%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO231+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:14:53 AM UTC 2026
% Result : Theorem 26.41s 6.25s
% Output : CNFRefutation 26.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 42 ( 15 unt; 0 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 69 ( 29 ~; 30 |; 3 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 63 ( 2 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(a1_defns,axiom,
! [X0,X1] :
( 'unequally$udirected$uopposite$ulines'(X0,X1)
<=> 'unequally$udirected$ulines'(X0,'reverse$uline'(X1)) ) ).
fof(a4_defns,axiom,
! [X0,X1] :
( 'equally$udirected$ulines'(X0,X1)
<=> ~ 'unequally$udirected$ulines'(X0,X1) ) ).
fof(a5_defns,axiom,
! [X0,X1] :
( 'equally$udirected$uopposite$ulines'(X0,X1)
<=> ~ 'unequally$udirected$uopposite$ulines'(X0,X1) ) ).
fof(ax5_basics,axiom,
! [X0] : 'equally$udirected$ulines'(X0,X0) ).
fof(ax6_basics,axiom,
! [X0,X1,X2] :
( 'unequally$udirected$ulines'(X0,X1)
=> ( 'unequally$udirected$ulines'(X1,X2)
| 'unequally$udirected$ulines'(X0,X2) ) ) ).
fof(ax8_basics,axiom,
! [X0,X1] :
( 'unequally$udirected$ulines'(X0,'reverse$uline'(X1))
| 'unequally$udirected$ulines'(X0,X1) ) ).
fof(ax9_basics,axiom,
! [X0,X1] :
( ( 'unequally$udirected$ulines'(X0,'reverse$uline'(X1))
& 'unequally$udirected$ulines'(X0,X1) )
=> ( 'left$uconvergent$ulines'(X0,'reverse$uline'(X1))
| 'left$uconvergent$ulines'(X0,X1) ) ) ).
fof(ax11_basics,axiom,
! [X0,X1] :
~ ( 'left$uconvergent$ulines'(X0,'reverse$uline'(X1))
| 'left$uconvergent$ulines'(X0,X1) ) ).
fof(con,conjecture,
! [X0,X1,X2] :
( ( 'equally$udirected$ulines'(X0,X2)
& 'equally$udirected$uopposite$ulines'(X0,X1) )
=> 'equally$udirected$uopposite$ulines'(X1,X2) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ( 'equally$udirected$ulines'(X0,X2)
& 'equally$udirected$uopposite$ulines'(X0,X1) )
=> 'equally$udirected$uopposite$ulines'(X1,X2) ),
inference(negate_conjecture,[status(cth)],[con]) ).
cnf(c0,plain,
( 'unequally$udirected$ulines'(X0,'reverse$uline'(X1))
| ~ 'unequally$udirected$uopposite$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[a1_defns]) ).
cnf(c1,plain,
( ~ 'unequally$udirected$ulines'(X0,'reverse$uline'(X1))
| 'unequally$udirected$uopposite$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[a1_defns]) ).
cnf(c6,plain,
( ~ 'unequally$udirected$ulines'(X0,X1)
| ~ 'equally$udirected$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[a4_defns]) ).
cnf(c8,plain,
( ~ 'unequally$udirected$uopposite$ulines'(X0,X1)
| ~ 'equally$udirected$uopposite$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[a5_defns]) ).
cnf(c9,plain,
( 'unequally$udirected$uopposite$ulines'(X0,X1)
| 'equally$udirected$uopposite$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[a5_defns]) ).
cnf(c43,plain,
'equally$udirected$ulines'(X0,X0),
inference(clausification,[status(esa)],[ax5_basics]) ).
cnf(c44,plain,
( 'unequally$udirected$ulines'(X1,X2)
| 'unequally$udirected$ulines'(X0,X2)
| ~ 'unequally$udirected$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[ax6_basics]) ).
cnf(c49,plain,
( 'unequally$udirected$ulines'(X0,'reverse$uline'(X1))
| 'unequally$udirected$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[ax8_basics]) ).
cnf(c50,plain,
( 'left$uconvergent$ulines'(X0,'reverse$uline'(X1))
| 'left$uconvergent$ulines'(X0,X1)
| ~ 'unequally$udirected$ulines'(X0,'reverse$uline'(X1))
| ~ 'unequally$udirected$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[ax9_basics]) ).
cnf(c53,plain,
~ 'left$uconvergent$ulines'(X0,X1),
inference(clausification,[status(esa)],[ax11_basics]) ).
cnf(c72,plain,
'equally$udirected$uopposite$ulines'(sK84,sK85),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c73,plain,
'equally$udirected$ulines'(sK84,sK86),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c74,plain,
~ 'equally$udirected$uopposite$ulines'(sK85,sK86),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
~ 'unequally$udirected$uopposite$ulines'(sK84,sK85),
inference(resolution,[status(thm)],[c8,c72]) ).
cnf(d1,plain,
( 'unequally$udirected$uopposite$ulines'(X0,X1)
| 'unequally$udirected$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[c49,c1]) ).
cnf(d2,plain,
( 'unequally$udirected$uopposite$ulines'(X2,X0)
| 'unequally$udirected$ulines'(X2,X1)
| 'unequally$udirected$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[c44,d1]) ).
cnf(d3,plain,
( 'unequally$udirected$ulines'(sK85,X0)
| 'unequally$udirected$ulines'(sK84,X0) ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( 'left$uconvergent$ulines'(X0,'reverse$uline'(X1))
| ~ 'unequally$udirected$ulines'(X0,'reverse$uline'(X1))
| ~ 'unequally$udirected$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[c53,c50]) ).
cnf(d5,plain,
( 'unequally$udirected$uopposite$ulines'(X0,'reverse$uline'(X1))
| 'left$uconvergent$ulines'(X0,'reverse$uline'(X1))
| ~ 'unequally$udirected$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
( ~ 'unequally$udirected$ulines'(X0,X1)
| 'unequally$udirected$uopposite$ulines'(X0,'reverse$uline'(X1)) ),
inference(resolution,[status(thm)],[c53,d5]) ).
cnf(d7,plain,
~ 'unequally$udirected$ulines'(X0,X0),
inference(resolution,[status(thm)],[c6,c43]) ).
cnf(d8,plain,
'unequally$udirected$uopposite$ulines'(sK85,sK86),
inference(resolution,[status(thm)],[c9,c74]) ).
cnf(d9,plain,
( ~ 'unequally$udirected$uopposite$ulines'(X2,X0)
| 'unequally$udirected$ulines'(X2,X1)
| 'unequally$udirected$ulines'('reverse$uline'(X0),X1) ),
inference(resolution,[status(thm)],[c44,c0]) ).
cnf(d10,plain,
( 'unequally$udirected$ulines'('reverse$uline'(sK86),X0)
| 'unequally$udirected$ulines'(sK85,X0) ),
inference(resolution,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
'unequally$udirected$ulines'(sK85,'reverse$uline'(sK86)),
inference(resolution,[status(thm)],[d10,d7]) ).
cnf(d12,plain,
( ~ 'unequally$udirected$uopposite$ulines'(X0,X1)
| 'left$uconvergent$ulines'(X0,'reverse$uline'(X1))
| ~ 'unequally$udirected$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[d4,c0]) ).
cnf(d13,plain,
( ~ 'unequally$udirected$ulines'(X0,X1)
| ~ 'unequally$udirected$uopposite$ulines'(X0,X1) ),
inference(resolution,[status(thm)],[c53,d12]) ).
cnf(d14,plain,
~ 'unequally$udirected$uopposite$ulines'(sK85,'reverse$uline'(sK86)),
inference(resolution,[status(thm)],[d13,d11]) ).
cnf(d15,plain,
~ 'unequally$udirected$ulines'(sK85,sK86),
inference(resolution,[status(thm)],[d14,d6]) ).
cnf(d16,plain,
'unequally$udirected$ulines'(sK84,sK86),
inference(resolution,[status(thm)],[d15,d3]) ).
cnf(d17,plain,
~ 'unequally$udirected$ulines'(sK84,sK86),
inference(resolution,[status(thm)],[c6,c73]) ).
cnf(d18,plain,
$false,
inference(resolution,[status(thm)],[d17,d16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO231+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n017.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 13:04:17 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.41/6.25 % SZS status Theorem for theBenchmark.p
% 26.41/6.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------