TSTP Solution File: GEO265+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO265+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 20:36:11 EDT 2022
% Result : Theorem 0.11s 0.38s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GEO265+3 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n009.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Wed Aug 31 07:10:35 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.32 Usage: tptp [options] [-file:]file
% 0.11/0.32 -h, -? prints this message.
% 0.11/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.32 -m, -model generate model.
% 0.11/0.32 -p, -proof generate proof.
% 0.11/0.32 -c, -core generate unsat core of named formulas.
% 0.11/0.32 -st, -statistics display statistics.
% 0.11/0.32 -t:timeout set timeout (in second).
% 0.11/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.32 -<param>:<value> configuration parameter and value.
% 0.11/0.32 -o:<output-file> file to place output in.
% 0.11/0.38 % SZS status Theorem
% 0.11/0.38 % SZS output start Proof
% 0.11/0.38 tff(unequally_directed_lines_type, type, (
% 0.11/0.38 unequally_directed_lines: ( $i * $i ) > $o)).
% 0.11/0.38 tff(reverse_line_type, type, (
% 0.11/0.38 reverse_line: $i > $i)).
% 0.11/0.38 tff(tptp_fun_M_0_type, type, (
% 0.11/0.38 tptp_fun_M_0: $i)).
% 0.11/0.38 tff(tptp_fun_L_1_type, type, (
% 0.11/0.38 tptp_fun_L_1: $i)).
% 0.11/0.38 tff(unequally_directed_opposite_lines_type, type, (
% 0.11/0.38 unequally_directed_opposite_lines: ( $i * $i ) > $o)).
% 0.11/0.38 tff(equally_directed_opposite_lines_type, type, (
% 0.11/0.38 equally_directed_opposite_lines: ( $i * $i ) > $o)).
% 0.11/0.38 tff(equally_directed_lines_type, type, (
% 0.11/0.38 equally_directed_lines: ( $i * $i ) > $o)).
% 0.11/0.38 tff(1,plain,
% 0.11/0.38 (^[X: $i, Y: $i] : refl((equally_directed_opposite_lines(X, Y) <=> (~unequally_directed_opposite_lines(X, Y))) <=> (equally_directed_opposite_lines(X, Y) <=> (~unequally_directed_opposite_lines(X, Y))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(2,plain,
% 0.11/0.38 (![X: $i, Y: $i] : (equally_directed_opposite_lines(X, Y) <=> (~unequally_directed_opposite_lines(X, Y))) <=> ![X: $i, Y: $i] : (equally_directed_opposite_lines(X, Y) <=> (~unequally_directed_opposite_lines(X, Y)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.38 tff(3,plain,
% 0.11/0.38 (![X: $i, Y: $i] : (equally_directed_opposite_lines(X, Y) <=> (~unequally_directed_opposite_lines(X, Y))) <=> ![X: $i, Y: $i] : (equally_directed_opposite_lines(X, Y) <=> (~unequally_directed_opposite_lines(X, Y)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(4,axiom,(![X: $i, Y: $i] : (equally_directed_opposite_lines(X, Y) <=> (~unequally_directed_opposite_lines(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','a5_defns')).
% 0.11/0.38 tff(5,plain,
% 0.11/0.38 (![X: $i, Y: $i] : (equally_directed_opposite_lines(X, Y) <=> (~unequally_directed_opposite_lines(X, Y)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.11/0.38 tff(6,plain,(
% 0.11/0.38 ![X: $i, Y: $i] : (equally_directed_opposite_lines(X, Y) <=> (~unequally_directed_opposite_lines(X, Y)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[5])).
% 0.11/0.38 tff(7,plain,
% 0.11/0.38 (![X: $i, Y: $i] : (equally_directed_opposite_lines(X, Y) <=> (~unequally_directed_opposite_lines(X, Y)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.11/0.38 tff(8,plain,
% 0.11/0.38 ((~![X: $i, Y: $i] : (equally_directed_opposite_lines(X, Y) <=> (~unequally_directed_opposite_lines(X, Y)))) | (equally_directed_opposite_lines(L!1, M!0) <=> (~unequally_directed_opposite_lines(L!1, M!0)))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(9,plain,
% 0.11/0.38 (equally_directed_opposite_lines(L!1, M!0) <=> (~unequally_directed_opposite_lines(L!1, M!0))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.11/0.38 tff(10,plain,
% 0.11/0.38 ((~![L: $i, M: $i] : ((~equally_directed_lines(L, reverse_line(M))) | equally_directed_opposite_lines(L, M))) <=> (~![L: $i, M: $i] : ((~equally_directed_lines(L, reverse_line(M))) | equally_directed_opposite_lines(L, M)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(11,plain,
% 0.11/0.38 ((~![L: $i, M: $i] : (equally_directed_lines(L, reverse_line(M)) => equally_directed_opposite_lines(L, M))) <=> (~![L: $i, M: $i] : ((~equally_directed_lines(L, reverse_line(M))) | equally_directed_opposite_lines(L, M)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(12,axiom,(~![L: $i, M: $i] : (equally_directed_lines(L, reverse_line(M)) => equally_directed_opposite_lines(L, M))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.11/0.38 tff(13,plain,
% 0.11/0.38 (~![L: $i, M: $i] : ((~equally_directed_lines(L, reverse_line(M))) | equally_directed_opposite_lines(L, M))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.11/0.38 tff(14,plain,
% 0.11/0.38 (~![L: $i, M: $i] : ((~equally_directed_lines(L, reverse_line(M))) | equally_directed_opposite_lines(L, M))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.11/0.38 tff(15,plain,
% 0.11/0.38 (~![L: $i, M: $i] : ((~equally_directed_lines(L, reverse_line(M))) | equally_directed_opposite_lines(L, M))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.11/0.38 tff(16,plain,
% 0.11/0.38 (~![L: $i, M: $i] : ((~equally_directed_lines(L, reverse_line(M))) | equally_directed_opposite_lines(L, M))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.11/0.38 tff(17,plain,
% 0.11/0.38 (~![L: $i, M: $i] : ((~equally_directed_lines(L, reverse_line(M))) | equally_directed_opposite_lines(L, M))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[16, 10])).
% 0.11/0.38 tff(18,plain,
% 0.11/0.38 (~![L: $i, M: $i] : ((~equally_directed_lines(L, reverse_line(M))) | equally_directed_opposite_lines(L, M))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.11/0.38 tff(19,plain,
% 0.11/0.38 (~![L: $i, M: $i] : ((~equally_directed_lines(L, reverse_line(M))) | equally_directed_opposite_lines(L, M))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[18, 10])).
% 0.11/0.38 tff(20,plain,(
% 0.11/0.38 ~((~equally_directed_lines(L!1, reverse_line(M!0))) | equally_directed_opposite_lines(L!1, M!0))),
% 0.11/0.38 inference(skolemize,[status(sab)],[19])).
% 0.11/0.38 tff(21,plain,
% 0.11/0.38 (~equally_directed_opposite_lines(L!1, M!0)),
% 0.11/0.38 inference(or_elim,[status(thm)],[20])).
% 0.11/0.38 tff(22,plain,
% 0.11/0.38 ((~(equally_directed_opposite_lines(L!1, M!0) <=> (~unequally_directed_opposite_lines(L!1, M!0)))) | equally_directed_opposite_lines(L!1, M!0) | unequally_directed_opposite_lines(L!1, M!0)),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(23,plain,
% 0.11/0.38 ((~(equally_directed_opposite_lines(L!1, M!0) <=> (~unequally_directed_opposite_lines(L!1, M!0)))) | unequally_directed_opposite_lines(L!1, M!0)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.11/0.38 tff(24,plain,
% 0.11/0.38 (unequally_directed_opposite_lines(L!1, M!0)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[23, 9])).
% 0.11/0.38 tff(25,plain,
% 0.11/0.38 (^[X: $i, Y: $i] : refl((equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y))) <=> (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(26,plain,
% 0.11/0.38 (![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y))) <=> ![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[25])).
% 0.11/0.38 tff(27,plain,
% 0.11/0.38 (![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y))) <=> ![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(28,axiom,(![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','a4_defns')).
% 0.11/0.38 tff(29,plain,
% 0.11/0.38 (![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.11/0.38 tff(30,plain,(
% 0.11/0.38 ![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[29])).
% 0.11/0.38 tff(31,plain,
% 0.11/0.38 (![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.11/0.38 tff(32,plain,
% 0.11/0.38 ((~![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y)))) | (equally_directed_lines(L!1, reverse_line(M!0)) <=> (~unequally_directed_lines(L!1, reverse_line(M!0))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(33,plain,
% 0.11/0.38 (equally_directed_lines(L!1, reverse_line(M!0)) <=> (~unequally_directed_lines(L!1, reverse_line(M!0)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.11/0.38 tff(34,plain,
% 0.11/0.38 (equally_directed_lines(L!1, reverse_line(M!0))),
% 0.11/0.38 inference(or_elim,[status(thm)],[20])).
% 0.11/0.38 tff(35,plain,
% 0.11/0.38 ((~(equally_directed_lines(L!1, reverse_line(M!0)) <=> (~unequally_directed_lines(L!1, reverse_line(M!0))))) | (~equally_directed_lines(L!1, reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(M!0)))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(36,plain,
% 0.11/0.38 ((~(equally_directed_lines(L!1, reverse_line(M!0)) <=> (~unequally_directed_lines(L!1, reverse_line(M!0))))) | (~unequally_directed_lines(L!1, reverse_line(M!0)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.11/0.38 tff(37,plain,
% 0.11/0.38 (~unequally_directed_lines(L!1, reverse_line(M!0))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[36, 33])).
% 0.11/0.38 tff(38,plain,
% 0.11/0.38 ((~(unequally_directed_opposite_lines(L!1, M!0) <=> unequally_directed_lines(L!1, reverse_line(M!0)))) | (~unequally_directed_opposite_lines(L!1, M!0)) | unequally_directed_lines(L!1, reverse_line(M!0))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(39,plain,
% 0.11/0.38 (~(unequally_directed_opposite_lines(L!1, M!0) <=> unequally_directed_lines(L!1, reverse_line(M!0)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[38, 37, 24])).
% 0.11/0.38 tff(40,plain,
% 0.11/0.38 (^[X: $i, Y: $i] : refl((unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y))) <=> (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(41,plain,
% 0.11/0.38 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y))) <=> ![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[40])).
% 0.11/0.38 tff(42,plain,
% 0.11/0.38 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y))) <=> ![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(43,axiom,(![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','a1_defns')).
% 0.11/0.38 tff(44,plain,
% 0.11/0.38 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.11/0.38 tff(45,plain,(
% 0.11/0.38 ![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[44])).
% 0.11/0.38 tff(46,plain,
% 0.11/0.38 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.11/0.38 tff(47,plain,
% 0.11/0.38 ((~![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))) | (unequally_directed_opposite_lines(L!1, M!0) <=> unequally_directed_lines(L!1, reverse_line(M!0)))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(48,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[47, 46, 39])).
% 0.11/0.38 % SZS output end Proof
%------------------------------------------------------------------------------