TSTP Solution File: GEO268+3 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GEO268+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n024.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 05:55:41 EDT 2022
% Result : Theorem 0.45s 1.04s
% Output : Refutation 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEO268+3 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n024.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sat Jun 18 12:22:32 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.45/1.03 ============================== Prover9 ===============================
% 0.45/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.45/1.03 Process 1403 was started by sandbox on n024.cluster.edu,
% 0.45/1.03 Sat Jun 18 12:22:33 2022
% 0.45/1.03 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_914_n024.cluster.edu".
% 0.45/1.03 ============================== end of head ===========================
% 0.45/1.03
% 0.45/1.03 ============================== INPUT =================================
% 0.45/1.03
% 0.45/1.03 % Reading from file /tmp/Prover9_914_n024.cluster.edu
% 0.45/1.03
% 0.45/1.03 set(prolog_style_variables).
% 0.45/1.03 set(auto2).
% 0.45/1.03 % set(auto2) -> set(auto).
% 0.45/1.03 % set(auto) -> set(auto_inference).
% 0.45/1.03 % set(auto) -> set(auto_setup).
% 0.45/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.45/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/1.03 % set(auto) -> set(auto_limits).
% 0.45/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/1.03 % set(auto) -> set(auto_denials).
% 0.45/1.03 % set(auto) -> set(auto_process).
% 0.45/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.45/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.45/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.45/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.45/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.45/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.45/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.45/1.03 % set(auto2) -> assign(stats, some).
% 0.45/1.03 % set(auto2) -> clear(echo_input).
% 0.45/1.03 % set(auto2) -> set(quiet).
% 0.45/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.45/1.03 % set(auto2) -> clear(print_given).
% 0.45/1.03 assign(lrs_ticks,-1).
% 0.45/1.03 assign(sos_limit,10000).
% 0.45/1.03 assign(order,kbo).
% 0.45/1.03 set(lex_order_vars).
% 0.45/1.03 clear(print_given).
% 0.45/1.03
% 0.45/1.03 % formulas(sos). % not echoed (37 formulas)
% 0.45/1.03
% 0.45/1.03 ============================== end of input ==========================
% 0.45/1.03
% 0.45/1.03 % From the command line: assign(max_seconds, 300).
% 0.45/1.03
% 0.45/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/1.03
% 0.45/1.03 % Formulas that are not ordinary clauses:
% 0.45/1.03 1 (all X all Y (unequally_directed_opposite_lines(X,Y) <-> unequally_directed_lines(X,reverse_line(Y)))) # label(a1_defns) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 2 (all X all Y (right_apart_point(X,Y) <-> left_apart_point(X,reverse_line(Y)))) # label(a2_defns) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 3 (all X all Y (right_convergent_lines(X,Y) <-> left_convergent_lines(X,reverse_line(Y)))) # label(a3_defns) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 4 (all X all Y (equally_directed_lines(X,Y) <-> -unequally_directed_lines(X,Y))) # label(a4_defns) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 5 (all X all Y (equally_directed_opposite_lines(X,Y) <-> -unequally_directed_opposite_lines(X,Y))) # label(a5_defns) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 6 (all A all L (apart_point_and_line(A,L) <-> left_apart_point(A,L) | right_apart_point(A,L))) # label(a6_defns) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 7 (all L all M (convergent_lines(L,M) <-> unequally_directed_lines(L,M) & unequally_directed_opposite_lines(L,M))) # label(a7_defns) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 8 (all A all B all L (divides_points(L,A,B) <-> left_apart_point(A,L) & right_apart_point(B,L) | right_apart_point(A,L) & left_apart_point(B,L))) # label(a8_defns) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 9 (all L all A all B (before_on_line(L,A,B) <-> distinct_points(A,B) & incident_point_and_line(A,L) & incident_point_and_line(B,L) & equally_directed_lines(L,line_connecting(A,B)))) # label(ax4_defns) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 10 (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(a9_defns) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 11 (all A -distinct_points(A,A)) # label(ax1_basics) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 12 (all A all B all C (distinct_points(A,B) -> distinct_points(A,C) | distinct_points(B,C))) # label(ax2_basics) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 13 (all L -distinct_lines(L,L)) # label(ax3_basics) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 14 (all L all M all N (distinct_lines(L,M) -> distinct_lines(L,N) | distinct_lines(M,N))) # label(ax4_basics) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 15 (all L equally_directed_lines(L,L)) # label(ax5_basics) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 16 (all L all M all N (unequally_directed_lines(L,M) -> unequally_directed_lines(L,N) | unequally_directed_lines(M,N))) # label(ax6_basics) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 17 (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(ax7_basics) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 18 (all L all M (unequally_directed_lines(L,M) | unequally_directed_lines(L,reverse_line(M)))) # label(ax8_basics) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 19 (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(ax9_basics) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 20 (all A all L -(left_apart_point(A,L) | left_apart_point(A,reverse_line(L)))) # label(ax10_basics) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 21 (all L all M -(left_convergent_lines(L,M) | left_convergent_lines(L,reverse_line(M)))) # label(ax11_basics) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 22 (all A all B (point(A) & point(B) & distinct_points(A,B) -> line(line_connecting(A,B)))) # label(ax1_cons_objs) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 23 (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(ax2_cons_objs) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 24 (all L all A (point(A) & line(L) -> line(parallel_through_point(L,A)))) # label(ax3_cons_objs) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 25 (all L (line(L) -> line(reverse_line(L)))) # label(ax4_cons_objs) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 26 (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(ax5_cons_objs) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 27 (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(ax6_cons_objs) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 28 (all A all L -apart_point_and_line(A,parallel_through_point(L,A))) # label(ax7_cons_objs) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 29 (all L -distinct_lines(L,reverse_line(L))) # label(ax8_cons_objs) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 30 (all A all B (distinct_points(A,B) -> equally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))))) # label(ax9_cons_objs) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 31 (all A all L equally_directed_lines(parallel_through_point(L,A),L)) # label(ax10_cons_objs) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 32 (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(ax1_uniq_cons) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 33 (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(ax2_uniq_cons) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 34 (all A all B all L (left_apart_point(A,L) -> distinct_points(A,B) | left_apart_point(B,L))) # label(ax1_subs) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 35 (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(ax2_subs) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 36 (all L all M all N (left_convergent_lines(L,M) -> unequally_directed_lines(M,N) | left_convergent_lines(L,N))) # label(ax3_subs) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 37 -(all L all M (unequally_directed_lines(L,M) <-> unequally_directed_opposite_lines(L,reverse_line(M)))) # label(con) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.45/1.03
% 0.45/1.03 ============================== end of process non-clausal formulas ===
% 0.45/1.03
% 0.45/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.45/1.03
% 0.45/1.03 ============================== PREDICATE ELIMINATION =================
% 0.45/1.03 38 -equally_directed_lines(A,B) | -unequally_directed_lines(A,B) # label(a4_defns) # label(axiom). [clausify(4)].
% 0.45/1.03 39 equally_directed_lines(A,A) # label(ax5_basics) # label(axiom). [clausify(15)].
% 0.45/1.03 40 equally_directed_lines(parallel_through_point(A,B),A) # label(ax10_cons_objs) # label(axiom). [clausify(31)].
% 0.45/1.03 41 equally_directed_lines(A,B) | unequally_directed_lines(A,B) # label(a4_defns) # label(axiom). [clausify(4)].
% 0.45/1.03 Derived: -unequally_directed_lines(A,A). [resolve(38,a,39,a)].
% 0.45/1.03 Derived: -unequally_directed_lines(parallel_through_point(A,B),A). [resolve(38,a,40,a)].
% 0.45/1.03 42 -before_on_line(A,B,C) | equally_directed_lines(A,line_connecting(B,C)) # label(ax4_defns) # label(axiom). [clausify(9)].
% 0.45/1.03 Derived: -before_on_line(A,B,C) | -unequally_directed_lines(A,line_connecting(B,C)). [resolve(42,b,38,a)].
% 0.45/1.03 43 -distinct_points(A,B) | equally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))) # label(ax9_cons_objs) # label(axiom). [clausify(30)].
% 0.45/1.03 Derived: -distinct_points(A,B) | -unequally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))). [resolve(43,b,38,a)].
% 0.45/1.03 44 before_on_line(A,B,C) | -distinct_points(B,C) | -incident_point_and_line(B,A) | -incident_point_and_line(C,A) | -equally_directed_lines(A,line_connecting(B,C)) # label(ax4_defns) # label(axiom). [clausify(9)].
% 0.45/1.03 Derived: before_on_line(line_connecting(A,B),A,B) | -distinct_points(A,B) | -incident_point_and_line(A,line_connecting(A,B)) | -incident_point_and_line(B,line_connecting(A,B)). [resolve(44,e,39,a)].
% 0.45/1.03 Derived: before_on_line(parallel_through_point(line_connecting(A,B),C),A,B) | -distinct_points(A,B) | -incident_point_and_line(A,parallel_through_point(line_connecting(A,B),C)) | -incident_point_and_line(B,parallel_through_point(line_connecting(A,B),C)). [resolve(44,e,40,a)].
% 0.45/1.03 Derived: before_on_line(A,B,C) | -distinct_points(B,C) | -incident_point_and_line(B,A) | -incident_point_and_line(C,A) | unequally_directed_lines(A,line_connecting(B,C)). [resolve(44,e,41,a)].
% 0.45/1.03 45 -equally_directed_opposite_lines(A,B) | -unequally_directed_opposite_lines(A,B) # label(a5_defns) # label(axiom). [clausify(5)].
% 0.45/1.03 46 equally_directed_opposite_lines(A,B) | unequally_directed_opposite_lines(A,B) # label(a5_defns) # label(axiom). [clausify(5)].
% 0.45/1.03 47 -unequally_directed_lines(c1,c2) | -unequally_directed_opposite_lines(c1,reverse_line(c2)) # label(con) # label(negated_conjecture). [clausify(37)].
% 0.45/1.03 48 unequally_directed_lines(c1,c2) | unequally_directed_opposite_lines(c1,reverse_line(c2)) # label(con) # label(negated_conjecture). [clausify(37)].
% 0.45/1.03 49 -convergent_lines(A,B) | unequally_directed_opposite_lines(A,B) # label(a7_defns) # label(axiom). [clausify(7)].
% 0.45/1.03 Derived: -convergent_lines(c1,reverse_line(c2)) | -unequally_directed_lines(c1,c2). [resolve(49,b,47,b)].
% 0.45/1.03 50 -unequally_directed_opposite_lines(A,B) | unequally_directed_lines(A,reverse_line(B)) # label(a1_defns) # label(axiom). [clausify(1)].
% 0.45/1.03 Derived: unequally_directed_lines(c1,reverse_line(reverse_line(c2))) | unequally_directed_lines(c1,c2). [resolve(50,a,48,b)].
% 0.45/1.03 Derived: unequally_directed_lines(A,reverse_line(B)) | -convergent_lines(A,B). [resolve(50,a,49,b)].
% 0.45/1.03 51 unequally_directed_opposite_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)) # label(a1_defns) # label(axiom). [clausify(1)].
% 0.45/1.03 Derived: -unequally_directed_lines(c1,reverse_line(reverse_line(c2))) | -unequally_directed_lines(c1,c2). [resolve(51,a,47,b)].
% 0.45/1.03 52 convergent_lines(A,B) | -unequally_directed_lines(A,B) | -unequally_directed_opposite_lines(A,B) # label(a7_defns) # label(axiom). [clausify(7)].
% 0.45/1.03 Derived: convergent_lines(c1,reverse_line(c2)) | -unequally_directed_lines(c1,reverse_line(c2)) | unequally_directed_lines(c1,c2). [resolve(52,c,48,b)].
% 0.45/1.03 Derived: convergent_lines(A,B) | -unequally_directed_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)). [resolve(52,c,51,a)].
% 0.45/1.03 53 apart_point_and_line(A,B) | -left_apart_point(A,B) # label(a6_defns) # label(axiom). [clausify(6)].
% 0.45/1.03 54 -apart_point_and_line(A,parallel_through_point(B,A)) # label(ax7_cons_objs) # label(axiom). [clausify(28)].
% 0.45/1.03 55 -distinct_points(A,B) | -apart_point_and_line(A,line_connecting(A,B)) # label(ax5_cons_objs) # label(axiom). [clausify(26)].
% 0.45/1.03 56 -distinct_points(A,B) | -apart_point_and_line(B,line_connecting(A,B)) # label(ax5_cons_objs) # label(axiom). [clausify(26)].
% 0.45/1.03 57 -unequally_directed_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)) | -apart_point_and_line(intersection_point(A,B),A) # label(ax6_cons_objs) # label(axiom). [clausify(27)].
% 0.45/1.03 58 -unequally_directed_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)) | -apart_point_and_line(intersection_point(A,B),B) # label(ax6_cons_objs) # label(axiom). [clausify(27)].
% 0.45/1.03 Derived: -left_apart_point(A,parallel_through_point(B,A)). [resolve(53,a,54,a)].
% 0.45/1.03 Derived: -left_apart_point(A,line_connecting(A,B)) | -distinct_points(A,B). [resolve(53,a,55,b)].
% 0.45/1.03 Derived: -left_apart_point(A,line_connecting(B,A)) | -distinct_points(B,A). [resolve(53,a,56,b)].
% 0.45/1.03 Derived: -left_apart_point(intersection_point(A,B),A) | -unequally_directed_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)). [resolve(53,a,57,c)].
% 0.45/1.03 Derived: -left_apart_point(intersection_point(A,B),B) | -unequally_directed_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)). [resolve(53,a,58,c)].
% 0.45/1.03 59 apart_point_and_line(A,B) | -right_apart_point(A,B) # label(a6_defns) # label(axiom). [clausify(6)].
% 0.45/1.03 Derived: -right_apart_point(A,parallel_through_point(B,A)). [resolve(59,a,54,a)].
% 0.45/1.03 Derived: -right_apart_point(A,line_connecting(A,B)) | -distinct_points(A,B). [resolve(59,a,55,b)].
% 0.45/1.03 Derived: -right_apart_point(A,line_connecting(B,A)) | -distinct_points(B,A). [resolve(59,a,56,b)].
% 0.45/1.03 Derived: -right_apart_point(intersection_point(A,B),A) | -unequally_directed_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)). [resolve(59,a,57,c)].
% 0.45/1.03 Derived: -right_apart_point(intersection_point(A,B),B) | -unequally_directed_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)). [resolve(59,a,58,c)].
% 0.45/1.03 60 -apart_point_and_line(A,B) | left_apart_point(A,B) | right_apart_point(A,B) # label(a6_defns) # label(axiom). [clausify(6)].
% 0.45/1.03 61 convergent_lines(c1,reverse_line(c2)) | -unequally_directed_lines(c1,reverse_line(c2)) | unequally_directed_lines(c1,c2). [resolve(52,c,48,b)].
% 0.45/1.03 62 -convergent_lines(A,B) | unequally_directed_lines(A,B) # label(a7_defns) # label(axiom). [clausify(7)].
% 0.45/1.03 63 -convergent_lines(c1,reverse_line(c2)) | -unequally_directed_lines(c1,c2). [resolve(49,b,47,b)].
% 0.45/1.03 64 unequally_directed_lines(A,reverse_line(B)) | -convergent_lines(A,B). [resolve(50,a,49,b)].
% 0.45/1.03 Derived: -unequally_directed_lines(c1,reverse_line(c2)) | unequally_directed_lines(c1,c2) | unequally_directed_lines(c1,reverse_line(reverse_line(c2))). [resolve(61,a,64,b)].
% 0.45/1.03 65 convergent_lines(A,B) | -unequally_directed_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)). [resolve(52,c,51,a)].
% 0.45/1.03 Derived: -unequally_directed_lines(c1,reverse_line(c2)) | -unequally_directed_lines(c1,reverse_line(reverse_line(c2))) | -unequally_directed_lines(c1,c2). [resolve(65,a,63,a)].
% 0.45/1.03 66 right_convergent_lines(A,B) | -left_convergent_lines(A,reverse_line(B)) # label(a3_defns) # label(axiom). [clausify(3)].
% 0.45/1.03 67 -right_convergent_lines(A,B) | left_convergent_lines(A,reverse_line(B)) # label(a3_defns) # label(axiom). [clausify(3)].
% 0.45/1.04 68 divides_points(A,B,C) | -left_apart_point(B,A) | -right_apart_point(C,A) # label(a8_defns) # label(axiom). [clausify(8)].
% 0.45/1.04 69 -divides_points(A,B,C) | left_apart_point(B,A) | right_apart_point(B,A) # label(a8_defns) # label(axiom). [clausify(8)].
% 0.45/1.04 70 -divides_points(A,B,C) | left_apart_point(B,A) | left_apart_point(C,A) # label(a8_defns) # label(axiom). [clausify(8)].
% 0.45/1.04 71 -divides_points(A,B,C) | right_apart_point(C,A) | right_apart_point(B,A) # label(a8_defns) # label(axiom). [clausify(8)].
% 0.45/1.04 72 -divides_points(A,B,C) | right_apart_point(C,A) | left_apart_point(C,A) # label(a8_defns) # label(axiom). [clausify(8)].
% 0.45/1.04 73 divides_points(A,B,C) | -right_apart_point(B,A) | -left_apart_point(C,A) # label(a8_defns) # label(axiom). [clausify(8)].
% 0.45/1.04 74 right_apart_point(A,B) | -left_apart_point(A,reverse_line(B)) # label(a2_defns) # label(axiom). [clausify(2)].
% 0.45/1.04 75 -right_apart_point(A,B) | left_apart_point(A,reverse_line(B)) # label(a2_defns) # label(axiom). [clausify(2)].
% 0.45/1.04 76 -right_apart_point(A,parallel_through_point(B,A)). [resolve(59,a,54,a)].
% 0.45/1.04 Derived: -left_apart_point(A,reverse_line(parallel_through_point(B,A))). [resolve(76,a,74,a)].
% 0.45/1.04 77 -right_apart_point(A,line_connecting(A,B)) | -distinct_points(A,B). [resolve(59,a,55,b)].
% 0.45/1.04 Derived: -distinct_points(A,B) | -left_apart_point(A,reverse_line(line_connecting(A,B))). [resolve(77,a,74,a)].
% 0.45/1.04 78 -right_apart_point(A,line_connecting(B,A)) | -distinct_points(B,A). [resolve(59,a,56,b)].
% 0.45/1.04 Derived: -distinct_points(A,B) | -left_apart_point(B,reverse_line(line_connecting(A,B))). [resolve(78,a,74,a)].
% 0.45/1.04 79 -right_apart_point(intersection_point(A,B),A) | -unequally_directed_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)). [resolve(59,a,57,c)].
% 0.45/1.04 Derived: -unequally_directed_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)) | -left_apart_point(intersection_point(A,B),reverse_line(A)). [resolve(79,a,74,a)].
% 0.45/1.04 80 -right_apart_point(intersection_point(A,B),B) | -unequally_directed_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)). [resolve(59,a,58,c)].
% 0.45/1.04 Derived: -unequally_directed_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)) | -left_apart_point(intersection_point(A,B),reverse_line(B)). [resolve(80,a,74,a)].
% 0.45/1.04 81 between_on_line(A,B,C,D) | -before_on_line(A,B,C) | -before_on_line(A,C,D) # label(a9_defns) # label(axiom). [clausify(10)].
% 0.45/1.04 82 -between_on_line(A,B,C,D) | before_on_line(A,B,C) | before_on_line(A,D,C) # label(a9_defns) # label(axiom). [clausify(10)].
% 0.45/1.04 83 -between_on_line(A,B,C,D) | before_on_line(A,B,C) | before_on_line(A,C,B) # label(a9_defns) # label(axiom). [clausify(10)].
% 0.45/1.04 84 -between_on_line(A,B,C,D) | before_on_line(A,C,D) | before_on_line(A,D,C) # label(a9_defns) # label(axiom). [clausify(10)].
% 0.45/1.04 85 -between_on_line(A,B,C,D) | before_on_line(A,C,D) | before_on_line(A,C,B) # label(a9_defns) # label(axiom). [clausify(10)].
% 0.45/1.04 86 between_on_line(A,B,C,D) | -before_on_line(A,D,C) | -before_on_line(A,C,B) # label(a9_defns) # label(axiom). [clausify(10)].
% 0.45/1.04 87 before_on_line(line_connecting(A,B),A,B) | -distinct_points(A,B) | -incident_point_and_line(A,line_connecting(A,B)) | -incident_point_and_line(B,line_connecting(A,B)). [resolve(44,e,39,a)].
% 0.45/1.04 88 -before_on_line(A,B,C) | distinct_points(B,C) # label(ax4_defns) # label(axiom). [clausify(9)].
% 0.45/1.04 89 -before_on_line(A,B,C) | incident_point_and_line(B,A) # label(ax4_defns) # label(axiom). [clausify(9)].
% 0.45/1.04 90 -before_on_line(A,B,C) | incident_point_and_line(C,A) # label(ax4_defns) # label(axiom). [clausify(9)].
% 0.45/1.04 91 -before_on_line(A,B,C) | -unequally_directed_lines(A,line_connecting(B,C)). [resolve(42,b,38,a)].
% 0.45/1.04 Derived: -distinct_points(A,B) | -incident_point_and_line(A,line_connecting(A,B)) | -incident_point_and_line(B,line_connecting(A,B)) | -unequally_directed_lines(line_connecting(A,B),line_connecting(A,B)). [resolve(87,a,91,a)].
% 0.45/1.04 92 before_on_line(parallel_through_point(line_connecting(A,B),C),A,B) | -distinct_points(A,B) | -incident_point_and_line(A,parallel_through_point(line_connecting(A,B),C)) | -incident_point_and_line(B,parallel_through_point(line_connecting(A,B),C)). [resolve(44,e,40,a)].
% 0.45/1.04 Derived: -distinct_points(A,B) | -incident_point_and_line(A,parallel_through_point(line_connecting(A,B),C)) | -incident_point_and_line(B,parallel_through_point(line_connecting(A,B),C)) | -unequally_directed_lines(parallel_through_point(line_connecting(A,B),C),line_connecting(A,B)). [resolve(92,a,91,a)].
% 0.45/1.04 93 before_on_line(A,B,C) | -distinct_points(B,C) | -incident_point_and_line(B,A) | -incident_point_and_line(C,A) | unequally_directed_lines(A,line_connecting(B,C)). [resolve(44,e,41,a)].
% 0.45/1.04
% 0.45/1.04 ============================== end predicate elimination =============
% 0.45/1.04
% 0.45/1.04 Auto_denials: (non-Horn, no changes).
% 0.45/1.04
% 0.45/1.04 Term ordering decisions:
% 0.45/1.04
% 0.45/1.04 % Assigning unary symbol reverse_line kb_weight 0 and highest precedence (14).
% 0.45/1.04 Function symbol KB weights: c1=1. c2=1. line_connecting=1. intersection_point=1. parallel_through_point=1. reverse_line=0.
% 0.45/1.04
% 0.45/1.04 ============================== end of process initial clauses ========
% 0.45/1.04
% 0.45/1.04 ============================== CLAUSES FOR SEARCH ====================
% 0.45/1.04
% 0.45/1.04 ============================== end of clauses for search =============
% 0.45/1.04
% 0.45/1.04 ============================== SEARCH ================================
% 0.45/1.04
% 0.45/1.04 % Starting search at 0.02 seconds.
% 0.45/1.04
% 0.45/1.04 ============================== PROOF =================================
% 0.45/1.04 % SZS status Theorem
% 0.45/1.04 % SZS output start Refutation
% 0.45/1.04
% 0.45/1.04 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.45/1.04 % Length of proof is 26.
% 0.45/1.04 % Level of proof is 7.
% 0.45/1.04 % Maximum clause weight is 11.000.
% 0.45/1.04 % Given clauses 26.
% 0.45/1.04
% 0.45/1.04 1 (all X all Y (unequally_directed_opposite_lines(X,Y) <-> unequally_directed_lines(X,reverse_line(Y)))) # label(a1_defns) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.04 16 (all L all M all N (unequally_directed_lines(L,M) -> unequally_directed_lines(L,N) | unequally_directed_lines(M,N))) # label(ax6_basics) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.04 18 (all L all M (unequally_directed_lines(L,M) | unequally_directed_lines(L,reverse_line(M)))) # label(ax8_basics) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.04 19 (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(ax9_basics) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.04 21 (all L all M -(left_convergent_lines(L,M) | left_convergent_lines(L,reverse_line(M)))) # label(ax11_basics) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.04 37 -(all L all M (unequally_directed_lines(L,M) <-> unequally_directed_opposite_lines(L,reverse_line(M)))) # label(con) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.45/1.04 47 -unequally_directed_lines(c1,c2) | -unequally_directed_opposite_lines(c1,reverse_line(c2)) # label(con) # label(negated_conjecture). [clausify(37)].
% 0.45/1.04 48 unequally_directed_lines(c1,c2) | unequally_directed_opposite_lines(c1,reverse_line(c2)) # label(con) # label(negated_conjecture). [clausify(37)].
% 0.45/1.04 50 -unequally_directed_opposite_lines(A,B) | unequally_directed_lines(A,reverse_line(B)) # label(a1_defns) # label(axiom). [clausify(1)].
% 0.45/1.04 51 unequally_directed_opposite_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)) # label(a1_defns) # label(axiom). [clausify(1)].
% 0.45/1.04 94 unequally_directed_lines(A,B) | unequally_directed_lines(A,reverse_line(B)) # label(ax8_basics) # label(axiom). [clausify(18)].
% 0.45/1.04 98 -left_convergent_lines(A,B) # label(ax11_basics) # label(axiom). [clausify(21)].
% 0.45/1.04 104 -unequally_directed_lines(A,B) | unequally_directed_lines(A,C) | unequally_directed_lines(B,C) # label(ax6_basics) # label(axiom). [clausify(16)].
% 0.45/1.04 111 -unequally_directed_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)) | left_convergent_lines(A,B) | left_convergent_lines(A,reverse_line(B)) # label(ax9_basics) # label(axiom). [clausify(19)].
% 0.45/1.04 112 -unequally_directed_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)). [copy(111),unit_del(c,98),unit_del(d,98)].
% 0.45/1.04 119 unequally_directed_lines(c1,reverse_line(reverse_line(c2))) | unequally_directed_lines(c1,c2). [resolve(50,a,48,b)].
% 0.45/1.04 120 -unequally_directed_lines(c1,reverse_line(reverse_line(c2))) | -unequally_directed_lines(c1,c2). [resolve(51,a,47,b)].
% 0.45/1.04 122 unequally_directed_lines(A,B) | unequally_directed_lines(reverse_line(C),B) | unequally_directed_lines(A,C). [resolve(104,a,94,b)].
% 0.45/1.04 125 unequally_directed_lines(reverse_line(A),A). [factor(122,b,c),merge(b)].
% 0.45/1.04 130 unequally_directed_lines(c1,c2) | unequally_directed_lines(c1,A) | unequally_directed_lines(reverse_line(reverse_line(c2)),A). [resolve(119,a,104,a)].
% 0.45/1.04 131 unequally_directed_lines(c1,c2) | unequally_directed_lines(reverse_line(reverse_line(c2)),c2). [factor(130,a,b)].
% 0.45/1.04 132 -unequally_directed_lines(c1,c2) | unequally_directed_lines(c1,reverse_line(c2)). [resolve(120,a,94,b)].
% 0.45/1.04 143 -unequally_directed_lines(reverse_line(reverse_line(A)),A). [resolve(125,a,112,b)].
% 0.45/1.04 145 unequally_directed_lines(c1,c2). [back_unit_del(131),unit_del(b,143)].
% 0.45/1.04 146 unequally_directed_lines(c1,reverse_line(c2)). [back_unit_del(132),unit_del(a,145)].
% 0.45/1.04 149 $F. [ur(112,a,145,a),unit_del(a,146)].
% 0.45/1.04
% 0.45/1.04 % SZS output end Refutation
% 0.45/1.04 ============================== end of proof ==========================
% 0.45/1.04
% 0.45/1.04 ============================== STATISTICS ============================
% 0.45/1.04
% 0.45/1.04 Given=26. Generated=124. Kept=49. proofs=1.
% 0.45/1.04 Usable=24. Sos=14. Demods=0. Limbo=1, Disabled=110. Hints=0.
% 0.45/1.04 Megabytes=0.13.
% 0.45/1.04 User_CPU=0.02, System_CPU=0.01, Wall_clock=0.
% 0.45/1.04
% 0.45/1.04 ============================== end of statistics =====================
% 0.45/1.04
% 0.45/1.04 ============================== end of search =========================
% 0.45/1.04
% 0.45/1.04 THEOREM PROVED
% 0.45/1.04 % SZS status Theorem
% 0.45/1.04
% 0.45/1.04 Exiting with 1 proof.
% 0.45/1.04
% 0.45/1.04 Process 1403 exit (max_proofs) Sat Jun 18 12:22:33 2022
% 0.45/1.04 Prover9 interrupted
%------------------------------------------------------------------------------