%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO042-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/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 07:13:59 AM UTC 2026
% Result : Unsatisfiable 38.93s 10.33s
% Output : CNFRefutation 38.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of clauses : 20 ( 9 unt; 0 nHn; 20 RR)
% Number of literals : 39 ( 3 equ; 21 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-5 aty)
% Number of variables : 39 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t1,axiom,
( between(X2,X1,X0)
| ~ between(X0,X1,X2) ) ).
cnf(v_between_u_and_x,hypothesis,
between(u,v,x) ).
cnf(w_between_v_and_x,hypothesis,
between(v,w,x) ).
cnf(prove_v_between_u_and_w,negated_conjecture,
~ between(u,v,w) ).
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(c26,plain,
( between(X2,X1,X0)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[t1]) ).
cnf(c32,plain,
between(u,v,x),
inference(clausification,[status(esa)],[v_between_u_and_x]) ).
cnf(c33,plain,
between(v,w,x),
inference(clausification,[status(esa)],[w_between_v_and_x]) ).
cnf(c34,plain,
~ between(u,v,w),
inference(clausification,[status(esa)],[prove_v_between_u_and_w]) ).
cnf(c41,plain,
( X0 = X1
| ~ between(X0,X1,X0) ),
inference(clausification,[status(esa)],[identity_for_betweeness]) ).
cnf(c42,plain,
( between(X1,'inner$upasch'(X0,X1,X2,X4,X3),X3)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[inner_pasch1]) ).
cnf(c43,plain,
( between(X4,'inner$upasch'(X0,X1,X2,X4,X3),X0)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[inner_pasch2]) ).
cnf(d_0,plain,
( X0 = 'inner$upasch'(X3,X0,X2,X1,X0)
| ~ between(X3,X0,X2)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[c42,c41]) ).
cnf(d_1,plain,
( ~ between(X1,X3,X2)
| ~ between(X0,X1,X2)
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2)
| between(X3,X1,X0) ),
inference(superposition,[status(thm)],[d_0,c43]) ).
cnf(d_2,plain,
( ~ between(v,X0,x)
| between(X0,v,u) ),
inference(resolution,[status(thm)],[d_1,c32]) ).
cnf(d_3,plain,
between(w,v,u),
inference(resolution,[status(thm)],[d_2,c33]) ).
cnf(d_4,plain,
between(u,v,w),
inference(resolution,[status(thm)],[d_3,c26]) ).
cnf(d_5,plain,
$false,
inference(resolution,[status(thm)],[c34,d_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO042-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n004.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Fri Sep 25 12:35:27 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 38.93/10.33 % SZS status Unsatisfiable for theBenchmark.p
% 38.93/10.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------