%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO220+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 : n015.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 0.28s 1.62s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 18
% Syntax : Number of formulae : 73 ( 17 unt; 0 def)
% Number of atoms : 196 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 228 ( 105 ~; 88 |; 14 &)
% ( 0 <=>; 21 =>; 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; 3 con; 0-2 aty)
% Number of variables : 159 ( 0 sgn 107 !; 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(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/sandbox/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/sandbox/benchmark/Axioms/GEO006+4.ax',couo1) ).
fof(coipo1,axiom,
! [X6,X7] :
~ ( ~ convergent_lines(X6,X7)
& ~ unorthogonal_lines(X6,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+4.ax',coipo1) ).
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,X7,X8] :
( ( ~ unorthogonal_lines(X6,X7)
& ~ unorthogonal_lines(X6,X8) )
=> ~ convergent_lines(X7,X8) ),
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(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(i_0_18,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_19,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_20,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_21,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_22,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_23,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_24,plain,
! [X6,X7] :
~ ( ~ convergent_lines(X6,X7)
& ~ unorthogonal_lines(X6,X7) ),
inference(fof_simplification,[status(thm)],[coipo1]) ).
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,X7,X8] :
( ( ~ unorthogonal_lines(X6,X7)
& ~ unorthogonal_lines(X6,X8) )
=> ~ convergent_lines(X7,X8) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[con])]) ).
fof(i_0_29,plain,
! [X73,X74,X75,X76] :
( ~ distinct_points(X73,X74)
| ~ distinct_lines(X75,X76)
| apart_point_and_line(X73,X75)
| apart_point_and_line(X73,X76)
| apart_point_and_line(X74,X75)
| apart_point_and_line(X74,X76) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cu1])]) ).
fof(i_0_30,plain,
! [X69,X70] :
( ~ convergent_lines(X69,X70)
| ~ apart_point_and_line(intersection_point(X69,X70),X69) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_18])]) ).
fof(i_0_31,plain,
! [X71,X72] :
( ~ convergent_lines(X71,X72)
| ~ apart_point_and_line(intersection_point(X71,X72),X72) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_19])]) ).
fof(i_0_32,plain,
! [X65,X66] :
( ~ distinct_points(X65,X66)
| ~ apart_point_and_line(X65,line_connecting(X65,X66)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_20])]) ).
fof(i_0_33,plain,
! [X67,X68] :
( ~ distinct_points(X67,X68)
| ~ apart_point_and_line(X68,line_connecting(X67,X68)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_21])]) ).
fof(i_0_34,plain,
! [X88,X89,X90] :
( ( convergent_lines(X88,X90)
| convergent_lines(X88,X89)
| ~ convergent_lines(X89,X90)
| ~ unorthogonal_lines(X89,X90) )
& ( unorthogonal_lines(X88,X90)
| convergent_lines(X88,X89)
| ~ convergent_lines(X89,X90)
| ~ unorthogonal_lines(X89,X90) )
& ( convergent_lines(X88,X90)
| unorthogonal_lines(X88,X89)
| ~ convergent_lines(X89,X90)
| ~ unorthogonal_lines(X89,X90) )
& ( unorthogonal_lines(X88,X90)
| unorthogonal_lines(X88,X89)
| ~ convergent_lines(X89,X90)
| ~ unorthogonal_lines(X89,X90) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_22])])]) ).
fof(i_0_35,plain,
! [X91,X92,X93] :
( unorthogonal_lines(X91,X92)
| unorthogonal_lines(X91,X93)
| ~ convergent_lines(X92,X93) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_23])]) ).
fof(i_0_36,plain,
! [X62,X63,X64] :
( ~ convergent_lines(X62,X63)
| convergent_lines(X62,X64)
| convergent_lines(X63,X64) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])]) ).
fof(i_0_37,plain,
! [X80,X81,X82] :
( ~ apart_point_and_line(X80,X81)
| distinct_lines(X81,X82)
| apart_point_and_line(X80,X82) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq2])]) ).
fof(i_0_38,plain,
! [X83,X84,X85] :
( ~ convergent_lines(X83,X84)
| distinct_lines(X84,X85)
| convergent_lines(X83,X85) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])]) ).
fof(i_0_39,plain,
! [X59,X60,X61] :
( ~ distinct_lines(X59,X60)
| distinct_lines(X59,X61)
| distinct_lines(X60,X61) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart5])]) ).
fof(i_0_40,plain,
! [X77,X78,X79] :
( ~ apart_point_and_line(X77,X78)
| distinct_points(X77,X79)
| apart_point_and_line(X79,X78) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq1])]) ).
fof(i_0_41,plain,
! [X56,X57,X58] :
( ~ distinct_points(X56,X57)
| distinct_points(X56,X58)
| distinct_points(X57,X58) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart4])]) ).
fof(i_0_42,plain,
! [X86,X87] :
( convergent_lines(X86,X87)
| unorthogonal_lines(X86,X87) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_24])]) ).
fof(i_0_43,plain,
! [X55] : ~ convergent_lines(X55,X55),
inference(variable_rename,[status(thm)],[i_0_25]) ).
fof(i_0_44,plain,
! [X54] : ~ distinct_lines(X54,X54),
inference(variable_rename,[status(thm)],[i_0_26]) ).
fof(i_0_45,plain,
! [X53] : ~ distinct_points(X53,X53),
inference(variable_rename,[status(thm)],[i_0_27]) ).
fof(i_0_46,negated_conjecture,
( ~ unorthogonal_lines(esk1_0,esk2_0)
& ~ unorthogonal_lines(esk1_0,esk3_0)
& convergent_lines(esk2_0,esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_28])])]) ).
cnf(i_0_47,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_48,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_49,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_31]),
[final] ).
cnf(i_0_50,plain,
( ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_32]),
[final] ).
cnf(i_0_51,plain,
( ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_52,plain,
( unorthogonal_lines(X1,X2)
| unorthogonal_lines(X1,X3)
| ~ convergent_lines(X3,X2)
| ~ unorthogonal_lines(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_34]),
[final] ).
cnf(i_0_53,plain,
( convergent_lines(X1,X2)
| unorthogonal_lines(X1,X3)
| ~ convergent_lines(X3,X2)
| ~ unorthogonal_lines(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_34]),
[final] ).
cnf(i_0_54,plain,
( unorthogonal_lines(X1,X2)
| convergent_lines(X1,X3)
| ~ convergent_lines(X3,X2)
| ~ unorthogonal_lines(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_34]),
[final] ).
cnf(i_0_55,plain,
( convergent_lines(X1,X2)
| convergent_lines(X1,X3)
| ~ convergent_lines(X3,X2)
| ~ unorthogonal_lines(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_34]),
[final] ).
cnf(i_0_56,plain,
( unorthogonal_lines(X1,X2)
| unorthogonal_lines(X1,X3)
| ~ convergent_lines(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_57,plain,
( convergent_lines(X1,X3)
| convergent_lines(X2,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_36]),
[final] ).
cnf(i_0_58,plain,
( distinct_lines(X2,X3)
| apart_point_and_line(X1,X3)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_37]),
[final] ).
cnf(i_0_59,plain,
( distinct_lines(X2,X3)
| convergent_lines(X1,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_60,plain,
( distinct_lines(X1,X3)
| distinct_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_39]),
[final] ).
cnf(i_0_61,plain,
( distinct_points(X1,X3)
| apart_point_and_line(X3,X2)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_40]),
[final] ).
cnf(i_0_62,plain,
( distinct_points(X1,X3)
| distinct_points(X2,X3)
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_63,plain,
( convergent_lines(X1,X2)
| unorthogonal_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_64,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_65,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_66,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_67,negated_conjecture,
~ unorthogonal_lines(esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_68,negated_conjecture,
~ unorthogonal_lines(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_69,negated_conjecture,
convergent_lines(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_70,plain,
convergent_lines(esk1_0,esk3_0),
inference(scs_inference,[],[i_0_67,i_0_63]) ).
cnf(i_0_71,plain,
( unorthogonal_lines(X1,X2)
| convergent_lines(X1,X2) ),
inference(rename_variables,[],[i_0_63]) ).
cnf(i_0_72,plain,
$false,
inference(scs_inference,[],[i_0_67,i_0_68,i_0_69,i_0_63,i_0_56]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO220+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
% 0.16/0.33 % Computer : n015.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 17:49:02 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 0.28/1.62 % Version : CSE_E---1.7
% 0.28/1.62 % Problem : theBenchmark.p
% 0.28/1.62 % SZS status Theorem for theBenchmark.p
% 0.28/1.62 % SZS output start CNFRefutation
% See solution above
% 0.28/1.63 % Total time : 1.272s
%------------------------------------------------------------------------------