%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO037-3 : 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 : n008.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 20.64s 6.31s
% Output : CNFRefutation 20.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of clauses : 22 ( 11 unt; 0 nHn; 16 RR)
% Number of literals : 37 ( 10 equ; 17 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 : 7 ( 7 usr; 6 con; 0-4 aty)
% Number of variables : 52 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(d2,axiom,
( equidistant(X2,X3,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ) ).
cnf(d5,axiom,
( equidistant(X0,X1,X4,X5)
| ~ equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ) ).
cnf(e2_1,axiom,
'lower$udimension$upoint$u1' != 'lower$udimension$upoint$u2' ).
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(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(c1,plain,
( equidistant(X2,X3,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[d2]) ).
cnf(c8,plain,
( equidistant(X0,X1,X4,X5)
| ~ equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[d5]) ).
cnf(c38,plain,
'lower$udimension$upoint$u1' != 'lower$udimension$upoint$u2',
inference(clausification,[status(esa)],[e2_1]) ).
cnf(c41,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(c44,plain,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(clausification,[status(esa)],[identity_for_equidistance]) ).
cnf(c45,plain,
between(X0,X1,extension(X0,X1,X2,X3)),
inference(clausification,[status(esa)],[segment_construction1]) ).
cnf(c46,plain,
equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(clausification,[status(esa)],[segment_construction2]) ).
cnf(d_0,plain,
equidistant(X0,X1,X2,extension(X3,X2,X0,X1)),
inference(resolution,[status(thm)],[c46,c1]) ).
cnf(d_1,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)],[c45,c41]) ).
cnf(d_2,plain,
( equidistant(X4,extension(X5,X4,X0,X1),X2,X3)
| ~ equidistant(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c46,c8]) ).
cnf(d_3,plain,
( v = extension(u,v,'lower$udimension$upoint$u1','lower$udimension$upoint$u2')
| ~ equidistant('lower$udimension$upoint$u1','lower$udimension$upoint$u2',x,extension(w,x,'lower$udimension$upoint$u1','lower$udimension$upoint$u2')) ),
inference(resolution,[status(thm)],[d_2,d_1]) ).
cnf(d_4,plain,
v = extension(u,v,'lower$udimension$upoint$u1','lower$udimension$upoint$u2'),
inference(resolution,[status(thm)],[d_0,d_3]) ).
cnf(d_5,plain,
equidistant('lower$udimension$upoint$u1','lower$udimension$upoint$u2',v,v),
inference(superposition,[status(thm)],[d_4,d_0]) ).
cnf(d_6,plain,
'lower$udimension$upoint$u1' = 'lower$udimension$upoint$u2',
inference(resolution,[status(thm)],[d_5,c44]) ).
cnf(d_7,plain,
$false,
inference(resolution,[status(thm)],[c38,d_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO037-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n008.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Fri Sep 25 12:35:41 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.64/6.31 % SZS status Unsatisfiable for theBenchmark.p
% 20.64/6.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------