%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO007-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/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 07:13:50 AM UTC 2026
% Result : Unsatisfiable 22.86s 8.70s
% Output : CNFRefutation 22.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 15
% Syntax : Number of clauses : 69 ( 29 unt; 12 nHn; 52 RR)
% Number of literals : 160 ( 31 equ; 77 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 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 : 161 ( 16 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_not_c,hypothesis,
a != c ).
cnf(a_between_a_and_c,hypothesis,
between(d,a,c) ).
cnf(a_between_a_and_e,hypothesis,
between(e,a,c) ).
cnf(e_not_between_d_and_a,hypothesis,
~ between(d,e,a) ).
cnf(prove_d_between_e_and_a,negated_conjecture,
~ between(e,d,a) ).
cnf(identity_for_betweeness,axiom,
( X0 = X1
| ~ between(X0,X1,X0) ) ).
cnf(transitivity_for_betweeness,axiom,
( between(X0,X1,X3)
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2) ) ).
cnf(connectivity_for_betweeness,axiom,
( between(X0,X3,X2)
| between(X0,X2,X3)
| X0 = X1
| ~ between(X0,X1,X3)
| ~ between(X0,X1,X2) ) ).
cnf(reflexivity_for_equidistance,axiom,
equidistant(X0,X1,X1,X0) ).
cnf(identity_for_equidistance,axiom,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ) ).
cnf(transitivity_for_equidistance,axiom,
( equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ) ).
cnf(outer_pasch1,axiom,
( between(X0,'outer$upasch'(X1,X0,X3,X4,X2),X3)
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ) ).
cnf(outer_pasch2,axiom,
( between(X4,X1,'outer$upasch'(X1,X0,X3,X4,X2))
| ~ between(X3,X2,X4)
| ~ between(X0,X1,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(c0,plain,
a != c,
inference(clausification,[status(esa)],[a_not_c]) ).
cnf(c1,plain,
between(d,a,c),
inference(clausification,[status(esa)],[a_between_a_and_c]) ).
cnf(c2,plain,
between(e,a,c),
inference(clausification,[status(esa)],[a_between_a_and_e]) ).
cnf(c3,plain,
~ between(d,e,a),
inference(clausification,[status(esa)],[e_not_between_d_and_a]) ).
cnf(c4,plain,
~ between(e,d,a),
inference(clausification,[status(esa)],[prove_d_between_e_and_a]) ).
cnf(c5,plain,
( X0 = X1
| ~ between(X0,X1,X0) ),
inference(clausification,[status(esa)],[identity_for_betweeness]) ).
cnf(c6,plain,
( between(X0,X1,X3)
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[transitivity_for_betweeness]) ).
cnf(c7,plain,
( between(X0,X3,X2)
| ~ between(X0,X1,X2)
| ~ between(X0,X1,X3)
| between(X0,X2,X3)
| X0 = X1 ),
inference(clausification,[status(esa)],[connectivity_for_betweeness]) ).
cnf(c8,plain,
equidistant(X0,X1,X1,X0),
inference(clausification,[status(esa)],[reflexivity_for_equidistance]) ).
cnf(c9,plain,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(clausification,[status(esa)],[identity_for_equidistance]) ).
cnf(c10,plain,
( equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[transitivity_for_equidistance]) ).
cnf(c11,plain,
( between(X0,'outer$upasch'(X1,X0,X3,X4,X2),X3)
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[outer_pasch1]) ).
cnf(c12,plain,
( between(X4,X1,'outer$upasch'(X1,X0,X3,X4,X2))
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[outer_pasch2]) ).
cnf(c17,plain,
between(X0,X1,extension(X0,X1,X2,X3)),
inference(clausification,[status(esa)],[segment_construction1]) ).
cnf(c18,plain,
equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(clausification,[status(esa)],[segment_construction2]) ).
cnf(d0,plain,
( between(d,a,X0)
| ~ between(a,X0,c) ),
inference(resolution,[status(thm)],[c6,c1]) ).
cnf(d1,plain,
( between(d,a,'outer$upasch'(X2,a,c,X1,X0))
| ~ between(a,X2,X0)
| ~ between(c,X0,X1) ),
inference(resolution,[status(thm)],[c11,d0]) ).
cnf(d2,plain,
( between(X4,X1,X5)
| ~ between(X1,X5,'outer$upasch'(X1,X0,X3,X4,X2))
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[c12,c6]) ).
cnf(d3,plain,
( ~ between(c,X1,X0)
| ~ between(a,d,X1)
| ~ between(a,d,X1)
| ~ between(c,X1,X0)
| between(X0,d,a) ),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
( between(e,a,X0)
| ~ between(a,X0,c) ),
inference(resolution,[status(thm)],[c6,c2]) ).
cnf(d5,plain,
( between(e,a,'outer$upasch'(X2,a,c,X1,X0))
| ~ between(a,X2,X0)
| ~ between(c,X0,X1) ),
inference(resolution,[status(thm)],[c11,d4]) ).
cnf(d6,plain,
( ~ between(c,X1,X0)
| ~ between(a,e,X1)
| ~ between(a,e,X1)
| ~ between(c,X1,X0)
| between(X0,e,a) ),
inference(resolution,[status(thm)],[d2,d5]) ).
cnf(d7,plain,
X0 = extension(X1,X0,X2,X2),
inference(resolution,[status(thm)],[c18,c9]) ).
cnf(d8,plain,
between(X0,X1,X1),
inference(superposition,[status(thm)],[d7,c17]) ).
cnf(d9,plain,
( between(X2,X0,X1)
| ~ between(X0,X1,X0) ),
inference(resolution,[status(thm)],[d8,c6]) ).
cnf(d10,plain,
( ~ between(X1,X2,X4)
| ~ between(X1,X4,X3)
| between(X0,X1,'outer$upasch'(X2,X1,X1,X3,X4)) ),
inference(resolution,[status(thm)],[d9,c11]) ).
cnf(d11,plain,
( ~ between(X0,X3,X1)
| ~ between(X0,X1,X2)
| between(X2,X3,X0)
| ~ between(X0,X3,X1)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[d10,d2]) ).
cnf(d12,plain,
( ~ between(X2,X1,X0)
| between(X0,X1,X2) ),
inference(resolution,[status(thm)],[d11,d8]) ).
cnf(d13,plain,
between(c,a,e),
inference(resolution,[status(thm)],[d12,c2]) ).
cnf(d14,plain,
( X0 = 'outer$upasch'(X3,X0,X0,X2,X1)
| ~ between(X0,X3,X1)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[c11,c5]) ).
cnf(d15,plain,
( ~ between(X0,X1,X2)
| X0 = 'outer$upasch'(X1,X0,X0,X2,X2) ),
inference(resolution,[status(thm)],[d14,d8]) ).
cnf(d16,plain,
d = 'outer$upasch'(a,d,d,c,c),
inference(resolution,[status(thm)],[d15,c1]) ).
cnf(d17,plain,
( ~ between(X4,X1,X5)
| between(X4,'outer$upasch'(X1,X0,X3,X4,X2),X5)
| between(X4,X5,'outer$upasch'(X1,X0,X3,X4,X2))
| X4 = X1
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[c12,c7]) ).
cnf(d18,plain,
( ~ between(d,a,c)
| ~ between(d,c,c)
| between(c,'outer$upasch'(a,d,d,c,c),X0)
| ~ between(c,a,X0)
| c = a
| between(c,X0,d) ),
inference(superposition,[status(thm)],[d16,d17]) ).
cnf(d19,plain,
( ~ between(d,c,c)
| ~ between(d,a,c)
| between(c,d,X0)
| ~ between(c,a,X0)
| between(c,X0,d)
| c = a ),
inference(demodulation,[status(thm)],[d18,d16]) ).
cnf(d20,plain,
( ~ between(d,c,c)
| between(c,d,X0)
| ~ between(c,a,X0)
| between(c,X0,d)
| c = a ),
inference(resolution,[status(thm)],[c1,d19]) ).
cnf(d21,plain,
( between(c,d,X0)
| ~ between(c,a,X0)
| between(c,X0,d)
| c = a ),
inference(resolution,[status(thm)],[d8,d20]) ).
cnf(d22,plain,
( between(c,d,e)
| between(c,e,d)
| c = a ),
inference(resolution,[status(thm)],[d21,d13]) ).
cnf(d23,plain,
( ~ between(a,e,e)
| between(d,e,a)
| between(c,d,e)
| c = a ),
inference(resolution,[status(thm)],[d22,d6]) ).
cnf(d24,plain,
( between(c,d,e)
| ~ between(a,e,e)
| c = a ),
inference(resolution,[status(thm)],[c3,d23]) ).
cnf(d25,plain,
( between(c,d,e)
| c = a ),
inference(resolution,[status(thm)],[d8,d24]) ).
cnf(d26,plain,
( ~ between(a,d,d)
| between(e,d,a)
| c = a ),
inference(resolution,[status(thm)],[d25,d3]) ).
cnf(d27,plain,
( ~ between(a,d,d)
| c = a ),
inference(resolution,[status(thm)],[c4,d26]) ).
cnf(d28,plain,
c = a,
inference(resolution,[status(thm)],[d8,d27]) ).
cnf(d29,plain,
a != a,
inference(demodulation,[status(thm)],[c0,d28]) ).
cnf(d30,plain,
( ~ between(X0,X1,X2)
| X0 = 'outer$upasch'(X1,X0,X0,extension(X0,X2,X3,X4),X2) ),
inference(resolution,[status(thm)],[d14,c17]) ).
cnf(d31,plain,
X0 = 'outer$upasch'(X1,X0,X0,extension(X0,X1,X2,X3),X1),
inference(resolution,[status(thm)],[d30,d8]) ).
cnf(d32,plain,
X0 = 'outer$upasch'(X1,X0,X0,extension(X0,X1,X2,X3),extension(X0,X1,X2,X3)),
inference(resolution,[status(thm)],[d15,c17]) ).
cnf(d33,plain,
( ~ equidistant(X1,X0,X2,X3)
| equidistant(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c10,c8]) ).
cnf(d34,plain,
equidistant(extension(X0,X1,X2,X3),X1,X2,X3),
inference(resolution,[status(thm)],[d33,c18]) ).
cnf(d35,plain,
extension(X0,X1,X2,X2) = X1,
inference(resolution,[status(thm)],[d34,c9]) ).
cnf(d36,plain,
X0 = 'outer$upasch'(X1,X0,X0,extension(X0,X1,X2,X2),X1),
inference(superposition,[status(thm)],[d35,d32]) ).
cnf(d37,plain,
X1 = X1,
inference(demodulation,[status(thm)],[d36,d31]) ).
cnf(d38,plain,
$false,
inference(resolution,[status(thm)],[d37,d29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO007-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n019.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Fri Sep 25 12:30:54 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.86/8.70 % SZS status Unsatisfiable for theBenchmark.p
% 22.86/8.70 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------