TSTP Solution File: GEO201+3 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GEO201+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n008.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 : 600s
% DateTime : Sat Jul 16 05:54:58 EDT 2022
% Result : Theorem 0.45s 1.05s
% Output : Refutation 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO201+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.32 % Computer : n008.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Sat Jun 18 01:12:07 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.45/1.05 ============================== Prover9 ===============================
% 0.45/1.05 Prover9 (32) version 2009-11A, November 2009.
% 0.45/1.05 Process 24756 was started by sandbox on n008.cluster.edu,
% 0.45/1.05 Sat Jun 18 01:12:08 2022
% 0.45/1.05 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_24590_n008.cluster.edu".
% 0.45/1.05 ============================== end of head ===========================
% 0.45/1.05
% 0.45/1.05 ============================== INPUT =================================
% 0.45/1.05
% 0.45/1.05 % Reading from file /tmp/Prover9_24590_n008.cluster.edu
% 0.45/1.05
% 0.45/1.05 set(prolog_style_variables).
% 0.45/1.05 set(auto2).
% 0.45/1.05 % set(auto2) -> set(auto).
% 0.45/1.05 % set(auto) -> set(auto_inference).
% 0.45/1.05 % set(auto) -> set(auto_setup).
% 0.45/1.05 % set(auto_setup) -> set(predicate_elim).
% 0.45/1.05 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/1.05 % set(auto) -> set(auto_limits).
% 0.45/1.05 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/1.05 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/1.05 % set(auto) -> set(auto_denials).
% 0.45/1.05 % set(auto) -> set(auto_process).
% 0.45/1.05 % set(auto2) -> assign(new_constants, 1).
% 0.45/1.05 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/1.05 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/1.05 % set(auto2) -> assign(max_hours, 1).
% 0.45/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/1.05 % set(auto2) -> assign(max_seconds, 0).
% 0.45/1.05 % set(auto2) -> assign(max_minutes, 5).
% 0.45/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/1.05 % set(auto2) -> set(sort_initial_sos).
% 0.45/1.05 % set(auto2) -> assign(sos_limit, -1).
% 0.45/1.05 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/1.05 % set(auto2) -> assign(max_megs, 400).
% 0.45/1.05 % set(auto2) -> assign(stats, some).
% 0.45/1.05 % set(auto2) -> clear(echo_input).
% 0.45/1.05 % set(auto2) -> set(quiet).
% 0.45/1.05 % set(auto2) -> clear(print_initial_clauses).
% 0.45/1.05 % set(auto2) -> clear(print_given).
% 0.45/1.05 assign(lrs_ticks,-1).
% 0.45/1.05 assign(sos_limit,10000).
% 0.45/1.05 assign(order,kbo).
% 0.45/1.05 set(lex_order_vars).
% 0.45/1.05 clear(print_given).
% 0.45/1.05
% 0.45/1.05 % formulas(sos). % not echoed (36 formulas)
% 0.45/1.05
% 0.45/1.05 ============================== end of input ==========================
% 0.45/1.05
% 0.45/1.05 % From the command line: assign(max_seconds, 300).
% 0.45/1.05
% 0.45/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/1.05
% 0.45/1.05 % Formulas that are not ordinary clauses:
% 0.45/1.05 1 (all X -distinct_points(X,X)) # label(apart1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 2 (all X -distinct_lines(X,X)) # label(apart2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 3 (all X -convergent_lines(X,X)) # label(apart3) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 4 (all X all Y all Z (distinct_points(X,Y) -> distinct_points(X,Z) | distinct_points(Y,Z))) # label(apart4) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 5 (all X all Y all Z (distinct_lines(X,Y) -> distinct_lines(X,Z) | distinct_lines(Y,Z))) # label(apart5) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 6 (all X all Y all Z (convergent_lines(X,Y) -> convergent_lines(X,Z) | convergent_lines(Y,Z))) # label(ax6) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 7 (all X all Y (distinct_points(X,Y) -> -apart_point_and_line(X,line_connecting(X,Y)))) # label(ci1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 8 (all X all Y (distinct_points(X,Y) -> -apart_point_and_line(Y,line_connecting(X,Y)))) # label(ci2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 9 (all X all Y (convergent_lines(X,Y) -> -apart_point_and_line(intersection_point(X,Y),X))) # label(ci3) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 10 (all X all Y (convergent_lines(X,Y) -> -apart_point_and_line(intersection_point(X,Y),Y))) # label(ci4) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 11 (all X all Y all U all V (distinct_points(X,Y) & distinct_lines(U,V) -> apart_point_and_line(X,U) | apart_point_and_line(X,V) | apart_point_and_line(Y,U) | apart_point_and_line(Y,V))) # label(cu1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 12 (all X all Y all Z (apart_point_and_line(X,Y) -> distinct_points(X,Z) | apart_point_and_line(Z,Y))) # label(ceq1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 13 (all X all Y all Z (apart_point_and_line(X,Y) -> distinct_lines(Y,Z) | apart_point_and_line(X,Z))) # label(ceq2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 14 (all X all Y all Z (convergent_lines(X,Y) -> distinct_lines(Y,Z) | convergent_lines(X,Z))) # label(ceq3) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 15 (all X all Y (distinct_lines(X,Y) -> convergent_lines(X,Y))) # label(p1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 16 (all X all Y -convergent_lines(parallel_through_point(Y,X),Y)) # label(cp1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 17 (all X all Y -apart_point_and_line(X,parallel_through_point(Y,X))) # label(cp2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 18 (all X all Y all Z (distinct_lines(Y,Z) -> apart_point_and_line(X,Y) | apart_point_and_line(X,Z) | convergent_lines(Y,Z))) # label(cup1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 19 (all L all M (convergent_lines(L,M) | unorthogonal_lines(L,M))) # label(occu1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 20 (all L all M all N (convergent_lines(L,M) & unorthogonal_lines(L,M) -> convergent_lines(L,N) & unorthogonal_lines(L,N) | convergent_lines(M,N) & unorthogonal_lines(M,N))) # label(oac1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 21 (all A all L -unorthogonal_lines(orthogonal_through_point(L,A),L)) # label(ooc1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 22 (all A all L -apart_point_and_line(A,orthogonal_through_point(L,A))) # label(ooc2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 23 (all A all L all M all N (distinct_lines(L,M) -> apart_point_and_line(A,L) | apart_point_and_line(A,M) | unorthogonal_lines(L,N) | unorthogonal_lines(M,N))) # label(ouo1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 24 (all L all M -(-convergent_lines(L,M) & -unorthogonal_lines(L,M))) # label(coipo1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 25 (all L all M all N ((-convergent_lines(L,M) | -unorthogonal_lines(L,M)) & (-convergent_lines(L,N) | -unorthogonal_lines(L,N)) -> -convergent_lines(M,N) | -unorthogonal_lines(M,N))) # label(cotno1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 26 (all L all M all N (-unorthogonal_lines(L,M) & -unorthogonal_lines(L,N) -> -convergent_lines(M,N))) # label(couo1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 27 (all A all B (point(A) & point(B) & distinct_points(A,B) -> line(line_connecting(A,B)))) # label(con1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 28 (all L all M (line(L) & line(M) & convergent_lines(L,M) -> point(intersection_point(L,M)))) # label(int1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 29 (all L all A (line(L) & point(A) -> line(parallel_through_point(L,A)))) # label(par1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 30 (all L all A (line(L) & point(A) -> line(orthogonal_through_point(L,A)))) # label(orth1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 31 (all X all Y (equal_points(X,Y) <-> -distinct_points(X,Y))) # label(ax1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 32 (all X all Y (equal_lines(X,Y) <-> -distinct_lines(X,Y))) # label(ax2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 33 (all X all Y (parallel_lines(X,Y) <-> -convergent_lines(X,Y))) # label(a3) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 34 (all X all Y (incident_point_and_line(X,Y) <-> -apart_point_and_line(X,Y))) # label(a4) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 35 (all X all Y (orthogonal_lines(X,Y) <-> -unorthogonal_lines(X,Y))) # label(a5) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 36 -(all X all Y (convergent_lines(X,Y) -> equal_points(intersection_point(X,Y),intersection_point(Y,X)))) # label(con) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.45/1.05
% 0.45/1.05 ============================== end of process non-clausal formulas ===
% 0.45/1.05
% 0.45/1.05 ============================== PROCESS INITIAL CLAUSES ===============
% 0.45/1.05
% 0.45/1.05 ============================== PREDICATE ELIMINATION =================
% 0.45/1.05 37 -equal_points(A,B) | -distinct_points(A,B) # label(ax1) # label(axiom). [clausify(31)].
% 0.45/1.05 38 equal_points(A,B) | distinct_points(A,B) # label(ax1) # label(axiom). [clausify(31)].
% 0.45/1.05 39 -equal_points(intersection_point(c1,c2),intersection_point(c2,c1)) # label(con) # label(negated_conjecture). [clausify(36)].
% 0.45/1.05 Derived: distinct_points(intersection_point(c1,c2),intersection_point(c2,c1)). [resolve(39,a,38,a)].
% 0.45/1.05 40 -equal_lines(A,B) | -distinct_lines(A,B) # label(ax2) # label(axiom). [clausify(32)].
% 0.45/1.05 41 equal_lines(A,B) | distinct_lines(A,B) # label(ax2) # label(axiom). [clausify(32)].
% 0.45/1.05 42 -parallel_lines(A,B) | -convergent_lines(A,B) # label(a3) # label(axiom). [clausify(33)].
% 0.45/1.05 43 parallel_lines(A,B) | convergent_lines(A,B) # label(a3) # label(axiom). [clausify(33)].
% 0.45/1.05 44 -incident_point_and_line(A,B) | -apart_point_and_line(A,B) # label(a4) # label(axiom). [clausify(34)].
% 0.45/1.05 45 incident_point_and_line(A,B) | apart_point_and_line(A,B) # label(a4) # label(axiom). [clausify(34)].
% 0.45/1.05 46 -orthogonal_lines(A,B) | -unorthogonal_lines(A,B) # label(a5) # label(axiom). [clausify(35)].
% 0.45/1.05 47 orthogonal_lines(A,B) | unorthogonal_lines(A,B) # label(a5) # label(axiom). [clausify(35)].
% 0.45/1.05
% 0.45/1.05 ============================== end predicate elimination =============
% 0.45/1.05
% 0.45/1.05 Auto_denials: (non-Horn, no changes).
% 0.45/1.05
% 0.45/1.05 Term ordering decisions:
% 0.45/1.05 Function symbol KB weights: c1=1. c2=1. intersection_point=1. line_connecting=1. orthogonal_through_point=1. parallel_through_point=1.
% 0.45/1.05
% 0.45/1.05 ============================== end of process initial clauses ========
% 0.45/1.05
% 0.45/1.05 ============================== CLAUSES FOR SEARCH ====================
% 0.45/1.05
% 0.45/1.05 ============================== end of clauses for search =============
% 0.45/1.05
% 0.45/1.05 ============================== SEARCH ================================
% 0.45/1.05
% 0.45/1.05 % Starting search at 0.01 seconds.
% 0.45/1.05
% 0.45/1.05 ============================== PROOF =================================
% 0.45/1.05 % SZS status Theorem
% 0.45/1.05 % SZS output start Refutation
% 0.45/1.05
% 0.45/1.05 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.45/1.05 % Length of proof is 37.
% 0.45/1.05 % Level of proof is 7.
% 0.45/1.05 % Maximum clause weight is 23.000.
% 0.45/1.05 % Given clauses 45.
% 0.45/1.05
% 0.45/1.05 2 (all X -distinct_lines(X,X)) # label(apart2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 3 (all X -convergent_lines(X,X)) # label(apart3) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 5 (all X all Y all Z (distinct_lines(X,Y) -> distinct_lines(X,Z) | distinct_lines(Y,Z))) # label(apart5) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 6 (all X all Y all Z (convergent_lines(X,Y) -> convergent_lines(X,Z) | convergent_lines(Y,Z))) # label(ax6) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 11 (all X all Y all U all V (distinct_points(X,Y) & distinct_lines(U,V) -> apart_point_and_line(X,U) | apart_point_and_line(X,V) | apart_point_and_line(Y,U) | apart_point_and_line(Y,V))) # label(cu1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 13 (all X all Y all Z (apart_point_and_line(X,Y) -> distinct_lines(Y,Z) | apart_point_and_line(X,Z))) # label(ceq2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 14 (all X all Y all Z (convergent_lines(X,Y) -> distinct_lines(Y,Z) | convergent_lines(X,Z))) # label(ceq3) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 15 (all X all Y (distinct_lines(X,Y) -> convergent_lines(X,Y))) # label(p1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 16 (all X all Y -convergent_lines(parallel_through_point(Y,X),Y)) # label(cp1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 17 (all X all Y -apart_point_and_line(X,parallel_through_point(Y,X))) # label(cp2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 31 (all X all Y (equal_points(X,Y) <-> -distinct_points(X,Y))) # label(ax1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 36 -(all X all Y (convergent_lines(X,Y) -> equal_points(intersection_point(X,Y),intersection_point(Y,X)))) # label(con) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.45/1.05 38 equal_points(A,B) | distinct_points(A,B) # label(ax1) # label(axiom). [clausify(31)].
% 0.45/1.05 39 -equal_points(intersection_point(c1,c2),intersection_point(c2,c1)) # label(con) # label(negated_conjecture). [clausify(36)].
% 0.45/1.05 48 convergent_lines(c1,c2) # label(con) # label(negated_conjecture). [clausify(36)].
% 0.45/1.05 51 -distinct_lines(A,A) # label(apart2) # label(axiom). [clausify(2)].
% 0.45/1.05 52 -convergent_lines(A,A) # label(apart3) # label(axiom). [clausify(3)].
% 0.45/1.05 53 -convergent_lines(parallel_through_point(A,B),A) # label(cp1) # label(axiom). [clausify(16)].
% 0.45/1.05 54 -apart_point_and_line(A,parallel_through_point(B,A)) # label(cp2) # label(axiom). [clausify(17)].
% 0.45/1.05 61 -distinct_lines(A,B) | convergent_lines(A,B) # label(p1) # label(axiom). [clausify(15)].
% 0.45/1.05 65 -distinct_lines(A,B) | distinct_lines(A,C) | distinct_lines(B,C) # label(apart5) # label(axiom). [clausify(5)].
% 0.45/1.05 66 -convergent_lines(A,B) | convergent_lines(A,C) | convergent_lines(B,C) # label(ax6) # label(axiom). [clausify(6)].
% 0.45/1.05 68 -apart_point_and_line(A,B) | distinct_lines(B,C) | apart_point_and_line(A,C) # label(ceq2) # label(axiom). [clausify(13)].
% 0.45/1.05 69 -convergent_lines(A,B) | distinct_lines(B,C) | convergent_lines(A,C) # label(ceq3) # label(axiom). [clausify(14)].
% 0.45/1.05 80 -distinct_points(A,B) | -distinct_lines(C,D) | apart_point_and_line(A,C) | apart_point_and_line(A,D) | apart_point_and_line(B,C) | apart_point_and_line(B,D) # label(cu1) # label(axiom). [clausify(11)].
% 0.45/1.05 81 distinct_points(intersection_point(c1,c2),intersection_point(c2,c1)). [resolve(39,a,38,a)].
% 0.45/1.05 85 -distinct_lines(parallel_through_point(A,B),A). [ur(61,b,53,a)].
% 0.45/1.05 88 -convergent_lines(A,parallel_through_point(A,B)). [ur(66,b,52,a,c,53,a)].
% 0.45/1.05 89 distinct_lines(c2,A) | convergent_lines(c1,A). [resolve(69,a,48,a)].
% 0.45/1.05 92 -distinct_lines(A,B) | apart_point_and_line(intersection_point(c1,c2),A) | apart_point_and_line(intersection_point(c1,c2),B) | apart_point_and_line(intersection_point(c2,c1),A) | apart_point_and_line(intersection_point(c2,c1),B). [resolve(81,a,80,a)].
% 0.45/1.05 108 -distinct_lines(A,parallel_through_point(A,B)). [ur(65,b,51,a,c,85,a)].
% 0.45/1.05 109 -convergent_lines(A,parallel_through_point(parallel_through_point(A,B),C)). [ur(69,b,85,a,c,88,a)].
% 0.45/1.05 128 convergent_lines(c1,A) | distinct_lines(c2,B) | distinct_lines(A,B). [resolve(89,a,65,a)].
% 0.45/1.05 131 -apart_point_and_line(A,B). [ur(68,b,108,a,c,54,a)].
% 0.45/1.05 135 -distinct_lines(A,B). [back_unit_del(92),unit_del(b,131),unit_del(c,131),unit_del(d,131),unit_del(e,131)].
% 0.45/1.05 136 convergent_lines(c1,A). [back_unit_del(128),unit_del(b,135),unit_del(c,135)].
% 0.45/1.05 137 $F. [resolve(136,a,109,a)].
% 0.45/1.05
% 0.45/1.05 % SZS output end Refutation
% 0.45/1.05 ============================== end of proof ==========================
% 0.45/1.05
% 0.45/1.05 ============================== STATISTICS ============================
% 0.45/1.05
% 0.45/1.05 Given=45. Generated=182. Kept=89. proofs=1.
% 0.45/1.05 Usable=28. Sos=24. Demods=0. Limbo=1, Disabled=84. Hints=0.
% 0.45/1.05 Megabytes=0.14.
% 0.45/1.05 User_CPU=0.01, System_CPU=0.00, Wall_clock=0.
% 0.45/1.05
% 0.45/1.05 ============================== end of statistics =====================
% 0.45/1.05
% 0.45/1.05 ============================== end of search =========================
% 0.45/1.05
% 0.45/1.05 THEOREM PROVED
% 0.45/1.05 % SZS status Theorem
% 0.45/1.05
% 0.45/1.05 Exiting with 1 proof.
% 0.45/1.05
% 0.45/1.05 Process 24756 exit (max_proofs) Sat Jun 18 01:12:08 2022
% 0.45/1.05 Prover9 interrupted
%------------------------------------------------------------------------------