TSTP Solution File: GEO146+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO146+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 20:35:06 EDT 2022
% Result : Theorem 0.18s 0.44s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.15 % Problem : GEO146+1 : TPTP v8.1.0. Released v2.4.0.
% 0.13/0.15 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 31 06:25:20 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 0.18/0.44 % SZS status Theorem
% 0.18/0.44 % SZS output start Proof
% 0.18/0.44 tff(once_type, type, (
% 0.18/0.44 once: $i > $o)).
% 0.18/0.44 tff(at_the_same_time_type, type, (
% 0.18/0.44 at_the_same_time: ( $i * $i ) > $i)).
% 0.18/0.44 tff(at_type, type, (
% 0.18/0.44 at: ( $i * $i ) > $i)).
% 0.18/0.44 tff(tptp_fun_P_25_type, type, (
% 0.18/0.44 tptp_fun_P_25: $i)).
% 0.18/0.44 tff(tptp_fun_X_27_type, type, (
% 0.18/0.44 tptp_fun_X_27: $i)).
% 0.18/0.44 tff(tptp_fun_Y_26_type, type, (
% 0.18/0.44 tptp_fun_Y_26: $i)).
% 0.18/0.44 tff(connect_type, type, (
% 0.18/0.44 connect: ( $i * $i * $i ) > $o)).
% 0.18/0.44 tff(1,assumption,(~connect(Y!26, X!27, P!25)), introduced(assumption)).
% 0.18/0.44 tff(2,plain,
% 0.18/0.44 (^[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)))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(3,plain,
% 0.18/0.44 (![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))))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[2])).
% 0.18/0.44 tff(4,plain,
% 0.18/0.44 (![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))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 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')).
% 0.18/0.44 tff(6,plain,
% 0.18/0.44 (![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> once(at_the_same_time(at(X, P), at(Y, P))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.18/0.44 tff(7,plain,(
% 0.18/0.44 ![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> once(at_the_same_time(at(X, P), at(Y, P))))),
% 0.18/0.44 inference(skolemize,[status(sab)],[6])).
% 0.18/0.44 tff(8,plain,
% 0.18/0.44 (![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> once(at_the_same_time(at(X, P), at(Y, P))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.18/0.44 tff(9,plain,
% 0.18/0.44 ((~![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> once(at_the_same_time(at(X, P), at(Y, P))))) | (connect(Y!26, X!27, P!25) <=> once(at_the_same_time(at(Y!26, P!25), at(X!27, P!25))))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(10,plain,
% 0.18/0.44 (connect(Y!26, X!27, P!25) <=> once(at_the_same_time(at(Y!26, P!25), at(X!27, P!25)))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.18/0.44 tff(11,plain,
% 0.18/0.44 ((~(connect(Y!26, X!27, P!25) <=> once(at_the_same_time(at(Y!26, P!25), at(X!27, P!25))))) | connect(Y!26, X!27, P!25) | (~once(at_the_same_time(at(Y!26, P!25), at(X!27, P!25))))),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(12,plain,
% 0.18/0.44 (connect(Y!26, X!27, P!25) | (~once(at_the_same_time(at(Y!26, P!25), at(X!27, P!25))))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.18/0.44 tff(13,plain,
% 0.18/0.44 (~once(at_the_same_time(at(Y!26, P!25), at(X!27, P!25)))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[12, 1])).
% 0.18/0.44 tff(14,plain,
% 0.18/0.44 ((~(connect(X!27, Y!26, P!25) <=> connect(Y!26, X!27, P!25))) <=> ((~connect(X!27, Y!26, P!25)) <=> connect(Y!26, X!27, P!25))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(15,plain,
% 0.18/0.44 ((~![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)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 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')).
% 0.18/0.44 tff(17,plain,
% 0.18/0.44 (~![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> connect(Y, X, P))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.18/0.44 tff(18,plain,
% 0.18/0.44 (~![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> connect(Y, X, P))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[17, 15])).
% 0.18/0.44 tff(19,plain,
% 0.18/0.44 (~![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> connect(Y, X, P))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[18, 15])).
% 0.18/0.44 tff(20,plain,
% 0.18/0.44 (~![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> connect(Y, X, P))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.18/0.44 tff(21,plain,
% 0.18/0.44 (~![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> connect(Y, X, P))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[20, 15])).
% 0.18/0.44 tff(22,plain,
% 0.18/0.44 (~![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> connect(Y, X, P))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[21, 15])).
% 0.18/0.44 tff(23,plain,
% 0.18/0.44 (~![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> connect(Y, X, P))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.18/0.44 tff(24,plain,(
% 0.18/0.44 ~(connect(X!27, Y!26, P!25) <=> connect(Y!26, X!27, P!25))),
% 0.18/0.44 inference(skolemize,[status(sab)],[23])).
% 0.18/0.44 tff(25,plain,
% 0.18/0.44 ((~connect(X!27, Y!26, P!25)) <=> connect(Y!26, X!27, P!25)),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[24, 14])).
% 0.18/0.44 tff(26,plain,
% 0.18/0.44 (connect(X!27, Y!26, P!25) | connect(Y!26, X!27, P!25) | (~((~connect(X!27, Y!26, P!25)) <=> connect(Y!26, X!27, P!25)))),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(27,plain,
% 0.18/0.44 (connect(X!27, Y!26, P!25) | connect(Y!26, X!27, P!25)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.18/0.44 tff(28,plain,
% 0.18/0.44 (connect(X!27, Y!26, P!25)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[27, 1])).
% 0.18/0.44 tff(29,plain,
% 0.18/0.44 ((~![X: $i, Y: $i, P: $i] : (connect(X, Y, P) <=> once(at_the_same_time(at(X, P), at(Y, P))))) | (connect(X!27, Y!26, P!25) <=> once(at_the_same_time(at(X!27, P!25), at(Y!26, P!25))))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(30,plain,
% 0.18/0.44 (connect(X!27, Y!26, P!25) <=> once(at_the_same_time(at(X!27, P!25), at(Y!26, P!25)))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[29, 8])).
% 0.18/0.44 tff(31,plain,
% 0.18/0.44 ((~(connect(X!27, Y!26, P!25) <=> once(at_the_same_time(at(X!27, P!25), at(Y!26, P!25))))) | (~connect(X!27, Y!26, P!25)) | once(at_the_same_time(at(X!27, P!25), at(Y!26, P!25)))),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(32,plain,
% 0.18/0.44 ((~connect(X!27, Y!26, P!25)) | once(at_the_same_time(at(X!27, P!25), at(Y!26, P!25)))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.18/0.44 tff(33,plain,
% 0.18/0.44 (once(at_the_same_time(at(X!27, P!25), at(Y!26, P!25)))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[32, 28])).
% 0.18/0.44 tff(34,plain,
% 0.18/0.44 (^[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))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(35,plain,
% 0.18/0.44 (![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)))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[34])).
% 0.18/0.44 tff(36,plain,
% 0.18/0.44 (![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)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(37,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')).
% 0.18/0.44 tff(38,plain,
% 0.18/0.44 (![A: $i, B: $i] : (once(at_the_same_time(A, B)) <=> once(at_the_same_time(B, A)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.18/0.44 tff(39,plain,(
% 0.18/0.44 ![A: $i, B: $i] : (once(at_the_same_time(A, B)) <=> once(at_the_same_time(B, A)))),
% 0.18/0.44 inference(skolemize,[status(sab)],[38])).
% 0.18/0.44 tff(40,plain,
% 0.18/0.44 (![A: $i, B: $i] : (once(at_the_same_time(A, B)) <=> once(at_the_same_time(B, A)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.18/0.44 tff(41,plain,
% 0.18/0.44 ((~![A: $i, B: $i] : (once(at_the_same_time(A, B)) <=> once(at_the_same_time(B, A)))) | (once(at_the_same_time(at(Y!26, P!25), at(X!27, P!25))) <=> once(at_the_same_time(at(X!27, P!25), at(Y!26, P!25))))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(42,plain,
% 0.18/0.44 (once(at_the_same_time(at(Y!26, P!25), at(X!27, P!25))) <=> once(at_the_same_time(at(X!27, P!25), at(Y!26, P!25)))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.18/0.44 tff(43,plain,
% 0.18/0.44 ((~(once(at_the_same_time(at(Y!26, P!25), at(X!27, P!25))) <=> once(at_the_same_time(at(X!27, P!25), at(Y!26, P!25))))) | once(at_the_same_time(at(Y!26, P!25), at(X!27, P!25))) | (~once(at_the_same_time(at(X!27, P!25), at(Y!26, P!25))))),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(44,plain,
% 0.18/0.44 (once(at_the_same_time(at(Y!26, P!25), at(X!27, P!25))) | (~once(at_the_same_time(at(X!27, P!25), at(Y!26, P!25))))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.18/0.45 tff(45,plain,
% 0.18/0.45 ($false),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[44, 33, 13])).
% 0.18/0.45 tff(46,plain,(connect(Y!26, X!27, P!25)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.45 tff(47,plain,
% 0.18/0.45 ((~(connect(Y!26, X!27, P!25) <=> once(at_the_same_time(at(Y!26, P!25), at(X!27, P!25))))) | (~connect(Y!26, X!27, P!25)) | once(at_the_same_time(at(Y!26, P!25), at(X!27, P!25)))),
% 0.18/0.45 inference(tautology,[status(thm)],[])).
% 0.18/0.45 tff(48,plain,
% 0.18/0.45 ((~connect(Y!26, X!27, P!25)) | once(at_the_same_time(at(Y!26, P!25), at(X!27, P!25)))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[47, 10])).
% 0.18/0.45 tff(49,plain,
% 0.18/0.45 (once(at_the_same_time(at(Y!26, P!25), at(X!27, P!25)))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[48, 46])).
% 0.18/0.45 tff(50,plain,
% 0.18/0.45 ((~connect(X!27, Y!26, P!25)) | (~connect(Y!26, X!27, P!25)) | (~((~connect(X!27, Y!26, P!25)) <=> connect(Y!26, X!27, P!25)))),
% 0.18/0.45 inference(tautology,[status(thm)],[])).
% 0.18/0.45 tff(51,plain,
% 0.18/0.45 ((~connect(X!27, Y!26, P!25)) | (~connect(Y!26, X!27, P!25))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[50, 25])).
% 0.18/0.45 tff(52,plain,
% 0.18/0.45 (~connect(X!27, Y!26, P!25)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[51, 46])).
% 0.18/0.45 tff(53,plain,
% 0.18/0.45 ((~(connect(X!27, Y!26, P!25) <=> once(at_the_same_time(at(X!27, P!25), at(Y!26, P!25))))) | connect(X!27, Y!26, P!25) | (~once(at_the_same_time(at(X!27, P!25), at(Y!26, P!25))))),
% 0.18/0.45 inference(tautology,[status(thm)],[])).
% 0.18/0.45 tff(54,plain,
% 0.18/0.45 (connect(X!27, Y!26, P!25) | (~once(at_the_same_time(at(X!27, P!25), at(Y!26, P!25))))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[53, 30])).
% 0.18/0.45 tff(55,plain,
% 0.18/0.45 (~once(at_the_same_time(at(X!27, P!25), at(Y!26, P!25)))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[54, 52])).
% 0.18/0.45 tff(56,plain,
% 0.18/0.45 ((~(once(at_the_same_time(at(Y!26, P!25), at(X!27, P!25))) <=> once(at_the_same_time(at(X!27, P!25), at(Y!26, P!25))))) | (~once(at_the_same_time(at(Y!26, P!25), at(X!27, P!25)))) | once(at_the_same_time(at(X!27, P!25), at(Y!26, P!25)))),
% 0.18/0.45 inference(tautology,[status(thm)],[])).
% 0.18/0.45 tff(57,plain,
% 0.18/0.45 ((~once(at_the_same_time(at(Y!26, P!25), at(X!27, P!25)))) | once(at_the_same_time(at(X!27, P!25), at(Y!26, P!25)))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[56, 42])).
% 0.18/0.45 tff(58,plain,
% 0.18/0.45 ($false),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[57, 55, 49])).
% 0.18/0.45 % SZS output end Proof
%------------------------------------------------------------------------------