TSTP Solution File: GEO235+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GEO235+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n004.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 05:55:23 EDT 2022
% Result : Theorem 0.64s 0.92s
% Output : Refutation 0.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GEO235+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.32 % Computer : n004.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 : 600
% 0.11/0.32 % DateTime : Sat Jun 18 07:21:08 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.64/0.91 ============================== Prover9 ===============================
% 0.64/0.91 Prover9 (32) version 2009-11A, November 2009.
% 0.64/0.91 Process 27447 was started by sandbox2 on n004.cluster.edu,
% 0.64/0.91 Sat Jun 18 07:21:09 2022
% 0.64/0.91 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_27069_n004.cluster.edu".
% 0.64/0.91 ============================== end of head ===========================
% 0.64/0.91
% 0.64/0.91 ============================== INPUT =================================
% 0.64/0.91
% 0.64/0.91 % Reading from file /tmp/Prover9_27069_n004.cluster.edu
% 0.64/0.91
% 0.64/0.91 set(prolog_style_variables).
% 0.64/0.91 set(auto2).
% 0.64/0.91 % set(auto2) -> set(auto).
% 0.64/0.91 % set(auto) -> set(auto_inference).
% 0.64/0.91 % set(auto) -> set(auto_setup).
% 0.64/0.91 % set(auto_setup) -> set(predicate_elim).
% 0.64/0.91 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.64/0.91 % set(auto) -> set(auto_limits).
% 0.64/0.91 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.64/0.91 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.64/0.91 % set(auto) -> set(auto_denials).
% 0.64/0.91 % set(auto) -> set(auto_process).
% 0.64/0.91 % set(auto2) -> assign(new_constants, 1).
% 0.64/0.91 % set(auto2) -> assign(fold_denial_max, 3).
% 0.64/0.91 % set(auto2) -> assign(max_weight, "200.000").
% 0.64/0.91 % set(auto2) -> assign(max_hours, 1).
% 0.64/0.91 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.64/0.91 % set(auto2) -> assign(max_seconds, 0).
% 0.64/0.91 % set(auto2) -> assign(max_minutes, 5).
% 0.64/0.91 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.64/0.91 % set(auto2) -> set(sort_initial_sos).
% 0.64/0.91 % set(auto2) -> assign(sos_limit, -1).
% 0.64/0.91 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.64/0.91 % set(auto2) -> assign(max_megs, 400).
% 0.64/0.91 % set(auto2) -> assign(stats, some).
% 0.64/0.91 % set(auto2) -> clear(echo_input).
% 0.64/0.91 % set(auto2) -> set(quiet).
% 0.64/0.91 % set(auto2) -> clear(print_initial_clauses).
% 0.64/0.91 % set(auto2) -> clear(print_given).
% 0.64/0.91 assign(lrs_ticks,-1).
% 0.64/0.91 assign(sos_limit,10000).
% 0.64/0.91 assign(order,kbo).
% 0.64/0.91 set(lex_order_vars).
% 0.64/0.91 clear(print_given).
% 0.64/0.91
% 0.64/0.91 % formulas(sos). % not echoed (32 formulas)
% 0.64/0.91
% 0.64/0.91 ============================== end of input ==========================
% 0.64/0.91
% 0.64/0.91 % From the command line: assign(max_seconds, 300).
% 0.64/0.91
% 0.64/0.91 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.64/0.91
% 0.64/0.91 % Formulas that are not ordinary clauses:
% 0.64/0.91 1 (all A all L (apart_point_and_line(A,L) <-> left_apart_point(A,L) | left_apart_point(A,reverse_line(L)))) # label(apt_def) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.91 2 (all L all M (convergent_lines(L,M) <-> unequally_directed_lines(L,M) & unequally_directed_lines(L,reverse_line(M)))) # label(con_def) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.91 3 (all A all B all L (divides_points(L,A,B) <-> left_apart_point(A,L) & left_apart_point(B,reverse_line(L)) | left_apart_point(A,reverse_line(L)) & left_apart_point(B,L))) # label(div_def) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.91 4 (all L all A all B (before_on_line(L,A,B) <-> distinct_points(A,B) & -(left_apart_point(A,L) | left_apart_point(A,reverse_line(L))) & -(left_apart_point(B,L) | left_apart_point(B,reverse_line(L))) & -unequally_directed_lines(L,line_connecting(A,B)))) # label(bf_def) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.91 5 (all L all A all B all C (between_on_line(L,A,B,C) <-> before_on_line(L,A,B) & before_on_line(L,B,C) | before_on_line(L,C,B) & before_on_line(L,B,A))) # label(bet_def) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.91 6 (all A -distinct_points(A,A)) # label(oag1) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.91 7 (all A all B all C (distinct_points(A,B) -> distinct_points(A,C) | distinct_points(B,C))) # label(oag2) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.91 8 (all L -distinct_lines(L,L)) # label(oag3) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.91 9 (all L all M all N (distinct_lines(L,M) -> distinct_lines(L,N) | distinct_lines(M,N))) # label(oag4) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.91 10 (all L -unequally_directed_lines(L,L)) # label(oag5) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.91 11 (all L all M all N (unequally_directed_lines(L,M) -> unequally_directed_lines(L,N) | unequally_directed_lines(M,N))) # label(oag6) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.91 12 (all L all M all N (unequally_directed_lines(L,M) & unequally_directed_lines(L,reverse_line(M)) -> unequally_directed_lines(L,N) & unequally_directed_lines(L,reverse_line(N)) | unequally_directed_lines(M,N) & unequally_directed_lines(M,reverse_line(N)))) # label(oag7) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.91 13 (all L all M (line(L) & line(M) -> unequally_directed_lines(L,M) | unequally_directed_lines(L,reverse_line(M)))) # label(oag8) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.91 14 (all L all M (unequally_directed_lines(L,M) & unequally_directed_lines(L,reverse_line(M)) -> left_convergent_lines(L,M) | left_convergent_lines(L,reverse_line(M)))) # label(oag9) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.91 15 (all A all L -(left_apart_point(A,L) | left_apart_point(A,reverse_line(L)))) # label(oag10) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.91 16 (all L all M -(left_convergent_lines(L,M) | left_convergent_lines(L,reverse_line(M)))) # label(oag11) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.91 17 (all A all B (point(A) & point(B) & distinct_points(A,B) -> line(line_connecting(A,B)))) # label(oagco1) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.91 18 (all L all M (line(L) & line(M) & unequally_directed_lines(L,M) & unequally_directed_lines(L,reverse_line(M)) -> point(intersection_point(L,M)))) # label(oagco2) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.91 19 (all L all A (point(A) & line(L) -> line(parallel_through_point(L,A)))) # label(oagco3) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.91 20 (all L (line(L) -> line(reverse_line(L)))) # label(oagco4) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.91 21 (all A all B (distinct_points(A,B) -> -apart_point_and_line(A,line_connecting(A,B)) & -apart_point_and_line(B,line_connecting(A,B)))) # label(oagco5) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.91 22 (all L all M (unequally_directed_lines(L,M) & unequally_directed_lines(L,reverse_line(M)) -> -apart_point_and_line(intersection_point(L,M),L) & -apart_point_and_line(intersection_point(L,M),M))) # label(oagco6) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.91 23 (all A all L -apart_point_and_line(A,parallel_through_point(L,A))) # label(oagco7) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.91 24 (all L -distinct_lines(L,reverse_line(L))) # label(oagco8) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.91 25 (all A all B -unequally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A)))) # label(oagco9) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.91 26 (all A all L -unequally_directed_lines(parallel_through_point(L,A),L)) # label(oagco10) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.91 27 (all A all B all L all M (distinct_points(A,B) & distinct_lines(L,M) -> left_apart_point(A,L) | left_apart_point(B,L) | left_apart_point(A,M) | left_apart_point(B,M) | left_apart_point(A,reverse_line(L)) | left_apart_point(B,reverse_line(L)) | left_apart_point(A,reverse_line(M)) | left_apart_point(B,reverse_line(M)))) # label(oaguc1) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.91 28 (all A all B all L (distinct_points(A,B) & left_apart_point(A,L) -> left_apart_point(B,L) | left_convergent_lines(line_connecting(A,B),L))) # label(oaguc2) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.91 29 (all A all B all L (left_apart_point(A,L) -> distinct_points(A,B) | left_apart_point(B,L))) # label(oagsub1) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.91 30 (all A all L all M (left_apart_point(A,L) & unequally_directed_lines(L,M) -> distinct_lines(L,M) | left_apart_point(A,reverse_line(M)))) # label(oagsub2) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.91 31 (all L all M all N (left_convergent_lines(L,M) -> unequally_directed_lines(M,N) | left_convergent_lines(L,N))) # label(oagsub3) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.91 32 -(all A all B all L (left_apart_point(A,L) & left_apart_point(B,reverse_line(L)) -> distinct_points(A,B))) # label(con) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.64/0.91
% 0.64/0.91 ============================== end of process non-clausal formulas ===
% 0.64/0.91
% 0.64/0.91 ============================== PROCESS INITIAL CLAUSES ===============
% 0.64/0.92
% 0.64/0.92 ============================== PREDICATE ELIMINATION =================
% 0.64/0.92 33 apart_point_and_line(A,B) | -left_apart_point(A,B) # label(apt_def) # label(axiom). [clausify(1)].
% 0.64/0.92 34 -apart_point_and_line(A,parallel_through_point(B,A)) # label(oagco7) # label(axiom). [clausify(23)].
% 0.64/0.92 35 -distinct_points(A,B) | -apart_point_and_line(A,line_connecting(A,B)) # label(oagco5) # label(axiom). [clausify(21)].
% 0.64/0.92 36 -distinct_points(A,B) | -apart_point_and_line(B,line_connecting(A,B)) # label(oagco5) # label(axiom). [clausify(21)].
% 0.64/0.92 37 -unequally_directed_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)) | -apart_point_and_line(intersection_point(A,B),A) # label(oagco6) # label(axiom). [clausify(22)].
% 0.64/0.92 38 -unequally_directed_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)) | -apart_point_and_line(intersection_point(A,B),B) # label(oagco6) # label(axiom). [clausify(22)].
% 0.64/0.92 Derived: -left_apart_point(A,parallel_through_point(B,A)). [resolve(33,a,34,a)].
% 0.64/0.92 Derived: -left_apart_point(A,line_connecting(A,B)) | -distinct_points(A,B). [resolve(33,a,35,b)].
% 0.64/0.92 Derived: -left_apart_point(A,line_connecting(B,A)) | -distinct_points(B,A). [resolve(33,a,36,b)].
% 0.64/0.92 Derived: -left_apart_point(intersection_point(A,B),A) | -unequally_directed_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)). [resolve(33,a,37,c)].
% 0.64/0.92 Derived: -left_apart_point(intersection_point(A,B),B) | -unequally_directed_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)). [resolve(33,a,38,c)].
% 0.64/0.92 39 apart_point_and_line(A,B) | -left_apart_point(A,reverse_line(B)) # label(apt_def) # label(axiom). [clausify(1)].
% 0.64/0.92 Derived: -left_apart_point(A,reverse_line(parallel_through_point(B,A))). [resolve(39,a,34,a)].
% 0.64/0.92 Derived: -left_apart_point(A,reverse_line(line_connecting(A,B))) | -distinct_points(A,B). [resolve(39,a,35,b)].
% 0.64/0.92 Derived: -left_apart_point(A,reverse_line(line_connecting(B,A))) | -distinct_points(B,A). [resolve(39,a,36,b)].
% 0.64/0.92 Derived: -left_apart_point(intersection_point(A,B),reverse_line(A)) | -unequally_directed_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)). [resolve(39,a,37,c)].
% 0.64/0.92 Derived: -left_apart_point(intersection_point(A,B),reverse_line(B)) | -unequally_directed_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)). [resolve(39,a,38,c)].
% 0.64/0.92 40 -apart_point_and_line(A,B) | left_apart_point(A,B) | left_apart_point(A,reverse_line(B)) # label(apt_def) # label(axiom). [clausify(1)].
% 0.64/0.92 41 convergent_lines(A,B) | -unequally_directed_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)) # label(con_def) # label(axiom). [clausify(2)].
% 0.64/0.92 42 -convergent_lines(A,B) | unequally_directed_lines(A,B) # label(con_def) # label(axiom). [clausify(2)].
% 0.64/0.92 43 -convergent_lines(A,B) | unequally_directed_lines(A,reverse_line(B)) # label(con_def) # label(axiom). [clausify(2)].
% 0.64/0.92 44 divides_points(A,B,C) | -left_apart_point(B,A) | -left_apart_point(C,reverse_line(A)) # label(div_def) # label(axiom). [clausify(3)].
% 0.64/0.92 45 -divides_points(A,B,C) | left_apart_point(B,A) | left_apart_point(C,A) # label(div_def) # label(axiom). [clausify(3)].
% 0.64/0.92 46 -divides_points(A,B,C) | left_apart_point(B,A) | left_apart_point(B,reverse_line(A)) # label(div_def) # label(axiom). [clausify(3)].
% 0.64/0.92 47 -divides_points(A,B,C) | left_apart_point(C,reverse_line(A)) | left_apart_point(C,A) # label(div_def) # label(axiom). [clausify(3)].
% 0.64/0.92 48 divides_points(A,B,C) | -left_apart_point(B,reverse_line(A)) | -left_apart_point(C,A) # label(div_def) # label(axiom). [clausify(3)].
% 0.64/0.92 49 -divides_points(A,B,C) | left_apart_point(C,reverse_line(A)) | left_apart_point(B,reverse_line(A)) # label(div_def) # label(axiom). [clausify(3)].
% 0.64/0.92 50 between_on_line(A,B,C,D) | -before_on_line(A,B,C) | -before_on_line(A,C,D) # label(bet_def) # label(axiom). [clausify(5)].
% 0.64/0.92 51 -between_on_line(A,B,C,D) | before_on_line(A,B,C) | before_on_line(A,D,C) # label(bet_def) # label(axiom). [clausify(5)].
% 0.64/0.92 52 -between_on_line(A,B,C,D) | before_on_line(A,B,C) | before_on_line(A,C,B) # label(bet_def) # label(axiom). [clausify(5)].
% 0.64/0.92 53 -between_on_line(A,B,C,D) | before_on_line(A,C,D) | before_on_line(A,D,C) # label(bet_def) # label(axiom). [clausify(5)].
% 0.64/0.92 54 -between_on_line(A,B,C,D) | before_on_line(A,C,D) | before_on_line(A,C,B) # label(bet_def) # label(axiom). [clausify(5)].
% 0.64/0.92 55 between_on_line(A,B,C,D) | -before_on_line(A,D,C) | -before_on_line(A,C,B) # label(bet_def) # label(axiom). [clausify(5)].
% 0.64/0.92 56 before_on_line(A,B,C) | -distinct_points(B,C) | left_apart_point(B,A) | left_apart_point(B,reverse_line(A)) | left_apart_point(C,A) | left_apart_point(C,reverse_line(A)) | unequally_directed_lines(A,line_connecting(B,C)) # label(bf_def) # label(axiom). [clausify(4)].
% 0.64/0.92 57 -before_on_line(A,B,C) | -left_apart_point(B,A) # label(bf_def) # label(axiom). [clausify(4)].
% 0.64/0.92 58 -before_on_line(A,B,C) | -left_apart_point(C,A) # label(bf_def) # label(axiom). [clausify(4)].
% 0.64/0.92 59 -before_on_line(A,B,C) | -left_apart_point(B,reverse_line(A)) # label(bf_def) # label(axiom). [clausify(4)].
% 0.64/0.92 60 -before_on_line(A,B,C) | -left_apart_point(C,reverse_line(A)) # label(bf_def) # label(axiom). [clausify(4)].
% 0.64/0.92 61 -before_on_line(A,B,C) | -unequally_directed_lines(A,line_connecting(B,C)) # label(bf_def) # label(axiom). [clausify(4)].
% 0.64/0.92 62 -before_on_line(A,B,C) | distinct_points(B,C) # label(bf_def) # label(axiom). [clausify(4)].
% 0.64/0.92
% 0.64/0.92 ============================== end predicate elimination =============
% 0.64/0.92
% 0.64/0.92 Auto_denials: (non-Horn, no changes).
% 0.64/0.92
% 0.64/0.92 Term ordering decisions:
% 0.64/0.92
% 0.64/0.92 % Assigning unary symbol reverse_line kb_weight 0 and highest precedence (14).
% 0.64/0.92 Function symbol KB weights: c1=1. c2=1. c3=1. line_connecting=1. intersection_point=1. parallel_through_point=1. reverse_line=0.
% 0.64/0.92
% 0.64/0.92 ============================== PROOF =================================
% 0.64/0.92 % SZS status Theorem
% 0.64/0.92 % SZS output start Refutation
% 0.64/0.92
% 0.64/0.92 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.64/0.92 % Length of proof is 5.
% 0.64/0.92 % Level of proof is 2.
% 0.64/0.92 % Maximum clause weight is 4.000.
% 0.64/0.92 % Given clauses 0.
% 0.64/0.92
% 0.64/0.92 15 (all A all L -(left_apart_point(A,L) | left_apart_point(A,reverse_line(L)))) # label(oag10) # label(axiom) # label(non_clause). [assumption].
% 0.64/0.92 32 -(all A all B all L (left_apart_point(A,L) & left_apart_point(B,reverse_line(L)) -> distinct_points(A,B))) # label(con) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.64/0.92 64 left_apart_point(c2,reverse_line(c3)) # label(con) # label(negated_conjecture). [clausify(32)].
% 0.64/0.92 68 -left_apart_point(A,B) # label(oag10) # label(axiom). [clausify(15)].
% 0.64/0.92 69 $F. [resolve(68,a,64,a)].
% 0.64/0.92
% 0.64/0.92 % SZS output end Refutation
% 0.64/0.92 ============================== end of proof ==========================
% 0.64/0.92
% 0.64/0.92 ============================== STATISTICS ============================
% 0.64/0.92
% 0.64/0.92 Given=0. Generated=6. Kept=6. proofs=1.
% 0.64/0.92 Usable=0. Sos=0. Demods=0. Limbo=5, Disabled=36. Hints=0.
% 0.64/0.92 Megabytes=0.08.
% 0.64/0.92 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.64/0.92
% 0.64/0.92 ============================== end of statistics =====================
% 0.64/0.92
% 0.64/0.92 ============================== end of search =========================
% 0.64/0.92
% 0.64/0.92 THEOREM PROVED
% 0.64/0.92 % SZS status Theorem
% 0.64/0.92
% 0.64/0.92 Exiting with 1 proof.
% 0.64/0.92
% 0.64/0.92 Process 27447 exit (max_proofs) Sat Jun 18 07:21:09 2022
% 0.64/0.92 Prover9 interrupted
%------------------------------------------------------------------------------