%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO042-2 : 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 : n001.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 15.37s 2.61s
% Output : CNFRefutation 15.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of clauses : 32 ( 17 unt; 0 nHn; 26 RR)
% Number of literals : 54 ( 10 equ; 26 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-5 aty)
% Number of variables : 59 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
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_equidistance,axiom,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ) ).
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(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,x),
inference(clausification,[status(esa)],[v_between_u_and_x]) ).
cnf(c1,plain,
between(v,w,x),
inference(clausification,[status(esa)],[w_between_v_and_x]) ).
cnf(c2,plain,
~ between(u,v,w),
inference(clausification,[status(esa)],[prove_v_between_u_and_w]) ).
cnf(c5,plain,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(clausification,[status(esa)],[identity_for_equidistance]) ).
cnf(c6,plain,
between(X0,X1,extension(X0,X1,X2,X3)),
inference(clausification,[status(esa)],[segment_construction1]) ).
cnf(c7,plain,
equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(clausification,[status(esa)],[segment_construction2]) ).
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 = extension(X1,X0,X2,X2),
inference(resolution,[status(thm)],[c7,c5]) ).
cnf(d1,plain,
between(X0,X1,X1),
inference(superposition,[status(thm)],[d0,c6]) ).
cnf(d2,plain,
( X0 = 'inner$upasch'(X3,X0,X2,X1,X0)
| ~ between(X3,X0,X2)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[c10,c9]) ).
cnf(d3,plain,
( ~ between(X1,X0,X2)
| X0 = 'inner$upasch'(X1,X0,X2,X2,X0) ),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
( ~ between(X0,v,x)
| v = 'inner$upasch'(X0,v,x,w,v) ),
inference(resolution,[status(thm)],[d2,c1]) ).
cnf(d5,plain,
v = 'inner$upasch'(u,v,x,w,v),
inference(resolution,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
( ~ between(u,v,x)
| ~ between(v,w,x)
| between(w,v,u) ),
inference(superposition,[status(thm)],[d5,c11]) ).
cnf(d7,plain,
( between(w,v,u)
| ~ between(v,w,x) ),
inference(resolution,[status(thm)],[c0,d6]) ).
cnf(d8,plain,
between(w,v,u),
inference(resolution,[status(thm)],[c1,d7]) ).
cnf(d9,plain,
v = 'inner$upasch'(w,v,u,u,v),
inference(resolution,[status(thm)],[d8,d3]) ).
cnf(d10,plain,
( ~ between(w,v,u)
| ~ between(v,u,u)
| between(u,v,w) ),
inference(superposition,[status(thm)],[d9,c11]) ).
cnf(d11,plain,
( ~ between(w,v,u)
| ~ between(v,u,u) ),
inference(resolution,[status(thm)],[c2,d10]) ).
cnf(d12,plain,
~ between(w,v,u),
inference(resolution,[status(thm)],[d1,d11]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[d8,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO042-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n001.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 12:41:11 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.37/2.61 % SZS status Unsatisfiable for theBenchmark.p
% 15.37/2.61 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------