%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO148+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO148+1 : TPTP v9.0.0. Released v2.4.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.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 14:37:48 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(once_type, type, (
% 0.19/0.39 once: $i > $o)).
% 0.19/0.39 tff(at_the_same_time_type, type, (
% 0.19/0.39 at_the_same_time: ( $i * $i ) > $i)).
% 0.19/0.39 tff(at_type, type, (
% 0.19/0.39 at: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_P_25_type, type, (
% 0.19/0.39 tptp_fun_P_25: $i)).
% 0.19/0.39 tff(tptp_fun_Y_23_type, type, (
% 0.19/0.39 tptp_fun_Y_23: $i)).
% 0.19/0.39 tff(tptp_fun_X_24_type, type, (
% 0.19/0.39 tptp_fun_X_24: $i)).
% 0.19/0.39 tff(connect_type, type, (
% 0.19/0.39 connect: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(ordered_by_type, type, (
% 0.19/0.39 ordered_by: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_Q1_27_type, type, (
% 0.19/0.39 tptp_fun_Q1_27: $i)).
% 0.19/0.39 tff(trajectory_of_type, type, (
% 0.19/0.39 trajectory_of: $i > $i)).
% 0.19/0.39 tff(tptp_fun_Q2_26_type, type, (
% 0.19/0.39 tptp_fun_Q2_26: $i)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (^[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)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (![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))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (![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))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(4,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')).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> once(at_the_same_time(at(X, P), at(Y, P))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.39 tff(6,plain,(
% 0.19/0.39 ![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> once(at_the_same_time(at(X, P), at(Y, P))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[5])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> once(at_the_same_time(at(X, P), at(Y, P))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 ((~![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))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (connect(X!24, Y!23, P!25) <=> once(at_the_same_time(at(X!24, P!25), at(Y!23, P!25)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 ((~![P: $i, X: $i, Y: $i] : ((~connect(X, Y, P)) | ![Q1: $i, Q2: $i] : ((~once(at_the_same_time(at(X, Q1), at(Y, Q2)))) | (~(ordered_by(trajectory_of(Y), Q2, P) & ordered_by(trajectory_of(X), P, Q1)))))) <=> (~![P: $i, X: $i, Y: $i] : ((~connect(X, Y, P)) | ![Q1: $i, Q2: $i] : ((~once(at_the_same_time(at(X, Q1), at(Y, Q2)))) | (~(ordered_by(trajectory_of(Y), Q2, P) & ordered_by(trajectory_of(X), P, Q1))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 ((~![P: $i, X: $i, Y: $i] : (connect(X, Y, P) => ![Q1: $i, Q2: $i] : ((ordered_by(trajectory_of(Y), Q2, P) & ordered_by(trajectory_of(X), P, Q1)) => (~once(at_the_same_time(at(X, Q1), at(Y, Q2))))))) <=> (~![P: $i, X: $i, Y: $i] : ((~connect(X, Y, P)) | ![Q1: $i, Q2: $i] : ((~once(at_the_same_time(at(X, Q1), at(Y, Q2)))) | (~(ordered_by(trajectory_of(Y), Q2, P) & ordered_by(trajectory_of(X), P, Q1))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(12,axiom,(~![P: $i, X: $i, Y: $i] : (connect(X, Y, P) => ![Q1: $i, Q2: $i] : ((ordered_by(trajectory_of(Y), Q2, P) & ordered_by(trajectory_of(X), P, Q1)) => (~once(at_the_same_time(at(X, Q1), at(Y, Q2))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t14')).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (~![P: $i, X: $i, Y: $i] : ((~connect(X, Y, P)) | ![Q1: $i, Q2: $i] : ((~once(at_the_same_time(at(X, Q1), at(Y, Q2)))) | (~(ordered_by(trajectory_of(Y), Q2, P) & ordered_by(trajectory_of(X), P, Q1)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (~![P: $i, X: $i, Y: $i] : ((~connect(X, Y, P)) | ![Q1: $i, Q2: $i] : ((~once(at_the_same_time(at(X, Q1), at(Y, Q2)))) | (~(ordered_by(trajectory_of(Y), Q2, P) & ordered_by(trajectory_of(X), P, Q1)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (~![P: $i, X: $i, Y: $i] : ((~connect(X, Y, P)) | ![Q1: $i, Q2: $i] : ((~once(at_the_same_time(at(X, Q1), at(Y, Q2)))) | (~(ordered_by(trajectory_of(Y), Q2, P) & ordered_by(trajectory_of(X), P, Q1)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (~![P: $i, X: $i, Y: $i] : ((~connect(X, Y, P)) | ![Q1: $i, Q2: $i] : ((~once(at_the_same_time(at(X, Q1), at(Y, Q2)))) | (~(ordered_by(trajectory_of(Y), Q2, P) & ordered_by(trajectory_of(X), P, Q1)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (connect(X!24, Y!23, P!25)),
% 0.19/0.39 inference(and_elim,[status(thm)],[16])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 ((~(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)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 ((~(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)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (once(at_the_same_time(at(X!24, P!25), at(Y!23, P!25)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[19, 9])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (~((~once(at_the_same_time(at(X!24, Q1!27), at(Y!23, Q2!26)))) | (~(ordered_by(trajectory_of(Y!23), Q2!26, P!25) & ordered_by(trajectory_of(X!24), P!25, Q1!27))))),
% 0.19/0.39 inference(and_elim,[status(thm)],[16])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (ordered_by(trajectory_of(Y!23), Q2!26, P!25) & ordered_by(trajectory_of(X!24), P!25, Q1!27)),
% 0.19/0.39 inference(or_elim,[status(thm)],[21])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (ordered_by(trajectory_of(X!24), P!25, Q1!27)),
% 0.19/0.39 inference(and_elim,[status(thm)],[22])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (ordered_by(trajectory_of(Y!23), Q2!26, P!25)),
% 0.19/0.39 inference(and_elim,[status(thm)],[22])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (once(at_the_same_time(at(X!24, Q1!27), at(Y!23, Q2!26)))),
% 0.19/0.39 inference(or_elim,[status(thm)],[21])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (^[P1: $i, P2: $i, Q1: $i, Q2: $i, X: $i, Y: $i] : refl(((~ordered_by(trajectory_of(X), P1, Q1)) | (~ordered_by(trajectory_of(Y), Q2, P2)) | (~once(at_the_same_time(at(X, P1), at(Y, P2)))) | (~once(at_the_same_time(at(X, Q1), at(Y, Q2))))) <=> ((~ordered_by(trajectory_of(X), P1, Q1)) | (~ordered_by(trajectory_of(Y), Q2, P2)) | (~once(at_the_same_time(at(X, P1), at(Y, P2)))) | (~once(at_the_same_time(at(X, Q1), at(Y, Q2))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (![P1: $i, P2: $i, Q1: $i, Q2: $i, X: $i, Y: $i] : ((~ordered_by(trajectory_of(X), P1, Q1)) | (~ordered_by(trajectory_of(Y), Q2, P2)) | (~once(at_the_same_time(at(X, P1), at(Y, P2)))) | (~once(at_the_same_time(at(X, Q1), at(Y, Q2))))) <=> ![P1: $i, P2: $i, Q1: $i, Q2: $i, X: $i, Y: $i] : ((~ordered_by(trajectory_of(X), P1, Q1)) | (~ordered_by(trajectory_of(Y), Q2, P2)) | (~once(at_the_same_time(at(X, P1), at(Y, P2)))) | (~once(at_the_same_time(at(X, Q1), at(Y, Q2)))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (^[P1: $i, P2: $i, Q1: $i, Q2: $i, X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((ordered_by(trajectory_of(X), P1, Q1) & ordered_by(trajectory_of(Y), Q2, P2)) <=> (~((~ordered_by(trajectory_of(X), P1, Q1)) | (~ordered_by(trajectory_of(Y), Q2, P2))))), ((~(ordered_by(trajectory_of(X), P1, Q1) & ordered_by(trajectory_of(Y), Q2, P2))) <=> (~(~((~ordered_by(trajectory_of(X), P1, Q1)) | (~ordered_by(trajectory_of(Y), Q2, P2))))))), rewrite((~(~((~ordered_by(trajectory_of(X), P1, Q1)) | (~ordered_by(trajectory_of(Y), Q2, P2))))) <=> ((~ordered_by(trajectory_of(X), P1, Q1)) | (~ordered_by(trajectory_of(Y), Q2, P2)))), ((~(ordered_by(trajectory_of(X), P1, Q1) & ordered_by(trajectory_of(Y), Q2, P2))) <=> ((~ordered_by(trajectory_of(X), P1, Q1)) | (~ordered_by(trajectory_of(Y), Q2, P2))))), trans(monotonicity(rewrite((once(at_the_same_time(at(X, P1), at(Y, P2))) & once(at_the_same_time(at(X, Q1), at(Y, Q2)))) <=> (~((~once(at_the_same_time(at(X, P1), at(Y, P2)))) | (~once(at_the_same_time(at(X, Q1), at(Y, Q2))))))), ((~(once(at_the_same_time(at(X, P1), at(Y, P2))) & once(at_the_same_time(at(X, Q1), at(Y, Q2))))) <=> (~(~((~once(at_the_same_time(at(X, P1), at(Y, P2)))) | (~once(at_the_same_time(at(X, Q1), at(Y, Q2))))))))), rewrite((~(~((~once(at_the_same_time(at(X, P1), at(Y, P2)))) | (~once(at_the_same_time(at(X, Q1), at(Y, Q2))))))) <=> ((~once(at_the_same_time(at(X, P1), at(Y, P2)))) | (~once(at_the_same_time(at(X, Q1), at(Y, Q2)))))), ((~(once(at_the_same_time(at(X, P1), at(Y, P2))) & once(at_the_same_time(at(X, Q1), at(Y, Q2))))) <=> ((~once(at_the_same_time(at(X, P1), at(Y, P2)))) | (~once(at_the_same_time(at(X, Q1), at(Y, Q2))))))), (((~(ordered_by(trajectory_of(X), P1, Q1) & ordered_by(trajectory_of(Y), Q2, P2))) | (~(once(at_the_same_time(at(X, P1), at(Y, P2))) & once(at_the_same_time(at(X, Q1), at(Y, Q2)))))) <=> (((~ordered_by(trajectory_of(X), P1, Q1)) | (~ordered_by(trajectory_of(Y), Q2, P2))) | ((~once(at_the_same_time(at(X, P1), at(Y, P2)))) | (~once(at_the_same_time(at(X, Q1), at(Y, Q2)))))))), rewrite((((~ordered_by(trajectory_of(X), P1, Q1)) | (~ordered_by(trajectory_of(Y), Q2, P2))) | ((~once(at_the_same_time(at(X, P1), at(Y, P2)))) | (~once(at_the_same_time(at(X, Q1), at(Y, Q2)))))) <=> ((~ordered_by(trajectory_of(X), P1, Q1)) | (~ordered_by(trajectory_of(Y), Q2, P2)) | (~once(at_the_same_time(at(X, P1), at(Y, P2)))) | (~once(at_the_same_time(at(X, Q1), at(Y, Q2)))))), (((~(ordered_by(trajectory_of(X), P1, Q1) & ordered_by(trajectory_of(Y), Q2, P2))) | (~(once(at_the_same_time(at(X, P1), at(Y, P2))) & once(at_the_same_time(at(X, Q1), at(Y, Q2)))))) <=> ((~ordered_by(trajectory_of(X), P1, Q1)) | (~ordered_by(trajectory_of(Y), Q2, P2)) | (~once(at_the_same_time(at(X, P1), at(Y, P2)))) | (~once(at_the_same_time(at(X, Q1), at(Y, Q2)))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (![P1: $i, P2: $i, Q1: $i, Q2: $i, X: $i, Y: $i] : ((~(ordered_by(trajectory_of(X), P1, Q1) & ordered_by(trajectory_of(Y), Q2, P2))) | (~(once(at_the_same_time(at(X, P1), at(Y, P2))) & once(at_the_same_time(at(X, Q1), at(Y, Q2)))))) <=> ![P1: $i, P2: $i, Q1: $i, Q2: $i, X: $i, Y: $i] : ((~ordered_by(trajectory_of(X), P1, Q1)) | (~ordered_by(trajectory_of(Y), Q2, P2)) | (~once(at_the_same_time(at(X, P1), at(Y, P2)))) | (~once(at_the_same_time(at(X, Q1), at(Y, Q2)))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[28])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (![P1: $i, P2: $i, Q1: $i, Q2: $i, X: $i, Y: $i] : ((~(ordered_by(trajectory_of(X), P1, Q1) & ordered_by(trajectory_of(Y), Q2, P2))) | (~(once(at_the_same_time(at(X, P1), at(Y, P2))) & once(at_the_same_time(at(X, Q1), at(Y, Q2)))))) <=> ![P1: $i, P2: $i, Q1: $i, Q2: $i, X: $i, Y: $i] : ((~(ordered_by(trajectory_of(X), P1, Q1) & ordered_by(trajectory_of(Y), Q2, P2))) | (~(once(at_the_same_time(at(X, P1), at(Y, P2))) & once(at_the_same_time(at(X, Q1), at(Y, Q2))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (^[P1: $i, P2: $i, Q1: $i, Q2: $i, X: $i, Y: $i] : rewrite(((once(at_the_same_time(at(X, P1), at(Y, P2))) & once(at_the_same_time(at(X, Q1), at(Y, Q2)))) => (~(ordered_by(trajectory_of(X), P1, Q1) & ordered_by(trajectory_of(Y), Q2, P2)))) <=> ((~(ordered_by(trajectory_of(X), P1, Q1) & ordered_by(trajectory_of(Y), Q2, P2))) | (~(once(at_the_same_time(at(X, P1), at(Y, P2))) & once(at_the_same_time(at(X, Q1), at(Y, Q2)))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (![P1: $i, P2: $i, Q1: $i, Q2: $i, X: $i, Y: $i] : ((once(at_the_same_time(at(X, P1), at(Y, P2))) & once(at_the_same_time(at(X, Q1), at(Y, Q2)))) => (~(ordered_by(trajectory_of(X), P1, Q1) & ordered_by(trajectory_of(Y), Q2, P2)))) <=> ![P1: $i, P2: $i, Q1: $i, Q2: $i, X: $i, Y: $i] : ((~(ordered_by(trajectory_of(X), P1, Q1) & ordered_by(trajectory_of(Y), Q2, P2))) | (~(once(at_the_same_time(at(X, P1), at(Y, P2))) & once(at_the_same_time(at(X, Q1), at(Y, Q2))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[31])).
% 0.19/0.39 tff(33,axiom,(![P1: $i, P2: $i, Q1: $i, Q2: $i, X: $i, Y: $i] : ((once(at_the_same_time(at(X, P1), at(Y, P2))) & once(at_the_same_time(at(X, Q1), at(Y, Q2)))) => (~(ordered_by(trajectory_of(X), P1, Q1) & ordered_by(trajectory_of(Y), Q2, P2))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004+3.ax','homogeneous_behaviour')).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 (![P1: $i, P2: $i, Q1: $i, Q2: $i, X: $i, Y: $i] : ((~(ordered_by(trajectory_of(X), P1, Q1) & ordered_by(trajectory_of(Y), Q2, P2))) | (~(once(at_the_same_time(at(X, P1), at(Y, P2))) & once(at_the_same_time(at(X, Q1), at(Y, Q2))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 (![P1: $i, P2: $i, Q1: $i, Q2: $i, X: $i, Y: $i] : ((~(ordered_by(trajectory_of(X), P1, Q1) & ordered_by(trajectory_of(Y), Q2, P2))) | (~(once(at_the_same_time(at(X, P1), at(Y, P2))) & once(at_the_same_time(at(X, Q1), at(Y, Q2))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.19/0.40 tff(36,plain,(
% 0.19/0.40 ![P1: $i, P2: $i, Q1: $i, Q2: $i, X: $i, Y: $i] : ((~(ordered_by(trajectory_of(X), P1, Q1) & ordered_by(trajectory_of(Y), Q2, P2))) | (~(once(at_the_same_time(at(X, P1), at(Y, P2))) & once(at_the_same_time(at(X, Q1), at(Y, Q2))))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[35])).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 (![P1: $i, P2: $i, Q1: $i, Q2: $i, X: $i, Y: $i] : ((~ordered_by(trajectory_of(X), P1, Q1)) | (~ordered_by(trajectory_of(Y), Q2, P2)) | (~once(at_the_same_time(at(X, P1), at(Y, P2)))) | (~once(at_the_same_time(at(X, Q1), at(Y, Q2)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 (![P1: $i, P2: $i, Q1: $i, Q2: $i, X: $i, Y: $i] : ((~ordered_by(trajectory_of(X), P1, Q1)) | (~ordered_by(trajectory_of(Y), Q2, P2)) | (~once(at_the_same_time(at(X, P1), at(Y, P2)))) | (~once(at_the_same_time(at(X, Q1), at(Y, Q2)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[37, 27])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 (((~![P1: $i, P2: $i, Q1: $i, Q2: $i, X: $i, Y: $i] : ((~ordered_by(trajectory_of(X), P1, Q1)) | (~ordered_by(trajectory_of(Y), Q2, P2)) | (~once(at_the_same_time(at(X, P1), at(Y, P2)))) | (~once(at_the_same_time(at(X, Q1), at(Y, Q2)))))) | ((~ordered_by(trajectory_of(X!24), P!25, Q1!27)) | (~ordered_by(trajectory_of(Y!23), Q2!26, 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, Q1!27), at(Y!23, Q2!26)))))) <=> ((~![P1: $i, P2: $i, Q1: $i, Q2: $i, X: $i, Y: $i] : ((~ordered_by(trajectory_of(X), P1, Q1)) | (~ordered_by(trajectory_of(Y), Q2, P2)) | (~once(at_the_same_time(at(X, P1), at(Y, P2)))) | (~once(at_the_same_time(at(X, Q1), at(Y, Q2)))))) | (~ordered_by(trajectory_of(X!24), P!25, Q1!27)) | (~ordered_by(trajectory_of(Y!23), Q2!26, 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, Q1!27), at(Y!23, Q2!26)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 ((~![P1: $i, P2: $i, Q1: $i, Q2: $i, X: $i, Y: $i] : ((~ordered_by(trajectory_of(X), P1, Q1)) | (~ordered_by(trajectory_of(Y), Q2, P2)) | (~once(at_the_same_time(at(X, P1), at(Y, P2)))) | (~once(at_the_same_time(at(X, Q1), at(Y, Q2)))))) | ((~ordered_by(trajectory_of(X!24), P!25, Q1!27)) | (~ordered_by(trajectory_of(Y!23), Q2!26, 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, Q1!27), at(Y!23, Q2!26)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 ((~![P1: $i, P2: $i, Q1: $i, Q2: $i, X: $i, Y: $i] : ((~ordered_by(trajectory_of(X), P1, Q1)) | (~ordered_by(trajectory_of(Y), Q2, P2)) | (~once(at_the_same_time(at(X, P1), at(Y, P2)))) | (~once(at_the_same_time(at(X, Q1), at(Y, Q2)))))) | (~ordered_by(trajectory_of(X!24), P!25, Q1!27)) | (~ordered_by(trajectory_of(Y!23), Q2!26, P!25)) | (~once(at_the_same_time(at(X!24, P!25), at(Y!23, P!25)))) | (~once(at_the_same_time(at(X!24, Q1!27), at(Y!23, Q2!26))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[41, 38, 25, 24, 23, 20])).
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------