%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO227+1 : TPTP v9.2.1. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 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 : 300s
% DateTime : Tue May 5 04:20:02 PM UTC 2026
% Result : Theorem 0.28s 1.61s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 32
% Syntax : Number of formulae : 146 ( 41 unt; 0 def)
% Number of atoms : 476 ( 0 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 557 ( 227 ~; 238 |; 65 &)
% ( 6 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 333 ( 27 sgn 163 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(bf_def,axiom,
! [X2,X1,X4] :
( before_on_line(X2,X1,X4)
<=> ( distinct_points(X1,X4)
& ~ ( left_apart_point(X1,X2)
| left_apart_point(X1,reverse_line(X2)) )
& ~ ( left_apart_point(X4,X2)
| left_apart_point(X4,reverse_line(X2)) )
& ~ unequally_directed_lines(X2,line_connecting(X1,X4)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',bf_def) ).
fof(oagco9,axiom,
! [X1,X4] : ~ unequally_directed_lines(line_connecting(X1,X4),reverse_line(line_connecting(X4,X1))),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oagco9) ).
fof(oagco6,axiom,
! [X2,X3] :
( ( unequally_directed_lines(X2,X3)
& unequally_directed_lines(X2,reverse_line(X3)) )
=> ( ~ apart_point_and_line(intersection_point(X2,X3),X2)
& ~ apart_point_and_line(intersection_point(X2,X3),X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oagco6) ).
fof(oagco5,axiom,
! [X1,X4] :
( distinct_points(X1,X4)
=> ( ~ apart_point_and_line(X1,line_connecting(X1,X4))
& ~ apart_point_and_line(X4,line_connecting(X1,X4)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oagco5) ).
fof(oagco10,axiom,
! [X1,X2] : ~ unequally_directed_lines(parallel_through_point(X2,X1),X2),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oagco10) ).
fof(oagco7,axiom,
! [X1,X2] : ~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oagco7) ).
fof(oagco8,axiom,
! [X2] : ~ distinct_lines(X2,reverse_line(X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oagco8) ).
fof(con,conjecture,
! [X2,X3] :
( ( line(X2)
& line(X3) )
=> ~ ( ~ unequally_directed_lines(X2,X3)
& ~ unequally_directed_lines(X2,reverse_line(X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(oag3,axiom,
! [X2] : ~ distinct_lines(X2,X2),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oag3) ).
fof(oag1,axiom,
! [X1] : ~ distinct_points(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oag1) ).
fof(oag5,axiom,
! [X2] : ~ unequally_directed_lines(X2,X2),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oag5) ).
fof(bet_def,axiom,
! [X2,X1,X4,X5] :
( between_on_line(X2,X1,X4,X5)
<=> ( ( before_on_line(X2,X1,X4)
& before_on_line(X2,X4,X5) )
| ( before_on_line(X2,X5,X4)
& before_on_line(X2,X4,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',bet_def) ).
fof(oaguc1,axiom,
! [X1,X4,X2,X3] :
( ( distinct_points(X1,X4)
& distinct_lines(X2,X3) )
=> ( left_apart_point(X1,X2)
| left_apart_point(X4,X2)
| left_apart_point(X1,X3)
| left_apart_point(X4,X3)
| left_apart_point(X1,reverse_line(X2))
| left_apart_point(X4,reverse_line(X2))
| left_apart_point(X1,reverse_line(X3))
| left_apart_point(X4,reverse_line(X3)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oaguc1) ).
fof(div_def,axiom,
! [X1,X4,X2] :
( divides_points(X2,X1,X4)
<=> ( ( left_apart_point(X1,X2)
& left_apart_point(X4,reverse_line(X2)) )
| ( left_apart_point(X1,reverse_line(X2))
& left_apart_point(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',div_def) ).
fof(oaguc2,axiom,
! [X1,X4,X2] :
( ( distinct_points(X1,X4)
& left_apart_point(X1,X2) )
=> ( left_apart_point(X4,X2)
| left_convergent_lines(line_connecting(X1,X4),X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oaguc2) ).
fof(oagco2,axiom,
! [X2,X3] :
( ( line(X2)
& line(X3)
& unequally_directed_lines(X2,X3)
& unequally_directed_lines(X2,reverse_line(X3)) )
=> point(intersection_point(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oagco2) ).
fof(oag7,axiom,
! [X2,X3,X6] :
( ( unequally_directed_lines(X2,X3)
& unequally_directed_lines(X2,reverse_line(X3)) )
=> ( ( unequally_directed_lines(X2,X6)
& unequally_directed_lines(X2,reverse_line(X6)) )
| ( unequally_directed_lines(X3,X6)
& unequally_directed_lines(X3,reverse_line(X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oag7) ).
fof(oag9,axiom,
! [X2,X3] :
( ( unequally_directed_lines(X2,X3)
& unequally_directed_lines(X2,reverse_line(X3)) )
=> ( left_convergent_lines(X2,X3)
| left_convergent_lines(X2,reverse_line(X3)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oag9) ).
fof(oagsub2,axiom,
! [X1,X2,X3] :
( ( left_apart_point(X1,X2)
& unequally_directed_lines(X2,X3) )
=> ( distinct_lines(X2,X3)
| left_apart_point(X1,reverse_line(X3)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oagsub2) ).
fof(con_def,axiom,
! [X2,X3] :
( convergent_lines(X2,X3)
<=> ( unequally_directed_lines(X2,X3)
& unequally_directed_lines(X2,reverse_line(X3)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',con_def) ).
fof(oagco1,axiom,
! [X1,X4] :
( ( point(X1)
& point(X4)
& distinct_points(X1,X4) )
=> line(line_connecting(X1,X4)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oagco1) ).
fof(apt_def,axiom,
! [X1,X2] :
( apart_point_and_line(X1,X2)
<=> ( left_apart_point(X1,X2)
| left_apart_point(X1,reverse_line(X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',apt_def) ).
fof(oag4,axiom,
! [X2,X3,X6] :
( distinct_lines(X2,X3)
=> ( distinct_lines(X2,X6)
| distinct_lines(X3,X6) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oag4) ).
fof(oag2,axiom,
! [X1,X4,X5] :
( distinct_points(X1,X4)
=> ( distinct_points(X1,X5)
| distinct_points(X4,X5) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oag2) ).
fof(oagsub3,axiom,
! [X2,X3,X6] :
( left_convergent_lines(X2,X3)
=> ( unequally_directed_lines(X3,X6)
| left_convergent_lines(X2,X6) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oagsub3) ).
fof(oag6,axiom,
! [X2,X3,X6] :
( unequally_directed_lines(X2,X3)
=> ( unequally_directed_lines(X2,X6)
| unequally_directed_lines(X3,X6) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oag6) ).
fof(oagsub1,axiom,
! [X1,X4,X2] :
( left_apart_point(X1,X2)
=> ( distinct_points(X1,X4)
| left_apart_point(X4,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oagsub1) ).
fof(oag8,axiom,
! [X2,X3] :
( ( line(X2)
& line(X3) )
=> ( unequally_directed_lines(X2,X3)
| unequally_directed_lines(X2,reverse_line(X3)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oag8) ).
fof(oagco3,axiom,
! [X2,X1] :
( ( point(X1)
& line(X2) )
=> line(parallel_through_point(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oagco3) ).
fof(oag11,axiom,
! [X2,X3] :
~ ( left_convergent_lines(X2,X3)
| left_convergent_lines(X2,reverse_line(X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oag11) ).
fof(oag10,axiom,
! [X1,X2] :
~ ( left_apart_point(X1,X2)
| left_apart_point(X1,reverse_line(X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oag10) ).
fof(oagco4,axiom,
! [X2] :
( line(X2)
=> line(reverse_line(X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oagco4) ).
fof(i_0_32,plain,
! [X2,X1,X4] :
( before_on_line(X2,X1,X4)
<=> ( distinct_points(X1,X4)
& ~ ( left_apart_point(X1,X2)
| left_apart_point(X1,reverse_line(X2)) )
& ~ ( left_apart_point(X4,X2)
| left_apart_point(X4,reverse_line(X2)) )
& ~ unequally_directed_lines(X2,line_connecting(X1,X4)) ) ),
inference(fof_simplification,[status(thm)],[bf_def]) ).
fof(i_0_33,plain,
! [X1,X4] : ~ unequally_directed_lines(line_connecting(X1,X4),reverse_line(line_connecting(X4,X1))),
inference(fof_simplification,[status(thm)],[oagco9]) ).
fof(i_0_34,plain,
! [X2,X3] :
( ( unequally_directed_lines(X2,X3)
& unequally_directed_lines(X2,reverse_line(X3)) )
=> ( ~ apart_point_and_line(intersection_point(X2,X3),X2)
& ~ apart_point_and_line(intersection_point(X2,X3),X3) ) ),
inference(fof_simplification,[status(thm)],[oagco6]) ).
fof(i_0_35,plain,
! [X1,X4] :
( distinct_points(X1,X4)
=> ( ~ apart_point_and_line(X1,line_connecting(X1,X4))
& ~ apart_point_and_line(X4,line_connecting(X1,X4)) ) ),
inference(fof_simplification,[status(thm)],[oagco5]) ).
fof(i_0_36,plain,
! [X1,X2] : ~ unequally_directed_lines(parallel_through_point(X2,X1),X2),
inference(fof_simplification,[status(thm)],[oagco10]) ).
fof(i_0_37,plain,
! [X1,X2] : ~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
inference(fof_simplification,[status(thm)],[oagco7]) ).
fof(i_0_38,plain,
! [X2] : ~ distinct_lines(X2,reverse_line(X2)),
inference(fof_simplification,[status(thm)],[oagco8]) ).
fof(i_0_39,negated_conjecture,
~ ! [X2,X3] :
( ( line(X2)
& line(X3) )
=> ~ ( ~ unequally_directed_lines(X2,X3)
& ~ unequally_directed_lines(X2,reverse_line(X3)) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[con])]) ).
fof(i_0_40,plain,
! [X2] : ~ distinct_lines(X2,X2),
inference(fof_simplification,[status(thm)],[oag3]) ).
fof(i_0_41,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[oag1]) ).
fof(i_0_42,plain,
! [X2] : ~ unequally_directed_lines(X2,X2),
inference(fof_simplification,[status(thm)],[oag5]) ).
fof(i_0_43,plain,
! [X90,X91,X92,X93] :
( ( before_on_line(X90,X93,X92)
| before_on_line(X90,X91,X92)
| ~ between_on_line(X90,X91,X92,X93) )
& ( before_on_line(X90,X92,X91)
| before_on_line(X90,X91,X92)
| ~ between_on_line(X90,X91,X92,X93) )
& ( before_on_line(X90,X93,X92)
| before_on_line(X90,X92,X93)
| ~ between_on_line(X90,X91,X92,X93) )
& ( before_on_line(X90,X92,X91)
| before_on_line(X90,X92,X93)
| ~ between_on_line(X90,X91,X92,X93) )
& ( ~ before_on_line(X90,X91,X92)
| ~ before_on_line(X90,X92,X93)
| between_on_line(X90,X91,X92,X93) )
& ( ~ before_on_line(X90,X93,X92)
| ~ before_on_line(X90,X92,X91)
| between_on_line(X90,X91,X92,X93) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[bet_def])])]) ).
fof(i_0_44,plain,
! [X87,X88,X89] :
( ( distinct_points(X88,X89)
| ~ before_on_line(X87,X88,X89) )
& ( ~ left_apart_point(X88,X87)
| ~ before_on_line(X87,X88,X89) )
& ( ~ left_apart_point(X88,reverse_line(X87))
| ~ before_on_line(X87,X88,X89) )
& ( ~ left_apart_point(X89,X87)
| ~ before_on_line(X87,X88,X89) )
& ( ~ left_apart_point(X89,reverse_line(X87))
| ~ before_on_line(X87,X88,X89) )
& ( ~ unequally_directed_lines(X87,line_connecting(X88,X89))
| ~ before_on_line(X87,X88,X89) )
& ( ~ distinct_points(X88,X89)
| left_apart_point(X88,X87)
| left_apart_point(X88,reverse_line(X87))
| left_apart_point(X89,X87)
| left_apart_point(X89,reverse_line(X87))
| unequally_directed_lines(X87,line_connecting(X88,X89))
| before_on_line(X87,X88,X89) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_32])])]) ).
fof(i_0_45,plain,
! [X135,X136,X137,X138] :
( ~ distinct_points(X135,X136)
| ~ distinct_lines(X137,X138)
| left_apart_point(X135,X137)
| left_apart_point(X136,X137)
| left_apart_point(X135,X138)
| left_apart_point(X136,X138)
| left_apart_point(X135,reverse_line(X137))
| left_apart_point(X136,reverse_line(X137))
| left_apart_point(X135,reverse_line(X138))
| left_apart_point(X136,reverse_line(X138)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oaguc1])]) ).
fof(i_0_46,plain,
! [X131,X132] : ~ unequally_directed_lines(line_connecting(X131,X132),reverse_line(line_connecting(X132,X131))),
inference(variable_rename,[status(thm)],[i_0_33]) ).
fof(i_0_47,plain,
! [X84,X85,X86] :
( ( left_apart_point(X84,reverse_line(X86))
| left_apart_point(X84,X86)
| ~ divides_points(X86,X84,X85) )
& ( left_apart_point(X85,X86)
| left_apart_point(X84,X86)
| ~ divides_points(X86,X84,X85) )
& ( left_apart_point(X84,reverse_line(X86))
| left_apart_point(X85,reverse_line(X86))
| ~ divides_points(X86,X84,X85) )
& ( left_apart_point(X85,X86)
| left_apart_point(X85,reverse_line(X86))
| ~ divides_points(X86,X84,X85) )
& ( ~ left_apart_point(X84,X86)
| ~ left_apart_point(X85,reverse_line(X86))
| divides_points(X86,X84,X85) )
& ( ~ left_apart_point(X84,reverse_line(X86))
| ~ left_apart_point(X85,X86)
| divides_points(X86,X84,X85) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[div_def])])]) ).
fof(i_0_48,plain,
! [X126,X127] :
( ( ~ apart_point_and_line(intersection_point(X126,X127),X126)
| ~ unequally_directed_lines(X126,X127)
| ~ unequally_directed_lines(X126,reverse_line(X127)) )
& ( ~ apart_point_and_line(intersection_point(X126,X127),X127)
| ~ unequally_directed_lines(X126,X127)
| ~ unequally_directed_lines(X126,reverse_line(X127)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_34])])]) ).
fof(i_0_49,plain,
! [X139,X140,X141] :
( ~ distinct_points(X139,X140)
| ~ left_apart_point(X139,X141)
| left_apart_point(X140,X141)
| left_convergent_lines(line_connecting(X139,X140),X141) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oaguc2])]) ).
fof(i_0_50,plain,
! [X119,X120] :
( ~ line(X119)
| ~ line(X120)
| ~ unequally_directed_lines(X119,X120)
| ~ unequally_directed_lines(X119,reverse_line(X120))
| point(intersection_point(X119,X120)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oagco2])]) ).
fof(i_0_51,plain,
! [X106,X107,X108] :
( ( unequally_directed_lines(X107,X108)
| unequally_directed_lines(X106,X108)
| ~ unequally_directed_lines(X106,X107)
| ~ unequally_directed_lines(X106,reverse_line(X107)) )
& ( unequally_directed_lines(X107,reverse_line(X108))
| unequally_directed_lines(X106,X108)
| ~ unequally_directed_lines(X106,X107)
| ~ unequally_directed_lines(X106,reverse_line(X107)) )
& ( unequally_directed_lines(X107,X108)
| unequally_directed_lines(X106,reverse_line(X108))
| ~ unequally_directed_lines(X106,X107)
| ~ unequally_directed_lines(X106,reverse_line(X107)) )
& ( unequally_directed_lines(X107,reverse_line(X108))
| unequally_directed_lines(X106,reverse_line(X108))
| ~ unequally_directed_lines(X106,X107)
| ~ unequally_directed_lines(X106,reverse_line(X107)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oag7])])]) ).
fof(i_0_52,plain,
! [X111,X112] :
( ~ unequally_directed_lines(X111,X112)
| ~ unequally_directed_lines(X111,reverse_line(X112))
| left_convergent_lines(X111,X112)
| left_convergent_lines(X111,reverse_line(X112)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oag9])]) ).
fof(i_0_53,plain,
! [X124,X125] :
( ( ~ apart_point_and_line(X124,line_connecting(X124,X125))
| ~ distinct_points(X124,X125) )
& ( ~ apart_point_and_line(X125,line_connecting(X124,X125))
| ~ distinct_points(X124,X125) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_35])])]) ).
fof(i_0_54,plain,
! [X145,X146,X147] :
( ~ left_apart_point(X145,X146)
| ~ unequally_directed_lines(X146,X147)
| distinct_lines(X146,X147)
| left_apart_point(X145,reverse_line(X147)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oagsub2])]) ).
fof(i_0_55,plain,
! [X82,X83] :
( ( unequally_directed_lines(X82,X83)
| ~ convergent_lines(X82,X83) )
& ( unequally_directed_lines(X82,reverse_line(X83))
| ~ convergent_lines(X82,X83) )
& ( ~ unequally_directed_lines(X82,X83)
| ~ unequally_directed_lines(X82,reverse_line(X83))
| convergent_lines(X82,X83) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[con_def])])]) ).
fof(i_0_56,plain,
! [X117,X118] :
( ~ point(X117)
| ~ point(X118)
| ~ distinct_points(X117,X118)
| line(line_connecting(X117,X118)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oagco1])]) ).
fof(i_0_57,plain,
! [X133,X134] : ~ unequally_directed_lines(parallel_through_point(X134,X133),X134),
inference(variable_rename,[status(thm)],[i_0_36]) ).
fof(i_0_58,plain,
! [X128,X129] : ~ apart_point_and_line(X128,parallel_through_point(X129,X128)),
inference(variable_rename,[status(thm)],[i_0_37]) ).
fof(i_0_59,plain,
! [X80,X81] :
( ( ~ apart_point_and_line(X80,X81)
| left_apart_point(X80,X81)
| left_apart_point(X80,reverse_line(X81)) )
& ( ~ left_apart_point(X80,X81)
| apart_point_and_line(X80,X81) )
& ( ~ left_apart_point(X80,reverse_line(X81))
| apart_point_and_line(X80,X81) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apt_def])])]) ).
fof(i_0_60,plain,
! [X99,X100,X101] :
( ~ distinct_lines(X99,X100)
| distinct_lines(X99,X101)
| distinct_lines(X100,X101) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oag4])]) ).
fof(i_0_61,plain,
! [X95,X96,X97] :
( ~ distinct_points(X95,X96)
| distinct_points(X95,X97)
| distinct_points(X96,X97) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oag2])]) ).
fof(i_0_62,plain,
! [X148,X149,X150] :
( ~ left_convergent_lines(X148,X149)
| unequally_directed_lines(X149,X150)
| left_convergent_lines(X148,X150) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oagsub3])]) ).
fof(i_0_63,plain,
! [X103,X104,X105] :
( ~ unequally_directed_lines(X103,X104)
| unequally_directed_lines(X103,X105)
| unequally_directed_lines(X104,X105) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oag6])]) ).
fof(i_0_64,plain,
! [X142,X143,X144] :
( ~ left_apart_point(X142,X144)
| distinct_points(X142,X143)
| left_apart_point(X143,X144) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oagsub1])]) ).
fof(i_0_65,plain,
! [X109,X110] :
( ~ line(X109)
| ~ line(X110)
| unequally_directed_lines(X109,X110)
| unequally_directed_lines(X109,reverse_line(X110)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oag8])]) ).
fof(i_0_66,plain,
! [X121,X122] :
( ~ point(X122)
| ~ line(X121)
| line(parallel_through_point(X121,X122)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oagco3])]) ).
fof(i_0_67,plain,
! [X115,X116] :
( ~ left_convergent_lines(X115,X116)
& ~ left_convergent_lines(X115,reverse_line(X116)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oag11])]) ).
fof(i_0_68,plain,
! [X130] : ~ distinct_lines(X130,reverse_line(X130)),
inference(variable_rename,[status(thm)],[i_0_38]) ).
fof(i_0_69,plain,
! [X113,X114] :
( ~ left_apart_point(X113,X114)
& ~ left_apart_point(X113,reverse_line(X114)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oag10])]) ).
fof(i_0_70,negated_conjecture,
( line(esk1_0)
& line(esk2_0)
& ~ unequally_directed_lines(esk1_0,esk2_0)
& ~ unequally_directed_lines(esk1_0,reverse_line(esk2_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_39])])]) ).
fof(i_0_71,plain,
! [X98] : ~ distinct_lines(X98,X98),
inference(variable_rename,[status(thm)],[i_0_40]) ).
fof(i_0_72,plain,
! [X94] : ~ distinct_points(X94,X94),
inference(variable_rename,[status(thm)],[i_0_41]) ).
fof(i_0_73,plain,
! [X102] : ~ unequally_directed_lines(X102,X102),
inference(variable_rename,[status(thm)],[i_0_42]) ).
fof(i_0_74,plain,
! [X123] :
( ~ line(X123)
| line(reverse_line(X123)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oagco4])]) ).
cnf(i_0_75,plain,
( before_on_line(X1,X2,X3)
| before_on_line(X1,X2,X4)
| ~ between_on_line(X1,X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_76,plain,
( before_on_line(X1,X2,X3)
| before_on_line(X1,X3,X2)
| ~ between_on_line(X1,X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_77,plain,
( before_on_line(X1,X2,X3)
| before_on_line(X1,X3,X2)
| ~ between_on_line(X1,X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_78,plain,
( before_on_line(X1,X2,X3)
| before_on_line(X1,X4,X3)
| ~ between_on_line(X1,X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_79,plain,
( between_on_line(X1,X2,X3,X4)
| ~ before_on_line(X1,X2,X3)
| ~ before_on_line(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_80,plain,
( between_on_line(X1,X4,X3,X2)
| ~ before_on_line(X1,X2,X3)
| ~ before_on_line(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_81,plain,
( left_apart_point(X1,X3)
| left_apart_point(X1,reverse_line(X3))
| left_apart_point(X2,X3)
| left_apart_point(X2,reverse_line(X3))
| unequally_directed_lines(X3,line_connecting(X1,X2))
| before_on_line(X3,X1,X2)
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_82,plain,
( left_apart_point(X1,X3)
| left_apart_point(X2,X3)
| left_apart_point(X1,X4)
| left_apart_point(X2,X4)
| left_apart_point(X1,reverse_line(X3))
| left_apart_point(X2,reverse_line(X3))
| left_apart_point(X1,reverse_line(X4))
| left_apart_point(X2,reverse_line(X4))
| ~ distinct_points(X1,X2)
| ~ distinct_lines(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_83,plain,
~ unequally_directed_lines(line_connecting(X1,X2),reverse_line(line_connecting(X2,X1))),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_84,plain,
( ~ unequally_directed_lines(X1,line_connecting(X2,X3))
| ~ before_on_line(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_85,plain,
( left_apart_point(X1,reverse_line(X2))
| left_apart_point(X3,reverse_line(X2))
| ~ divides_points(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_86,plain,
( left_apart_point(X1,reverse_line(X2))
| left_apart_point(X1,X2)
| ~ divides_points(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_87,plain,
( left_apart_point(X1,X2)
| left_apart_point(X1,reverse_line(X2))
| ~ divides_points(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_88,plain,
( ~ apart_point_and_line(intersection_point(X1,X2),X1)
| ~ unequally_directed_lines(X1,X2)
| ~ unequally_directed_lines(X1,reverse_line(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_89,plain,
( ~ apart_point_and_line(intersection_point(X1,X2),X2)
| ~ unequally_directed_lines(X1,X2)
| ~ unequally_directed_lines(X1,reverse_line(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_90,plain,
( ~ left_apart_point(X1,reverse_line(X2))
| ~ before_on_line(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_91,plain,
( ~ left_apart_point(X1,reverse_line(X2))
| ~ before_on_line(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_92,plain,
( left_apart_point(X1,X2)
| left_apart_point(X3,X2)
| ~ divides_points(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_93,plain,
( divides_points(X2,X1,X3)
| ~ left_apart_point(X1,X2)
| ~ left_apart_point(X3,reverse_line(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_94,plain,
( divides_points(X2,X1,X3)
| ~ left_apart_point(X1,reverse_line(X2))
| ~ left_apart_point(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_95,plain,
( ~ left_apart_point(X1,X2)
| ~ before_on_line(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_96,plain,
( ~ left_apart_point(X1,X2)
| ~ before_on_line(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_97,plain,
( distinct_points(X1,X2)
| ~ before_on_line(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_98,plain,
( left_apart_point(X2,X3)
| left_convergent_lines(line_connecting(X1,X2),X3)
| ~ distinct_points(X1,X2)
| ~ left_apart_point(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_99,plain,
( point(intersection_point(X1,X2))
| ~ line(X1)
| ~ line(X2)
| ~ unequally_directed_lines(X1,X2)
| ~ unequally_directed_lines(X1,reverse_line(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_100,plain,
( unequally_directed_lines(X1,reverse_line(X2))
| unequally_directed_lines(X3,reverse_line(X2))
| ~ unequally_directed_lines(X3,X1)
| ~ unequally_directed_lines(X3,reverse_line(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_101,plain,
( left_convergent_lines(X1,X2)
| left_convergent_lines(X1,reverse_line(X2))
| ~ unequally_directed_lines(X1,X2)
| ~ unequally_directed_lines(X1,reverse_line(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_102,plain,
( unequally_directed_lines(X1,X2)
| unequally_directed_lines(X3,reverse_line(X2))
| ~ unequally_directed_lines(X3,X1)
| ~ unequally_directed_lines(X3,reverse_line(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_103,plain,
( unequally_directed_lines(X1,reverse_line(X2))
| unequally_directed_lines(X3,X2)
| ~ unequally_directed_lines(X3,X1)
| ~ unequally_directed_lines(X3,reverse_line(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_104,plain,
( ~ apart_point_and_line(X1,line_connecting(X1,X2))
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_105,plain,
( ~ apart_point_and_line(X1,line_connecting(X2,X1))
| ~ distinct_points(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_106,plain,
( unequally_directed_lines(X1,X2)
| unequally_directed_lines(X3,X2)
| ~ unequally_directed_lines(X3,X1)
| ~ unequally_directed_lines(X3,reverse_line(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_107,plain,
( distinct_lines(X2,X3)
| left_apart_point(X1,reverse_line(X3))
| ~ left_apart_point(X1,X2)
| ~ unequally_directed_lines(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_108,plain,
( convergent_lines(X1,X2)
| ~ unequally_directed_lines(X1,X2)
| ~ unequally_directed_lines(X1,reverse_line(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_109,plain,
( line(line_connecting(X1,X2))
| ~ point(X1)
| ~ point(X2)
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_110,plain,
~ unequally_directed_lines(parallel_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_111,plain,
~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
inference(split_conjunct,[status(thm)],[i_0_58]),
[final] ).
cnf(i_0_112,plain,
( left_apart_point(X1,X2)
| left_apart_point(X1,reverse_line(X2))
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_113,plain,
( distinct_lines(X1,X3)
| distinct_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_114,plain,
( distinct_points(X1,X3)
| distinct_points(X2,X3)
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_115,plain,
( unequally_directed_lines(X2,X3)
| left_convergent_lines(X1,X3)
| ~ left_convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_116,plain,
( unequally_directed_lines(X1,X3)
| unequally_directed_lines(X2,X3)
| ~ unequally_directed_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_117,plain,
( distinct_points(X1,X3)
| left_apart_point(X3,X2)
| ~ left_apart_point(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_118,plain,
( unequally_directed_lines(X1,X2)
| unequally_directed_lines(X1,reverse_line(X2))
| ~ line(X1)
| ~ line(X2) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_119,plain,
( apart_point_and_line(X1,X2)
| ~ left_apart_point(X1,reverse_line(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_120,plain,
( line(parallel_through_point(X2,X1))
| ~ point(X1)
| ~ line(X2) ),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_121,plain,
( unequally_directed_lines(X1,reverse_line(X2))
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_122,plain,
( unequally_directed_lines(X1,X2)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_123,plain,
( apart_point_and_line(X1,X2)
| ~ left_apart_point(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_124,plain,
~ left_convergent_lines(X1,reverse_line(X2)),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_125,plain,
~ distinct_lines(X1,reverse_line(X1)),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_126,plain,
~ left_apart_point(X1,reverse_line(X2)),
inference(split_conjunct,[status(thm)],[i_0_69]),
[final] ).
cnf(i_0_127,negated_conjecture,
~ unequally_directed_lines(esk1_0,reverse_line(esk2_0)),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_128,plain,
~ left_convergent_lines(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_129,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_130,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_131,plain,
~ unequally_directed_lines(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_73]),
[final] ).
cnf(i_0_132,plain,
~ left_apart_point(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_69]),
[final] ).
cnf(i_0_133,negated_conjecture,
~ unequally_directed_lines(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_134,plain,
( line(reverse_line(X1))
| ~ line(X1) ),
inference(split_conjunct,[status(thm)],[i_0_74]),
[final] ).
cnf(i_0_135,negated_conjecture,
line(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_136,negated_conjecture,
line(esk1_0),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_137,plain,
~ convergent_lines(esk1_0,esk2_0),
inference(scs_inference,[],[i_0_127,i_0_121]) ).
cnf(i_0_138,plain,
( unequally_directed_lines(X1,reverse_line(X2))
| ~ convergent_lines(X1,X2) ),
inference(rename_variables,[],[i_0_121]) ).
cnf(i_0_139,plain,
~ before_on_line(X1,X2,X2),
inference(scs_inference,[],[i_0_127,i_0_130,i_0_121,i_0_97]) ).
cnf(i_0_140,plain,
( distinct_points(X1,X2)
| ~ before_on_line(X3,X1,X2) ),
inference(rename_variables,[],[i_0_97]) ).
cnf(i_0_141,plain,
~ between_on_line(X1,X2,X2,X3),
inference(scs_inference,[],[i_0_127,i_0_130,i_0_121,i_0_97,i_0_76]) ).
cnf(i_0_142,plain,
( before_on_line(X1,X2,X3)
| before_on_line(X1,X3,X2)
| ~ between_on_line(X1,X2,X3,X4) ),
inference(rename_variables,[],[i_0_76]) ).
cnf(i_0_143,plain,
~ between_on_line(X1,X2,X3,X3),
inference(scs_inference,[],[i_0_127,i_0_130,i_0_121,i_0_97,i_0_76,i_0_77]) ).
cnf(i_0_144,plain,
( before_on_line(X1,X2,X3)
| before_on_line(X1,X3,X2)
| ~ between_on_line(X1,X4,X2,X3) ),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_145,plain,
$false,
inference(scs_inference,[],[i_0_127,i_0_133,i_0_135,i_0_136,i_0_130,i_0_121,i_0_97,i_0_76,i_0_77,i_0_118]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GEO227+1 : TPTP v9.2.1. Bugfixed v6.4.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n027.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 17:49:35 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 0.28/1.61 % Version : CSE_E---1.7
% 0.28/1.61 % Problem : theBenchmark.p
% 0.28/1.61 % SZS status Theorem for theBenchmark.p
% 0.28/1.61 % SZS output start CNFRefutation
% See solution above
% 0.28/1.64 % Total time : 1.272s
%------------------------------------------------------------------------------