%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO040-2 : 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 : n003.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 07:13:58 AM UTC 2026
% Result : Unsatisfiable 13.34s 3.37s
% Output : CNFRefutation 13.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of clauses : 21 ( 11 unt; 0 nHn; 21 RR)
% Number of literals : 37 ( 12 equ; 19 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-5 aty)
% Number of variables : 34 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(v_between_u_and_w,hypothesis,
between(u,v,w) ).
cnf(u_between_v_and_w,hypothesis,
between(v,u,w) ).
cnf(prove_u_is_v,negated_conjecture,
u != v ).
cnf(identity_for_betweeness,axiom,
( X0 = X1
| ~ between(X0,X1,X0) ) ).
cnf(inner_pasch1,axiom,
( between(X1,'inner$upasch'(X0,X1,X2,X4,X3),X3)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ) ).
cnf(inner_pasch2,axiom,
( between(X4,'inner$upasch'(X0,X1,X2,X4,X3),X0)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ) ).
cnf(c0,plain,
between(u,v,w),
inference(clausification,[status(esa)],[v_between_u_and_w]) ).
cnf(c1,plain,
between(v,u,w),
inference(clausification,[status(esa)],[u_between_v_and_w]) ).
cnf(c2,plain,
u != v,
inference(clausification,[status(esa)],[prove_u_is_v]) ).
cnf(c9,plain,
( X0 = X1
| ~ between(X0,X1,X0) ),
inference(clausification,[status(esa)],[identity_for_betweeness]) ).
cnf(c10,plain,
( between(X1,'inner$upasch'(X0,X1,X2,X4,X3),X3)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[inner_pasch1]) ).
cnf(c11,plain,
( between(X4,'inner$upasch'(X0,X1,X2,X4,X3),X0)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[inner_pasch2]) ).
cnf(d0,plain,
( X0 = 'inner$upasch'(X3,X0,X2,X1,X0)
| ~ between(X3,X0,X2)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[c10,c9]) ).
cnf(d1,plain,
( ~ between(X0,u,w)
| u = 'inner$upasch'(X0,u,w,v,u) ),
inference(resolution,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
u = 'inner$upasch'(v,u,w,v,u),
inference(resolution,[status(thm)],[d1,c1]) ).
cnf(d3,plain,
( X1 = 'inner$upasch'(X1,X3,X2,X1,X0)
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[c11,c9]) ).
cnf(d4,plain,
( ~ between(v,X0,w)
| v = 'inner$upasch'(v,X0,w,v,u) ),
inference(resolution,[status(thm)],[d3,c0]) ).
cnf(d5,plain,
v = 'inner$upasch'(v,u,w,v,u),
inference(resolution,[status(thm)],[d4,c1]) ).
cnf(d6,plain,
v = u,
inference(demodulation,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
u != u,
inference(demodulation,[status(thm)],[c2,d6]) ).
cnf(d8,plain,
$false,
inference(equality_resolution,[status(thm)],[d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO040-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n003.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Fri Sep 25 12:36:38 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.34/3.37 % SZS status Unsatisfiable for theBenchmark.p
% 13.34/3.37 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------