%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO211+1 : TPTP v9.2.1. Released v3.3.0.
% 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 : n017.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 04:19:56 PM UTC 2026
% Result : Theorem 0.29s 1.62s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 23
% Syntax : Number of formulae : 85 ( 33 unt; 0 def)
% Number of atoms : 208 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 214 ( 91 ~; 98 |; 7 &)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 189 ( 4 sgn 127 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(ci1,axiom,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci1) ).
fof(ci2,axiom,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci2) ).
fof(ooc1,axiom,
! [X9,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X9),X6),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',ooc1) ).
fof(cp1,axiom,
! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cp1) ).
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(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(apart3,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(apart2,axiom,
! [X1] : ~ distinct_lines(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart2) ).
fof(apart1,axiom,
! [X1] : ~ distinct_points(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart1) ).
fof(con,conjecture,
! [X6] : unorthogonal_lines(X6,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(cu1,axiom,
! [X1,X2,X4,X5] :
( ( distinct_points(X1,X2)
& distinct_lines(X4,X5) )
=> ( apart_point_and_line(X1,X4)
| apart_point_and_line(X1,X5)
| apart_point_and_line(X2,X4)
| apart_point_and_line(X2,X5) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',cu1) ).
fof(ouo1,axiom,
! [X9,X6,X7,X8] :
( distinct_lines(X6,X7)
=> ( apart_point_and_line(X9,X6)
| apart_point_and_line(X9,X7)
| unorthogonal_lines(X6,X8)
| unorthogonal_lines(X7,X8) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',ouo1) ).
fof(oac1,axiom,
! [X6,X7,X8] :
( ( convergent_lines(X6,X7)
& unorthogonal_lines(X6,X7) )
=> ( ( convergent_lines(X6,X8)
& unorthogonal_lines(X6,X8) )
| ( convergent_lines(X7,X8)
& unorthogonal_lines(X7,X8) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',oac1) ).
fof(cup1,axiom,
! [X1,X2,X3] :
( distinct_lines(X2,X3)
=> ( apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3)
| convergent_lines(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cup1) ).
fof(ax6,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( convergent_lines(X1,X3)
| convergent_lines(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ax6) ).
fof(ceq2,axiom,
! [X1,X2,X3] :
( apart_point_and_line(X1,X2)
=> ( distinct_lines(X2,X3)
| apart_point_and_line(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq2) ).
fof(ceq3,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( distinct_lines(X2,X3)
| convergent_lines(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq3) ).
fof(apart5,axiom,
! [X1,X2,X3] :
( distinct_lines(X1,X2)
=> ( distinct_lines(X1,X3)
| distinct_lines(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart5) ).
fof(ceq1,axiom,
! [X1,X2,X3] :
( apart_point_and_line(X1,X2)
=> ( distinct_points(X1,X3)
| apart_point_and_line(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq1) ).
fof(apart4,axiom,
! [X1,X2,X3] :
( distinct_points(X1,X2)
=> ( distinct_points(X1,X3)
| distinct_points(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart4) ).
fof(occu1,axiom,
! [X6,X7] :
( convergent_lines(X6,X7)
| unorthogonal_lines(X6,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',occu1) ).
fof(i_0_23,plain,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(fof_simplification,[status(thm)],[ci3]) ).
fof(i_0_24,plain,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(fof_simplification,[status(thm)],[ci4]) ).
fof(i_0_25,plain,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
inference(fof_simplification,[status(thm)],[ci1]) ).
fof(i_0_26,plain,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
inference(fof_simplification,[status(thm)],[ci2]) ).
fof(i_0_27,plain,
! [X9,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X9),X6),
inference(fof_simplification,[status(thm)],[ooc1]) ).
fof(i_0_28,plain,
! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
inference(fof_simplification,[status(thm)],[cp1]) ).
fof(i_0_29,plain,
! [X9,X6] : ~ apart_point_and_line(X9,orthogonal_through_point(X6,X9)),
inference(fof_simplification,[status(thm)],[ooc2]) ).
fof(i_0_30,plain,
! [X1,X2] : ~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
inference(fof_simplification,[status(thm)],[cp2]) ).
fof(i_0_31,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart3]) ).
fof(i_0_32,plain,
! [X1] : ~ distinct_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart2]) ).
fof(i_0_33,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[apart1]) ).
fof(i_0_34,negated_conjecture,
~ ! [X6] : unorthogonal_lines(X6,X6),
inference(assume_negation,[status(cth)],[con]) ).
fof(i_0_35,plain,
! [X84,X85,X86,X87] :
( ~ distinct_points(X84,X85)
| ~ distinct_lines(X86,X87)
| apart_point_and_line(X84,X86)
| apart_point_and_line(X84,X87)
| apart_point_and_line(X85,X86)
| apart_point_and_line(X85,X87) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cu1])]) ).
fof(i_0_36,plain,
! [X80,X81] :
( ~ convergent_lines(X80,X81)
| ~ apart_point_and_line(intersection_point(X80,X81),X80) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_23])]) ).
fof(i_0_37,plain,
! [X82,X83] :
( ~ convergent_lines(X82,X83)
| ~ apart_point_and_line(intersection_point(X82,X83),X83) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_24])]) ).
fof(i_0_38,plain,
! [X76,X77] :
( ~ distinct_points(X76,X77)
| ~ apart_point_and_line(X76,line_connecting(X76,X77)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_25])]) ).
fof(i_0_39,plain,
! [X78,X79] :
( ~ distinct_points(X78,X79)
| ~ apart_point_and_line(X79,line_connecting(X78,X79)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_26])]) ).
fof(i_0_40,plain,
! [X113,X114,X115,X116] :
( ~ distinct_lines(X114,X115)
| apart_point_and_line(X113,X114)
| apart_point_and_line(X113,X115)
| unorthogonal_lines(X114,X116)
| unorthogonal_lines(X115,X116) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ouo1])]) ).
fof(i_0_41,plain,
! [X106,X107,X108] :
( ( convergent_lines(X107,X108)
| convergent_lines(X106,X108)
| ~ convergent_lines(X106,X107)
| ~ unorthogonal_lines(X106,X107) )
& ( unorthogonal_lines(X107,X108)
| convergent_lines(X106,X108)
| ~ convergent_lines(X106,X107)
| ~ unorthogonal_lines(X106,X107) )
& ( convergent_lines(X107,X108)
| unorthogonal_lines(X106,X108)
| ~ convergent_lines(X106,X107)
| ~ unorthogonal_lines(X106,X107) )
& ( unorthogonal_lines(X107,X108)
| unorthogonal_lines(X106,X108)
| ~ convergent_lines(X106,X107)
| ~ unorthogonal_lines(X106,X107) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oac1])])]) ).
fof(i_0_42,plain,
! [X101,X102,X103] :
( ~ distinct_lines(X102,X103)
| apart_point_and_line(X101,X102)
| apart_point_and_line(X101,X103)
| convergent_lines(X102,X103) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cup1])]) ).
fof(i_0_43,plain,
! [X109,X110] : ~ unorthogonal_lines(orthogonal_through_point(X110,X109),X110),
inference(variable_rename,[status(thm)],[i_0_27]) ).
fof(i_0_44,plain,
! [X97,X98] : ~ convergent_lines(parallel_through_point(X98,X97),X98),
inference(variable_rename,[status(thm)],[i_0_28]) ).
fof(i_0_45,plain,
! [X111,X112] : ~ apart_point_and_line(X111,orthogonal_through_point(X112,X111)),
inference(variable_rename,[status(thm)],[i_0_29]) ).
fof(i_0_46,plain,
! [X99,X100] : ~ apart_point_and_line(X99,parallel_through_point(X100,X99)),
inference(variable_rename,[status(thm)],[i_0_30]) ).
fof(i_0_47,plain,
! [X73,X74,X75] :
( ~ convergent_lines(X73,X74)
| convergent_lines(X73,X75)
| convergent_lines(X74,X75) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])]) ).
fof(i_0_48,plain,
! [X91,X92,X93] :
( ~ apart_point_and_line(X91,X92)
| distinct_lines(X92,X93)
| apart_point_and_line(X91,X93) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq2])]) ).
fof(i_0_49,plain,
! [X94,X95,X96] :
( ~ convergent_lines(X94,X95)
| distinct_lines(X95,X96)
| convergent_lines(X94,X96) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])]) ).
fof(i_0_50,plain,
! [X70,X71,X72] :
( ~ distinct_lines(X70,X71)
| distinct_lines(X70,X72)
| distinct_lines(X71,X72) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart5])]) ).
fof(i_0_51,plain,
! [X88,X89,X90] :
( ~ apart_point_and_line(X88,X89)
| distinct_points(X88,X90)
| apart_point_and_line(X90,X89) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq1])]) ).
fof(i_0_52,plain,
! [X67,X68,X69] :
( ~ distinct_points(X67,X68)
| distinct_points(X67,X69)
| distinct_points(X68,X69) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart4])]) ).
fof(i_0_53,plain,
! [X104,X105] :
( convergent_lines(X104,X105)
| unorthogonal_lines(X104,X105) ),
inference(variable_rename,[status(thm)],[occu1]) ).
fof(i_0_54,plain,
! [X66] : ~ convergent_lines(X66,X66),
inference(variable_rename,[status(thm)],[i_0_31]) ).
fof(i_0_55,plain,
! [X65] : ~ distinct_lines(X65,X65),
inference(variable_rename,[status(thm)],[i_0_32]) ).
fof(i_0_56,plain,
! [X64] : ~ distinct_points(X64,X64),
inference(variable_rename,[status(thm)],[i_0_33]) ).
fof(i_0_57,negated_conjecture,
~ unorthogonal_lines(esk1_0,esk1_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_34])])]) ).
cnf(i_0_58,plain,
( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X4)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X4)
| ~ distinct_points(X1,X2)
| ~ distinct_lines(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_59,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_36]),
[final] ).
cnf(i_0_60,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_37]),
[final] ).
cnf(i_0_61,plain,
( ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_62,plain,
( ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_39]),
[final] ).
cnf(i_0_63,plain,
( apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X2)
| unorthogonal_lines(X1,X4)
| unorthogonal_lines(X2,X4)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_40]),
[final] ).
cnf(i_0_64,plain,
( unorthogonal_lines(X1,X2)
| unorthogonal_lines(X3,X2)
| ~ convergent_lines(X3,X1)
| ~ unorthogonal_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_65,plain,
( convergent_lines(X1,X2)
| unorthogonal_lines(X3,X2)
| ~ convergent_lines(X3,X1)
| ~ unorthogonal_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_66,plain,
( unorthogonal_lines(X1,X2)
| convergent_lines(X3,X2)
| ~ convergent_lines(X3,X1)
| ~ unorthogonal_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_67,plain,
( convergent_lines(X1,X2)
| convergent_lines(X3,X2)
| ~ convergent_lines(X3,X1)
| ~ unorthogonal_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_68,plain,
( apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X2)
| convergent_lines(X1,X2)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_69,plain,
~ unorthogonal_lines(orthogonal_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_70,plain,
~ convergent_lines(parallel_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_71,plain,
~ apart_point_and_line(X1,orthogonal_through_point(X2,X1)),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_72,plain,
~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_73,plain,
( convergent_lines(X1,X3)
| convergent_lines(X2,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_74,plain,
( distinct_lines(X2,X3)
| apart_point_and_line(X1,X3)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_75,plain,
( distinct_lines(X2,X3)
| convergent_lines(X1,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_76,plain,
( distinct_lines(X1,X3)
| distinct_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_77,plain,
( distinct_points(X1,X3)
| apart_point_and_line(X3,X2)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_78,plain,
( distinct_points(X1,X3)
| distinct_points(X2,X3)
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_79,plain,
( convergent_lines(X1,X2)
| unorthogonal_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_80,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_81,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_82,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_83,negated_conjecture,
~ unorthogonal_lines(esk1_0,esk1_0),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_84,plain,
$false,
inference(scs_inference,[],[i_0_80,i_0_83,i_0_79]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO211+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % 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
% 0.16/0.34 % Computer : n017.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon May 4 17:46:12 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 0.29/1.62 % Version : CSE_E---1.7
% 0.29/1.62 % Problem : theBenchmark.p
% 0.29/1.62 % SZS status Theorem for theBenchmark.p
% 0.29/1.62 % SZS output start CNFRefutation
% See solution above
% 0.29/1.64 % Total time : 1.274s
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