%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO077-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 07:14:06 AM UTC 2026
% Result : Unsatisfiable 70.13s 18.19s
% Output : CNFRefutation 70.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 16
% Syntax : Number of clauses : 51 ( 24 unt; 27 nHn; 51 RR)
% Number of literals : 259 ( 98 equ; 136 neg)
% Maximal clause size : 18 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 56 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(point1,hypothesis,
point(point1) ).
cnf(point2,hypothesis,
point(point2) ).
cnf(point3,hypothesis,
point(point3) ).
cnf(line,hypothesis,
line('a$uline') ).
cnf(point1_on_line,hypothesis,
on(point1,'a$uline') ).
cnf(point2_on_line,hypothesis,
on(point2,'a$uline') ).
cnf(point3_not_on_line,hypothesis,
~ on(point3,'a$uline') ).
cnf(point1_not_point2,hypothesis,
point1 != point2 ).
cnf(point1_not_point3,hypothesis,
point1 != point3 ).
cnf(point2_not_point3,hypothesis,
point2 != point3 ).
cnf(prove_points_noncollinear,negated_conjecture,
collinear(point1,point2,point3) ).
cnf(axiom_G1D,axiom,
( ~ line(X3)
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ on(X2,X3)
| ~ on(X0,X3)
| X1 = X3
| ~ on(X2,X1)
| X0 = X2
| ~ on(X0,X1) ) ).
cnf(axiom_G10A,axiom,
( ~ collinear(X0,X1,X2)
| on(X0,'line$uthrough$u3$upoints'(X0,X1,X2))
| X1 = X2
| X0 = X2
| X0 = X1
| ~ point(X2)
| ~ point(X1)
| ~ point(X0) ) ).
cnf(axiom_G10B,axiom,
( ~ collinear(X0,X1,X2)
| on(X1,'line$uthrough$u3$upoints'(X0,X1,X2))
| X1 = X2
| X0 = X2
| X0 = X1
| ~ point(X2)
| ~ point(X1)
| ~ point(X0) ) ).
cnf(axiom_G10C,axiom,
( ~ collinear(X0,X1,X2)
| on(X2,'line$uthrough$u3$upoints'(X0,X1,X2))
| X1 = X2
| X0 = X2
| X0 = X1
| ~ point(X2)
| ~ point(X1)
| ~ point(X0) ) ).
cnf(axiom_G10D,axiom,
( ~ collinear(X0,X1,X2)
| line('line$uthrough$u3$upoints'(X0,X1,X2))
| X1 = X2
| X0 = X2
| X0 = X1
| ~ point(X2)
| ~ point(X1)
| ~ point(X0) ) ).
cnf(c0,plain,
point(point1),
inference(clausification,[status(esa)],[point1]) ).
cnf(c1,plain,
point(point2),
inference(clausification,[status(esa)],[point2]) ).
cnf(c2,plain,
point(point3),
inference(clausification,[status(esa)],[point3]) ).
cnf(c3,plain,
line('a$uline'),
inference(clausification,[status(esa)],[line]) ).
cnf(c4,plain,
on(point1,'a$uline'),
inference(clausification,[status(esa)],[point1_on_line]) ).
cnf(c5,plain,
on(point2,'a$uline'),
inference(clausification,[status(esa)],[point2_on_line]) ).
cnf(c6,plain,
~ on(point3,'a$uline'),
inference(clausification,[status(esa)],[point3_not_on_line]) ).
cnf(c7,plain,
point1 != point2,
inference(clausification,[status(esa)],[point1_not_point2]) ).
cnf(c8,plain,
point1 != point3,
inference(clausification,[status(esa)],[point1_not_point3]) ).
cnf(c9,plain,
point2 != point3,
inference(clausification,[status(esa)],[point2_not_point3]) ).
cnf(c10,plain,
collinear(point1,point2,point3),
inference(clausification,[status(esa)],[prove_points_noncollinear]) ).
cnf(c14,plain,
( ~ point(X2)
| ~ line(X0)
| ~ on(X3,X0)
| ~ point(X3)
| ~ on(X3,X1)
| ~ on(X2,X1)
| ~ line(X1)
| X2 = X3
| ~ on(X2,X0)
| X0 = X1 ),
inference(clausification,[status(esa)],[axiom_G1D]) ).
cnf(c37,plain,
( ~ point(X0)
| X1 = X2
| X0 = X1
| ~ point(X2)
| ~ point(X1)
| X0 = X2
| ~ collinear(X0,X1,X2)
| on(X0,'line$uthrough$u3$upoints'(X0,X1,X2)) ),
inference(clausification,[status(esa)],[axiom_G10A]) ).
cnf(c38,plain,
( X2 = X1
| X2 = X0
| ~ point(X1)
| on(X1,'line$uthrough$u3$upoints'(X2,X1,X0))
| ~ collinear(X2,X1,X0)
| ~ point(X2)
| X1 = X0
| ~ point(X0) ),
inference(clausification,[status(esa)],[axiom_G10B]) ).
cnf(c39,plain,
( ~ point(X2)
| X1 = X0
| X1 = X2
| on(X2,'line$uthrough$u3$upoints'(X1,X0,X2))
| ~ point(X1)
| X0 = X2
| ~ collinear(X1,X0,X2)
| ~ point(X0) ),
inference(clausification,[status(esa)],[axiom_G10C]) ).
cnf(c40,plain,
( ~ point(X1)
| X1 = X0
| X1 = X2
| line('line$uthrough$u3$upoints'(X1,X2,X0))
| ~ point(X2)
| X2 = X0
| ~ collinear(X1,X2,X0)
| ~ point(X0) ),
inference(clausification,[status(esa)],[axiom_G10D]) ).
cnf(d0,plain,
( ~ on(point1,X0)
| ~ on(X1,'a$uline')
| ~ on(X1,X0)
| ~ line('a$uline')
| ~ line(X0)
| ~ point(point1)
| ~ point(X1)
| point1 = X1
| X0 = 'a$uline' ),
inference(resolution,[status(thm)],[c14,c4]) ).
cnf(d1,plain,
( ~ on(point1,X0)
| ~ on(X1,'a$uline')
| ~ on(X1,X0)
| ~ line('a$uline')
| ~ line(X0)
| ~ point(X1)
| point1 = X1
| X0 = 'a$uline' ),
inference(resolution,[status(thm)],[c0,d0]) ).
cnf(d2,plain,
( ~ on(point1,X0)
| ~ on(X1,'a$uline')
| ~ on(X1,X0)
| ~ line(X0)
| ~ point(X1)
| point1 = X1
| X0 = 'a$uline' ),
inference(resolution,[status(thm)],[c3,d1]) ).
cnf(d3,plain,
( ~ on(X2,'a$uline')
| ~ on(X2,'line$uthrough$u3$upoints'(point1,X0,X1))
| ~ line('line$uthrough$u3$upoints'(point1,X0,X1))
| ~ point(X2)
| point1 = X2
| 'line$uthrough$u3$upoints'(point1,X0,X1) = 'a$uline'
| ~ collinear(point1,X0,X1)
| ~ point(X1)
| ~ point(point1)
| ~ point(X0)
| point1 = X1
| point1 = X0
| X0 = X1 ),
inference(resolution,[status(thm)],[c37,d2]) ).
cnf(d4,plain,
( ~ collinear(point1,X0,X1)
| ~ on(X2,'line$uthrough$u3$upoints'(point1,X0,X1))
| ~ on(X2,'a$uline')
| ~ line('line$uthrough$u3$upoints'(point1,X0,X1))
| ~ point(X0)
| ~ point(X1)
| ~ point(X2)
| 'line$uthrough$u3$upoints'(point1,X0,X1) = 'a$uline'
| point1 = X0
| point1 = X1
| point1 = X2
| X0 = X1 ),
inference(resolution,[status(thm)],[c0,d3]) ).
cnf(d5,plain,
( ~ collinear(point1,X0,X1)
| ~ point(X0)
| ~ point(point1)
| ~ point(X1)
| X0 = X1
| point1 = X0
| point1 = X1
| ~ collinear(point1,X0,X1)
| ~ on(X0,'a$uline')
| ~ line('line$uthrough$u3$upoints'(point1,X0,X1))
| ~ point(X0)
| ~ point(X1)
| ~ point(X0)
| 'line$uthrough$u3$upoints'(point1,X0,X1) = 'a$uline'
| point1 = X0
| point1 = X1
| point1 = X0
| X0 = X1 ),
inference(resolution,[status(thm)],[d4,c38]) ).
cnf(d6,plain,
( ~ collinear(point1,X0,X1)
| ~ on(X0,'a$uline')
| ~ line('line$uthrough$u3$upoints'(point1,X0,X1))
| ~ point(X0)
| ~ point(X1)
| 'line$uthrough$u3$upoints'(point1,X0,X1) = 'a$uline'
| point1 = X0
| point1 = X1
| X0 = X1 ),
inference(resolution,[status(thm)],[c0,d5]) ).
cnf(d7,plain,
( ~ collinear(point1,X0,X1)
| ~ on(X0,'a$uline')
| ~ line('line$uthrough$u3$upoints'(point1,X0,X1))
| ~ point(X0)
| ~ point(X1)
| point1 = X0
| point1 = X1
| X0 = X1
| ~ collinear(point1,X0,X1)
| ~ point(point1)
| ~ point(X0)
| ~ point(X1)
| point1 = X0
| point1 = X1
| X0 = X1
| on(X1,'a$uline') ),
inference(superposition,[status(thm)],[d6,c39]) ).
cnf(d8,plain,
( ~ collinear(point1,X0,X1)
| ~ on(X0,'a$uline')
| on(X1,'a$uline')
| ~ line('line$uthrough$u3$upoints'(point1,X0,X1))
| ~ point(X0)
| ~ point(X1)
| point1 = X0
| point1 = X1
| X0 = X1 ),
inference(resolution,[status(thm)],[c0,d7]) ).
cnf(d9,plain,
( ~ collinear(point1,X0,X1)
| ~ point(point1)
| ~ point(X0)
| ~ point(X1)
| point1 = X0
| point1 = X1
| X0 = X1
| ~ collinear(point1,X0,X1)
| ~ on(X0,'a$uline')
| on(X1,'a$uline')
| ~ point(X0)
| ~ point(X1)
| point1 = X0
| point1 = X1
| X0 = X1 ),
inference(resolution,[status(thm)],[d8,c40]) ).
cnf(d10,plain,
( ~ collinear(point1,X0,X1)
| ~ on(X0,'a$uline')
| on(X1,'a$uline')
| ~ point(X0)
| ~ point(X1)
| point1 = X0
| point1 = X1
| X0 = X1 ),
inference(resolution,[status(thm)],[c0,d9]) ).
cnf(d11,plain,
( ~ on(point2,'a$uline')
| on(point3,'a$uline')
| ~ point(point2)
| ~ point(point3)
| point1 = point2
| point1 = point3
| point2 = point3 ),
inference(resolution,[status(thm)],[d10,c10]) ).
cnf(d12,plain,
( on(point3,'a$uline')
| ~ on(point2,'a$uline')
| ~ point(point3)
| point2 = point3
| point1 = point3
| point1 = point2 ),
inference(resolution,[status(thm)],[c1,d11]) ).
cnf(d13,plain,
( on(point3,'a$uline')
| ~ on(point2,'a$uline')
| point2 = point3
| point1 = point3
| point1 = point2 ),
inference(resolution,[status(thm)],[c2,d12]) ).
cnf(d14,plain,
( on(point3,'a$uline')
| point2 = point3
| point1 = point3
| point1 = point2 ),
inference(resolution,[status(thm)],[c5,d13]) ).
cnf(d15,plain,
( point2 = point3
| point1 = point3
| point1 = point2 ),
inference(resolution,[status(thm)],[c6,d14]) ).
cnf(d16,plain,
( point2 = point3
| point1 = point3 ),
inference(resolution,[status(thm)],[c7,d15]) ).
cnf(d17,plain,
point2 = point3,
inference(resolution,[status(thm)],[c8,d16]) ).
cnf(d18,plain,
$false,
inference(resolution,[status(thm)],[c9,d17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO077-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n018.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Fri Sep 25 12:41:35 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 70.13/18.19 % SZS status Unsatisfiable for theBenchmark.p
% 70.13/18.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------