%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO006-2 : 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 : 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 07:13:50 AM UTC 2026
% Result : Unsatisfiable 11.31s 2.31s
% Output : CNFRefutation 11.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of clauses : 38 ( 16 unt; 9 nHn; 32 RR)
% Number of literals : 70 ( 20 equ; 28 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 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 : 63 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_not_c,hypothesis,
a != c ).
cnf(c_not_d,hypothesis,
c != d ).
cnf(c_between_a_and_d,hypothesis,
between(a,c,d) ).
cnf(prove_not_between_others,negated_conjecture,
( between(a,d,c)
| between(c,a,d) ) ).
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,
a != c,
inference(clausification,[status(esa)],[a_not_c]) ).
cnf(c2,plain,
c != d,
inference(clausification,[status(esa)],[c_not_d]) ).
cnf(c3,plain,
between(a,c,d),
inference(clausification,[status(esa)],[c_between_a_and_d]) ).
cnf(c4,plain,
( between(a,d,c)
| between(c,a,d) ),
inference(clausification,[status(esa)],[prove_not_between_others]) ).
cnf(c7,plain,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(clausification,[status(esa)],[identity_for_equidistance]) ).
cnf(c8,plain,
between(X0,X1,extension(X0,X1,X2,X3)),
inference(clausification,[status(esa)],[segment_construction1]) ).
cnf(c9,plain,
equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(clausification,[status(esa)],[segment_construction2]) ).
cnf(c11,plain,
( X0 = X1
| ~ between(X0,X1,X0) ),
inference(clausification,[status(esa)],[identity_for_betweeness]) ).
cnf(c12,plain,
( between(X1,'inner$upasch'(X0,X1,X2,X4,X3),X3)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[inner_pasch1]) ).
cnf(c13,plain,
( between(X4,'inner$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 = 'inner$upasch'(X3,X0,X2,X1,X0)
| ~ between(X3,X0,X2)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[c12,c11]) ).
cnf(d1,plain,
( ~ between(X1,X3,X2)
| ~ between(X0,X1,X2)
| ~ between(X0,X1,X2)
| ~ between(X1,X3,X2)
| between(X3,X1,X0) ),
inference(superposition,[status(thm)],[d0,c13]) ).
cnf(d2,plain,
X0 = extension(X1,X0,X2,X2),
inference(resolution,[status(thm)],[c9,c7]) ).
cnf(d3,plain,
between(X0,X1,X1),
inference(superposition,[status(thm)],[d2,c8]) ).
cnf(d4,plain,
( ~ between(c,X0,d)
| between(X0,c,a) ),
inference(resolution,[status(thm)],[d1,c3]) ).
cnf(d5,plain,
between(d,c,a),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( ~ between(c,X0,a)
| between(X0,c,d) ),
inference(resolution,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
( between(a,d,c)
| ~ between(a,X0,d)
| between(X0,a,c) ),
inference(resolution,[status(thm)],[d1,c4]) ).
cnf(d8,plain,
( between(a,d,c)
| between(c,a,c) ),
inference(resolution,[status(thm)],[d7,c3]) ).
cnf(d9,plain,
( c = a
| between(a,d,c) ),
inference(resolution,[status(thm)],[d8,c11]) ).
cnf(d10,plain,
( ~ between(d,X0,c)
| between(X0,d,a)
| c = a ),
inference(resolution,[status(thm)],[d9,d1]) ).
cnf(d11,plain,
( between(c,d,a)
| c = a ),
inference(resolution,[status(thm)],[d10,d3]) ).
cnf(d12,plain,
( between(d,c,d)
| c = a ),
inference(resolution,[status(thm)],[d11,d6]) ).
cnf(d13,plain,
( d = c
| c = a ),
inference(resolution,[status(thm)],[d12,c11]) ).
cnf(d14,plain,
( c = a
| c != c ),
inference(superposition,[status(thm)],[d13,c2]) ).
cnf(d15,plain,
c = a,
inference(equality_resolution,[status(thm)],[d14]) ).
cnf(d16,plain,
a != a,
inference(demodulation,[status(thm)],[c0,d15]) ).
cnf(d17,plain,
$false,
inference(equality_resolution,[status(thm)],[d16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO006-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Fri Sep 25 12:30:21 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.31/2.31 % SZS status Unsatisfiable for theBenchmark.p
% 11.31/2.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------