%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO211+2 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n003.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 0.28s 1.61s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 21
% Syntax : Number of formulae : 77 ( 33 unt; 0 def)
% Number of atoms : 205 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 211 ( 83 ~; 104 |; 10 &)
% ( 0 <=>; 14 =>; 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 : 178 ( 4 sgn 113 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ooc1,axiom,
! [X9,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X9),X6),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',ooc1) ).
fof(cp1,axiom,
! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax',cp1) ).
fof(ooc2,axiom,
! [X9,X6] : ~ apart_point_and_line(X9,orthogonal_through_point(X6,X9)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',ooc2) ).
fof(cp2,axiom,
! [X1,X2] : ~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax',cp2) ).
fof(apart3,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart3) ).
fof(apart2,axiom,
! [X1] : ~ distinct_lines(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart2) ).
fof(apart1,axiom,
! [X1] : ~ distinct_points(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart1) ).
fof(con,conjecture,
! [X6] : unorthogonal_lines(X6,X6),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GEO008+0.ax',cu1) ).
fof(con1,axiom,
! [X1,X2,X3] :
( distinct_points(X1,X2)
=> ( apart_point_and_line(X3,line_connecting(X1,X2))
=> ( distinct_points(X3,X1)
& distinct_points(X3,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',con1) ).
fof(con2,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( ( apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X2) )
=> distinct_points(X3,intersection_point(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',con2) ).
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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/GEO006+2.ax',cup1) ).
fof(apart6,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( convergent_lines(X1,X3)
| convergent_lines(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart6) ).
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/sandbox2/benchmark/Axioms/GEO008+0.ax',ceq2) ).
fof(apart5,axiom,
! [X1,X2,X3] :
( distinct_lines(X1,X2)
=> ( distinct_lines(X1,X3)
| distinct_lines(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+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/sandbox2/benchmark/Axioms/GEO008+0.ax',ceq1) ).
fof(apart4,axiom,
! [X1,X2,X3] :
( distinct_points(X1,X2)
=> ( distinct_points(X1,X3)
| distinct_points(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart4) ).
fof(ceq3,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> distinct_lines(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',ceq3) ).
fof(occu1,axiom,
! [X6,X7] :
( convergent_lines(X6,X7)
| unorthogonal_lines(X6,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',occu1) ).
fof(i_0_21,plain,
! [X9,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X9),X6),
inference(fof_simplification,[status(thm)],[ooc1]) ).
fof(i_0_22,plain,
! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
inference(fof_simplification,[status(thm)],[cp1]) ).
fof(i_0_23,plain,
! [X9,X6] : ~ apart_point_and_line(X9,orthogonal_through_point(X6,X9)),
inference(fof_simplification,[status(thm)],[ooc2]) ).
fof(i_0_24,plain,
! [X1,X2] : ~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
inference(fof_simplification,[status(thm)],[cp2]) ).
fof(i_0_25,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart3]) ).
fof(i_0_26,plain,
! [X1] : ~ distinct_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart2]) ).
fof(i_0_27,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[apart1]) ).
fof(i_0_28,negated_conjecture,
~ ! [X6] : unorthogonal_lines(X6,X6),
inference(assume_negation,[status(cth)],[con]) ).
fof(i_0_29,plain,
! [X79,X80,X81,X82] :
( ~ distinct_points(X79,X80)
| ~ distinct_lines(X81,X82)
| apart_point_and_line(X79,X81)
| apart_point_and_line(X79,X82)
| apart_point_and_line(X80,X81)
| apart_point_and_line(X80,X82) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cu1])]) ).
fof(i_0_30,plain,
! [X73,X74,X75] :
( ( distinct_points(X75,X73)
| ~ apart_point_and_line(X75,line_connecting(X73,X74))
| ~ distinct_points(X73,X74) )
& ( distinct_points(X75,X74)
| ~ apart_point_and_line(X75,line_connecting(X73,X74))
| ~ distinct_points(X73,X74) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[con1])])]) ).
fof(i_0_31,plain,
! [X76,X77,X78] :
( ( ~ apart_point_and_line(X78,X76)
| distinct_points(X78,intersection_point(X76,X77))
| ~ convergent_lines(X76,X77) )
& ( ~ apart_point_and_line(X78,X77)
| distinct_points(X78,intersection_point(X76,X77))
| ~ convergent_lines(X76,X77) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[con2])])]) ).
fof(i_0_32,plain,
! [X107,X108,X109,X110] :
( ~ distinct_lines(X108,X109)
| apart_point_and_line(X107,X108)
| apart_point_and_line(X107,X109)
| unorthogonal_lines(X108,X110)
| unorthogonal_lines(X109,X110) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ouo1])]) ).
fof(i_0_33,plain,
! [X100,X101,X102] :
( ( convergent_lines(X101,X102)
| convergent_lines(X100,X102)
| ~ convergent_lines(X100,X101)
| ~ unorthogonal_lines(X100,X101) )
& ( unorthogonal_lines(X101,X102)
| convergent_lines(X100,X102)
| ~ convergent_lines(X100,X101)
| ~ unorthogonal_lines(X100,X101) )
& ( convergent_lines(X101,X102)
| unorthogonal_lines(X100,X102)
| ~ convergent_lines(X100,X101)
| ~ unorthogonal_lines(X100,X101) )
& ( unorthogonal_lines(X101,X102)
| unorthogonal_lines(X100,X102)
| ~ convergent_lines(X100,X101)
| ~ unorthogonal_lines(X100,X101) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oac1])])]) ).
fof(i_0_34,plain,
! [X95,X96,X97] :
( ~ distinct_lines(X96,X97)
| apart_point_and_line(X95,X96)
| apart_point_and_line(X95,X97)
| convergent_lines(X96,X97) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cup1])]) ).
fof(i_0_35,plain,
! [X103,X104] : ~ unorthogonal_lines(orthogonal_through_point(X104,X103),X104),
inference(variable_rename,[status(thm)],[i_0_21]) ).
fof(i_0_36,plain,
! [X91,X92] : ~ convergent_lines(parallel_through_point(X92,X91),X92),
inference(variable_rename,[status(thm)],[i_0_22]) ).
fof(i_0_37,plain,
! [X105,X106] : ~ apart_point_and_line(X105,orthogonal_through_point(X106,X105)),
inference(variable_rename,[status(thm)],[i_0_23]) ).
fof(i_0_38,plain,
! [X93,X94] : ~ apart_point_and_line(X93,parallel_through_point(X94,X93)),
inference(variable_rename,[status(thm)],[i_0_24]) ).
fof(i_0_39,plain,
! [X70,X71,X72] :
( ~ convergent_lines(X70,X71)
| convergent_lines(X70,X72)
| convergent_lines(X71,X72) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart6])]) ).
fof(i_0_40,plain,
! [X86,X87,X88] :
( ~ apart_point_and_line(X86,X87)
| distinct_lines(X87,X88)
| apart_point_and_line(X86,X88) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq2])]) ).
fof(i_0_41,plain,
! [X67,X68,X69] :
( ~ distinct_lines(X67,X68)
| distinct_lines(X67,X69)
| distinct_lines(X68,X69) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart5])]) ).
fof(i_0_42,plain,
! [X83,X84,X85] :
( ~ apart_point_and_line(X83,X84)
| distinct_points(X83,X85)
| apart_point_and_line(X85,X84) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq1])]) ).
fof(i_0_43,plain,
! [X64,X65,X66] :
( ~ distinct_points(X64,X65)
| distinct_points(X64,X66)
| distinct_points(X65,X66) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart4])]) ).
fof(i_0_44,plain,
! [X89,X90] :
( ~ convergent_lines(X89,X90)
| distinct_lines(X89,X90) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])]) ).
fof(i_0_45,plain,
! [X98,X99] :
( convergent_lines(X98,X99)
| unorthogonal_lines(X98,X99) ),
inference(variable_rename,[status(thm)],[occu1]) ).
fof(i_0_46,plain,
! [X63] : ~ convergent_lines(X63,X63),
inference(variable_rename,[status(thm)],[i_0_25]) ).
fof(i_0_47,plain,
! [X62] : ~ distinct_lines(X62,X62),
inference(variable_rename,[status(thm)],[i_0_26]) ).
fof(i_0_48,plain,
! [X61] : ~ distinct_points(X61,X61),
inference(variable_rename,[status(thm)],[i_0_27]) ).
fof(i_0_49,negated_conjecture,
~ unorthogonal_lines(esk1_0,esk1_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_28])])]) ).
cnf(i_0_50,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_29]),
[final] ).
cnf(i_0_51,plain,
( distinct_points(X1,X2)
| ~ apart_point_and_line(X1,line_connecting(X2,X3))
| ~ distinct_points(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_52,plain,
( distinct_points(X1,X2)
| ~ apart_point_and_line(X1,line_connecting(X3,X2))
| ~ distinct_points(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_53,plain,
( distinct_points(X1,intersection_point(X2,X3))
| ~ apart_point_and_line(X1,X2)
| ~ convergent_lines(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_31]),
[final] ).
cnf(i_0_54,plain,
( distinct_points(X1,intersection_point(X3,X2))
| ~ apart_point_and_line(X1,X2)
| ~ convergent_lines(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_31]),
[final] ).
cnf(i_0_55,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_32]),
[final] ).
cnf(i_0_56,plain,
( unorthogonal_lines(X1,X2)
| unorthogonal_lines(X3,X2)
| ~ convergent_lines(X3,X1)
| ~ unorthogonal_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_57,plain,
( convergent_lines(X1,X2)
| unorthogonal_lines(X3,X2)
| ~ convergent_lines(X3,X1)
| ~ unorthogonal_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_58,plain,
( unorthogonal_lines(X1,X2)
| convergent_lines(X3,X2)
| ~ convergent_lines(X3,X1)
| ~ unorthogonal_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_59,plain,
( convergent_lines(X1,X2)
| convergent_lines(X3,X2)
| ~ convergent_lines(X3,X1)
| ~ unorthogonal_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_60,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_34]),
[final] ).
cnf(i_0_61,plain,
~ unorthogonal_lines(orthogonal_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_62,plain,
~ convergent_lines(parallel_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_36]),
[final] ).
cnf(i_0_63,plain,
~ apart_point_and_line(X1,orthogonal_through_point(X2,X1)),
inference(split_conjunct,[status(thm)],[i_0_37]),
[final] ).
cnf(i_0_64,plain,
~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_65,plain,
( convergent_lines(X1,X3)
| convergent_lines(X2,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_39]),
[final] ).
cnf(i_0_66,plain,
( distinct_lines(X2,X3)
| apart_point_and_line(X1,X3)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_40]),
[final] ).
cnf(i_0_67,plain,
( distinct_lines(X1,X3)
| distinct_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_68,plain,
( distinct_points(X1,X3)
| apart_point_and_line(X3,X2)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_69,plain,
( distinct_points(X1,X3)
| distinct_points(X2,X3)
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_70,plain,
( distinct_lines(X1,X2)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_71,plain,
( convergent_lines(X1,X2)
| unorthogonal_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_72,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_73,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_74,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_75,negated_conjecture,
~ unorthogonal_lines(esk1_0,esk1_0),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_76,plain,
$false,
inference(scs_inference,[],[i_0_72,i_0_75,i_0_71]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO211+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n003.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 17:47:26 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % 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
% 0.28/1.63 % Total time : 1.271s
%------------------------------------------------------------------------------