%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO067-2 : 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 : n004.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 07:14:04 AM UTC 2026
% Result : Unsatisfiable 12.68s 3.29s
% Output : CNFRefutation 12.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of clauses : 31 ( 12 unt; 0 nHn; 22 RR)
% Number of literals : 63 ( 8 equ; 40 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 51 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(part_1,negated_conjecture,
( x = y
| ~ colinear(y,x,x)
| ~ colinear(x,y,x)
| ~ colinear(x,x,y) ) ).
cnf(part_2,negated_conjecture,
( ~ colinear(x,z,y)
| ~ colinear(y,x,x)
| ~ colinear(x,y,x)
| ~ colinear(x,x,y) ) ).
cnf(identity_for_equidistance,axiom,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ) ).
cnf(segment_construction1,axiom,
between(X0,X1,extension(X0,X1,X2,X3)) ).
cnf(segment_construction2,axiom,
equidistant(X0,extension(X1,X0,X2,X3),X2,X3) ).
cnf(colinearity1,axiom,
( colinear(X0,X1,X2)
| ~ between(X0,X1,X2) ) ).
cnf(colinearity2,axiom,
( colinear(X2,X0,X1)
| ~ between(X0,X1,X2) ) ).
cnf(colinearity3,axiom,
( colinear(X1,X2,X0)
| ~ between(X0,X1,X2) ) ).
cnf(c0,plain,
( x = y
| ~ colinear(y,x,x)
| ~ colinear(x,y,x)
| ~ colinear(x,x,y) ),
inference(clausification,[status(esa)],[part_1]) ).
cnf(c1,plain,
( ~ colinear(x,z,y)
| ~ colinear(y,x,x)
| ~ colinear(x,y,x)
| ~ colinear(x,x,y) ),
inference(clausification,[status(esa)],[part_2]) ).
cnf(c4,plain,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(clausification,[status(esa)],[identity_for_equidistance]) ).
cnf(c5,plain,
between(X0,X1,extension(X0,X1,X2,X3)),
inference(clausification,[status(esa)],[segment_construction1]) ).
cnf(c6,plain,
equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(clausification,[status(esa)],[segment_construction2]) ).
cnf(c20,plain,
( colinear(X0,X1,X2)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[colinearity1]) ).
cnf(c21,plain,
( colinear(X2,X0,X1)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[colinearity2]) ).
cnf(c22,plain,
( colinear(X1,X2,X0)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[colinearity3]) ).
cnf(d0,plain,
X0 = extension(X1,X0,X2,X2),
inference(resolution,[status(thm)],[c6,c4]) ).
cnf(d1,plain,
between(X0,X1,X1),
inference(superposition,[status(thm)],[d0,c5]) ).
cnf(d2,plain,
colinear(X0,X1,X0),
inference(resolution,[status(thm)],[c21,d1]) ).
cnf(d3,plain,
colinear(X0,X1,X1),
inference(resolution,[status(thm)],[d1,c20]) ).
cnf(d4,plain,
( ~ colinear(x,y,x)
| ~ colinear(x,x,y)
| x = y ),
inference(resolution,[status(thm)],[d3,c0]) ).
cnf(d5,plain,
( ~ colinear(x,x,y)
| x = y ),
inference(resolution,[status(thm)],[d2,d4]) ).
cnf(d6,plain,
colinear(X0,X0,X1),
inference(resolution,[status(thm)],[c22,d1]) ).
cnf(d7,plain,
x = y,
inference(resolution,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
( ~ colinear(x,z,y)
| ~ colinear(x,y,x)
| ~ colinear(x,x,y) ),
inference(resolution,[status(thm)],[d3,c1]) ).
cnf(d9,plain,
( ~ colinear(x,z,y)
| ~ colinear(x,y,x)
| ~ colinear(x,x,x) ),
inference(demodulation,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
( ~ colinear(x,z,y)
| ~ colinear(x,x,x)
| ~ colinear(x,x,x) ),
inference(demodulation,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
( ~ colinear(x,z,x)
| ~ colinear(x,x,x)
| ~ colinear(x,x,x) ),
inference(demodulation,[status(thm)],[d10,d7]) ).
cnf(d12,plain,
( ~ colinear(x,z,x)
| ~ colinear(x,x,x) ),
inference(resolution,[status(thm)],[d3,d11]) ).
cnf(d13,plain,
~ colinear(x,z,x),
inference(resolution,[status(thm)],[d2,d12]) ).
cnf(d14,plain,
$false,
inference(resolution,[status(thm)],[d13,d2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO067-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.41 % Computer : n004.cluster.edu
% 0.17/0.41 % Model : x86_64 x86_64
% 0.17/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.41 % Memory : 8046.5625MB
% 0.17/0.41 % OS : Linux 6.8.0-71-generic
% 0.17/0.41 % CPULimit : 300
% 0.17/0.41 % WCLimit : 300
% 0.17/0.41 % DateTime : Fri Sep 25 12:37:50 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.68/3.29 % SZS status Unsatisfiable for theBenchmark.p
% 12.68/3.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------