%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO044-3 : 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 : n009.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 07:14:00 AM UTC 2026
% Result : Unsatisfiable 32.00s 5.91s
% Output : CNFRefutation 32.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 24 ( 16 unt; 4 nHn; 18 RR)
% Number of literals : 43 ( 12 equ; 19 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 45 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(d9,axiom,
( X2 = X3
| X0 = X1
| ~ equidistant(X1,X2,X1,X3)
| ~ between(X0,X1,X3)
| ~ between(X0,X1,X2) ) ).
cnf(b5,axiom,
( between(X1,X2,X3)
| ~ between(X0,X2,X3)
| ~ between(X0,X1,X2) ) ).
cnf(v_between_u_and_w,hypothesis,
between(u,v,w) ).
cnf(w_between_v_and_x,hypothesis,
between(v,w,x) ).
cnf(v_not_w,hypothesis,
v != w ).
cnf(prove_w_between_u_and_x,negated_conjecture,
~ between(u,w,x) ).
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(c18,plain,
( ~ equidistant(X1,X3,X1,X2)
| X2 = X3
| X1 = X0
| ~ between(X0,X1,X3)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[d9]) ).
cnf(c32,plain,
( between(X3,X1,X2)
| ~ between(X0,X3,X1)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[b5]) ).
cnf(c33,plain,
between(u,v,w),
inference(clausification,[status(esa)],[v_between_u_and_w]) ).
cnf(c34,plain,
between(v,w,x),
inference(clausification,[status(esa)],[w_between_v_and_x]) ).
cnf(c35,plain,
w != v,
inference(clausification,[status(esa)],[v_not_w]) ).
cnf(c36,plain,
~ between(u,w,x),
inference(clausification,[status(esa)],[prove_w_between_u_and_x]) ).
cnf(c40,plain,
between(X0,X1,extension(X0,X1,X2,X3)),
inference(clausification,[status(esa)],[segment_construction1]) ).
cnf(c41,plain,
equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(clausification,[status(esa)],[segment_construction2]) ).
cnf(d_0,plain,
( ~ between(X2,X0,X1)
| between(X0,X1,extension(X2,X1,X3,X4)) ),
inference(resolution,[status(thm)],[c40,c32]) ).
cnf(d_1,plain,
between(v,w,extension(u,w,X0,X1)),
inference(resolution,[status(thm)],[d_0,c33]) ).
cnf(d_2,plain,
( ~ between(X3,X2,extension(X1,X2,X2,X0))
| ~ between(X3,X2,X0)
| X2 = X3
| X0 = extension(X1,X2,X2,X0) ),
inference(resolution,[status(thm)],[c41,c18]) ).
cnf(d_3,plain,
( ~ between(v,w,extension(X0,w,w,x))
| x = extension(X0,w,w,x)
| w = v ),
inference(resolution,[status(thm)],[d_2,c34]) ).
cnf(d_4,plain,
( ~ between(v,w,extension(X0,w,w,x))
| x = extension(X0,w,w,x) ),
inference(resolution,[status(thm)],[c35,d_3]) ).
cnf(d_5,plain,
x = extension(u,w,w,x),
inference(resolution,[status(thm)],[d_4,d_1]) ).
cnf(d_6,plain,
between(u,w,x),
inference(superposition,[status(thm)],[d_5,c40]) ).
cnf(d_7,plain,
$false,
inference(resolution,[status(thm)],[c36,d_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO044-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 12:35:44 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 32.00/5.91 % SZS status Unsatisfiable for theBenchmark.p
% 32.00/5.91 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------