TSTP Solution File: GEO218+3 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GEO218+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n023.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 05:55:12 EDT 2022
% Result : Theorem 0.72s 1.03s
% Output : Refutation 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GEO218+3 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n023.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 : 600
% 0.12/0.33 % DateTime : Sat Jun 18 04:45:34 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.72/1.02 ============================== Prover9 ===============================
% 0.72/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.72/1.02 Process 31722 was started by sandbox2 on n023.cluster.edu,
% 0.72/1.02 Sat Jun 18 04:45:35 2022
% 0.72/1.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_31568_n023.cluster.edu".
% 0.72/1.02 ============================== end of head ===========================
% 0.72/1.02
% 0.72/1.02 ============================== INPUT =================================
% 0.72/1.02
% 0.72/1.02 % Reading from file /tmp/Prover9_31568_n023.cluster.edu
% 0.72/1.02
% 0.72/1.02 set(prolog_style_variables).
% 0.72/1.02 set(auto2).
% 0.72/1.02 % set(auto2) -> set(auto).
% 0.72/1.02 % set(auto) -> set(auto_inference).
% 0.72/1.02 % set(auto) -> set(auto_setup).
% 0.72/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.72/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.72/1.02 % set(auto) -> set(auto_limits).
% 0.72/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.72/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.72/1.02 % set(auto) -> set(auto_denials).
% 0.72/1.02 % set(auto) -> set(auto_process).
% 0.72/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.72/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.72/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.72/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.72/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.72/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.72/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.72/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.72/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.72/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.72/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.72/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.72/1.02 % set(auto2) -> assign(stats, some).
% 0.72/1.02 % set(auto2) -> clear(echo_input).
% 0.72/1.02 % set(auto2) -> set(quiet).
% 0.72/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.72/1.02 % set(auto2) -> clear(print_given).
% 0.72/1.02 assign(lrs_ticks,-1).
% 0.72/1.02 assign(sos_limit,10000).
% 0.72/1.02 assign(order,kbo).
% 0.72/1.02 set(lex_order_vars).
% 0.72/1.02 clear(print_given).
% 0.72/1.02
% 0.72/1.02 % formulas(sos). % not echoed (36 formulas)
% 0.72/1.02
% 0.72/1.02 ============================== end of input ==========================
% 0.72/1.02
% 0.72/1.02 % From the command line: assign(max_seconds, 300).
% 0.72/1.02
% 0.72/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.72/1.02
% 0.72/1.02 % Formulas that are not ordinary clauses:
% 0.72/1.02 1 (all X -distinct_points(X,X)) # label(apart1) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.02 2 (all X -distinct_lines(X,X)) # label(apart2) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.02 3 (all X -convergent_lines(X,X)) # label(apart3) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.02 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].
% 0.72/1.02 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].
% 0.72/1.02 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].
% 0.72/1.02 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].
% 0.72/1.02 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].
% 0.72/1.02 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].
% 0.72/1.02 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].
% 0.72/1.02 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].
% 0.72/1.02 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].
% 0.72/1.02 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].
% 0.72/1.03 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].
% 0.72/1.03 15 (all X all Y (distinct_lines(X,Y) -> convergent_lines(X,Y))) # label(p1) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.03 16 (all X all Y -convergent_lines(parallel_through_point(Y,X),Y)) # label(cp1) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.03 17 (all X all Y -apart_point_and_line(X,parallel_through_point(Y,X))) # label(cp2) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.03 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].
% 0.72/1.03 19 (all L all M (convergent_lines(L,M) | unorthogonal_lines(L,M))) # label(occu1) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.03 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].
% 0.72/1.03 21 (all A all L -unorthogonal_lines(orthogonal_through_point(L,A),L)) # label(ooc1) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.03 22 (all A all L -apart_point_and_line(A,orthogonal_through_point(L,A))) # label(ooc2) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.03 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].
% 0.72/1.03 24 (all L all M -(-convergent_lines(L,M) & -unorthogonal_lines(L,M))) # label(coipo1) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.03 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].
% 0.72/1.03 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].
% 0.72/1.03 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].
% 0.72/1.03 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].
% 0.72/1.03 29 (all L all A (line(L) & point(A) -> line(parallel_through_point(L,A)))) # label(par1) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.03 30 (all L all A (line(L) & point(A) -> line(orthogonal_through_point(L,A)))) # label(orth1) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.03 31 (all X all Y (equal_points(X,Y) <-> -distinct_points(X,Y))) # label(ax1) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.03 32 (all X all Y (equal_lines(X,Y) <-> -distinct_lines(X,Y))) # label(ax2) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.03 33 (all X all Y (parallel_lines(X,Y) <-> -convergent_lines(X,Y))) # label(a3) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.03 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].
% 0.72/1.03 35 (all X all Y (orthogonal_lines(X,Y) <-> -unorthogonal_lines(X,Y))) # label(a5) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.03 36 -(all L all M all N (parallel_lines(L,M) & orthogonal_lines(L,N) -> orthogonal_lines(M,N))) # label(con) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.72/1.03
% 0.72/1.03 ============================== end of process non-clausal formulas ===
% 0.72/1.03
% 0.72/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.72/1.03
% 0.72/1.03 ============================== PREDICATE ELIMINATION =================
% 0.72/1.03 37 -parallel_lines(A,B) | -convergent_lines(A,B) # label(a3) # label(axiom). [clausify(33)].
% 0.72/1.03 38 parallel_lines(c1,c2) # label(con) # label(negated_conjecture). [clausify(36)].
% 0.72/1.03 39 parallel_lines(A,B) | convergent_lines(A,B) # label(a3) # label(axiom). [clausify(33)].
% 0.72/1.03 Derived: -convergent_lines(c1,c2). [resolve(37,a,38,a)].
% 0.72/1.03 40 -orthogonal_lines(c2,c3) # label(con) # label(negated_conjecture). [clausify(36)].
% 0.72/1.03 41 orthogonal_lines(c1,c3) # label(con) # label(negated_conjecture). [clausify(36)].
% 0.72/1.03 42 orthogonal_lines(A,B) | unorthogonal_lines(A,B) # label(a5) # label(axiom). [clausify(35)].
% 0.72/1.03 Derived: unorthogonal_lines(c2,c3). [resolve(40,a,42,a)].
% 0.72/1.03 43 -orthogonal_lines(A,B) | -unorthogonal_lines(A,B) # label(a5) # label(axiom). [clausify(35)].
% 0.72/1.03 Derived: -unorthogonal_lines(c1,c3). [resolve(43,a,41,a)].
% 0.72/1.03 44 -equal_points(A,B) | -distinct_points(A,B) # label(ax1) # label(axiom). [clausify(31)].
% 0.72/1.03 45 equal_points(A,B) | distinct_points(A,B) # label(ax1) # label(axiom). [clausify(31)].
% 0.72/1.03 46 -equal_lines(A,B) | -distinct_lines(A,B) # label(ax2) # label(axiom). [clausify(32)].
% 0.72/1.03 47 equal_lines(A,B) | distinct_lines(A,B) # label(ax2) # label(axiom). [clausify(32)].
% 0.72/1.03 48 -incident_point_and_line(A,B) | -apart_point_and_line(A,B) # label(a4) # label(axiom). [clausify(34)].
% 0.72/1.03 49 incident_point_and_line(A,B) | apart_point_and_line(A,B) # label(a4) # label(axiom). [clausify(34)].
% 0.72/1.03
% 0.72/1.03 ============================== end predicate elimination =============
% 0.72/1.03
% 0.72/1.03 Auto_denials: (non-Horn, no changes).
% 0.72/1.03
% 0.72/1.03 Term ordering decisions:
% 0.72/1.03 Function symbol KB weights: c1=1. c2=1. c3=1. intersection_point=1. line_connecting=1. orthogonal_through_point=1. parallel_through_point=1.
% 0.72/1.03
% 0.72/1.03 ============================== end of process initial clauses ========
% 0.72/1.03
% 0.72/1.03 ============================== CLAUSES FOR SEARCH ====================
% 0.72/1.03
% 0.72/1.03 ============================== end of clauses for search =============
% 0.72/1.03
% 0.72/1.03 ============================== SEARCH ================================
% 0.72/1.03
% 0.72/1.03 % Starting search at 0.02 seconds.
% 0.72/1.03
% 0.72/1.03 ============================== PROOF =================================
% 0.72/1.03 % SZS status Theorem
% 0.72/1.03 % SZS output start Refutation
% 0.72/1.03
% 0.72/1.03 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.72/1.03 % Length of proof is 24.
% 0.72/1.03 % Level of proof is 5.
% 0.72/1.03 % Maximum clause weight is 12.000.
% 0.72/1.03 % Given clauses 46.
% 0.72/1.03
% 0.72/1.03 3 (all X -convergent_lines(X,X)) # label(apart3) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.03 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].
% 0.72/1.03 19 (all L all M (convergent_lines(L,M) | unorthogonal_lines(L,M))) # label(occu1) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.03 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].
% 0.72/1.03 33 (all X all Y (parallel_lines(X,Y) <-> -convergent_lines(X,Y))) # label(a3) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.03 35 (all X all Y (orthogonal_lines(X,Y) <-> -unorthogonal_lines(X,Y))) # label(a5) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.03 36 -(all L all M all N (parallel_lines(L,M) & orthogonal_lines(L,N) -> orthogonal_lines(M,N))) # label(con) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.72/1.03 37 -parallel_lines(A,B) | -convergent_lines(A,B) # label(a3) # label(axiom). [clausify(33)].
% 0.72/1.03 38 parallel_lines(c1,c2) # label(con) # label(negated_conjecture). [clausify(36)].
% 0.72/1.03 40 -orthogonal_lines(c2,c3) # label(con) # label(negated_conjecture). [clausify(36)].
% 0.72/1.03 41 orthogonal_lines(c1,c3) # label(con) # label(negated_conjecture). [clausify(36)].
% 0.72/1.03 42 orthogonal_lines(A,B) | unorthogonal_lines(A,B) # label(a5) # label(axiom). [clausify(35)].
% 0.72/1.03 43 -orthogonal_lines(A,B) | -unorthogonal_lines(A,B) # label(a5) # label(axiom). [clausify(35)].
% 0.72/1.03 50 convergent_lines(A,B) | unorthogonal_lines(A,B) # label(occu1) # label(axiom). [clausify(19)].
% 0.72/1.03 53 -convergent_lines(A,A) # label(apart3) # label(axiom). [clausify(3)].
% 0.72/1.03 67 -convergent_lines(A,B) | convergent_lines(A,C) | convergent_lines(B,C) # label(ax6) # label(axiom). [clausify(6)].
% 0.72/1.03 78 convergent_lines(A,B) | unorthogonal_lines(A,C) | -convergent_lines(B,C) | -unorthogonal_lines(B,C) # label(cotno1) # label(axiom). [clausify(25)].
% 0.72/1.03 82 -convergent_lines(c1,c2). [resolve(37,a,38,a)].
% 0.72/1.03 83 unorthogonal_lines(c2,c3). [resolve(40,a,42,a)].
% 0.72/1.03 84 -unorthogonal_lines(c1,c3). [resolve(43,a,41,a)].
% 0.72/1.03 99 convergent_lines(c1,c3). [resolve(84,a,50,b)].
% 0.72/1.03 100 -convergent_lines(c2,c3). [ur(78,a,82,a,b,84,a,d,83,a)].
% 0.72/1.03 111 -convergent_lines(c3,c2). [ur(67,b,53,a,c,100,a)].
% 0.72/1.03 147 $F. [ur(67,b,82,a,c,111,a),unit_del(a,99)].
% 0.72/1.03
% 0.72/1.03 % SZS output end Refutation
% 0.72/1.03 ============================== end of proof ==========================
% 0.72/1.03
% 0.72/1.03 ============================== STATISTICS ============================
% 0.72/1.03
% 0.72/1.03 Given=46. Generated=198. Kept=97. proofs=1.
% 0.72/1.03 Usable=46. Sos=37. Demods=0. Limbo=2, Disabled=64. Hints=0.
% 0.72/1.03 Megabytes=0.14.
% 0.72/1.03 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.72/1.03
% 0.72/1.03 ============================== end of statistics =====================
% 0.72/1.03
% 0.72/1.03 ============================== end of search =========================
% 0.72/1.03
% 0.72/1.03 THEOREM PROVED
% 0.72/1.03 % SZS status Theorem
% 0.72/1.03
% 0.72/1.03 Exiting with 1 proof.
% 0.72/1.03
% 0.72/1.03 Process 31722 exit (max_proofs) Sat Jun 18 04:45:35 2022
% 0.72/1.03 Prover9 interrupted
%------------------------------------------------------------------------------