%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO069-3 : 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 : n014.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 07:14:05 AM UTC 2026
% Result : Unsatisfiable 17.37s 5.83s
% Output : CNFRefutation 17.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 28 ( 14 unt; 6 nHn; 28 RR)
% Number of literals : 52 ( 8 equ; 23 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 32 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t10_1,axiom,
( colinear(X2,X1,X0)
| ~ colinear(X0,X1,X2) ) ).
cnf(t10_2,axiom,
( colinear(X1,X2,X0)
| ~ colinear(X0,X1,X2) ) ).
cnf(t12_1,axiom,
( X0 = X1
| colinear(X0,X2,X3)
| ~ colinear(X0,X1,X3)
| ~ colinear(X0,X1,X2) ) ).
cnf(t12_2,axiom,
( X0 = X1
| colinear(X1,X2,X3)
| ~ colinear(X0,X1,X3)
| ~ colinear(X0,X1,X2) ) ).
cnf(u_not_v,hypothesis,
u != v ).
cnf(wvu_colinear,hypothesis,
colinear(w,v,u) ).
cnf(xvu_colinear,hypothesis,
colinear(x,v,u) ).
cnf(prove_xwu_and_xwv_colinear,negated_conjecture,
( ~ colinear(x,w,v)
| ~ colinear(x,w,u) ) ).
cnf(c_66,plain,
( colinear(X2,X1,X0)
| ~ colinear(X0,X1,X2) ),
inference(clausification,[status(esa)],[t10_1]) ).
cnf(c_67,plain,
( colinear(X1,X2,X0)
| ~ colinear(X0,X1,X2) ),
inference(clausification,[status(esa)],[t10_2]) ).
cnf(c_77,plain,
( X0 = X1
| colinear(X0,X2,X3)
| ~ colinear(X0,X1,X3)
| ~ colinear(X0,X1,X2) ),
inference(clausification,[status(esa)],[t12_1]) ).
cnf(c_78,plain,
( X0 = X1
| colinear(X1,X2,X3)
| ~ colinear(X0,X1,X3)
| ~ colinear(X0,X1,X2) ),
inference(clausification,[status(esa)],[t12_2]) ).
cnf(c_79,plain,
u != v,
inference(clausification,[status(esa)],[u_not_v]) ).
cnf(c_80,plain,
colinear(w,v,u),
inference(clausification,[status(esa)],[wvu_colinear]) ).
cnf(c_81,plain,
colinear(x,v,u),
inference(clausification,[status(esa)],[xvu_colinear]) ).
cnf(c_82,plain,
( ~ colinear(x,w,v)
| ~ colinear(x,w,u) ),
inference(clausification,[status(esa)],[prove_xwu_and_xwv_colinear]) ).
cnf(d_0,plain,
colinear(u,v,w),
inference(resolution,[status(thm)],[c_66,c_80]) ).
cnf(d_1,plain,
colinear(u,v,x),
inference(resolution,[status(thm)],[c_66,c_81]) ).
cnf(d_2,plain,
( ~ colinear(u,v,X0)
| colinear(v,x,X0)
| u = v ),
inference(resolution,[status(thm)],[c_78,d_1]) ).
cnf(d_3,plain,
( colinear(v,x,X0)
| ~ colinear(u,v,X0) ),
inference(resolution,[status(thm)],[c_79,d_2]) ).
cnf(d_4,plain,
colinear(v,x,w),
inference(resolution,[status(thm)],[d_3,d_0]) ).
cnf(d_5,plain,
colinear(x,w,v),
inference(resolution,[status(thm)],[d_4,c_67]) ).
cnf(d_6,plain,
( ~ colinear(u,v,X0)
| colinear(u,x,X0)
| u = v ),
inference(resolution,[status(thm)],[d_1,c_77]) ).
cnf(d_7,plain,
( colinear(u,x,X0)
| ~ colinear(u,v,X0) ),
inference(resolution,[status(thm)],[c_79,d_6]) ).
cnf(d_8,plain,
colinear(u,x,w),
inference(resolution,[status(thm)],[d_7,d_0]) ).
cnf(d_9,plain,
colinear(x,w,u),
inference(resolution,[status(thm)],[d_8,c_67]) ).
cnf(d_10,plain,
~ colinear(x,w,v),
inference(resolution,[status(thm)],[d_9,c_82]) ).
cnf(d_11,plain,
$false,
inference(resolution,[status(thm)],[d_10,d_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO069-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 12:38:34 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.37/5.83 % SZS status Unsatisfiable for theBenchmark.p
% 17.37/5.83 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------