TSTP Solution File: GEO236+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO236+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 20:35:58 EDT 2022
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GEO236+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n012.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 07:06:50 EDT 2022
% 0.12/0.34 % 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.
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(left_apart_point_type, type, (
% 0.12/0.39 left_apart_point: ( $i * $i ) > $o)).
% 0.12/0.39 tff(reverse_line_type, type, (
% 0.12/0.39 reverse_line: $i > $i)).
% 0.12/0.39 tff(tptp_fun_M_0_type, type, (
% 0.12/0.39 tptp_fun_M_0: $i)).
% 0.12/0.39 tff(tptp_fun_A_2_type, type, (
% 0.12/0.39 tptp_fun_A_2: $i)).
% 0.12/0.39 tff(right_apart_point_type, type, (
% 0.12/0.39 right_apart_point: ( $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_L_1_type, type, (
% 0.12/0.39 tptp_fun_L_1: $i)).
% 0.12/0.39 tff(distinct_lines_type, type, (
% 0.12/0.39 distinct_lines: ( $i * $i ) > $o)).
% 0.12/0.39 tff(unequally_directed_lines_type, type, (
% 0.12/0.39 unequally_directed_lines: ( $i * $i ) > $o)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 (^[X: $i, Y: $i] : refl((right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y))) <=> (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y))) <=> ![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y))) <=> ![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(4,axiom,(![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','a2_defns')).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.39 tff(6,plain,(
% 0.12/0.39 ![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[5])).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 ((~![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))) | (right_apart_point(A!2, M!0) <=> left_apart_point(A!2, reverse_line(M!0)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (right_apart_point(A!2, M!0) <=> left_apart_point(A!2, reverse_line(M!0))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 ((~(unequally_directed_lines(L!1, M!0) | distinct_lines(L!1, M!0) | (~(left_apart_point(A!2, L!1) & right_apart_point(A!2, M!0))))) <=> (~(unequally_directed_lines(L!1, M!0) | distinct_lines(L!1, M!0) | (~(left_apart_point(A!2, L!1) & right_apart_point(A!2, M!0)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 ((~![A: $i, L: $i, M: $i] : (unequally_directed_lines(L, M) | distinct_lines(L, M) | (~(left_apart_point(A, L) & right_apart_point(A, M))))) <=> (~![A: $i, L: $i, M: $i] : (unequally_directed_lines(L, M) | distinct_lines(L, M) | (~(left_apart_point(A, L) & right_apart_point(A, M)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 ((~![A: $i, L: $i, M: $i] : ((left_apart_point(A, L) & right_apart_point(A, M)) => (unequally_directed_lines(L, M) | distinct_lines(L, M)))) <=> (~![A: $i, L: $i, M: $i] : (unequally_directed_lines(L, M) | distinct_lines(L, M) | (~(left_apart_point(A, L) & right_apart_point(A, M)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(13,axiom,(~![A: $i, L: $i, M: $i] : ((left_apart_point(A, L) & right_apart_point(A, M)) => (unequally_directed_lines(L, M) | distinct_lines(L, M)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (~![A: $i, L: $i, M: $i] : (unequally_directed_lines(L, M) | distinct_lines(L, M) | (~(left_apart_point(A, L) & right_apart_point(A, M))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (~![A: $i, L: $i, M: $i] : (unequally_directed_lines(L, M) | distinct_lines(L, M) | (~(left_apart_point(A, L) & right_apart_point(A, M))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (~![A: $i, L: $i, M: $i] : (unequally_directed_lines(L, M) | distinct_lines(L, M) | (~(left_apart_point(A, L) & right_apart_point(A, M))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.12/0.40 tff(17,plain,
% 0.12/0.40 (~![A: $i, L: $i, M: $i] : (unequally_directed_lines(L, M) | distinct_lines(L, M) | (~(left_apart_point(A, L) & right_apart_point(A, M))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.12/0.40 tff(18,plain,
% 0.12/0.40 (~![A: $i, L: $i, M: $i] : (unequally_directed_lines(L, M) | distinct_lines(L, M) | (~(left_apart_point(A, L) & right_apart_point(A, M))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[17, 11])).
% 0.12/0.40 tff(19,plain,
% 0.12/0.40 (~![A: $i, L: $i, M: $i] : (unequally_directed_lines(L, M) | distinct_lines(L, M) | (~(left_apart_point(A, L) & right_apart_point(A, M))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.12/0.40 tff(20,plain,
% 0.12/0.40 (~![A: $i, L: $i, M: $i] : (unequally_directed_lines(L, M) | distinct_lines(L, M) | (~(left_apart_point(A, L) & right_apart_point(A, M))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[19, 11])).
% 0.12/0.40 tff(21,plain,(
% 0.12/0.40 ~(unequally_directed_lines(L!1, M!0) | distinct_lines(L!1, M!0) | (~(left_apart_point(A!2, L!1) & right_apart_point(A!2, M!0))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[20])).
% 0.12/0.40 tff(22,plain,
% 0.12/0.40 (~(unequally_directed_lines(L!1, M!0) | distinct_lines(L!1, M!0) | (~(left_apart_point(A!2, L!1) & right_apart_point(A!2, M!0))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[21, 10])).
% 0.12/0.40 tff(23,plain,
% 0.12/0.40 (left_apart_point(A!2, L!1) & right_apart_point(A!2, M!0)),
% 0.12/0.40 inference(or_elim,[status(thm)],[22])).
% 0.12/0.40 tff(24,plain,
% 0.12/0.40 (right_apart_point(A!2, M!0)),
% 0.12/0.40 inference(and_elim,[status(thm)],[23])).
% 0.12/0.40 tff(25,plain,
% 0.12/0.40 ((~(right_apart_point(A!2, M!0) <=> left_apart_point(A!2, reverse_line(M!0)))) | (~right_apart_point(A!2, M!0)) | left_apart_point(A!2, reverse_line(M!0))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(26,plain,
% 0.12/0.40 ((~(right_apart_point(A!2, M!0) <=> left_apart_point(A!2, reverse_line(M!0)))) | left_apart_point(A!2, reverse_line(M!0))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.12/0.40 tff(27,plain,
% 0.12/0.40 (left_apart_point(A!2, reverse_line(M!0))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[26, 9])).
% 0.12/0.40 tff(28,plain,
% 0.12/0.40 ((left_apart_point(A!2, M!0) | left_apart_point(A!2, reverse_line(M!0))) | (~left_apart_point(A!2, reverse_line(M!0)))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(29,plain,
% 0.12/0.40 (left_apart_point(A!2, M!0) | left_apart_point(A!2, reverse_line(M!0))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.12/0.40 tff(30,plain,
% 0.12/0.40 (^[A: $i, L: $i] : refl((~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) <=> (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(31,plain,
% 0.12/0.40 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) <=> ![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[30])).
% 0.12/0.40 tff(32,plain,
% 0.12/0.40 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) <=> ![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(33,axiom,(![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','ax10_basics')).
% 0.12/0.40 tff(34,plain,
% 0.12/0.40 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.12/0.40 tff(35,plain,(
% 0.12/0.40 ![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[34])).
% 0.12/0.40 tff(36,plain,
% 0.12/0.40 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.12/0.40 tff(37,plain,
% 0.12/0.40 ((~![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (~(left_apart_point(A!2, M!0) | left_apart_point(A!2, reverse_line(M!0))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(38,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[37, 36, 29])).
% 0.12/0.40 % SZS output end Proof
%------------------------------------------------------------------------------