TSTP Solution File: GEO248+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO248+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 20:36:03 EDT 2022
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEO248+3 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 06:55:01 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(left_apart_point_type, type, (
% 0.13/0.40 left_apart_point: ( $i * $i ) > $o)).
% 0.13/0.40 tff(reverse_line_type, type, (
% 0.13/0.40 reverse_line: $i > $i)).
% 0.13/0.40 tff(tptp_fun_L_0_type, type, (
% 0.13/0.40 tptp_fun_L_0: $i)).
% 0.13/0.40 tff(tptp_fun_A_2_type, type, (
% 0.13/0.40 tptp_fun_A_2: $i)).
% 0.13/0.40 tff(right_apart_point_type, type, (
% 0.13/0.40 right_apart_point: ( $i * $i ) > $o)).
% 0.13/0.40 tff(apart_point_and_line_type, type, (
% 0.13/0.40 apart_point_and_line: ( $i * $i ) > $o)).
% 0.13/0.40 tff(incident_point_and_line_type, type, (
% 0.13/0.40 incident_point_and_line: ( $i * $i ) > $o)).
% 0.13/0.40 tff(parallel_lines_type, type, (
% 0.13/0.40 parallel_lines: ( $i * $i ) > $i)).
% 0.13/0.40 tff(tptp_fun_B_1_type, type, (
% 0.13/0.40 tptp_fun_B_1: $i)).
% 0.13/0.40 tff(1,assumption,(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0))), introduced(assumption)).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 (^[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)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 (![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))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.13/0.40 tff(4,plain,
% 0.13/0.40 (![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))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(5,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')).
% 0.13/0.40 tff(6,plain,
% 0.13/0.40 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.13/0.40 tff(7,plain,(
% 0.13/0.40 ![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[6])).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 ((~![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.13/0.40 tff(11,plain,(~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 ((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0))) | (~left_apart_point(A!2, reverse_line(L!0)))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 (~left_apart_point(A!2, reverse_line(L!0))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 ((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0))) | (~left_apart_point(A!2, L!0))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (~left_apart_point(A!2, L!0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[14, 11])).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 (^[A: $i, L: $i] : refl((apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L))) <=> (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L))) <=> ![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[16])).
% 0.13/0.40 tff(18,plain,
% 0.13/0.40 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L))) <=> ![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(19,axiom,(![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','a6_defns')).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.13/0.40 tff(21,plain,(
% 0.13/0.40 ![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[20])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 ((~![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))) | (apart_point_and_line(A!2, L!0) <=> (left_apart_point(A!2, L!0) | right_apart_point(A!2, L!0)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 (apart_point_and_line(A!2, L!0) <=> (left_apart_point(A!2, L!0) | right_apart_point(A!2, L!0))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 ((~![A: $i, B: $i, L: $i] : ((~(apart_point_and_line(A, L) & incident_point_and_line(B, parallel_lines(L, A)))) | apart_point_and_line(B, L))) <=> (~![A: $i, B: $i, L: $i] : ((~(apart_point_and_line(A, L) & incident_point_and_line(B, parallel_lines(L, A)))) | apart_point_and_line(B, L)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(26,plain,
% 0.13/0.41 ((~![A: $i, B: $i, L: $i] : ((apart_point_and_line(A, L) & incident_point_and_line(B, parallel_lines(L, A))) => apart_point_and_line(B, L))) <=> (~![A: $i, B: $i, L: $i] : ((~(apart_point_and_line(A, L) & incident_point_and_line(B, parallel_lines(L, A)))) | apart_point_and_line(B, L)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(27,axiom,(~![A: $i, B: $i, L: $i] : ((apart_point_and_line(A, L) & incident_point_and_line(B, parallel_lines(L, A))) => apart_point_and_line(B, L))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.13/0.41 tff(28,plain,
% 0.13/0.41 (~![A: $i, B: $i, L: $i] : ((~(apart_point_and_line(A, L) & incident_point_and_line(B, parallel_lines(L, A)))) | apart_point_and_line(B, L))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.13/0.41 tff(29,plain,
% 0.13/0.41 (~![A: $i, B: $i, L: $i] : ((~(apart_point_and_line(A, L) & incident_point_and_line(B, parallel_lines(L, A)))) | apart_point_and_line(B, L))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[28, 25])).
% 0.13/0.41 tff(30,plain,
% 0.13/0.41 (~![A: $i, B: $i, L: $i] : ((~(apart_point_and_line(A, L) & incident_point_and_line(B, parallel_lines(L, A)))) | apart_point_and_line(B, L))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.13/0.41 tff(31,plain,
% 0.13/0.41 (~![A: $i, B: $i, L: $i] : ((~(apart_point_and_line(A, L) & incident_point_and_line(B, parallel_lines(L, A)))) | apart_point_and_line(B, L))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[30, 25])).
% 0.13/0.41 tff(32,plain,
% 0.13/0.41 (~![A: $i, B: $i, L: $i] : ((~(apart_point_and_line(A, L) & incident_point_and_line(B, parallel_lines(L, A)))) | apart_point_and_line(B, L))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[31, 25])).
% 0.13/0.41 tff(33,plain,
% 0.13/0.41 (~![A: $i, B: $i, L: $i] : ((~(apart_point_and_line(A, L) & incident_point_and_line(B, parallel_lines(L, A)))) | apart_point_and_line(B, L))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.13/0.41 tff(34,plain,
% 0.13/0.41 (~![A: $i, B: $i, L: $i] : ((~(apart_point_and_line(A, L) & incident_point_and_line(B, parallel_lines(L, A)))) | apart_point_and_line(B, L))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[33, 25])).
% 0.13/0.41 tff(35,plain,(
% 0.13/0.41 ~((~(apart_point_and_line(A!2, L!0) & incident_point_and_line(B!1, parallel_lines(L!0, A!2)))) | apart_point_and_line(B!1, L!0))),
% 0.13/0.41 inference(skolemize,[status(sab)],[34])).
% 0.13/0.41 tff(36,plain,
% 0.13/0.41 (apart_point_and_line(A!2, L!0) & incident_point_and_line(B!1, parallel_lines(L!0, A!2))),
% 0.13/0.41 inference(or_elim,[status(thm)],[35])).
% 0.13/0.41 tff(37,plain,
% 0.13/0.41 (apart_point_and_line(A!2, L!0)),
% 0.13/0.41 inference(and_elim,[status(thm)],[36])).
% 0.13/0.41 tff(38,plain,
% 0.13/0.41 ((~(apart_point_and_line(A!2, L!0) <=> (left_apart_point(A!2, L!0) | right_apart_point(A!2, L!0)))) | (~apart_point_and_line(A!2, L!0)) | (left_apart_point(A!2, L!0) | right_apart_point(A!2, L!0))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(39,plain,
% 0.13/0.41 ((~(apart_point_and_line(A!2, L!0) <=> (left_apart_point(A!2, L!0) | right_apart_point(A!2, L!0)))) | (left_apart_point(A!2, L!0) | right_apart_point(A!2, L!0))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.13/0.41 tff(40,plain,
% 0.13/0.41 (left_apart_point(A!2, L!0) | right_apart_point(A!2, L!0)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[39, 24])).
% 0.13/0.41 tff(41,plain,
% 0.13/0.41 ((~(left_apart_point(A!2, L!0) | right_apart_point(A!2, L!0))) | left_apart_point(A!2, L!0) | right_apart_point(A!2, L!0)),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(42,plain,
% 0.13/0.41 (left_apart_point(A!2, L!0) | right_apart_point(A!2, L!0)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.13/0.41 tff(43,plain,
% 0.13/0.41 (right_apart_point(A!2, L!0)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[42, 15])).
% 0.13/0.41 tff(44,plain,
% 0.13/0.41 ((~(right_apart_point(A!2, L!0) <=> left_apart_point(A!2, reverse_line(L!0)))) | (~right_apart_point(A!2, L!0)) | left_apart_point(A!2, reverse_line(L!0))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(45,plain,
% 0.13/0.41 (~(right_apart_point(A!2, L!0) <=> left_apart_point(A!2, reverse_line(L!0)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[44, 43, 13])).
% 0.13/0.41 tff(46,plain,
% 0.13/0.41 (^[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))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(47,plain,
% 0.13/0.41 (![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)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[46])).
% 0.13/0.41 tff(48,plain,
% 0.13/0.41 (![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)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(49,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')).
% 0.13/0.41 tff(50,plain,
% 0.13/0.41 (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.13/0.41 tff(51,plain,(
% 0.13/0.41 ![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.13/0.41 inference(skolemize,[status(sab)],[50])).
% 0.13/0.41 tff(52,plain,
% 0.13/0.41 (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.13/0.41 tff(53,plain,
% 0.13/0.41 ((~![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))) | (right_apart_point(A!2, L!0) <=> left_apart_point(A!2, reverse_line(L!0)))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(54,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[53, 52, 45])).
% 0.13/0.41 % SZS output end Proof
%------------------------------------------------------------------------------