%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO043-2 : 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 : n019.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 16.23s 9.56s
% Output : CNFRefutation 16.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of clauses : 37 ( 19 unt; 0 nHn; 31 RR)
% Number of literals : 64 ( 12 equ; 31 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 : 63 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(v_between_u_and_w,hypothesis,
between(u,v,w) ).
cnf(w_between_u_and_x,hypothesis,
between(u,w,x) ).
cnf(prove_w_between_v_and_x,negated_conjecture,
~ between(v,w,x) ).
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,w),
inference(clausification,[status(esa)],[v_between_u_and_w]) ).
cnf(c1,plain,
between(u,w,x),
inference(clausification,[status(esa)],[w_between_u_and_x]) ).
cnf(c2,plain,
~ between(v,w,x),
inference(clausification,[status(esa)],[prove_w_between_v_and_x]) ).
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,
v = 'inner$upasch'(u,v,w,w,v),
inference(resolution,[status(thm)],[d3,c0]) ).
cnf(d5,plain,
( ~ between(u,v,w)
| ~ between(v,w,w)
| between(w,v,u) ),
inference(superposition,[status(thm)],[d4,c11]) ).
cnf(d6,plain,
( between(w,v,u)
| ~ between(v,w,w) ),
inference(resolution,[status(thm)],[c0,d5]) ).
cnf(d7,plain,
between(w,v,u),
inference(resolution,[status(thm)],[d1,d6]) ).
cnf(d8,plain,
( X1 = 'inner$upasch'(X1,X3,X2,X1,X0)
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[c11,c9]) ).
cnf(d9,plain,
w = 'inner$upasch'(u,w,x,x,w),
inference(resolution,[status(thm)],[d3,c1]) ).
cnf(d10,plain,
( ~ between(u,w,x)
| ~ between(w,x,x)
| between(x,w,u) ),
inference(superposition,[status(thm)],[d9,c11]) ).
cnf(d11,plain,
( between(x,w,u)
| ~ between(w,x,x) ),
inference(resolution,[status(thm)],[c1,d10]) ).
cnf(d12,plain,
between(x,w,u),
inference(resolution,[status(thm)],[d1,d11]) ).
cnf(d13,plain,
( ~ between(w,X0,u)
| w = 'inner$upasch'(w,X0,u,w,x) ),
inference(resolution,[status(thm)],[d12,d8]) ).
cnf(d14,plain,
w = 'inner$upasch'(w,v,u,w,x),
inference(resolution,[status(thm)],[d13,d7]) ).
cnf(d15,plain,
( ~ between(w,v,u)
| ~ between(x,w,u)
| between(v,w,x) ),
inference(superposition,[status(thm)],[d14,c10]) ).
cnf(d16,plain,
( ~ between(x,w,u)
| ~ between(w,v,u) ),
inference(resolution,[status(thm)],[c2,d15]) ).
cnf(d17,plain,
~ between(w,v,u),
inference(resolution,[status(thm)],[d12,d16]) ).
cnf(d18,plain,
$false,
inference(resolution,[status(thm)],[d7,d17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO043-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.43 % Computer : n019.cluster.edu
% 0.16/5.43 % Model : x86_64 x86_64
% 0.16/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.43 % Memory : 8046.5625MB
% 0.16/5.43 % OS : Linux 6.8.0-71-generic
% 0.16/5.43 % CPULimit : 300
% 0.16/5.43 % WCLimit : 300
% 0.16/5.43 % DateTime : Fri Sep 25 12:35:43 UTC 2026
% 0.16/5.43 % CPUTime :
% 0.16/5.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.23/9.56 % SZS status Unsatisfiable for theBenchmark.p
% 16.23/9.56 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------