TSTP Solution File: GEO147+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO147+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 : Fri Sep 16 20:35:07 EDT 2022
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO147+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n025.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 : Wed Aug 31 06:32:45 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(incident_o_type, type, (
% 0.19/0.40 incident_o: ( $i * $i ) > $o)).
% 0.19/0.40 tff(trajectory_of_type, type, (
% 0.19/0.40 trajectory_of: $i > $i)).
% 0.19/0.40 tff(tptp_fun_Y_25_type, type, (
% 0.19/0.40 tptp_fun_Y_25: $i)).
% 0.19/0.40 tff(tptp_fun_P_27_type, type, (
% 0.19/0.40 tptp_fun_P_27: $i)).
% 0.19/0.40 tff(once_type, type, (
% 0.19/0.40 once: $i > $o)).
% 0.19/0.40 tff(at_type, type, (
% 0.19/0.40 at: ( $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_X_26_type, type, (
% 0.19/0.40 tptp_fun_X_26: $i)).
% 0.19/0.40 tff(at_the_same_time_type, type, (
% 0.19/0.40 at_the_same_time: ( $i * $i ) > $i)).
% 0.19/0.40 tff(connect_type, type, (
% 0.19/0.40 connect: ( $i * $i * $i ) > $o)).
% 0.19/0.40 tff(1,plain,
% 0.19/0.40 (^[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))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.40 tff(3,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 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')).
% 0.19/0.40 tff(5,plain,
% 0.19/0.40 (![X: $i, P: $i] : (once(at(X, P)) <=> incident_o(P, trajectory_of(X)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.40 tff(6,plain,(
% 0.19/0.40 ![X: $i, P: $i] : (once(at(X, P)) <=> incident_o(P, trajectory_of(X)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[5])).
% 0.19/0.40 tff(7,plain,
% 0.19/0.40 (![X: $i, P: $i] : (once(at(X, P)) <=> incident_o(P, trajectory_of(X)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.40 tff(8,plain,
% 0.19/0.40 ((~![X: $i, P: $i] : (once(at(X, P)) <=> incident_o(P, trajectory_of(X)))) | (once(at(Y!25, P!27)) <=> incident_o(P!27, trajectory_of(Y!25)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 (once(at(Y!25, P!27)) <=> incident_o(P!27, trajectory_of(Y!25))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 (^[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)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(11,plain,
% 0.19/0.40 (![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))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (![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))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 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')).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 (![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> once(at_the_same_time(at(X, P), at(Y, P))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.40 tff(15,plain,(
% 0.19/0.40 ![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> once(at_the_same_time(at(X, P), at(Y, P))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[14])).
% 0.19/0.40 tff(16,plain,
% 0.19/0.40 (![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> once(at_the_same_time(at(X, P), at(Y, P))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 ((~![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> once(at_the_same_time(at(X, P), at(Y, P))))) | (connect(X!26, Y!25, P!27) <=> once(at_the_same_time(at(X!26, P!27), at(Y!25, P!27))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 (connect(X!26, Y!25, P!27) <=> once(at_the_same_time(at(X!26, P!27), at(Y!25, P!27)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 ((~![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)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 ((~![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)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 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')).
% 0.19/0.41 tff(22,plain,
% 0.19/0.41 (~![P: $i, X: $i, Y: $i] : ((~connect(X, Y, P)) | (incident_o(P, trajectory_of(X)) & incident_o(P, trajectory_of(Y))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 (~![P: $i, X: $i, Y: $i] : ((~connect(X, Y, P)) | (incident_o(P, trajectory_of(X)) & incident_o(P, trajectory_of(Y))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[22, 19])).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 (~![P: $i, X: $i, Y: $i] : ((~connect(X, Y, P)) | (incident_o(P, trajectory_of(X)) & incident_o(P, trajectory_of(Y))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 (~![P: $i, X: $i, Y: $i] : ((~connect(X, Y, P)) | (incident_o(P, trajectory_of(X)) & incident_o(P, trajectory_of(Y))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[24, 19])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 (~![P: $i, X: $i, Y: $i] : ((~connect(X, Y, P)) | (incident_o(P, trajectory_of(X)) & incident_o(P, trajectory_of(Y))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[25, 19])).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 (~![P: $i, X: $i, Y: $i] : ((~connect(X, Y, P)) | (incident_o(P, trajectory_of(X)) & incident_o(P, trajectory_of(Y))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (~![P: $i, X: $i, Y: $i] : ((~connect(X, Y, P)) | (incident_o(P, trajectory_of(X)) & incident_o(P, trajectory_of(Y))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[27, 19])).
% 0.19/0.41 tff(29,plain,(
% 0.19/0.41 ~((~connect(X!26, Y!25, P!27)) | (incident_o(P!27, trajectory_of(X!26)) & incident_o(P!27, trajectory_of(Y!25))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[28])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 (connect(X!26, Y!25, P!27)),
% 0.19/0.41 inference(or_elim,[status(thm)],[29])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 ((~(connect(X!26, Y!25, P!27) <=> once(at_the_same_time(at(X!26, P!27), at(Y!25, P!27))))) | (~connect(X!26, Y!25, P!27)) | once(at_the_same_time(at(X!26, P!27), at(Y!25, P!27)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 ((~(connect(X!26, Y!25, P!27) <=> once(at_the_same_time(at(X!26, P!27), at(Y!25, P!27))))) | once(at_the_same_time(at(X!26, P!27), at(Y!25, P!27)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 (once(at_the_same_time(at(X!26, P!27), at(Y!25, P!27)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[32, 18])).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 (^[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))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 (![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)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[34])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 (^[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))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 (![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)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[36])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[39])).
% 0.19/0.41 tff(41,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')).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 (![A: $i, B: $i] : ((~once(at_the_same_time(A, B))) | (once(A) & once(B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 (![A: $i, B: $i] : ((~once(at_the_same_time(A, B))) | (once(A) & once(B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.19/0.41 tff(44,plain,(
% 0.19/0.41 ![A: $i, B: $i] : ((~once(at_the_same_time(A, B))) | (once(A) & once(B)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[43])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 (![A: $i, B: $i] : ((~once(at_the_same_time(A, B))) | (~((~once(B)) | (~once(A)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 (![A: $i, B: $i] : ((~once(at_the_same_time(A, B))) | (~((~once(B)) | (~once(A)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[45, 35])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 (((~![A: $i, B: $i] : ((~once(at_the_same_time(A, B))) | (~((~once(B)) | (~once(A)))))) | ((~once(at_the_same_time(at(X!26, P!27), at(Y!25, P!27)))) | (~((~once(at(Y!25, P!27))) | (~once(at(X!26, P!27))))))) <=> ((~![A: $i, B: $i] : ((~once(at_the_same_time(A, B))) | (~((~once(B)) | (~once(A)))))) | (~once(at_the_same_time(at(X!26, P!27), at(Y!25, P!27)))) | (~((~once(at(Y!25, P!27))) | (~once(at(X!26, P!27))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : ((~once(at_the_same_time(A, B))) | (~((~once(B)) | (~once(A)))))) | ((~once(at_the_same_time(at(X!26, P!27), at(Y!25, P!27)))) | (~((~once(at(Y!25, P!27))) | (~once(at(X!26, P!27))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : ((~once(at_the_same_time(A, B))) | (~((~once(B)) | (~once(A)))))) | (~once(at_the_same_time(at(X!26, P!27), at(Y!25, P!27)))) | (~((~once(at(Y!25, P!27))) | (~once(at(X!26, P!27)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 (~((~once(at(Y!25, P!27))) | (~once(at(X!26, P!27))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[49, 46, 33])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (((~once(at(Y!25, P!27))) | (~once(at(X!26, P!27)))) | once(at(Y!25, P!27))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 (once(at(Y!25, P!27))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 ((~(once(at(Y!25, P!27)) <=> incident_o(P!27, trajectory_of(Y!25)))) | (~once(at(Y!25, P!27))) | incident_o(P!27, trajectory_of(Y!25))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 (incident_o(P!27, trajectory_of(Y!25))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[53, 52, 9])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 ((~![X: $i, P: $i] : (once(at(X, P)) <=> incident_o(P, trajectory_of(X)))) | (once(at(X!26, P!27)) <=> incident_o(P!27, trajectory_of(X!26)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 (once(at(X!26, P!27)) <=> incident_o(P!27, trajectory_of(X!26))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[55, 7])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 (((~once(at(Y!25, P!27))) | (~once(at(X!26, P!27)))) | once(at(X!26, P!27))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 (once(at(X!26, P!27))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[57, 50])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 ((~(once(at(X!26, P!27)) <=> incident_o(P!27, trajectory_of(X!26)))) | (~once(at(X!26, P!27))) | incident_o(P!27, trajectory_of(X!26))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 (incident_o(P!27, trajectory_of(X!26))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[59, 58, 56])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 ((~(~((~incident_o(P!27, trajectory_of(X!26))) | (~incident_o(P!27, trajectory_of(Y!25)))))) <=> ((~incident_o(P!27, trajectory_of(X!26))) | (~incident_o(P!27, trajectory_of(Y!25))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 ((incident_o(P!27, trajectory_of(X!26)) & incident_o(P!27, trajectory_of(Y!25))) <=> (~((~incident_o(P!27, trajectory_of(X!26))) | (~incident_o(P!27, trajectory_of(Y!25)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 ((~(incident_o(P!27, trajectory_of(X!26)) & incident_o(P!27, trajectory_of(Y!25)))) <=> (~(~((~incident_o(P!27, trajectory_of(X!26))) | (~incident_o(P!27, trajectory_of(Y!25))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[62])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 ((~(incident_o(P!27, trajectory_of(X!26)) & incident_o(P!27, trajectory_of(Y!25)))) <=> ((~incident_o(P!27, trajectory_of(X!26))) | (~incident_o(P!27, trajectory_of(Y!25))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[63, 61])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 (~(incident_o(P!27, trajectory_of(X!26)) & incident_o(P!27, trajectory_of(Y!25)))),
% 0.19/0.41 inference(or_elim,[status(thm)],[29])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 ((~incident_o(P!27, trajectory_of(X!26))) | (~incident_o(P!27, trajectory_of(Y!25)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[66, 60, 54])).
% 0.19/0.41 % SZS output end Proof
%------------------------------------------------------------------------------