%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO262+3 : TPTP v9.2.1. Released v4.0.0.
% 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 : n021.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 04:20:11 PM UTC 2026
% Result : Theorem 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 5 unt; 0 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 68 ( 22 ~; 19 |; 22 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 42 ( 2 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(a1_defns,axiom,
! [X1,X2] :
( unequally_directed_opposite_lines(X1,X2)
<=> unequally_directed_lines(X1,reverse_line(X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',a1_defns) ).
fof(a7_defns,axiom,
! [X4,X5] :
( convergent_lines(X4,X5)
<=> ( unequally_directed_lines(X4,X5)
& unequally_directed_opposite_lines(X4,X5) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',a7_defns) ).
fof(con,conjecture,
! [X4,X5,X8,X3,X6,X7] :
( ( between_on_line(X4,X3,X6,X7)
& convergent_lines(X4,X5)
& incident_point_and_line(X6,X5)
& convergent_lines(X4,X8)
& convergent_lines(X5,X8)
& incident_point_and_line(X6,X8) )
=> between_on_line(X5,intersection_point(X5,parallel_through_point(X8,X3)),X6,intersection_point(X5,parallel_through_point(X8,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(ax9_basics,axiom,
! [X4,X5] :
( ( unequally_directed_lines(X4,X5)
& unequally_directed_lines(X4,reverse_line(X5)) )
=> ( left_convergent_lines(X4,X5)
| left_convergent_lines(X4,reverse_line(X5)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',ax9_basics) ).
fof(ax11_basics,axiom,
! [X4,X5] :
~ ( left_convergent_lines(X4,X5)
| left_convergent_lines(X4,reverse_line(X5)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',ax11_basics) ).
fof(c_0_5,plain,
! [X96,X97] :
( ( ~ unequally_directed_opposite_lines(X96,X97)
| unequally_directed_lines(X96,reverse_line(X97)) )
& ( ~ unequally_directed_lines(X96,reverse_line(X97))
| unequally_directed_opposite_lines(X96,X97) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[a1_defns])]) ).
fof(c_0_6,plain,
! [X108,X109] :
( ( unequally_directed_lines(X108,X109)
| ~ convergent_lines(X108,X109) )
& ( unequally_directed_opposite_lines(X108,X109)
| ~ convergent_lines(X108,X109) )
& ( ~ unequally_directed_lines(X108,X109)
| ~ unequally_directed_opposite_lines(X108,X109)
| convergent_lines(X108,X109) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[a7_defns])])]) ).
fof(c_0_7,negated_conjecture,
~ ! [X4,X5,X8,X3,X6,X7] :
( ( between_on_line(X4,X3,X6,X7)
& convergent_lines(X4,X5)
& incident_point_and_line(X6,X5)
& convergent_lines(X4,X8)
& convergent_lines(X5,X8)
& incident_point_and_line(X6,X8) )
=> between_on_line(X5,intersection_point(X5,parallel_through_point(X8,X3)),X6,intersection_point(X5,parallel_through_point(X8,X7))) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(c_0_8,plain,
! [X137,X138] :
( ~ unequally_directed_lines(X137,X138)
| ~ unequally_directed_lines(X137,reverse_line(X138))
| left_convergent_lines(X137,X138)
| left_convergent_lines(X137,reverse_line(X138)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax9_basics])]) ).
fof(c_0_9,plain,
! [X141,X142] :
( ~ left_convergent_lines(X141,X142)
& ~ left_convergent_lines(X141,reverse_line(X142)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax11_basics])]) ).
cnf(c_0_10,plain,
( unequally_directed_lines(X1,reverse_line(X2))
| ~ unequally_directed_opposite_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,plain,
( unequally_directed_opposite_lines(X1,X2)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_12,negated_conjecture,
( between_on_line(esk1_0,esk4_0,esk5_0,esk6_0)
& convergent_lines(esk1_0,esk2_0)
& incident_point_and_line(esk5_0,esk2_0)
& convergent_lines(esk1_0,esk3_0)
& convergent_lines(esk2_0,esk3_0)
& incident_point_and_line(esk5_0,esk3_0)
& ~ between_on_line(esk2_0,intersection_point(esk2_0,parallel_through_point(esk3_0,esk4_0)),esk5_0,intersection_point(esk2_0,parallel_through_point(esk3_0,esk6_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_13,plain,
( left_convergent_lines(X1,X2)
| left_convergent_lines(X1,reverse_line(X2))
| ~ unequally_directed_lines(X1,X2)
| ~ unequally_directed_lines(X1,reverse_line(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
~ left_convergent_lines(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( unequally_directed_lines(X1,reverse_line(X2))
| ~ convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,negated_conjecture,
convergent_lines(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( unequally_directed_lines(X1,X2)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_18,plain,
( ~ unequally_directed_lines(X1,reverse_line(X2))
| ~ unequally_directed_lines(X1,X2) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_13,c_0_14]),c_0_14]) ).
cnf(c_0_19,negated_conjecture,
unequally_directed_lines(esk2_0,reverse_line(esk3_0)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
unequally_directed_lines(esk2_0,esk3_0),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO262+3 : TPTP v9.2.1. Released v4.0.0.
% 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
% 0.14/0.33 % Computer : n021.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 17:52:10 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.27/1.72 % Version : CSE_E---1.7
% 1.27/1.72 % Problem : theBenchmark.p
% 1.27/1.72 % SZS status Theorem for theBenchmark.p
% 1.27/1.72 % SZS output start CNFRefutation
% See solution above
% 1.27/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------