%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GEO223+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:27:52 PM UTC 2026
% Result : Theorem 0.18s 0.53s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of formulae : 82 ( 36 unt; 0 def)
% Number of atoms : 184 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 164 ( 62 ~; 87 |; 6 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 148 ( 8 sgn 84 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,conjecture,
! [X9,X6] : ~ distinct_lines(parallel_through_point(X6,X9),orthogonal_through_point(orthogonal_through_point(X6,X9),X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(apart5,axiom,
! [X1,X2,X3] :
( distinct_lines(X1,X2)
=> ( distinct_lines(X2,X3)
| distinct_lines(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart5) ).
fof(apart2,axiom,
! [X1] : ~ distinct_lines(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart2) ).
fof(cup1,axiom,
! [X1,X2,X3] :
( distinct_lines(X2,X3)
=> ( convergent_lines(X2,X3)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cup1) ).
fof(ooc2,axiom,
! [X9,X6] : ~ apart_point_and_line(X9,orthogonal_through_point(X6,X9)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',ooc2) ).
fof(ax6,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( convergent_lines(X2,X3)
| convergent_lines(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ax6) ).
fof(cp2,axiom,
! [X1,X2] : ~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cp2) ).
fof(ci4,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci4) ).
fof(apart3,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(ooc1,axiom,
! [X9,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X9),X6),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',ooc1) ).
fof(ouo1,axiom,
! [X9,X6,X7,X8] :
( distinct_lines(X6,X7)
=> ( unorthogonal_lines(X7,X8)
| unorthogonal_lines(X6,X8)
| apart_point_and_line(X9,X7)
| apart_point_and_line(X9,X6) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',ouo1) ).
fof(ci3,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci3) ).
fof(occu1,axiom,
! [X6,X7] :
( unorthogonal_lines(X6,X7)
| convergent_lines(X6,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',occu1) ).
fof(oac1,axiom,
! [X6,X7,X8] :
( ( unorthogonal_lines(X6,X7)
& convergent_lines(X6,X7) )
=> ( ( unorthogonal_lines(X7,X8)
& convergent_lines(X7,X8) )
| ( unorthogonal_lines(X6,X8)
& convergent_lines(X6,X8) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',oac1) ).
fof(cp1,axiom,
! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cp1) ).
fof(c_0_15,negated_conjecture,
~ ! [X9,X6] : ~ distinct_lines(parallel_through_point(X6,X9),orthogonal_through_point(orthogonal_through_point(X6,X9),X9)),
inference(assume_negation,[status(cth)],[con]) ).
fof(c_0_16,negated_conjecture,
~ ! [X9,X6] : ~ distinct_lines(parallel_through_point(X6,X9),orthogonal_through_point(orthogonal_through_point(X6,X9),X9)),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_17,plain,
! [X16,X17,X18] :
( distinct_lines(X17,X18)
| distinct_lines(X16,X18)
| ~ distinct_lines(X16,X17) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart5])])]) ).
fof(c_0_18,negated_conjecture,
distinct_lines(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
cnf(c_0_19,plain,
( ~ distinct_lines(X1,X2)
| distinct_lines(X2,X3)
| distinct_lines(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_20,negated_conjecture,
distinct_lines(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_21,negated_conjecture,
( distinct_lines(parallel_through_point(esk2_0,esk1_0),X1)
| distinct_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_22,plain,
! [X1] : ~ distinct_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart2]) ).
cnf(c_0_23,negated_conjecture,
( distinct_lines(X2,X1)
| distinct_lines(parallel_through_point(esk2_0,esk1_0),X2)
| distinct_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_21]) ).
fof(c_0_24,plain,
! [X11] : ~ distinct_lines(X11,X11),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_22])]) ).
fof(c_0_25,plain,
! [X47,X48,X49] :
( convergent_lines(X48,X49)
| apart_point_and_line(X47,X49)
| apart_point_and_line(X47,X48)
| ~ distinct_lines(X48,X49) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cup1])])]) ).
cnf(c_0_26,negated_conjecture,
( distinct_lines(X1,X3)
| distinct_lines(X2,X3)
| distinct_lines(parallel_through_point(esk2_0,esk1_0),X2)
| distinct_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_23]) ).
cnf(c_0_27,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_28,plain,
! [X9,X6] : ~ apart_point_and_line(X9,orthogonal_through_point(X6,X9)),
inference(fof_simplification,[status(thm)],[ooc2]) ).
fof(c_0_29,plain,
! [X19,X20,X21] :
( convergent_lines(X20,X21)
| convergent_lines(X19,X21)
| ~ convergent_lines(X19,X20) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])])]) ).
cnf(c_0_30,plain,
( ~ distinct_lines(X1,X2)
| convergent_lines(X1,X2)
| apart_point_and_line(X3,X2)
| apart_point_and_line(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_31,plain,
! [X1,X2] : ~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
inference(fof_simplification,[status(thm)],[cp2]) ).
fof(c_0_32,plain,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(fof_simplification,[status(thm)],[ci4]) ).
cnf(c_0_33,negated_conjecture,
( distinct_lines(X1,parallel_through_point(esk2_0,esk1_0))
| distinct_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1) ),
inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_26]),c_0_27]) ).
fof(c_0_34,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart3]) ).
fof(c_0_35,plain,
! [X57,X58] : ~ apart_point_and_line(X57,orthogonal_through_point(X58,X57)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_28])]) ).
cnf(c_0_36,plain,
( ~ convergent_lines(X1,X2)
| convergent_lines(X2,X3)
| convergent_lines(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_37,negated_conjecture,
( convergent_lines(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0))
| apart_point_and_line(X1,parallel_through_point(esk2_0,esk1_0))
| apart_point_and_line(X1,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)) ),
inference(spm,[status(thm)],[c_0_30,c_0_20]) ).
fof(c_0_38,plain,
! [X45,X46] : ~ apart_point_and_line(X45,parallel_through_point(X46,X45)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_31])]) ).
fof(c_0_39,plain,
! [X9,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X9),X6),
inference(fof_simplification,[status(thm)],[ooc1]) ).
fof(c_0_40,plain,
! [X59,X60,X61,X62] :
( unorthogonal_lines(X61,X62)
| unorthogonal_lines(X60,X62)
| apart_point_and_line(X59,X61)
| apart_point_and_line(X59,X60)
| ~ distinct_lines(X60,X61) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ouo1])])]) ).
fof(c_0_41,plain,
! [X28,X29] :
( ~ apart_point_and_line(intersection_point(X28,X29),X29)
| ~ convergent_lines(X28,X29) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])]) ).
cnf(c_0_42,negated_conjecture,
distinct_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),parallel_through_point(esk2_0,esk1_0)),
inference(spm,[status(thm)],[c_0_27,c_0_33]) ).
fof(c_0_43,plain,
! [X12] : ~ convergent_lines(X12,X12),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_34])]) ).
cnf(c_0_44,plain,
~ apart_point_and_line(X1,orthogonal_through_point(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_45,negated_conjecture,
( convergent_lines(parallel_through_point(esk2_0,esk1_0),X2)
| convergent_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X2)
| apart_point_and_line(X1,parallel_through_point(esk2_0,esk1_0))
| apart_point_and_line(X1,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_46,plain,
~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_47,plain,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(fof_simplification,[status(thm)],[ci3]) ).
fof(c_0_48,plain,
! [X55,X56] : ~ unorthogonal_lines(orthogonal_through_point(X56,X55),X56),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_39])]) ).
cnf(c_0_49,plain,
( ~ distinct_lines(X1,X2)
| unorthogonal_lines(X2,X4)
| unorthogonal_lines(X1,X4)
| apart_point_and_line(X3,X2)
| apart_point_and_line(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_50,plain,
( ~ apart_point_and_line(intersection_point(X1,X2),X2)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_51,negated_conjecture,
( convergent_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),parallel_through_point(esk2_0,esk1_0))
| apart_point_and_line(X1,parallel_through_point(esk2_0,esk1_0))
| apart_point_and_line(X1,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)) ),
inference(spm,[status(thm)],[c_0_30,c_0_42]) ).
cnf(c_0_52,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_53,negated_conjecture,
( convergent_lines(parallel_through_point(esk2_0,esk1_0),X1)
| convergent_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]) ).
fof(c_0_54,plain,
! [X26,X27] :
( ~ apart_point_and_line(intersection_point(X26,X27),X26)
| ~ convergent_lines(X26,X27) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_47])])]) ).
cnf(c_0_55,plain,
~ unorthogonal_lines(orthogonal_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_56,negated_conjecture,
( apart_point_and_line(X2,parallel_through_point(esk2_0,esk1_0))
| apart_point_and_line(X2,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0))
| unorthogonal_lines(parallel_through_point(esk2_0,esk1_0),X1)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_20]) ).
cnf(c_0_57,negated_conjecture,
( ~ convergent_lines(X1,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0))
| convergent_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),parallel_through_point(esk2_0,esk1_0))
| apart_point_and_line(intersection_point(X1,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),parallel_through_point(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_58,negated_conjecture,
convergent_lines(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
fof(c_0_59,plain,
! [X50,X51] :
( unorthogonal_lines(X50,X51)
| convergent_lines(X50,X51) ),
inference(variable_rename,[status(thm)],[occu1]) ).
cnf(c_0_60,plain,
( ~ apart_point_and_line(intersection_point(X1,X2),X1)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_61,negated_conjecture,
( apart_point_and_line(X1,parallel_through_point(esk2_0,esk1_0))
| apart_point_and_line(X1,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0))
| unorthogonal_lines(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_62,negated_conjecture,
( convergent_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),parallel_through_point(esk2_0,esk1_0))
| apart_point_and_line(intersection_point(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),parallel_through_point(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_63,plain,
( unorthogonal_lines(X1,X2)
| convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_64,negated_conjecture,
( ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
| apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1),parallel_through_point(esk2_0,esk1_0))
| unorthogonal_lines(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_65,negated_conjecture,
convergent_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),parallel_through_point(esk2_0,esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_62]),c_0_58])]) ).
cnf(c_0_66,plain,
convergent_lines(orthogonal_through_point(X1,X2),X1),
inference(spm,[status(thm)],[c_0_55,c_0_63]) ).
fof(c_0_67,plain,
! [X52,X53,X54] :
( ( ~ unorthogonal_lines(X52,X53)
| ~ convergent_lines(X52,X53)
| unorthogonal_lines(X52,X54)
| unorthogonal_lines(X53,X54) )
& ( ~ unorthogonal_lines(X52,X53)
| ~ convergent_lines(X52,X53)
| unorthogonal_lines(X52,X54)
| convergent_lines(X53,X54) )
& ( ~ unorthogonal_lines(X52,X53)
| ~ convergent_lines(X52,X53)
| convergent_lines(X52,X54)
| unorthogonal_lines(X53,X54) )
& ( ~ unorthogonal_lines(X52,X53)
| ~ convergent_lines(X52,X53)
| convergent_lines(X52,X54)
| convergent_lines(X53,X54) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oac1])])])]) ).
cnf(c_0_68,negated_conjecture,
( apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),parallel_through_point(esk2_0,esk1_0)),parallel_through_point(esk2_0,esk1_0))
| unorthogonal_lines(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_69,plain,
( convergent_lines(X1,X3)
| convergent_lines(orthogonal_through_point(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_36,c_0_66]) ).
cnf(c_0_70,plain,
( ~ unorthogonal_lines(X3,X1)
| ~ convergent_lines(X3,X1)
| convergent_lines(X3,X2)
| unorthogonal_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_71,negated_conjecture,
unorthogonal_lines(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(esk2_0,esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_68]),c_0_65])]) ).
cnf(c_0_72,plain,
( convergent_lines(X4,X3)
| convergent_lines(X1,X4)
| convergent_lines(orthogonal_through_point(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_36,c_0_69]) ).
fof(c_0_73,plain,
! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
inference(fof_simplification,[status(thm)],[cp1]) ).
cnf(c_0_74,negated_conjecture,
( ~ convergent_lines(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(esk2_0,esk1_0))
| convergent_lines(parallel_through_point(esk2_0,esk1_0),X1)
| unorthogonal_lines(orthogonal_through_point(esk2_0,esk1_0),X1) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_75,plain,
( convergent_lines(X2,X1)
| convergent_lines(X1,orthogonal_through_point(X2,X3)) ),
inference(spm,[status(thm)],[c_0_52,c_0_72]) ).
fof(c_0_76,plain,
! [X43,X44] : ~ convergent_lines(parallel_through_point(X44,X43),X44),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_73])]) ).
cnf(c_0_77,negated_conjecture,
( convergent_lines(parallel_through_point(esk2_0,esk1_0),X1)
| convergent_lines(esk2_0,parallel_through_point(esk2_0,esk1_0))
| unorthogonal_lines(orthogonal_through_point(esk2_0,esk1_0),X1) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_78,plain,
~ convergent_lines(parallel_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_79,negated_conjecture,
convergent_lines(esk2_0,parallel_through_point(esk2_0,esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_77]),c_0_78]) ).
cnf(c_0_80,negated_conjecture,
( convergent_lines(esk2_0,X1)
| convergent_lines(parallel_through_point(esk2_0,esk1_0),X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_79]) ).
cnf(c_0_81,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_80]),c_0_52]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO223+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n011.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 20 13:48:40 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.53 % Version: 3.5.1
% 0.18/0.53 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.18/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.18/0.53 % Starting new_bool_3 with 300s (1) cores
% 0.18/0.53 % Starting new_bool_1 with 300s (1) cores
% 0.18/0.53 % Starting sh5l with 300s (1) cores
% 0.18/0.53 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3756187 completed with status 0
% 0.18/0.53 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.18/0.53 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.18/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.18/0.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.18/0.53 % No SInE strategy applied
% 0.18/0.53 % Search class: FGHNF-FFMF22-SFFFFFNN
% 0.18/0.53 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/0.53 % Starting SubtermCWHack with 136s (1) cores
% 0.18/0.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.18/0.53 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.18/0.53 % Starting new_bool_3 with 136s (1) cores
% 0.18/0.53 % Starting new_bool_1 with 136s (1) cores
% 0.18/0.53 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3756196 completed with status 0
% 0.18/0.53 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.18/0.53 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.18/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.18/0.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.18/0.53 % No SInE strategy applied
% 0.18/0.53 % Search class: FGHNF-FFMF22-SFFFFFNN
% 0.18/0.53 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/0.53 % Starting SubtermCWHack with 136s (1) cores
% 0.18/0.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.18/0.53 % Preprocessing time : 0.002 s
% 0.18/0.53 % Presaturation interreduction done
% 0.18/0.53
% 0.18/0.53 % Proof found!
% 0.18/0.53 % SZS status Theorem
% 0.18/0.53 % SZS output start CNFRefutation
% See solution above
% 0.18/0.53 % Parsed axioms : 23
% 0.18/0.53 % Removed by relevancy pruning/SinE : 0
% 0.18/0.53 % Initial clauses : 26
% 0.18/0.53 % Removed in clause preprocessing : 0
% 0.18/0.53 % Initial clauses in saturation : 26
% 0.18/0.53 % Processed clauses : 285
% 0.18/0.53 % ...of these trivial : 3
% 0.18/0.53 % ...subsumed : 101
% 0.18/0.53 % ...remaining for further processing : 181
% 0.18/0.53 % Other redundant clauses eliminated : 0
% 0.18/0.53 % Clauses deleted for lack of memory : 0
% 0.18/0.53 % Backward-subsumed : 12
% 0.18/0.53 % Backward-rewritten : 11
% 0.18/0.53 % Generated clauses : 1575
% 0.18/0.53 % ...of the previous two non-redundant : 1464
% 0.18/0.53 % ...aggressively subsumed : 0
% 0.18/0.53 % Contextual simplify-reflections : 0
% 0.18/0.53 % Paramodulations : 1475
% 0.18/0.53 % Factorizations : 100
% 0.18/0.53 % NegExts : 0
% 0.18/0.53 % Equation resolutions : 0
% 0.18/0.53 % Disequality decompositions : 0
% 0.18/0.53 % Total rewrite steps : 123
% 0.18/0.53 % ...of those cached : 89
% 0.18/0.53 % Propositional unsat checks : 0
% 0.18/0.53 % Propositional check models : 0
% 0.18/0.53 % Propositional check unsatisfiable : 0
% 0.18/0.53 % Propositional clauses : 0
% 0.18/0.53 % Propositional clauses after purity: 0
% 0.18/0.53 % Propositional unsat core size : 0
% 0.18/0.53 % Propositional preprocessing time : 0.000
% 0.18/0.53 % Propositional encoding time : 0.000
% 0.18/0.53 % Propositional solver time : 0.000
% 0.18/0.53 % Success case prop preproc time : 0.000
% 0.18/0.53 % Success case prop encoding time : 0.000
% 0.18/0.53 % Success case prop solver time : 0.000
% 0.18/0.53 % Current number of processed clauses : 133
% 0.18/0.53 % Positive orientable unit clauses : 20
% 0.18/0.53 % Positive unorientable unit clauses: 0
% 0.18/0.53 % Negative unit clauses : 7
% 0.18/0.53 % Non-unit-clauses : 106
% 0.18/0.53 % Current number of unprocessed clauses: 1168
% 0.18/0.53 % ...number of literals in the above : 5782
% 0.18/0.53 % Current number of archived formulas : 0
% 0.18/0.53 % Current number of archived clauses : 48
% 0.18/0.53 % Clause-clause subsumption calls (NU) : 2430
% 0.18/0.53 % Rec. Clause-clause subsumption calls : 1244
% 0.18/0.53 % Non-unit clause-clause subsumptions : 105
% 0.18/0.53 % Unit Clause-clause subsumption calls : 318
% 0.18/0.53 % Rewrite failures with RHS unbound : 0
% 0.18/0.53 % BW rewrite match attempts : 27
% 0.18/0.53 % BW rewrite match successes : 6
% 0.18/0.53 % Condensation attempts : 0
% 0.18/0.53 % Condensation successes : 0
% 0.18/0.53 % Termbank termtop insertions : 24700
% 0.18/0.53 % Search garbage collected termcells : 247
% 0.18/0.53
% 0.18/0.53 % -------------------------------------------------
% 0.18/0.53 % User time : 0.070 s
% 0.18/0.53 % System time : 0.006 s
% 0.18/0.53 % Total time : 0.076 s
% 0.18/0.53 % Maximum resident set size: 3660 pages
% 0.18/0.53
% 0.18/0.53 % -------------------------------------------------
% 0.18/0.53 % User time : 0.278 s
% 0.18/0.53 % System time : 0.019 s
% 0.18/0.53 % Total time : 0.297 s
% 0.18/0.53 % Maximum resident set size: 4864 pages
% 0.18/0.53 % E exiting
%------------------------------------------------------------------------------