%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO067-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 07:14:04 AM UTC 2026
% Result : Unsatisfiable 7.86s 4.32s
% Output : CNFRefutation 7.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of clauses : 25 ( 10 unt; 0 nHn; 18 RR)
% Number of literals : 58 ( 5 equ; 41 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 26 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t3,axiom,
between(X0,X1,X1) ).
cnf(t2,axiom,
between(X0,X0,X1) ).
cnf(c2_1,axiom,
( colinear(X2,X1,X0)
| ~ between(X0,X1,X2) ) ).
cnf(c2_2,axiom,
( colinear(X0,X2,X1)
| ~ between(X0,X1,X2) ) ).
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(c24,plain,
between(X0,X1,X1),
inference(clausification,[status(esa)],[t3]) ).
cnf(c27,plain,
between(X0,X0,X1),
inference(clausification,[status(esa)],[t2]) ).
cnf(c63,plain,
( colinear(X2,X1,X0)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[c2_1]) ).
cnf(c64,plain,
( colinear(X0,X2,X1)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[c2_2]) ).
cnf(c72,plain,
( x = y
| ~ colinear(y,x,x)
| ~ colinear(x,y,x)
| ~ colinear(x,x,y) ),
inference(clausification,[status(esa)],[part_1]) ).
cnf(c73,plain,
( ~ colinear(x,z,y)
| ~ colinear(y,x,x)
| ~ colinear(x,y,x)
| ~ colinear(x,x,y) ),
inference(clausification,[status(esa)],[part_2]) ).
cnf(d_0,plain,
colinear(X0,X1,X1),
inference(resolution,[status(thm)],[c63,c27]) ).
cnf(d_1,plain,
( ~ colinear(x,y,x)
| ~ colinear(x,x,y)
| x = y ),
inference(resolution,[status(thm)],[d_0,c72]) ).
cnf(d_2,plain,
colinear(X0,X0,X1),
inference(resolution,[status(thm)],[c63,c24]) ).
cnf(d_3,plain,
( ~ colinear(x,y,x)
| x = y ),
inference(resolution,[status(thm)],[d_2,d_1]) ).
cnf(d_4,plain,
colinear(X0,X1,X0),
inference(resolution,[status(thm)],[c64,c27]) ).
cnf(d_5,plain,
x = y,
inference(resolution,[status(thm)],[d_4,d_3]) ).
cnf(d_6,plain,
( ~ colinear(y,x,x)
| ~ colinear(x,z,y)
| ~ colinear(x,y,x)
| ~ colinear(x,x,x) ),
inference(demodulation,[status(thm)],[c73,d_5]) ).
cnf(d_7,plain,
( ~ colinear(y,x,x)
| ~ colinear(x,z,y)
| ~ colinear(x,x,x)
| ~ colinear(x,x,x) ),
inference(demodulation,[status(thm)],[d_6,d_5]) ).
cnf(d_8,plain,
( ~ colinear(y,x,x)
| ~ colinear(x,z,x)
| ~ colinear(x,x,x)
| ~ colinear(x,x,x) ),
inference(demodulation,[status(thm)],[d_7,d_5]) ).
cnf(d_9,plain,
( ~ colinear(x,x,x)
| ~ colinear(x,z,x)
| ~ colinear(x,x,x)
| ~ colinear(x,x,x) ),
inference(demodulation,[status(thm)],[d_8,d_5]) ).
cnf(d_10,plain,
( ~ colinear(x,x,x)
| ~ colinear(x,z,x)
| ~ colinear(x,x,x) ),
inference(resolution,[status(thm)],[d_0,d_9]) ).
cnf(d_11,plain,
~ colinear(x,z,x),
inference(resolution,[status(thm)],[d_2,d_10]) ).
cnf(d_12,plain,
$false,
inference(resolution,[status(thm)],[d_4,d_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO067-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n017.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 12:33:17 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.86/4.32 % SZS status Unsatisfiable for theBenchmark.p
% 7.86/4.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------