%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO037-2 : 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 : n009.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 25.39s 3.64s
% Output : CNFRefutation 25.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of clauses : 45 ( 24 unt; 0 nHn; 26 RR)
% Number of literals : 76 ( 13 equ; 34 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-5 aty)
% Number of variables : 142 ( 25 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_lengthen,negated_conjecture,
( ~ between(u,v,extension(u,v,'lower$udimension$upoint$u1','lower$udimension$upoint$u2'))
| ~ equidistant(v,extension(u,v,'lower$udimension$upoint$u1','lower$udimension$upoint$u2'),x,extension(w,x,'lower$udimension$upoint$u1','lower$udimension$upoint$u2'))
| v = extension(u,v,'lower$udimension$upoint$u1','lower$udimension$upoint$u2') ) ).
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(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(lower_dimension1,axiom,
~ between('lower$udimension$upoint$u1','lower$udimension$upoint$u2','lower$udimension$upoint$u3') ).
cnf(c0,plain,
( ~ between(u,v,extension(u,v,'lower$udimension$upoint$u1','lower$udimension$upoint$u2'))
| ~ equidistant(v,extension(u,v,'lower$udimension$upoint$u1','lower$udimension$upoint$u2'),x,extension(w,x,'lower$udimension$upoint$u1','lower$udimension$upoint$u2'))
| v = extension(u,v,'lower$udimension$upoint$u1','lower$udimension$upoint$u2') ),
inference(clausification,[status(esa)],[prove_lengthen]) ).
cnf(c1,plain,
equidistant(X0,X1,X1,X0),
inference(clausification,[status(esa)],[reflexivity_for_equidistance]) ).
cnf(c2,plain,
( equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[transitivity_for_equidistance]) ).
cnf(c3,plain,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(clausification,[status(esa)],[identity_for_equidistance]) ).
cnf(c4,plain,
between(X0,X1,extension(X0,X1,X2,X3)),
inference(clausification,[status(esa)],[segment_construction1]) ).
cnf(c5,plain,
equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(clausification,[status(esa)],[segment_construction2]) ).
cnf(c7,plain,
( X0 = X1
| ~ between(X0,X1,X0) ),
inference(clausification,[status(esa)],[identity_for_betweeness]) ).
cnf(c8,plain,
( between(X1,'inner$upasch'(X0,X1,X2,X4,X3),X3)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[inner_pasch1]) ).
cnf(c9,plain,
( between(X4,'inner$upasch'(X0,X1,X2,X4,X3),X0)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[inner_pasch2]) ).
cnf(c10,plain,
~ between('lower$udimension$upoint$u1','lower$udimension$upoint$u2','lower$udimension$upoint$u3'),
inference(clausification,[status(esa)],[lower_dimension1]) ).
cnf(d0,plain,
( ~ equidistant(X3,X2,X0,X1)
| equidistant(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c2,c1]) ).
cnf(d1,plain,
equidistant(X0,X1,extension(X2,X3,X0,X1),X3),
inference(resolution,[status(thm)],[d0,c5]) ).
cnf(d2,plain,
equidistant(extension(X0,X1,X2,X3),X1,X3,X2),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
equidistant(X0,X1,X2,extension(X3,X2,X1,X0)),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( ~ equidistant(v,extension(u,v,'lower$udimension$upoint$u1','lower$udimension$upoint$u2'),x,extension(w,x,'lower$udimension$upoint$u1','lower$udimension$upoint$u2'))
| v = extension(u,v,'lower$udimension$upoint$u1','lower$udimension$upoint$u2') ),
inference(resolution,[status(thm)],[c4,c0]) ).
cnf(d5,plain,
( ~ equidistant(X4,extension(X5,X4,X2,X3),X0,X1)
| equidistant(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c5,c2]) ).
cnf(d6,plain,
( ~ equidistant(X4,X5,X0,X1)
| equidistant(X0,X1,extension(X2,X3,X4,X5),X3) ),
inference(resolution,[status(thm)],[d1,c2]) ).
cnf(d7,plain,
( equidistant(extension(X6,X7,X0,X1),X7,X4,X5)
| ~ equidistant(X0,X1,X2,extension(X3,X2,X4,X5)) ),
inference(resolution,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
equidistant(extension(X0,X1,X2,extension(X3,X2,X4,X5)),X1,X4,X5),
inference(resolution,[status(thm)],[d5,d1]) ).
cnf(d9,plain,
equidistant(X0,X1,X2,extension(X3,X2,X4,extension(X5,X4,X0,X1))),
inference(resolution,[status(thm)],[d8,d0]) ).
cnf(d10,plain,
equidistant(extension(X0,X1,X2,X3),X1,X4,extension(X5,X4,X2,X3)),
inference(resolution,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
equidistant(X0,extension(X1,X0,X2,X3),X4,extension(X5,X4,X2,X3)),
inference(resolution,[status(thm)],[d10,d0]) ).
cnf(d12,plain,
v = extension(u,v,'lower$udimension$upoint$u1','lower$udimension$upoint$u2'),
inference(resolution,[status(thm)],[d11,d4]) ).
cnf(d13,plain,
equidistant('lower$udimension$upoint$u2','lower$udimension$upoint$u1',v,v),
inference(superposition,[status(thm)],[d12,d3]) ).
cnf(d14,plain,
'lower$udimension$upoint$u2' = 'lower$udimension$upoint$u1',
inference(resolution,[status(thm)],[d13,c3]) ).
cnf(d15,plain,
~ between('lower$udimension$upoint$u1','lower$udimension$upoint$u1','lower$udimension$upoint$u3'),
inference(demodulation,[status(thm)],[c10,d14]) ).
cnf(d16,plain,
X0 = extension(X1,X0,X2,X2),
inference(resolution,[status(thm)],[c5,c3]) ).
cnf(d17,plain,
between(X0,X1,X1),
inference(superposition,[status(thm)],[d16,c4]) ).
cnf(d18,plain,
( X0 = 'inner$upasch'(X3,X0,X2,X1,X0)
| ~ between(X3,X0,X2)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[c8,c7]) ).
cnf(d19,plain,
( ~ between(X1,X0,X2)
| X0 = 'inner$upasch'(X1,X0,X2,X2,X0) ),
inference(resolution,[status(thm)],[d18,d17]) ).
cnf(d20,plain,
X0 = 'inner$upasch'(X1,X0,X0,X0,X0),
inference(resolution,[status(thm)],[d19,d17]) ).
cnf(d21,plain,
( ~ between(X0,X1,X1)
| ~ between(X1,X1,X1)
| between(X1,X1,X0) ),
inference(superposition,[status(thm)],[d20,c9]) ).
cnf(d22,plain,
( ~ between(X1,X0,X0)
| between(X0,X0,X1) ),
inference(resolution,[status(thm)],[d17,d21]) ).
cnf(d23,plain,
between(X0,X0,X1),
inference(resolution,[status(thm)],[d22,d17]) ).
cnf(d24,plain,
$false,
inference(resolution,[status(thm)],[d23,d15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO037-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 12:34:59 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.39/3.64 % SZS status Unsatisfiable for theBenchmark.p
% 25.39/3.64 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------