TSTP Solution File: GEO265+3 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GEO265+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 05:55:40 EDT 2022
% Result : Theorem 0.83s 1.10s
% Output : Refutation 0.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GEO265+3 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.36 % Computer : n027.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Fri Jun 17 22:29:22 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.83/1.09 ============================== Prover9 ===============================
% 0.83/1.09 Prover9 (32) version 2009-11A, November 2009.
% 0.83/1.09 Process 14134 was started by sandbox2 on n027.cluster.edu,
% 0.83/1.09 Fri Jun 17 22:29:23 2022
% 0.83/1.09 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_13981_n027.cluster.edu".
% 0.83/1.09 ============================== end of head ===========================
% 0.83/1.09
% 0.83/1.09 ============================== INPUT =================================
% 0.83/1.09
% 0.83/1.09 % Reading from file /tmp/Prover9_13981_n027.cluster.edu
% 0.83/1.09
% 0.83/1.09 set(prolog_style_variables).
% 0.83/1.09 set(auto2).
% 0.83/1.09 % set(auto2) -> set(auto).
% 0.83/1.09 % set(auto) -> set(auto_inference).
% 0.83/1.09 % set(auto) -> set(auto_setup).
% 0.83/1.09 % set(auto_setup) -> set(predicate_elim).
% 0.83/1.09 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.83/1.09 % set(auto) -> set(auto_limits).
% 0.83/1.09 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.83/1.09 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.83/1.09 % set(auto) -> set(auto_denials).
% 0.83/1.09 % set(auto) -> set(auto_process).
% 0.83/1.09 % set(auto2) -> assign(new_constants, 1).
% 0.83/1.09 % set(auto2) -> assign(fold_denial_max, 3).
% 0.83/1.09 % set(auto2) -> assign(max_weight, "200.000").
% 0.83/1.09 % set(auto2) -> assign(max_hours, 1).
% 0.83/1.09 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.83/1.09 % set(auto2) -> assign(max_seconds, 0).
% 0.83/1.09 % set(auto2) -> assign(max_minutes, 5).
% 0.83/1.09 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.83/1.09 % set(auto2) -> set(sort_initial_sos).
% 0.83/1.09 % set(auto2) -> assign(sos_limit, -1).
% 0.83/1.09 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.83/1.09 % set(auto2) -> assign(max_megs, 400).
% 0.83/1.09 % set(auto2) -> assign(stats, some).
% 0.83/1.09 % set(auto2) -> clear(echo_input).
% 0.83/1.09 % set(auto2) -> set(quiet).
% 0.83/1.09 % set(auto2) -> clear(print_initial_clauses).
% 0.83/1.09 % set(auto2) -> clear(print_given).
% 0.83/1.09 assign(lrs_ticks,-1).
% 0.83/1.09 assign(sos_limit,10000).
% 0.83/1.09 assign(order,kbo).
% 0.83/1.09 set(lex_order_vars).
% 0.83/1.09 clear(print_given).
% 0.83/1.09
% 0.83/1.09 % formulas(sos). % not echoed (37 formulas)
% 0.83/1.09
% 0.83/1.09 ============================== end of input ==========================
% 0.83/1.09
% 0.83/1.09 % From the command line: assign(max_seconds, 300).
% 0.83/1.09
% 0.83/1.09 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.83/1.09
% 0.83/1.09 % Formulas that are not ordinary clauses:
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 4 (all X all Y (equally_directed_lines(X,Y) <-> -unequally_directed_lines(X,Y))) # label(a4_defns) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 11 (all A -distinct_points(A,A)) # label(ax1_basics) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.09 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].
% 0.83/1.09 13 (all L -distinct_lines(L,L)) # label(ax3_basics) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.09 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].
% 0.83/1.09 15 (all L equally_directed_lines(L,L)) # label(ax5_basics) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 25 (all L (line(L) -> line(reverse_line(L)))) # label(ax4_cons_objs) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 29 (all L -distinct_lines(L,reverse_line(L))) # label(ax8_cons_objs) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.09 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].
% 0.83/1.09 31 (all A all L equally_directed_lines(parallel_through_point(L,A),L)) # label(ax10_cons_objs) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 37 -(all L all M (equally_directed_lines(L,reverse_line(M)) -> equally_directed_opposite_lines(L,M))) # label(con) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.83/1.09
% 0.83/1.09 ============================== end of process non-clausal formulas ===
% 0.83/1.09
% 0.83/1.09 ============================== PROCESS INITIAL CLAUSES ===============
% 0.83/1.09
% 0.83/1.09 ============================== PREDICATE ELIMINATION =================
% 0.83/1.09 38 -equally_directed_lines(A,B) | -unequally_directed_lines(A,B) # label(a4_defns) # label(axiom). [clausify(4)].
% 0.83/1.09 39 equally_directed_lines(A,A) # label(ax5_basics) # label(axiom). [clausify(15)].
% 0.83/1.09 40 equally_directed_lines(c1,reverse_line(c2)) # label(con) # label(negated_conjecture). [clausify(37)].
% 0.83/1.09 41 equally_directed_lines(parallel_through_point(A,B),A) # label(ax10_cons_objs) # label(axiom). [clausify(31)].
% 0.83/1.09 42 equally_directed_lines(A,B) | unequally_directed_lines(A,B) # label(a4_defns) # label(axiom). [clausify(4)].
% 0.83/1.09 Derived: -unequally_directed_lines(A,A). [resolve(38,a,39,a)].
% 0.83/1.09 Derived: -unequally_directed_lines(c1,reverse_line(c2)). [resolve(38,a,40,a)].
% 0.83/1.09 Derived: -unequally_directed_lines(parallel_through_point(A,B),A). [resolve(38,a,41,a)].
% 0.83/1.09 43 -before_on_line(A,B,C) | equally_directed_lines(A,line_connecting(B,C)) # label(ax4_defns) # label(axiom). [clausify(9)].
% 0.83/1.09 Derived: -before_on_line(A,B,C) | -unequally_directed_lines(A,line_connecting(B,C)). [resolve(43,b,38,a)].
% 0.83/1.09 44 -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)].
% 0.83/1.09 Derived: -distinct_points(A,B) | -unequally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))). [resolve(44,b,38,a)].
% 0.83/1.09 45 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)].
% 0.83/1.09 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(45,e,39,a)].
% 0.83/1.09 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(45,e,41,a)].
% 0.83/1.09 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(45,e,42,a)].
% 0.83/1.09 46 -equally_directed_opposite_lines(c1,c2) # label(con) # label(negated_conjecture). [clausify(37)].
% 0.83/1.09 47 equally_directed_opposite_lines(A,B) | unequally_directed_opposite_lines(A,B) # label(a5_defns) # label(axiom). [clausify(5)].
% 0.83/1.09 Derived: unequally_directed_opposite_lines(c1,c2). [resolve(46,a,47,a)].
% 0.83/1.09 48 -equally_directed_opposite_lines(A,B) | -unequally_directed_opposite_lines(A,B) # label(a5_defns) # label(axiom). [clausify(5)].
% 0.83/1.09 49 apart_point_and_line(A,B) | -left_apart_point(A,B) # label(a6_defns) # label(axiom). [clausify(6)].
% 0.83/1.09 50 -apart_point_and_line(A,parallel_through_point(B,A)) # label(ax7_cons_objs) # label(axiom). [clausify(28)].
% 0.83/1.09 51 -distinct_points(A,B) | -apart_point_and_line(A,line_connecting(A,B)) # label(ax5_cons_objs) # label(axiom). [clausify(26)].
% 0.83/1.09 52 -distinct_points(A,B) | -apart_point_and_line(B,line_connecting(A,B)) # label(ax5_cons_objs) # label(axiom). [clausify(26)].
% 0.83/1.09 53 -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)].
% 0.83/1.09 54 -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)].
% 0.83/1.09 Derived: -left_apart_point(A,parallel_through_point(B,A)). [resolve(49,a,50,a)].
% 0.83/1.09 Derived: -left_apart_point(A,line_connecting(A,B)) | -distinct_points(A,B). [resolve(49,a,51,b)].
% 0.83/1.09 Derived: -left_apart_point(A,line_connecting(B,A)) | -distinct_points(B,A). [resolve(49,a,52,b)].
% 0.83/1.09 Derived: -left_apart_point(intersection_point(A,B),A) | -unequally_directed_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)). [resolve(49,a,53,c)].
% 0.83/1.09 Derived: -left_apart_point(intersection_point(A,B),B) | -unequally_directed_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)). [resolve(49,a,54,c)].
% 0.83/1.09 55 apart_point_and_line(A,B) | -right_apart_point(A,B) # label(a6_defns) # label(axiom). [clausify(6)].
% 0.83/1.09 Derived: -right_apart_point(A,parallel_through_point(B,A)). [resolve(55,a,50,a)].
% 0.83/1.09 Derived: -right_apart_point(A,line_connecting(A,B)) | -distinct_points(A,B). [resolve(55,a,51,b)].
% 0.83/1.09 Derived: -right_apart_point(A,line_connecting(B,A)) | -distinct_points(B,A). [resolve(55,a,52,b)].
% 0.83/1.09 Derived: -right_apart_point(intersection_point(A,B),A) | -unequally_directed_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)). [resolve(55,a,53,c)].
% 0.83/1.09 Derived: -right_apart_point(intersection_point(A,B),B) | -unequally_directed_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)). [resolve(55,a,54,c)].
% 0.83/1.09 56 -apart_point_and_line(A,B) | left_apart_point(A,B) | right_apart_point(A,B) # label(a6_defns) # label(axiom). [clausify(6)].
% 0.83/1.09 57 convergent_lines(A,B) | -unequally_directed_lines(A,B) | -unequally_directed_opposite_lines(A,B) # label(a7_defns) # label(axiom). [clausify(7)].
% 0.83/1.09 58 -convergent_lines(A,B) | unequally_directed_lines(A,B) # label(a7_defns) # label(axiom). [clausify(7)].
% 0.83/1.09 59 -convergent_lines(A,B) | unequally_directed_opposite_lines(A,B) # label(a7_defns) # label(axiom). [clausify(7)].
% 0.83/1.09 60 unequally_directed_opposite_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)) # label(a1_defns) # label(axiom). [clausify(1)].
% 0.83/1.09 61 -unequally_directed_opposite_lines(A,B) | unequally_directed_lines(A,reverse_line(B)) # label(a1_defns) # label(axiom). [clausify(1)].
% 0.83/1.09 62 unequally_directed_opposite_lines(c1,c2). [resolve(46,a,47,a)].
% 0.83/1.09 Derived: unequally_directed_lines(c1,reverse_line(c2)). [resolve(62,a,61,a)].
% 0.83/1.09 63 right_convergent_lines(A,B) | -left_convergent_lines(A,reverse_line(B)) # label(a3_defns) # label(axiom). [clausify(3)].
% 0.83/1.09 64 -right_convergent_lines(A,B) | left_convergent_lines(A,reverse_line(B)) # label(a3_defns) # label(axiom). [clausify(3)].
% 0.83/1.09 65 divides_points(A,B,C) | -left_apart_point(B,A) | -right_apart_point(C,A) # label(a8_defns) # label(axiom). [clausify(8)].
% 0.83/1.09 66 -divides_points(A,B,C) | left_apart_point(B,A) | right_apart_point(B,A) # label(a8_defns) # label(axiom). [clausify(8)].
% 0.83/1.09 67 -divides_points(A,B,C) | left_apart_point(B,A) | left_apart_point(C,A) # label(a8_defns) # label(axiom). [clausify(8)].
% 0.83/1.09 68 -divides_points(A,B,C) | right_apart_point(C,A) | right_apart_point(B,A) # label(a8_defns) # label(axiom). [clausify(8)].
% 0.83/1.09 69 -divides_points(A,B,C) | right_apart_point(C,A) | left_apart_point(C,A) # label(a8_defns) # label(axiom). [clausify(8)].
% 0.83/1.09 70 divides_points(A,B,C) | -right_apart_point(B,A) | -left_apart_point(C,A) # label(a8_defns) # label(axiom). [clausify(8)].
% 0.83/1.09 71 right_apart_point(A,B) | -left_apart_point(A,reverse_line(B)) # label(a2_defns) # label(axiom). [clausify(2)].
% 0.83/1.09 72 -right_apart_point(A,B) | left_apart_point(A,reverse_line(B)) # label(a2_defns) # label(axiom). [clausify(2)].
% 0.83/1.09 73 -right_apart_point(A,parallel_through_point(B,A)). [resolve(55,a,50,a)].
% 0.83/1.09 Derived: -left_apart_point(A,reverse_line(parallel_through_point(B,A))). [resolve(73,a,71,a)].
% 0.83/1.09 74 -right_apart_point(A,line_connecting(A,B)) | -distinct_points(A,B). [resolve(55,a,51,b)].
% 0.83/1.09 Derived: -distinct_points(A,B) | -left_apart_point(A,reverse_line(line_connecting(A,B))). [resolve(74,a,71,a)].
% 0.83/1.10 75 -right_apart_point(A,line_connecting(B,A)) | -distinct_points(B,A). [resolve(55,a,52,b)].
% 0.83/1.10 Derived: -distinct_points(A,B) | -left_apart_point(B,reverse_line(line_connecting(A,B))). [resolve(75,a,71,a)].
% 0.83/1.10 76 -right_apart_point(intersection_point(A,B),A) | -unequally_directed_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)). [resolve(55,a,53,c)].
% 0.83/1.10 Derived: -unequally_directed_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)) | -left_apart_point(intersection_point(A,B),reverse_line(A)). [resolve(76,a,71,a)].
% 0.83/1.10 77 -right_apart_point(intersection_point(A,B),B) | -unequally_directed_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)). [resolve(55,a,54,c)].
% 0.83/1.10 Derived: -unequally_directed_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)) | -left_apart_point(intersection_point(A,B),reverse_line(B)). [resolve(77,a,71,a)].
% 0.83/1.10 78 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)].
% 0.83/1.10 79 -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)].
% 0.83/1.10 80 -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)].
% 0.83/1.10 81 -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)].
% 0.83/1.10 82 -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)].
% 0.83/1.10 83 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)].
% 0.83/1.10 84 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(45,e,39,a)].
% 0.83/1.10 85 -before_on_line(A,B,C) | distinct_points(B,C) # label(ax4_defns) # label(axiom). [clausify(9)].
% 0.83/1.10 86 -before_on_line(A,B,C) | incident_point_and_line(B,A) # label(ax4_defns) # label(axiom). [clausify(9)].
% 0.83/1.10 87 -before_on_line(A,B,C) | incident_point_and_line(C,A) # label(ax4_defns) # label(axiom). [clausify(9)].
% 0.83/1.10 88 -before_on_line(A,B,C) | -unequally_directed_lines(A,line_connecting(B,C)). [resolve(43,b,38,a)].
% 0.83/1.10 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(84,a,88,a)].
% 0.83/1.10 89 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(45,e,41,a)].
% 0.83/1.10 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(89,a,88,a)].
% 0.83/1.10 90 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(45,e,42,a)].
% 0.83/1.10
% 0.83/1.10 ============================== end predicate elimination =============
% 0.83/1.10
% 0.83/1.10 Auto_denials: (non-Horn, no changes).
% 0.83/1.10
% 0.83/1.10 Term ordering decisions:
% 0.83/1.10
% 0.83/1.10 % Assigning unary symbol reverse_line kb_weight 0 and highest precedence (14).
% 0.83/1.10 Function symbol KB weights: c1=1. c2=1. line_connecting=1. intersection_point=1. parallel_through_point=1. reverse_line=0.
% 0.83/1.10
% 0.83/1.10 ============================== PROOF =================================
% 0.83/1.10 % SZS status Theorem
% 0.83/1.10 % SZS output start Refutation
% 0.83/1.10
% 0.83/1.10 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.83/1.10 % Length of proof is 13.
% 0.83/1.10 % Level of proof is 4.
% 0.83/1.10 % Maximum clause weight is 4.000.
% 0.83/1.10 % Given clauses 0.
% 0.83/1.10
% 0.83/1.10 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].
% 0.83/1.10 4 (all X all Y (equally_directed_lines(X,Y) <-> -unequally_directed_lines(X,Y))) # label(a4_defns) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 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].
% 0.83/1.10 37 -(all L all M (equally_directed_lines(L,reverse_line(M)) -> equally_directed_opposite_lines(L,M))) # label(con) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.83/1.10 38 -equally_directed_lines(A,B) | -unequally_directed_lines(A,B) # label(a4_defns) # label(axiom). [clausify(4)].
% 0.83/1.10 40 equally_directed_lines(c1,reverse_line(c2)) # label(con) # label(negated_conjecture). [clausify(37)].
% 0.83/1.10 46 -equally_directed_opposite_lines(c1,c2) # label(con) # label(negated_conjecture). [clausify(37)].
% 0.83/1.10 47 equally_directed_opposite_lines(A,B) | unequally_directed_opposite_lines(A,B) # label(a5_defns) # label(axiom). [clausify(5)].
% 0.83/1.10 61 -unequally_directed_opposite_lines(A,B) | unequally_directed_lines(A,reverse_line(B)) # label(a1_defns) # label(axiom). [clausify(1)].
% 0.83/1.10 62 unequally_directed_opposite_lines(c1,c2). [resolve(46,a,47,a)].
% 0.83/1.10 114 -unequally_directed_lines(c1,reverse_line(c2)). [resolve(38,a,40,a)].
% 0.83/1.10 117 unequally_directed_lines(c1,reverse_line(c2)). [resolve(62,a,61,a)].
% 0.83/1.10 118 $F. [copy(117),unit_del(a,114)].
% 0.83/1.10
% 0.83/1.10 % SZS output end Refutation
% 0.83/1.10 ============================== end of proof ==========================
% 0.83/1.10
% 0.83/1.10 ============================== STATISTICS ============================
% 0.83/1.10
% 0.83/1.10 Given=0. Generated=35. Kept=20. proofs=1.
% 0.83/1.10 Usable=0. Sos=0. Demods=0. Limbo=20, Disabled=88. Hints=0.
% 0.83/1.10 Megabytes=0.10.
% 0.83/1.10 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.83/1.10
% 0.83/1.10 ============================== end of statistics =====================
% 0.83/1.10
% 0.83/1.10 ============================== end of search =========================
% 0.83/1.10
% 0.83/1.10 THEOREM PROVED
% 0.83/1.10 % SZS status Theorem
% 0.83/1.10
% 0.83/1.10 Exiting with 1 proof.
% 0.83/1.10
% 0.83/1.10 Process 14134 exit (max_proofs) Fri Jun 17 22:29:23 2022
% 0.83/1.10 Prover9 interrupted
%------------------------------------------------------------------------------