TSTP Solution File: GEO237+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GEO237+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 05:55:25 EDT 2022
% Result : Theorem 0.40s 0.98s
% Output : Refutation 0.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GEO237+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n018.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 14:01:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.40/0.97 ============================== Prover9 ===============================
% 0.40/0.97 Prover9 (32) version 2009-11A, November 2009.
% 0.40/0.97 Process 23582 was started by sandbox on n018.cluster.edu,
% 0.40/0.97 Sat Jun 18 14:01:33 2022
% 0.40/0.97 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_23425_n018.cluster.edu".
% 0.40/0.97 ============================== end of head ===========================
% 0.40/0.97
% 0.40/0.97 ============================== INPUT =================================
% 0.40/0.97
% 0.40/0.97 % Reading from file /tmp/Prover9_23425_n018.cluster.edu
% 0.40/0.97
% 0.40/0.97 set(prolog_style_variables).
% 0.40/0.97 set(auto2).
% 0.40/0.97 % set(auto2) -> set(auto).
% 0.40/0.97 % set(auto) -> set(auto_inference).
% 0.40/0.97 % set(auto) -> set(auto_setup).
% 0.40/0.97 % set(auto_setup) -> set(predicate_elim).
% 0.40/0.97 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.40/0.97 % set(auto) -> set(auto_limits).
% 0.40/0.97 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.40/0.97 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.40/0.97 % set(auto) -> set(auto_denials).
% 0.40/0.97 % set(auto) -> set(auto_process).
% 0.40/0.97 % set(auto2) -> assign(new_constants, 1).
% 0.40/0.97 % set(auto2) -> assign(fold_denial_max, 3).
% 0.40/0.97 % set(auto2) -> assign(max_weight, "200.000").
% 0.40/0.97 % set(auto2) -> assign(max_hours, 1).
% 0.40/0.97 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.40/0.97 % set(auto2) -> assign(max_seconds, 0).
% 0.40/0.97 % set(auto2) -> assign(max_minutes, 5).
% 0.40/0.97 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.40/0.97 % set(auto2) -> set(sort_initial_sos).
% 0.40/0.97 % set(auto2) -> assign(sos_limit, -1).
% 0.40/0.97 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.40/0.97 % set(auto2) -> assign(max_megs, 400).
% 0.40/0.97 % set(auto2) -> assign(stats, some).
% 0.40/0.97 % set(auto2) -> clear(echo_input).
% 0.40/0.97 % set(auto2) -> set(quiet).
% 0.40/0.97 % set(auto2) -> clear(print_initial_clauses).
% 0.40/0.97 % set(auto2) -> clear(print_given).
% 0.40/0.97 assign(lrs_ticks,-1).
% 0.40/0.97 assign(sos_limit,10000).
% 0.40/0.97 assign(order,kbo).
% 0.40/0.97 set(lex_order_vars).
% 0.40/0.97 clear(print_given).
% 0.40/0.97
% 0.40/0.97 % formulas(sos). % not echoed (37 formulas)
% 0.40/0.97
% 0.40/0.97 ============================== end of input ==========================
% 0.40/0.97
% 0.40/0.97 % From the command line: assign(max_seconds, 300).
% 0.40/0.97
% 0.40/0.97 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.40/0.97
% 0.40/0.97 % Formulas that are not ordinary clauses:
% 0.40/0.97 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].
% 0.40/0.97 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].
% 0.40/0.97 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].
% 0.40/0.97 4 (all X all Y (equally_directed_lines(X,Y) <-> -unequally_directed_lines(X,Y))) # label(a4_defns) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.97 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].
% 0.40/0.97 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].
% 0.40/0.97 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].
% 0.40/0.97 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].
% 0.40/0.97 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].
% 0.40/0.97 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].
% 0.40/0.97 11 (all A -distinct_points(A,A)) # label(ax1_basics) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.97 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].
% 0.40/0.97 13 (all L -distinct_lines(L,L)) # label(ax3_basics) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.97 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].
% 0.40/0.97 15 (all L equally_directed_lines(L,L)) # label(ax5_basics) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.97 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].
% 0.40/0.97 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].
% 0.40/0.97 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].
% 0.40/0.97 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].
% 0.40/0.97 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].
% 0.40/0.97 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].
% 0.40/0.97 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].
% 0.40/0.97 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].
% 0.40/0.97 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].
% 0.40/0.97 25 (all L (line(L) -> line(reverse_line(L)))) # label(ax4_cons_objs) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.97 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].
% 0.40/0.97 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].
% 0.40/0.97 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].
% 0.40/0.97 29 (all L -distinct_lines(L,reverse_line(L))) # label(ax8_cons_objs) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.97 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].
% 0.40/0.97 31 (all A all L equally_directed_lines(parallel_through_point(L,A),L)) # label(ax10_cons_objs) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.97 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].
% 0.40/0.97 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].
% 0.40/0.98 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].
% 0.40/0.98 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].
% 0.40/0.98 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].
% 0.40/0.98 37 -(all A all B all C all L (apart_point_and_line(C,L) -> (divides_points(L,A,B) -> divides_points(L,A,C) | divides_points(L,B,C)))) # label(con) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.40/0.98
% 0.40/0.98 ============================== end of process non-clausal formulas ===
% 0.40/0.98
% 0.40/0.98 ============================== PROCESS INITIAL CLAUSES ===============
% 0.40/0.98
% 0.40/0.98 ============================== PREDICATE ELIMINATION =================
% 0.40/0.98 38 -equally_directed_lines(A,B) | -unequally_directed_lines(A,B) # label(a4_defns) # label(axiom). [clausify(4)].
% 0.40/0.98 39 equally_directed_lines(A,A) # label(ax5_basics) # label(axiom). [clausify(15)].
% 0.40/0.98 40 equally_directed_lines(parallel_through_point(A,B),A) # label(ax10_cons_objs) # label(axiom). [clausify(31)].
% 0.40/0.98 41 equally_directed_lines(A,B) | unequally_directed_lines(A,B) # label(a4_defns) # label(axiom). [clausify(4)].
% 0.40/0.98 Derived: -unequally_directed_lines(A,A). [resolve(38,a,39,a)].
% 0.40/0.98 Derived: -unequally_directed_lines(parallel_through_point(A,B),A). [resolve(38,a,40,a)].
% 0.40/0.98 42 -before_on_line(A,B,C) | equally_directed_lines(A,line_connecting(B,C)) # label(ax4_defns) # label(axiom). [clausify(9)].
% 0.40/0.98 Derived: -before_on_line(A,B,C) | -unequally_directed_lines(A,line_connecting(B,C)). [resolve(42,b,38,a)].
% 0.40/0.98 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)].
% 0.40/0.98 Derived: -distinct_points(A,B) | -unequally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))). [resolve(43,b,38,a)].
% 0.40/0.98 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)].
% 0.40/0.98 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)].
% 0.40/0.98 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)].
% 0.40/0.98 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)].
% 0.40/0.98 45 -apart_point_and_line(A,parallel_through_point(B,A)) # label(ax7_cons_objs) # label(axiom). [clausify(28)].
% 0.40/0.98 46 apart_point_and_line(c3,c4) # label(con) # label(negated_conjecture). [clausify(37)].
% 0.40/0.98 47 -distinct_points(A,B) | -apart_point_and_line(A,line_connecting(A,B)) # label(ax5_cons_objs) # label(axiom). [clausify(26)].
% 0.40/0.98 48 -distinct_points(A,B) | -apart_point_and_line(B,line_connecting(A,B)) # label(ax5_cons_objs) # label(axiom). [clausify(26)].
% 0.40/0.98 49 -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)].
% 0.40/0.98 50 -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)].
% 0.40/0.98 51 apart_point_and_line(A,B) | -left_apart_point(A,B) # label(a6_defns) # label(axiom). [clausify(6)].
% 0.40/0.98 Derived: -left_apart_point(A,parallel_through_point(B,A)). [resolve(51,a,45,a)].
% 0.40/0.98 Derived: -left_apart_point(A,line_connecting(A,B)) | -distinct_points(A,B). [resolve(51,a,47,b)].
% 0.40/0.98 Derived: -left_apart_point(A,line_connecting(B,A)) | -distinct_points(B,A). [resolve(51,a,48,b)].
% 0.40/0.98 Derived: -left_apart_point(intersection_point(A,B),A) | -unequally_directed_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)). [resolve(51,a,49,c)].
% 0.40/0.98 Derived: -left_apart_point(intersection_point(A,B),B) | -unequally_directed_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)). [resolve(51,a,50,c)].
% 0.40/0.98 52 apart_point_and_line(A,B) | -right_apart_point(A,B) # label(a6_defns) # label(axiom). [clausify(6)].
% 0.40/0.98 Derived: -right_apart_point(A,parallel_through_point(B,A)). [resolve(52,a,45,a)].
% 0.40/0.98 Derived: -right_apart_point(A,line_connecting(A,B)) | -distinct_points(A,B). [resolve(52,a,47,b)].
% 0.40/0.98 Derived: -right_apart_point(A,line_connecting(B,A)) | -distinct_points(B,A). [resolve(52,a,48,b)].
% 0.40/0.98 Derived: -right_apart_point(intersection_point(A,B),A) | -unequally_directed_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)). [resolve(52,a,49,c)].
% 0.40/0.98 Derived: -right_apart_point(intersection_point(A,B),B) | -unequally_directed_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)). [resolve(52,a,50,c)].
% 0.40/0.98 53 -apart_point_and_line(A,B) | left_apart_point(A,B) | right_apart_point(A,B) # label(a6_defns) # label(axiom). [clausify(6)].
% 0.40/0.98 Derived: left_apart_point(c3,c4) | right_apart_point(c3,c4). [resolve(53,a,46,a)].
% 0.40/0.98 54 -divides_points(c4,c1,c3) # label(con) # label(negated_conjecture). [clausify(37)].
% 0.40/0.98 55 divides_points(c4,c1,c2) # label(con) # label(negated_conjecture). [clausify(37)].
% 0.40/0.98 56 -divides_points(c4,c2,c3) # label(con) # label(negated_conjecture). [clausify(37)].
% 0.40/0.98 57 -divides_points(A,B,C) | left_apart_point(B,A) | right_apart_point(B,A) # label(a8_defns) # label(axiom). [clausify(8)].
% 0.40/0.98 Derived: left_apart_point(c1,c4) | right_apart_point(c1,c4). [resolve(57,a,55,a)].
% 0.40/0.98 58 -divides_points(A,B,C) | left_apart_point(B,A) | left_apart_point(C,A) # label(a8_defns) # label(axiom). [clausify(8)].
% 0.40/0.98 Derived: left_apart_point(c1,c4) | left_apart_point(c2,c4). [resolve(58,a,55,a)].
% 0.40/0.98 59 -divides_points(A,B,C) | right_apart_point(C,A) | right_apart_point(B,A) # label(a8_defns) # label(axiom). [clausify(8)].
% 0.40/0.98 Derived: right_apart_point(c2,c4) | right_apart_point(c1,c4). [resolve(59,a,55,a)].
% 0.40/0.98 60 -divides_points(A,B,C) | right_apart_point(C,A) | left_apart_point(C,A) # label(a8_defns) # label(axiom). [clausify(8)].
% 0.40/0.98 Derived: right_apart_point(c2,c4) | left_apart_point(c2,c4). [resolve(60,a,55,a)].
% 0.40/0.98 61 divides_points(A,B,C) | -left_apart_point(B,A) | -right_apart_point(C,A) # label(a8_defns) # label(axiom). [clausify(8)].
% 0.40/0.98 Derived: -left_apart_point(c1,c4) | -right_apart_point(c3,c4). [resolve(61,a,54,a)].
% 0.40/0.98 Derived: -left_apart_point(c2,c4) | -right_apart_point(c3,c4). [resolve(61,a,56,a)].
% 0.40/0.98 62 divides_points(A,B,C) | -right_apart_point(B,A) | -left_apart_point(C,A) # label(a8_defns) # label(axiom). [clausify(8)].
% 0.40/0.98 Derived: -right_apart_point(c1,c4) | -left_apart_point(c3,c4). [resolve(62,a,54,a)].
% 0.40/0.98 Derived: -right_apart_point(c2,c4) | -left_apart_point(c3,c4). [resolve(62,a,56,a)].
% 0.40/0.98 63 -equally_directed_opposite_lines(A,B) | -unequally_directed_opposite_lines(A,B) # label(a5_defns) # label(axiom). [clausify(5)].
% 0.40/0.98 64 equally_directed_opposite_lines(A,B) | unequally_directed_opposite_lines(A,B) # label(a5_defns) # label(axiom). [clausify(5)].
% 0.40/0.98 65 convergent_lines(A,B) | -unequally_directed_lines(A,B) | -unequally_directed_opposite_lines(A,B) # label(a7_defns) # label(axiom). [clausify(7)].
% 0.40/0.98 66 -convergent_lines(A,B) | unequally_directed_lines(A,B) # label(a7_defns) # label(axiom). [clausify(7)].
% 0.40/0.98 67 -convergent_lines(A,B) | unequally_directed_opposite_lines(A,B) # label(a7_defns) # label(axiom). [clausify(7)].
% 0.40/0.98 68 unequally_directed_opposite_lines(A,B) | -unequally_directed_lines(A,reverse_line(B)) # label(a1_defns) # label(axiom). [clausify(1)].
% 0.40/0.98 69 -unequally_directed_opposite_lines(A,B) | unequally_directed_lines(A,reverse_line(B)) # label(a1_defns) # label(axiom). [clausify(1)].
% 0.40/0.98 70 right_convergent_lines(A,B) | -left_convergent_lines(A,reverse_line(B)) # label(a3_defns) # label(axiom). [clausify(3)].
% 0.40/0.98 71 -right_convergent_lines(A,B) | left_convergent_lines(A,reverse_line(B)) # label(a3_defns) # label(axiom). [clausify(3)].
% 0.40/0.98 72 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)].
% 0.40/0.98 73 -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)].
% 0.40/0.98 74 -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)].
% 0.40/0.98 75 -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)].
% 0.40/0.98 76 -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)].
% 0.40/0.98 77 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)].
% 0.40/0.98 78 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)].
% 0.40/0.98 79 -before_on_line(A,B,C) | distinct_points(B,C) # label(ax4_defns) # label(axiom). [clausify(9)].
% 0.40/0.98 80 -before_on_line(A,B,C) | incident_point_and_line(B,A) # label(ax4_defns) # label(axiom). [clausify(9)].
% 0.40/0.98 81 -before_on_line(A,B,C) | incident_point_and_line(C,A) # label(ax4_defns) # label(axiom). [clausify(9)].
% 0.40/0.98 82 -before_on_line(A,B,C) | -unequally_directed_lines(A,line_connecting(B,C)). [resolve(42,b,38,a)].
% 0.40/0.98 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(78,a,82,a)].
% 0.40/0.98 83 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)].
% 0.40/0.98 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(83,a,82,a)].
% 0.40/0.98 84 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)].
% 0.40/0.98
% 0.40/0.98 ============================== end predicate elimination =============
% 0.40/0.98
% 0.40/0.98 Auto_denials: (non-Horn, no changes).
% 0.40/0.98
% 0.40/0.98 Term ordering decisions:
% 0.40/0.98
% 0.40/0.98 % Assigning unary symbol reverse_line kb_weight 0 and highest precedence (17).
% 0.40/0.98 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. line_connecting=1. intersection_point=1. parallel_through_point=1. reverse_line=0.
% 0.40/0.98
% 0.40/0.98 ============================== PROOF =================================
% 0.40/0.98 % SZS status Theorem
% 0.40/0.98 % SZS output start Refutation
% 0.40/0.98
% 0.40/0.98 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.40/0.98 % Length of proof is 11.
% 0.40/0.98 % Level of proof is 3.
% 0.40/0.98 % Maximum clause weight is 3.000.
% 0.40/0.98 % Given clauses 0.
% 0.40/0.98
% 0.40/0.98 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].
% 0.40/0.98 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].
% 0.40/0.98 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].
% 0.40/0.98 37 -(all A all B all C all L (apart_point_and_line(C,L) -> (divides_points(L,A,B) -> divides_points(L,A,C) | divides_points(L,B,C)))) # label(con) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.40/0.98 46 apart_point_and_line(c3,c4) # label(con) # label(negated_conjecture). [clausify(37)].
% 0.40/0.98 53 -apart_point_and_line(A,B) | left_apart_point(A,B) | right_apart_point(A,B) # label(a6_defns) # label(axiom). [clausify(6)].
% 0.40/0.98 88 -left_apart_point(A,B) # label(ax10_basics) # label(axiom). [clausify(20)].
% 0.40/0.98 92 -right_apart_point(A,B) | left_apart_point(A,reverse_line(B)) # label(a2_defns) # label(axiom). [clausify(2)].
% 0.40/0.98 93 -right_apart_point(A,B). [copy(92),unit_del(b,88)].
% 0.40/0.98 113 left_apart_point(c3,c4) | right_apart_point(c3,c4). [resolve(53,a,46,a)].
% 0.40/0.98 114 $F. [copy(113),unit_del(a,88),unit_del(b,93)].
% 0.40/0.98
% 0.40/0.98 % SZS output end Refutation
% 0.40/0.98 ============================== end of proof ==========================
% 0.40/0.98
% 0.40/0.98 ============================== STATISTICS ============================
% 0.40/0.98
% 0.40/0.98 Given=0. Generated=41. Kept=20. proofs=1.
% 0.40/0.98 Usable=0. Sos=0. Demods=0. Limbo=20, Disabled=88. Hints=0.
% 0.40/0.98 Megabytes=0.10.
% 0.40/0.98 User_CPU=0.02, System_CPU=0.00, Wall_clock=1.
% 0.40/0.98
% 0.40/0.98 ============================== end of statistics =====================
% 0.40/0.98
% 0.40/0.98 ============================== end of search =========================
% 0.40/0.98
% 0.40/0.98 THEOREM PROVED
% 0.40/0.98 % SZS status Theorem
% 0.40/0.98
% 0.40/0.98 Exiting with 1 proof.
% 0.40/0.98
% 0.40/0.98 Process 23582 exit (max_proofs) Sat Jun 18 14:01:34 2022
% 0.40/0.98 Prover9 interrupted
%------------------------------------------------------------------------------