%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO053-2 : 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 : n012.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 07:14:01 AM UTC 2026
% Result : Unsatisfiable 16.15s 14.41s
% Output : CNFRefutation 16.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of clauses : 62 ( 33 unt; 4 nHn; 50 RR)
% Number of literals : 128 ( 29 equ; 65 neg)
% Maximal clause size : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-5 aty)
% Number of variables : 130 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(v_between_u_and_w,hypothesis,
between(u,v,w) ).
cnf(u_to_v_equals_u_to_w,hypothesis,
equidistant(u,v,u,w) ).
cnf(prove_v_equals_w,negated_conjecture,
v != w ).
cnf(reflexivity_for_equidistance,axiom,
equidistant(X0,X1,X1,X0) ).
cnf(transitivity_for_equidistance,axiom,
( equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ) ).
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(outer_five_segment,axiom,
( equidistant(X4,X6,X5,X7)
| X0 = X1
| ~ between(X2,X3,X5)
| ~ between(X0,X1,X4)
| ~ equidistant(X1,X6,X3,X7)
| ~ equidistant(X0,X6,X2,X7)
| ~ equidistant(X1,X4,X3,X5)
| ~ equidistant(X0,X1,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,
equidistant(u,v,u,w),
inference(clausification,[status(esa)],[u_to_v_equals_u_to_w]) ).
cnf(c2,plain,
v != w,
inference(clausification,[status(esa)],[prove_v_equals_w]) ).
cnf(c3,plain,
equidistant(X0,X1,X1,X0),
inference(clausification,[status(esa)],[reflexivity_for_equidistance]) ).
cnf(c4,plain,
( equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[transitivity_for_equidistance]) ).
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(c8,plain,
( ~ equidistant(X1,X6,X3,X7)
| X0 = X1
| ~ between(X2,X3,X5)
| equidistant(X4,X6,X5,X7)
| ~ equidistant(X0,X6,X2,X7)
| ~ between(X0,X1,X4)
| ~ equidistant(X1,X4,X3,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[outer_five_segment]) ).
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,
( X1 = 'inner$upasch'(X1,X3,X2,X1,X0)
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[c11,c9]) ).
cnf(d1,plain,
X0 = extension(X1,X0,X2,X2),
inference(resolution,[status(thm)],[c7,c5]) ).
cnf(d2,plain,
between(X0,X1,X1),
inference(superposition,[status(thm)],[d1,c6]) ).
cnf(d3,plain,
( X0 = 'inner$upasch'(X3,X0,X2,X1,X0)
| ~ between(X3,X0,X2)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[c10,c9]) ).
cnf(d4,plain,
( ~ between(X1,X0,X2)
| X0 = 'inner$upasch'(X1,X0,X2,X2,X0) ),
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
v = 'inner$upasch'(u,v,w,w,v),
inference(resolution,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
( ~ between(u,v,w)
| ~ between(v,w,w)
| between(w,v,u) ),
inference(superposition,[status(thm)],[d5,c11]) ).
cnf(d7,plain,
( between(w,v,u)
| ~ between(v,w,w) ),
inference(resolution,[status(thm)],[c0,d6]) ).
cnf(d8,plain,
between(w,v,u),
inference(resolution,[status(thm)],[d2,d7]) ).
cnf(d9,plain,
( ~ between(v,X0,u)
| v = 'inner$upasch'(v,X0,u,v,w) ),
inference(resolution,[status(thm)],[d8,d0]) ).
cnf(d10,plain,
( ~ equidistant(X3,X2,X0,X1)
| equidistant(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c4,c3]) ).
cnf(d11,plain,
equidistant(u,w,v,u),
inference(resolution,[status(thm)],[d10,c1]) ).
cnf(d12,plain,
equidistant(v,u,w,u),
inference(resolution,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
( ~ equidistant(X0,X4,X1,X5)
| ~ equidistant(X1,X3,X0,X2)
| ~ equidistant(X1,X4,X0,X5)
| equidistant(X3,X4,X2,X5)
| ~ between(X0,X1,X3)
| ~ between(X1,X0,X2)
| X0 = X1 ),
inference(resolution,[status(thm)],[c8,c3]) ).
cnf(d14,plain,
( ~ equidistant(w,X1,v,X0)
| ~ equidistant(w,u,v,u)
| equidistant(X1,u,X0,u)
| ~ between(v,w,X1)
| ~ between(w,v,X0)
| v = w ),
inference(resolution,[status(thm)],[d13,d12]) ).
cnf(d15,plain,
( ~ equidistant(w,u,v,u)
| ~ equidistant(w,X0,v,X1)
| equidistant(X0,u,X1,u)
| ~ between(w,v,X1)
| ~ between(v,w,X0) ),
inference(resolution,[status(thm)],[c2,d14]) ).
cnf(d16,plain,
( ~ equidistant(u,v,X0,X1)
| equidistant(X0,X1,u,w) ),
inference(resolution,[status(thm)],[c4,c1]) ).
cnf(d17,plain,
equidistant(v,u,u,w),
inference(resolution,[status(thm)],[d16,c3]) ).
cnf(d18,plain,
equidistant(u,w,u,v),
inference(resolution,[status(thm)],[d17,d10]) ).
cnf(d19,plain,
equidistant(u,v,w,u),
inference(resolution,[status(thm)],[d18,d10]) ).
cnf(d20,plain,
equidistant(w,u,v,u),
inference(resolution,[status(thm)],[d19,d10]) ).
cnf(d21,plain,
( ~ equidistant(w,X0,v,X1)
| equidistant(X0,u,X1,u)
| ~ between(w,v,X1)
| ~ between(v,w,X0) ),
inference(resolution,[status(thm)],[d20,d15]) ).
cnf(d22,plain,
( equidistant(extension(X0,w,v,X1),u,X1,u)
| ~ between(w,v,X1)
| ~ between(v,w,extension(X0,w,v,X1)) ),
inference(resolution,[status(thm)],[d21,c7]) ).
cnf(d23,plain,
( extension(X0,w,v,u) = u
| ~ between(w,v,u)
| ~ between(v,w,extension(X0,w,v,u)) ),
inference(resolution,[status(thm)],[d22,c5]) ).
cnf(d24,plain,
( ~ between(v,w,extension(X0,w,v,u))
| extension(X0,w,v,u) = u ),
inference(resolution,[status(thm)],[d8,d23]) ).
cnf(d25,plain,
extension(v,w,v,u) = u,
inference(resolution,[status(thm)],[d24,c6]) ).
cnf(d26,plain,
between(v,w,u),
inference(superposition,[status(thm)],[d25,c6]) ).
cnf(d27,plain,
v = 'inner$upasch'(v,w,u,v,w),
inference(resolution,[status(thm)],[d26,d9]) ).
cnf(d28,plain,
( ~ between(X0,w,u)
| w = 'inner$upasch'(X0,w,u,v,w) ),
inference(resolution,[status(thm)],[d8,d3]) ).
cnf(d29,plain,
w = 'inner$upasch'(v,w,u,v,w),
inference(resolution,[status(thm)],[d26,d28]) ).
cnf(d30,plain,
w = v,
inference(demodulation,[status(thm)],[d29,d27]) ).
cnf(d31,plain,
v != v,
inference(demodulation,[status(thm)],[c2,d30]) ).
cnf(d32,plain,
X0 = 'inner$upasch'(X1,X0,X0,X0,X0),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d33,plain,
( ~ between(X1,X0,extension(X0,X2,X3,X4))
| X0 = 'inner$upasch'(X1,X0,extension(X0,X2,X3,X4),X2,X0) ),
inference(resolution,[status(thm)],[d3,c6]) ).
cnf(d34,plain,
X0 = 'inner$upasch'(X0,X0,extension(X0,X0,X1,X2),X0,X0),
inference(resolution,[status(thm)],[d33,c6]) ).
cnf(d35,plain,
X0 = 'inner$upasch'(X0,X0,X0,X0,X0),
inference(superposition,[status(thm)],[d1,d34]) ).
cnf(d36,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d35,d32]) ).
cnf(d37,plain,
$false,
inference(resolution,[status(thm)],[d36,d31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO053-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n012.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 25 12:36:35 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.15/14.41 % SZS status Unsatisfiable for theBenchmark.p
% 16.15/14.41 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------