%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO219+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 : n008.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 04:19:59 PM UTC 2026
% Result : Theorem 0.22s 1.61s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 16
% Syntax : Number of formulae : 80 ( 26 unt; 0 def)
% Number of atoms : 219 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 249 ( 110 ~; 105 |; 17 &)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 168 ( 0 sgn 93 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cotno1,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+4.ax',cotno1) ).
fof(couo1,axiom,
! [X6,X7,X8] :
( ( ~ unorthogonal_lines(X6,X7)
& ~ unorthogonal_lines(X6,X8) )
=> ~ convergent_lines(X7,X8) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+4.ax',couo1) ).
fof(coipo1,axiom,
! [X6,X7] :
~ ( ~ convergent_lines(X6,X7)
& ~ unorthogonal_lines(X6,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+4.ax',coipo1) ).
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,X7,X8] :
( ( ~ unorthogonal_lines(X6,X7)
& ~ convergent_lines(X6,X8) )
=> ~ unorthogonal_lines(X7,X8) ),
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(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(i_0_16,plain,
! [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) ) ),
inference(fof_simplification,[status(thm)],[cotno1]) ).
fof(i_0_17,plain,
! [X6,X7,X8] :
( ( ~ unorthogonal_lines(X6,X7)
& ~ unorthogonal_lines(X6,X8) )
=> ~ convergent_lines(X7,X8) ),
inference(fof_simplification,[status(thm)],[couo1]) ).
fof(i_0_18,plain,
! [X6,X7] :
~ ( ~ convergent_lines(X6,X7)
& ~ unorthogonal_lines(X6,X7) ),
inference(fof_simplification,[status(thm)],[coipo1]) ).
fof(i_0_19,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart3]) ).
fof(i_0_20,plain,
! [X1] : ~ distinct_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart2]) ).
fof(i_0_21,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[apart1]) ).
fof(i_0_22,negated_conjecture,
~ ! [X6,X7,X8] :
( ( ~ unorthogonal_lines(X6,X7)
& ~ convergent_lines(X6,X8) )
=> ~ unorthogonal_lines(X7,X8) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[con])]) ).
fof(i_0_23,plain,
! [X68,X69,X70,X71] :
( ~ distinct_points(X68,X69)
| ~ distinct_lines(X70,X71)
| apart_point_and_line(X68,X70)
| apart_point_and_line(X68,X71)
| apart_point_and_line(X69,X70)
| apart_point_and_line(X69,X71) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cu1])]) ).
fof(i_0_24,plain,
! [X62,X63,X64] :
( ( distinct_points(X64,X62)
| ~ apart_point_and_line(X64,line_connecting(X62,X63))
| ~ distinct_points(X62,X63) )
& ( distinct_points(X64,X63)
| ~ apart_point_and_line(X64,line_connecting(X62,X63))
| ~ distinct_points(X62,X63) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[con1])])]) ).
fof(i_0_25,plain,
! [X65,X66,X67] :
( ( ~ apart_point_and_line(X67,X65)
| distinct_points(X67,intersection_point(X65,X66))
| ~ convergent_lines(X65,X66) )
& ( ~ apart_point_and_line(X67,X66)
| distinct_points(X67,intersection_point(X65,X66))
| ~ convergent_lines(X65,X66) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[con2])])]) ).
fof(i_0_26,plain,
! [X82,X83,X84] :
( ( convergent_lines(X82,X84)
| convergent_lines(X82,X83)
| ~ convergent_lines(X83,X84)
| ~ unorthogonal_lines(X83,X84) )
& ( unorthogonal_lines(X82,X84)
| convergent_lines(X82,X83)
| ~ convergent_lines(X83,X84)
| ~ unorthogonal_lines(X83,X84) )
& ( convergent_lines(X82,X84)
| unorthogonal_lines(X82,X83)
| ~ convergent_lines(X83,X84)
| ~ unorthogonal_lines(X83,X84) )
& ( unorthogonal_lines(X82,X84)
| unorthogonal_lines(X82,X83)
| ~ convergent_lines(X83,X84)
| ~ unorthogonal_lines(X83,X84) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_16])])]) ).
fof(i_0_27,plain,
! [X85,X86,X87] :
( unorthogonal_lines(X85,X86)
| unorthogonal_lines(X85,X87)
| ~ convergent_lines(X86,X87) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_17])]) ).
fof(i_0_28,plain,
! [X59,X60,X61] :
( ~ convergent_lines(X59,X60)
| convergent_lines(X59,X61)
| convergent_lines(X60,X61) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart6])]) ).
fof(i_0_29,plain,
! [X75,X76,X77] :
( ~ apart_point_and_line(X75,X76)
| distinct_lines(X76,X77)
| apart_point_and_line(X75,X77) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq2])]) ).
fof(i_0_30,plain,
! [X56,X57,X58] :
( ~ distinct_lines(X56,X57)
| distinct_lines(X56,X58)
| distinct_lines(X57,X58) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart5])]) ).
fof(i_0_31,plain,
! [X72,X73,X74] :
( ~ apart_point_and_line(X72,X73)
| distinct_points(X72,X74)
| apart_point_and_line(X74,X73) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq1])]) ).
fof(i_0_32,plain,
! [X53,X54,X55] :
( ~ distinct_points(X53,X54)
| distinct_points(X53,X55)
| distinct_points(X54,X55) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart4])]) ).
fof(i_0_33,plain,
! [X78,X79] :
( ~ convergent_lines(X78,X79)
| distinct_lines(X78,X79) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])]) ).
fof(i_0_34,plain,
! [X80,X81] :
( convergent_lines(X80,X81)
| unorthogonal_lines(X80,X81) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_18])]) ).
fof(i_0_35,plain,
! [X52] : ~ convergent_lines(X52,X52),
inference(variable_rename,[status(thm)],[i_0_19]) ).
fof(i_0_36,plain,
! [X51] : ~ distinct_lines(X51,X51),
inference(variable_rename,[status(thm)],[i_0_20]) ).
fof(i_0_37,plain,
! [X50] : ~ distinct_points(X50,X50),
inference(variable_rename,[status(thm)],[i_0_21]) ).
fof(i_0_38,negated_conjecture,
( ~ unorthogonal_lines(esk1_0,esk2_0)
& ~ convergent_lines(esk1_0,esk3_0)
& unorthogonal_lines(esk2_0,esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_22])])]) ).
cnf(i_0_39,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_23]),
[final] ).
cnf(i_0_40,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_24]),
[final] ).
cnf(i_0_41,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_24]),
[final] ).
cnf(i_0_42,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_25]),
[final] ).
cnf(i_0_43,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_25]),
[final] ).
cnf(i_0_44,plain,
( unorthogonal_lines(X1,X2)
| unorthogonal_lines(X1,X3)
| ~ convergent_lines(X3,X2)
| ~ unorthogonal_lines(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_45,plain,
( convergent_lines(X1,X2)
| unorthogonal_lines(X1,X3)
| ~ convergent_lines(X3,X2)
| ~ unorthogonal_lines(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_46,plain,
( unorthogonal_lines(X1,X2)
| convergent_lines(X1,X3)
| ~ convergent_lines(X3,X2)
| ~ unorthogonal_lines(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_47,plain,
( convergent_lines(X1,X2)
| convergent_lines(X1,X3)
| ~ convergent_lines(X3,X2)
| ~ unorthogonal_lines(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_48,plain,
( unorthogonal_lines(X1,X2)
| unorthogonal_lines(X1,X3)
| ~ convergent_lines(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_49,plain,
( convergent_lines(X1,X3)
| convergent_lines(X2,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_50,plain,
( distinct_lines(X2,X3)
| apart_point_and_line(X1,X3)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_51,plain,
( distinct_lines(X1,X3)
| distinct_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_52,plain,
( distinct_points(X1,X3)
| apart_point_and_line(X3,X2)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_31]),
[final] ).
cnf(i_0_53,plain,
( distinct_points(X1,X3)
| distinct_points(X2,X3)
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_32]),
[final] ).
cnf(i_0_54,plain,
( distinct_lines(X1,X2)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_55,plain,
( convergent_lines(X1,X2)
| unorthogonal_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_34]),
[final] ).
cnf(i_0_56,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_57,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_36]),
[final] ).
cnf(i_0_58,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_37]),
[final] ).
cnf(i_0_59,negated_conjecture,
~ unorthogonal_lines(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_60,negated_conjecture,
~ convergent_lines(esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_61,negated_conjecture,
unorthogonal_lines(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_62,plain,
convergent_lines(esk1_0,esk2_0),
inference(scs_inference,[],[i_0_59,i_0_55]) ).
cnf(i_0_63,plain,
( unorthogonal_lines(X1,X2)
| convergent_lines(X1,X2) ),
inference(rename_variables,[],[i_0_55]) ).
cnf(i_0_64,plain,
distinct_lines(esk1_0,esk2_0),
inference(scs_inference,[],[i_0_59,i_0_55,i_0_54]) ).
cnf(i_0_65,plain,
( ~ convergent_lines(X1,X2)
| distinct_lines(X1,X2) ),
inference(rename_variables,[],[i_0_54]) ).
cnf(i_0_66,plain,
~ apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0),
inference(scs_inference,[],[i_0_59,i_0_58,i_0_55,i_0_54,i_0_42]) ).
cnf(i_0_67,plain,
~ distinct_points(X1,X1),
inference(rename_variables,[],[i_0_58]) ).
cnf(i_0_68,plain,
( distinct_points(X1,intersection_point(X2,X3))
| ~ apart_point_and_line(X1,X2)
| ~ convergent_lines(X2,X3) ),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_69,plain,
unorthogonal_lines(esk1_0,esk1_0),
inference(scs_inference,[],[i_0_59,i_0_58,i_0_55,i_0_54,i_0_42,i_0_48]) ).
cnf(i_0_70,plain,
( ~ convergent_lines(X1,X2)
| unorthogonal_lines(X3,X1)
| unorthogonal_lines(X3,X2) ),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_71,plain,
convergent_lines(esk2_0,esk3_0),
inference(scs_inference,[],[i_0_59,i_0_60,i_0_58,i_0_55,i_0_54,i_0_42,i_0_48,i_0_49]) ).
cnf(i_0_72,plain,
( ~ convergent_lines(X1,X2)
| convergent_lines(X1,X3)
| convergent_lines(X2,X3) ),
inference(rename_variables,[],[i_0_49]) ).
cnf(i_0_73,plain,
~ apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0),
inference(scs_inference,[],[i_0_59,i_0_60,i_0_58,i_0_67,i_0_55,i_0_54,i_0_42,i_0_48,i_0_49,i_0_43]) ).
cnf(i_0_74,plain,
~ distinct_points(X1,X1),
inference(rename_variables,[],[i_0_58]) ).
cnf(i_0_75,plain,
( distinct_points(X1,intersection_point(X2,X3))
| ~ apart_point_and_line(X1,X3)
| ~ convergent_lines(X2,X3) ),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_76,plain,
distinct_lines(esk2_0,esk1_0),
inference(scs_inference,[],[i_0_59,i_0_60,i_0_57,i_0_58,i_0_67,i_0_55,i_0_54,i_0_42,i_0_48,i_0_49,i_0_43,i_0_51]) ).
cnf(i_0_77,plain,
~ distinct_lines(X1,X1),
inference(rename_variables,[],[i_0_57]) ).
cnf(i_0_78,plain,
( ~ distinct_lines(X1,X2)
| distinct_lines(X1,X3)
| distinct_lines(X2,X3) ),
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_79,plain,
$false,
inference(scs_inference,[],[i_0_59,i_0_60,i_0_61,i_0_57,i_0_58,i_0_67,i_0_55,i_0_54,i_0_42,i_0_48,i_0_49,i_0_43,i_0_51,i_0_45]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO219+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
% 0.12/0.32 % Computer : n008.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon May 4 17:48:58 EDT 2026
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % start to proof: theBenchmark
% 0.22/1.61 % Version : CSE_E---1.7
% 0.22/1.61 % Problem : theBenchmark.p
% 0.22/1.61 % SZS status Theorem for theBenchmark.p
% 0.22/1.61 % SZS output start CNFRefutation
% See solution above
% 0.22/1.66 % Total time : 1.273s
%------------------------------------------------------------------------------