A)))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[33])).
% 0.19/0.38 tff(35,plain,
% 0.19/0.38 (![A: $i, B: $i] : ((~once(at_the_same_time(A, B))) | (once(A) & once(B))) <=> ![A: $i, B: $i] : ((~once(at_the_same_time(A, B))) | (once(A) & once(B)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(36,plain,
% 0.19/0.38 (^[A: $i, B: $i] : rewrite((once(at_the_same_time(A, B)) => (once(A) & once(B))) <=> ((~once(at_the_same_time(A, B))) | (once(A) & once(B))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(37,plain,
% 0.19/0.38 (![A: $i, B: $i] : (once(at_the_same_time(A, B)) => (once(A) & once(B))) <=> ![A: $i, B: $i] : ((~once(at_the_same_time(A, B))) | (once(A) & once(B)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[36])).
% 0.19/0.38 tff(38,axiom,(![A: $i, B: $i] : (once(at_the_same_time(A, B)) => (once(A) & once(B)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004+3.ax','conjunction_at_the_same_time')).
% 0.19/0.38 tff(39,plain,
% 0.19/0.38 (![A: $i, B: $i] : ((~once(at_the_same_time(A, B))) | (once(A) & once(B)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (![A: $i, B: $i] : ((~once(at_the_same_time(A, B))) | (once(A) & once(B)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.19/0.39 tff(41,plain,(
% 0.19/0.39 ![A: $i, B: $i] : ((~once(at_the_same_time(A, B))) | (once(A) & once(B)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[40])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (![A: $i, B: $i] : ((~once(at_the_same_time(A, B))) | (~((~once(B)) | (~once(A)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 (![A: $i, B: $i] : ((~once(at_the_same_time(A, B))) | (~((~once(B)) | (~once(A)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[42, 32])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 (((~![A: $i, B: $i] : ((~once(at_the_same_time(A, B))) | (~((~once(B)) | (~once(A)))))) | ((~once(at_the_same_time(at(X!24, P!25), at(Y!23, P!25)))) | (~((~once(at(Y!23, P!25))) | (~once(at(X!24, P!25))))))) <=> ((~![A: $i, B: $i] : ((~once(at_the_same_time(A, B))) | (~((~once(B)) | (~once(A)))))) | (~once(at_the_same_time(at(X!24, P!25), at(Y!23, P!25)))) | (~((~once(at(Y!23, P!25))) | (~once(at(X!24, P!25))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : ((~once(at_the_same_time(A, B))) | (~((~once(B)) | (~once(A)))))) | ((~once(at_the_same_time(at(X!24, P!25), at(Y!23, P!25)))) | (~((~once(at(Y!23, P!25))) | (~once(at(X!24, P!25))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : ((~once(at_the_same_time(A, B))) | (~((~once(B)) | (~once(A)))))) | (~once(at_the_same_time(at(X!24, P!25), at(Y!23, P!25)))) | (~((~once(at(Y!23, P!25))) | (~once(at(X!24, P!25)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 (~((~once(at(Y!23, P!25))) | (~once(at(X!24, P!25))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[46, 43, 30])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 (((~once(at(Y!23, P!25))) | (~once(at(X!24, P!25)))) | once(at(Y!23, P!25))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 (once(at(Y!23, P!25))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 ((~(once(at(Y!23, P!25)) <=> incident_o(P!25, trajectory_of(Y!23)))) | (~once(at(Y!23, P!25))) | incident_o(P!25, trajectory_of(Y!23))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 (incident_o(P!25, trajectory_of(Y!23))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[50, 49, 9])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 ((~![X: $i, P: $i] : (once(at(X, P)) <=> incident_o(P, trajectory_of(X)))) | (once(at(X!24, P!25)) <=> incident_o(P!25, trajectory_of(X!24)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 (once(at(X!24, P!25)) <=> incident_o(P!25, trajectory_of(X!24))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[52, 7])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 (((~once(at(Y!23, P!25))) | (~once(at(X!24, P!25)))) | once(at(X!24, P!25))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 (once(at(X!24, P!25))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[54, 47])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 ((~(once(at(X!24, P!25)) <=> incident_o(P!25, trajectory_of(X!24)))) | (~once(at(X!24, P!25))) | incident_o(P!25, trajectory_of(X!24))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 (incident_o(P!25, trajectory_of(X!24))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[56, 55, 53])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 ((~(~((~incident_o(P!25, trajectory_of(X!24))) | (~incident_o(P!25, trajectory_of(Y!23)))))) <=> ((~incident_o(P!25, trajectory_of(X!24))) | (~incident_o(P!25, trajectory_of(Y!23))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 ((incident_o(P!25, trajectory_of(X!24)) & incident_o(P!25, trajectory_of(Y!23))) <=> (~((~incident_o(P!25, trajectory_of(X!24))) | (~incident_o(P!25, trajectory_of(Y!23)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 ((~(incident_o(P!25, trajectory_of(X!24)) & incident_o(P!25, trajectory_of(Y!23)))) <=> (~(~((~incident_o(P!25, trajectory_of(X!24))) | (~incident_o(P!25, trajectory_of(Y!23))))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[59])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 ((~(incident_o(P!25, trajectory_of(X!24)) & incident_o(P!25, trajectory_of(Y!23)))) <=> ((~incident_o(P!25, trajectory_of(X!24))) | (~incident_o(P!25, trajectory_of(Y!23))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[60, 58])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 (~(incident_o(P!25, trajectory_of(X!24)) & incident_o(P!25, trajectory_of(Y!23)))),
% 0.19/0.39 inference(or_elim,[status(thm)],[26])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 ((~incident_o(P!25, trajectory_of(X!24))) | (~incident_o(P!25, trajectory_of(Y!23)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[63, 57, 51])).
% 0.19/0.39 % SZS output end Proof
% 0.19/0.39 % E exiting
%------------------------------------------------------------------------------