%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO231+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 : n007.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 04:20:03 PM UTC 2026
% Result : Theorem 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 12 unt; 0 def)
% Number of atoms : 88 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 82 ( 35 ~; 29 |; 9 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 62 ( 2 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(con,conjecture,
! [X4,X5,X8] :
( ( equally_directed_opposite_lines(X4,X5)
& equally_directed_lines(X4,X8) )
=> equally_directed_opposite_lines(X5,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
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(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(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(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(ax6_basics,axiom,
! [X4,X5,X8] :
( unequally_directed_lines(X4,X5)
=> ( unequally_directed_lines(X4,X8)
| unequally_directed_lines(X5,X8) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax',ax6_basics) ).
fof(c_0_8,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_9,negated_conjecture,
~ ! [X4,X5,X8] :
( ( equally_directed_opposite_lines(X4,X5)
& equally_directed_lines(X4,X8) )
=> equally_directed_opposite_lines(X5,X8) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(c_0_10,plain,
! [X101,X102] :
( ( ~ equally_directed_opposite_lines(X101,X102)
| ~ unequally_directed_opposite_lines(X101,X102) )
& ( unequally_directed_opposite_lines(X101,X102)
| equally_directed_opposite_lines(X101,X102) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])]) ).
fof(c_0_11,negated_conjecture,
( equally_directed_opposite_lines(esk1_0,esk2_0)
& equally_directed_lines(esk1_0,esk3_0)
& ~ equally_directed_opposite_lines(esk2_0,esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
cnf(c_0_12,plain,
( ~ equally_directed_opposite_lines(X1,X2)
| ~ unequally_directed_opposite_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,negated_conjecture,
equally_directed_opposite_lines(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_14,plain,
! [X93,X94] :
( ( ~ unequally_directed_opposite_lines(X93,X94)
| unequally_directed_lines(X93,reverse_line(X94)) )
& ( ~ unequally_directed_lines(X93,reverse_line(X94))
| unequally_directed_opposite_lines(X93,X94) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[a1_defns])]) ).
fof(c_0_15,plain,
! [X134,X135] :
( ~ unequally_directed_lines(X134,X135)
| ~ unequally_directed_lines(X134,reverse_line(X135))
| left_convergent_lines(X134,X135)
| left_convergent_lines(X134,reverse_line(X135)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax9_basics])]) ).
fof(c_0_16,plain,
! [X138,X139] :
( ~ left_convergent_lines(X138,X139)
& ~ left_convergent_lines(X138,reverse_line(X139)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax11_basics])]) ).
cnf(c_0_17,negated_conjecture,
~ equally_directed_opposite_lines(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( unequally_directed_opposite_lines(X1,X2)
| equally_directed_opposite_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,negated_conjecture,
~ unequally_directed_opposite_lines(esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_20,plain,
( unequally_directed_opposite_lines(X1,X2)
| ~ unequally_directed_lines(X1,reverse_line(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_21,plain,
! [X132,X133] :
( unequally_directed_lines(X132,X133)
| unequally_directed_lines(X132,reverse_line(X133)) ),
inference(variable_rename,[status(thm)],[ax8_basics]) ).
fof(c_0_22,plain,
! [X1,X2] :
( equally_directed_lines(X1,X2)
<=> ~ unequally_directed_lines(X1,X2) ),
inference(fof_simplification,[status(thm)],[a4_defns]) ).
cnf(c_0_23,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_15]) ).
cnf(c_0_24,plain,
~ left_convergent_lines(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,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_26,negated_conjecture,
unequally_directed_opposite_lines(esk2_0,esk3_0),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_27,plain,
! [X126,X127,X128] :
( ~ unequally_directed_lines(X126,X127)
| unequally_directed_lines(X126,X128)
| unequally_directed_lines(X127,X128) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6_basics])]) ).
cnf(c_0_28,negated_conjecture,
~ unequally_directed_lines(esk1_0,reverse_line(esk2_0)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_29,plain,
( unequally_directed_lines(X1,X2)
| unequally_directed_lines(X1,reverse_line(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_30,plain,
! [X99,X100] :
( ( ~ equally_directed_lines(X99,X100)
| ~ unequally_directed_lines(X99,X100) )
& ( unequally_directed_lines(X99,X100)
| equally_directed_lines(X99,X100) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])]) ).
cnf(c_0_31,plain,
( ~ unequally_directed_lines(X1,reverse_line(X2))
| ~ unequally_directed_lines(X1,X2) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_23,c_0_24]),c_0_24]) ).
cnf(c_0_32,negated_conjecture,
unequally_directed_lines(esk2_0,reverse_line(esk3_0)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,plain,
( unequally_directed_lines(X1,X3)
| unequally_directed_lines(X2,X3)
| ~ unequally_directed_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,negated_conjecture,
unequally_directed_lines(esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,plain,
( ~ equally_directed_lines(X1,X2)
| ~ unequally_directed_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,negated_conjecture,
equally_directed_lines(esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_37,negated_conjecture,
~ unequally_directed_lines(esk2_0,esk3_0),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_38,negated_conjecture,
( unequally_directed_lines(esk1_0,X1)
| unequally_directed_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
~ unequally_directed_lines(esk1_0,esk3_0),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO231+3 : TPTP v9.2.1. Released v4.0.0.
% 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 : n007.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 17:49:09 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % 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 : 1.370s
%------------------------------------------------------------------------------