%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO269+3 : TPTP v9.2.1. Released v4.0.0.
% 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 : n027.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 04:20:12 PM UTC 2026
% Result : Theorem 1.27s 1.71s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 33 ( 13 unt; 0 def)
% Number of atoms : 65 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 60 ( 28 ~; 21 |; 5 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 48 ( 2 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,conjecture,
! [X4] : equally_directed_opposite_lines(X4,reverse_line(X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(a5_defns,axiom,
! [X1,X2] :
( equally_directed_opposite_lines(X1,X2)
<=> ~ unequally_directed_opposite_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax',a5_defns) ).
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/sandbox/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/sandbox/benchmark/Axioms/GEO009+0.ax',ax11_basics) ).
fof(a1_defns,axiom,
! [X1,X2] :
( unequally_directed_opposite_lines(X1,X2)
<=> unequally_directed_lines(X1,reverse_line(X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax',a1_defns) ).
fof(a4_defns,axiom,
! [X1,X2] :
( equally_directed_lines(X1,X2)
<=> ~ unequally_directed_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax',a4_defns) ).
fof(ax5_basics,axiom,
! [X4] : equally_directed_lines(X4,X4),
file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax',ax5_basics) ).
fof(ax8_basics,axiom,
! [X4,X5] :
( unequally_directed_lines(X4,X5)
| unequally_directed_lines(X4,reverse_line(X5)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax',ax8_basics) ).
fof(c_0_8,negated_conjecture,
~ ! [X4] : equally_directed_opposite_lines(X4,reverse_line(X4)),
inference(assume_negation,[status(cth)],[con]) ).
fof(c_0_9,plain,
! [X1,X2] :
( equally_directed_opposite_lines(X1,X2)
<=> ~ unequally_directed_opposite_lines(X1,X2) ),
inference(fof_simplification,[status(thm)],[a5_defns]) ).
fof(c_0_10,negated_conjecture,
~ equally_directed_opposite_lines(esk1_0,reverse_line(esk1_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_11,plain,
! [X99,X100] :
( ( ~ equally_directed_opposite_lines(X99,X100)
| ~ unequally_directed_opposite_lines(X99,X100) )
& ( unequally_directed_opposite_lines(X99,X100)
| equally_directed_opposite_lines(X99,X100) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])]) ).
fof(c_0_12,plain,
! [X132,X133] :
( ~ unequally_directed_lines(X132,X133)
| ~ unequally_directed_lines(X132,reverse_line(X133))
| left_convergent_lines(X132,X133)
| left_convergent_lines(X132,reverse_line(X133)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax9_basics])]) ).
fof(c_0_13,plain,
! [X136,X137] :
( ~ left_convergent_lines(X136,X137)
& ~ left_convergent_lines(X136,reverse_line(X137)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax11_basics])]) ).
fof(c_0_14,plain,
! [X91,X92] :
( ( ~ unequally_directed_opposite_lines(X91,X92)
| unequally_directed_lines(X91,reverse_line(X92)) )
& ( ~ unequally_directed_lines(X91,reverse_line(X92))
| unequally_directed_opposite_lines(X91,X92) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[a1_defns])]) ).
cnf(c_0_15,negated_conjecture,
~ equally_directed_opposite_lines(esk1_0,reverse_line(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( unequally_directed_opposite_lines(X1,X2)
| equally_directed_opposite_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,plain,
! [X1,X2] :
( equally_directed_lines(X1,X2)
<=> ~ unequally_directed_lines(X1,X2) ),
inference(fof_simplification,[status(thm)],[a4_defns]) ).
cnf(c_0_18,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_12]) ).
cnf(c_0_19,plain,
~ left_convergent_lines(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( unequally_directed_lines(X1,reverse_line(X2))
| ~ unequally_directed_opposite_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,negated_conjecture,
unequally_directed_opposite_lines(esk1_0,reverse_line(esk1_0)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_22,plain,
! [X97,X98] :
( ( ~ equally_directed_lines(X97,X98)
| ~ unequally_directed_lines(X97,X98) )
& ( unequally_directed_lines(X97,X98)
| equally_directed_lines(X97,X98) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])]) ).
fof(c_0_23,plain,
! [X123] : equally_directed_lines(X123,X123),
inference(variable_rename,[status(thm)],[ax5_basics]) ).
cnf(c_0_24,plain,
( ~ unequally_directed_lines(X1,reverse_line(X2))
| ~ unequally_directed_lines(X1,X2) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_18,c_0_19]),c_0_19]) ).
cnf(c_0_25,negated_conjecture,
unequally_directed_lines(esk1_0,reverse_line(reverse_line(esk1_0))),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_26,plain,
! [X130,X131] :
( unequally_directed_lines(X130,X131)
| unequally_directed_lines(X130,reverse_line(X131)) ),
inference(variable_rename,[status(thm)],[ax8_basics]) ).
cnf(c_0_27,plain,
( ~ equally_directed_lines(X1,X2)
| ~ unequally_directed_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
equally_directed_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,negated_conjecture,
~ unequally_directed_lines(esk1_0,reverse_line(esk1_0)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,plain,
( unequally_directed_lines(X1,X2)
| unequally_directed_lines(X1,reverse_line(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,plain,
~ unequally_directed_lines(X1,X1),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GEO269+3 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n027.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 17:51:49 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.27/1.71 % Version : CSE_E---1.7
% 1.27/1.71 % Problem : theBenchmark.p
% 1.27/1.71 % SZS status Theorem for theBenchmark.p
% 1.27/1.71 % SZS output start CNFRefutation
% See solution above
% 1.27/1.71 % Total time : 1.372s
%------------------------------------------------------------------------------