%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO202+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 : n011.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 04:19:52 PM UTC 2026
% Result : Theorem 1.57s 1.81s
% Output : CNFRefutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 60 ( 21 unt; 0 def)
% Number of atoms : 150 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 137 ( 47 ~; 68 |; 11 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 102 ( 0 sgn 57 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,conjecture,
! [X1,X2,X3] :
( ( distinct_points(X1,X2)
& distinct_points(X1,X3)
& convergent_lines(line_connecting(X1,X2),line_connecting(X1,X3)) )
=> ~ distinct_points(intersection_point(line_connecting(X1,X2),line_connecting(X1,X3)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
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(apart3,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart3) ).
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(ceq3,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> distinct_lines(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',ceq3) ).
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(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(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(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(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(c_0_11,negated_conjecture,
~ ! [X1,X2,X3] :
( ( distinct_points(X1,X2)
& distinct_points(X1,X3)
& convergent_lines(line_connecting(X1,X2),line_connecting(X1,X3)) )
=> ~ distinct_points(intersection_point(line_connecting(X1,X2),line_connecting(X1,X3)),X1) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[con])]) ).
fof(c_0_12,plain,
! [X48,X49,X50] :
( ~ convergent_lines(X48,X49)
| convergent_lines(X48,X50)
| convergent_lines(X49,X50) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart6])]) ).
fof(c_0_13,negated_conjecture,
( distinct_points(esk1_0,esk2_0)
& distinct_points(esk1_0,esk3_0)
& convergent_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0))
& distinct_points(intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),esk1_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_14,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart3]) ).
cnf(c_0_15,plain,
( convergent_lines(X1,X3)
| convergent_lines(X2,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
convergent_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_17,plain,
! [X41] : ~ convergent_lines(X41,X41),
inference(variable_rename,[status(thm)],[c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( convergent_lines(line_connecting(esk1_0,esk2_0),X1)
| convergent_lines(line_connecting(esk1_0,esk3_0),X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_20,negated_conjecture,
( convergent_lines(line_connecting(esk1_0,esk2_0),X1)
| convergent_lines(line_connecting(esk1_0,esk3_0),X2)
| convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
( convergent_lines(X1,line_connecting(esk1_0,esk3_0))
| convergent_lines(line_connecting(esk1_0,esk2_0),X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_22,plain,
! [X45,X46,X47] :
( ~ distinct_lines(X45,X46)
| distinct_lines(X45,X47)
| distinct_lines(X46,X47) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart5])]) ).
fof(c_0_23,plain,
! [X67,X68] :
( ~ convergent_lines(X67,X68)
| distinct_lines(X67,X68) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])]) ).
cnf(c_0_24,negated_conjecture,
( convergent_lines(X1,line_connecting(esk1_0,esk3_0))
| convergent_lines(line_connecting(esk1_0,esk2_0),X2)
| convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_21]) ).
fof(c_0_25,plain,
! [X1] : ~ distinct_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart2]) ).
cnf(c_0_26,plain,
( distinct_lines(X1,X3)
| distinct_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
( distinct_lines(X1,X2)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,negated_conjecture,
( convergent_lines(X1,line_connecting(esk1_0,esk2_0))
| convergent_lines(X1,line_connecting(esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_19,c_0_24]) ).
fof(c_0_29,plain,
! [X40] : ~ distinct_lines(X40,X40),
inference(variable_rename,[status(thm)],[c_0_25]) ).
cnf(c_0_30,plain,
( distinct_lines(X1,X2)
| distinct_lines(X3,X2)
| ~ convergent_lines(X1,X3) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,negated_conjecture,
convergent_lines(line_connecting(esk1_0,esk3_0),line_connecting(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_19,c_0_28]) ).
fof(c_0_32,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[apart1]) ).
fof(c_0_33,plain,
! [X42,X43,X44] :
( ~ distinct_points(X42,X43)
| distinct_points(X42,X44)
| distinct_points(X43,X44) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart4])]) ).
fof(c_0_34,plain,
! [X57,X58,X59,X60] :
( ~ distinct_points(X57,X58)
| ~ distinct_lines(X59,X60)
| apart_point_and_line(X57,X59)
| apart_point_and_line(X57,X60)
| apart_point_and_line(X58,X59)
| apart_point_and_line(X58,X60) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cu1])]) ).
cnf(c_0_35,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,negated_conjecture,
( distinct_lines(line_connecting(esk1_0,esk2_0),X1)
| distinct_lines(line_connecting(esk1_0,esk3_0),X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
fof(c_0_37,plain,
! [X39] : ~ distinct_points(X39,X39),
inference(variable_rename,[status(thm)],[c_0_32]) ).
cnf(c_0_38,plain,
( distinct_points(X1,X3)
| distinct_points(X2,X3)
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_39,negated_conjecture,
distinct_points(intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_40,plain,
! [X54,X55,X56] :
( ( ~ apart_point_and_line(X56,X54)
| distinct_points(X56,intersection_point(X54,X55))
| ~ convergent_lines(X54,X55) )
& ( ~ apart_point_and_line(X56,X55)
| distinct_points(X56,intersection_point(X54,X55))
| ~ convergent_lines(X54,X55) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[con2])])]) ).
cnf(c_0_41,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_34]) ).
cnf(c_0_42,negated_conjecture,
distinct_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_43,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_44,negated_conjecture,
( distinct_points(intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),X1)
| distinct_points(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_45,plain,
( distinct_points(X1,intersection_point(X3,X2))
| ~ apart_point_and_line(X1,X2)
| ~ convergent_lines(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_46,negated_conjecture,
( apart_point_and_line(X1,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(X1,line_connecting(esk1_0,esk3_0))
| apart_point_and_line(X2,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(X2,line_connecting(esk1_0,esk3_0))
| ~ distinct_points(X1,X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,negated_conjecture,
distinct_points(esk1_0,intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0))),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_48,plain,
( distinct_points(X1,intersection_point(X2,X3))
| ~ apart_point_and_line(X1,X2)
| ~ convergent_lines(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_49,plain,
( ~ apart_point_and_line(intersection_point(X1,X2),X2)
| ~ convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_43,c_0_45]) ).
cnf(c_0_50,negated_conjecture,
( apart_point_and_line(intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),line_connecting(esk1_0,esk3_0))
| apart_point_and_line(intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
fof(c_0_51,plain,
! [X51,X52,X53] :
( ( distinct_points(X53,X51)
| ~ apart_point_and_line(X53,line_connecting(X51,X52))
| ~ distinct_points(X51,X52) )
& ( distinct_points(X53,X52)
| ~ apart_point_and_line(X53,line_connecting(X51,X52))
| ~ distinct_points(X51,X52) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[con1])])]) ).
cnf(c_0_52,plain,
( ~ apart_point_and_line(intersection_point(X1,X2),X1)
| ~ convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_43,c_0_48]) ).
cnf(c_0_53,negated_conjecture,
( apart_point_and_line(intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_16])]) ).
cnf(c_0_54,plain,
( distinct_points(X1,X2)
| ~ apart_point_and_line(X1,line_connecting(X2,X3))
| ~ distinct_points(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_55,negated_conjecture,
( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_16])]) ).
cnf(c_0_56,negated_conjecture,
distinct_points(esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_57,negated_conjecture,
apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56])]),c_0_43]) ).
cnf(c_0_58,negated_conjecture,
distinct_points(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_59,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_57]),c_0_58])]),c_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO202+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
% 0.15/0.33 % Computer : n011.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 17:48:02 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.57/1.81 % Version : CSE_E---1.7
% 1.57/1.81 % Problem : theBenchmark.p
% 1.57/1.81 % SZS status Theorem for theBenchmark.p
% 1.57/1.81 % SZS output start CNFRefutation
% See solution above
% 1.57/1.81 % Total time : 1.368s
%------------------------------------------------------------------------------