%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO195+1 : 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 : n005.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 04:19:49 PM UTC 2026
% Result : Theorem 1.35s 1.75s
% Output : CNFRefutation 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of formulae : 69 ( 23 unt; 0 def)
% Number of atoms : 171 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 146 ( 44 ~; 79 |; 9 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 110 ( 0 sgn 65 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,conjecture,
! [X1,X2,X3] :
( ( convergent_lines(X1,X2)
& convergent_lines(X3,X2)
& convergent_lines(X1,X3) )
=> ( apart_point_and_line(intersection_point(X1,X2),X3)
=> apart_point_and_line(intersection_point(X2,X1),X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
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/GEO006+0.ax',ceq2) ).
fof(ci4,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci4) ).
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/GEO006+0.ax',ceq1) ).
fof(apart3,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(ax6,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( convergent_lines(X1,X3)
| convergent_lines(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ax6) ).
fof(apart2,axiom,
! [X1] : ~ distinct_lines(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart2) ).
fof(ceq3,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( distinct_lines(X2,X3)
| convergent_lines(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq3) ).
fof(apart1,axiom,
! [X1] : ~ distinct_points(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart1) ).
fof(apart4,axiom,
! [X1,X2,X3] :
( distinct_points(X1,X2)
=> ( distinct_points(X1,X3)
| distinct_points(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart4) ).
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/GEO006+0.ax',cu1) ).
fof(ci3,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci3) ).
fof(c_0_12,negated_conjecture,
~ ! [X1,X2,X3] :
( ( convergent_lines(X1,X2)
& convergent_lines(X3,X2)
& convergent_lines(X1,X3) )
=> ( apart_point_and_line(intersection_point(X1,X2),X3)
=> apart_point_and_line(intersection_point(X2,X1),X3) ) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(c_0_13,plain,
! [X69,X70,X71] :
( ~ apart_point_and_line(X69,X70)
| distinct_lines(X70,X71)
| apart_point_and_line(X69,X71) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq2])]) ).
fof(c_0_14,negated_conjecture,
( convergent_lines(esk1_0,esk2_0)
& convergent_lines(esk3_0,esk2_0)
& convergent_lines(esk1_0,esk3_0)
& apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0)
& ~ apart_point_and_line(intersection_point(esk2_0,esk1_0),esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
fof(c_0_15,plain,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(fof_simplification,[status(thm)],[ci4]) ).
fof(c_0_16,plain,
! [X66,X67,X68] :
( ~ apart_point_and_line(X66,X67)
| distinct_points(X66,X68)
| apart_point_and_line(X68,X67) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq1])]) ).
cnf(c_0_17,plain,
( distinct_lines(X2,X3)
| apart_point_and_line(X1,X3)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_19,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart3]) ).
fof(c_0_20,plain,
! [X51,X52,X53] :
( ~ convergent_lines(X51,X52)
| convergent_lines(X51,X53)
| convergent_lines(X52,X53) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])]) ).
fof(c_0_21,plain,
! [X60,X61] :
( ~ convergent_lines(X60,X61)
| ~ apart_point_and_line(intersection_point(X60,X61),X61) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])]) ).
cnf(c_0_22,plain,
( distinct_points(X1,X3)
| apart_point_and_line(X3,X2)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),X1)
| distinct_lines(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_24,plain,
! [X44] : ~ convergent_lines(X44,X44),
inference(variable_rename,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
( convergent_lines(X1,X3)
| convergent_lines(X2,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,negated_conjecture,
convergent_lines(esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_27,plain,
! [X1] : ~ distinct_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart2]) ).
cnf(c_0_28,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,negated_conjecture,
( apart_point_and_line(X1,X2)
| distinct_lines(esk3_0,X2)
| distinct_points(intersection_point(esk1_0,esk2_0),X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,negated_conjecture,
( convergent_lines(esk3_0,X1)
| convergent_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
fof(c_0_32,plain,
! [X43] : ~ distinct_lines(X43,X43),
inference(variable_rename,[status(thm)],[c_0_27]) ).
fof(c_0_33,plain,
! [X72,X73,X74] :
( ~ convergent_lines(X72,X73)
| distinct_lines(X73,X74)
| convergent_lines(X72,X74) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])]) ).
fof(c_0_34,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[apart1]) ).
fof(c_0_35,plain,
! [X45,X46,X47] :
( ~ distinct_points(X45,X46)
| distinct_points(X45,X47)
| distinct_points(X46,X47) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart4])]) ).
cnf(c_0_36,negated_conjecture,
( distinct_lines(esk3_0,X1)
| distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(X2,X1))
| ~ convergent_lines(X2,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_37,negated_conjecture,
convergent_lines(esk2_0,esk3_0),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_38,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_39,plain,
! [X62,X63,X64,X65] :
( ~ distinct_points(X62,X63)
| ~ distinct_lines(X64,X65)
| apart_point_and_line(X62,X64)
| apart_point_and_line(X62,X65)
| apart_point_and_line(X63,X64)
| apart_point_and_line(X63,X65) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cu1])]) ).
cnf(c_0_40,plain,
( distinct_lines(X2,X3)
| convergent_lines(X1,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,negated_conjecture,
convergent_lines(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_42,plain,
! [X42] : ~ distinct_points(X42,X42),
inference(variable_rename,[status(thm)],[c_0_34]) ).
cnf(c_0_43,plain,
( distinct_points(X1,X3)
| distinct_points(X2,X3)
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_44,negated_conjecture,
distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(esk2_0,esk3_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
fof(c_0_45,plain,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(fof_simplification,[status(thm)],[ci3]) ).
cnf(c_0_46,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)],[c_0_39]) ).
cnf(c_0_47,negated_conjecture,
( convergent_lines(esk1_0,X1)
| distinct_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_48,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_49,negated_conjecture,
( distinct_points(intersection_point(esk1_0,esk2_0),X1)
| distinct_points(intersection_point(esk2_0,esk3_0),X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
fof(c_0_50,plain,
! [X58,X59] :
( ~ convergent_lines(X58,X59)
| ~ apart_point_and_line(intersection_point(X58,X59),X58) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])]) ).
cnf(c_0_51,negated_conjecture,
( apart_point_and_line(X1,esk2_0)
| apart_point_and_line(X2,esk2_0)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X2,X3)
| convergent_lines(esk1_0,X3)
| ~ distinct_points(X1,X2) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,negated_conjecture,
distinct_points(intersection_point(esk2_0,esk3_0),intersection_point(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_54,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0)
| apart_point_and_line(intersection_point(esk2_0,esk3_0),esk2_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),X1)
| apart_point_and_line(intersection_point(esk2_0,esk3_0),X1)
| convergent_lines(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_55,negated_conjecture,
( apart_point_and_line(intersection_point(esk2_0,esk3_0),esk1_0)
| apart_point_and_line(intersection_point(esk2_0,esk3_0),esk2_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_41])]),c_0_30]) ).
cnf(c_0_56,negated_conjecture,
distinct_lines(esk3_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_23]),c_0_41])]) ).
cnf(c_0_57,negated_conjecture,
( apart_point_and_line(intersection_point(esk2_0,esk3_0),esk2_0)
| apart_point_and_line(intersection_point(esk2_0,esk3_0),esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_55]),c_0_41])]) ).
cnf(c_0_58,negated_conjecture,
( apart_point_and_line(X1,esk3_0)
| apart_point_and_line(X1,esk2_0)
| apart_point_and_line(X2,esk3_0)
| apart_point_and_line(X2,esk2_0)
| ~ distinct_points(X1,X2) ),
inference(spm,[status(thm)],[c_0_46,c_0_56]) ).
cnf(c_0_59,negated_conjecture,
( apart_point_and_line(intersection_point(esk2_0,esk3_0),esk2_0)
| apart_point_and_line(X1,esk1_0)
| distinct_points(intersection_point(esk2_0,esk3_0),X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_57]) ).
cnf(c_0_60,negated_conjecture,
( apart_point_and_line(intersection_point(esk2_0,esk3_0),esk2_0)
| apart_point_and_line(intersection_point(esk2_0,esk3_0),esk3_0)
| apart_point_and_line(X1,esk1_0)
| apart_point_and_line(X1,esk2_0)
| apart_point_and_line(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_61,negated_conjecture,
( apart_point_and_line(intersection_point(esk2_0,esk3_0),esk2_0)
| apart_point_and_line(X1,esk3_0)
| apart_point_and_line(X1,esk2_0)
| apart_point_and_line(X1,esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_60]),c_0_37])]) ).
cnf(c_0_62,negated_conjecture,
~ apart_point_and_line(intersection_point(esk2_0,esk1_0),esk3_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_63,negated_conjecture,
( apart_point_and_line(X1,esk1_0)
| apart_point_and_line(X1,esk2_0)
| apart_point_and_line(X1,esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_61]),c_0_37])]) ).
cnf(c_0_64,negated_conjecture,
( convergent_lines(esk1_0,X1)
| convergent_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_41]) ).
cnf(c_0_65,negated_conjecture,
( apart_point_and_line(intersection_point(esk2_0,esk1_0),esk2_0)
| apart_point_and_line(intersection_point(esk2_0,esk1_0),esk1_0) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_66,negated_conjecture,
convergent_lines(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_30,c_0_64]) ).
cnf(c_0_67,negated_conjecture,
apart_point_and_line(intersection_point(esk2_0,esk1_0),esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_65]),c_0_66])]) ).
cnf(c_0_68,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_67]),c_0_66])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO195+1 : 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
% 0.14/0.32 % Computer : n005.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 17:47:15 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.35/1.75 % Version : CSE_E---1.7
% 1.35/1.75 % Problem : theBenchmark.p
% 1.35/1.75 % SZS status Theorem for theBenchmark.p
% 1.35/1.75 % SZS output start CNFRefutation
% See solution above
% 1.35/1.75 % Total time : 1.371s
%------------------------------------------------------------------------------