%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO112-1 : TPTP v9.3.1. Released v2.4.0.
% 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 07:14:12 AM UTC 2026
% Result : Unsatisfiable 184.34s 30.39s
% Output : CNFRefutation 184.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of clauses : 28 ( 12 unt; 6 nHn; 28 RR)
% Number of literals : 58 ( 9 equ; 29 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 59 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(theorem_3_8_2_77,negated_conjecture,
'between$uc'(sk15,sk16,sk17,sk18) ).
cnf(theorem_3_8_2_78,negated_conjecture,
~ 'between$uc'(sk15,sk18,sk17,sk16) ).
cnf(between_c_defn_1,axiom,
( X1 != X3
| ~ 'between$uc'(X0,X1,X2,X3) ) ).
cnf(between_c_defn_2,axiom,
( 'part$uof'('ax1$usk1'(X3,X2,X1,X0),X0)
| ~ 'between$uc'(X0,X1,X2,X3) ) ).
cnf(between_c_defn_3,axiom,
( 'end$upoint'(X1,'ax1$usk1'(X3,X2,X1,X0))
| ~ 'between$uc'(X0,X1,X2,X3) ) ).
cnf(between_c_defn_4,axiom,
( 'end$upoint'(X3,'ax1$usk1'(X3,X2,X1,X0))
| ~ 'between$uc'(X0,X1,X2,X3) ) ).
cnf(between_c_defn_5,axiom,
( 'inner$upoint'(X2,'ax1$usk1'(X3,X2,X1,X0))
| ~ 'between$uc'(X0,X1,X2,X3) ) ).
cnf(between_c_defn_6,axiom,
( 'between$uc'(X3,X0,X4,X1)
| ~ 'inner$upoint'(X4,X2)
| ~ 'end$upoint'(X1,X2)
| ~ 'end$upoint'(X0,X2)
| ~ 'part$uof'(X2,X3)
| X0 = X1 ) ).
cnf(c0,plain,
'between$uc'(sk15,sk16,sk17,sk18),
inference(clausification,[status(esa)],[theorem_3_8_2_77]) ).
cnf(c1,plain,
~ 'between$uc'(sk15,sk18,sk17,sk16),
inference(clausification,[status(esa)],[theorem_3_8_2_78]) ).
cnf(c45,plain,
( X3 != X1
| ~ 'between$uc'(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[between_c_defn_1]) ).
cnf(c46,plain,
( 'part$uof'('ax1$usk1'(X3,X2,X1,X0),X0)
| ~ 'between$uc'(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[between_c_defn_2]) ).
cnf(c47,plain,
( 'end$upoint'(X1,'ax1$usk1'(X3,X2,X1,X0))
| ~ 'between$uc'(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[between_c_defn_3]) ).
cnf(c48,plain,
( 'end$upoint'(X3,'ax1$usk1'(X3,X2,X1,X0))
| ~ 'between$uc'(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[between_c_defn_4]) ).
cnf(c49,plain,
( 'inner$upoint'(X2,'ax1$usk1'(X3,X2,X1,X0))
| ~ 'between$uc'(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[between_c_defn_5]) ).
cnf(c50,plain,
( ~ 'end$upoint'(X2,X0)
| ~ 'end$upoint'(X4,X0)
| X4 = X2
| ~ 'inner$upoint'(X3,X0)
| 'between$uc'(X1,X2,X3,X4)
| ~ 'part$uof'(X0,X1) ),
inference(clausification,[status(esa)],[between_c_defn_6]) ).
cnf(d0,plain,
'inner$upoint'(sk17,'ax1$usk1'(sk18,sk17,sk16,sk15)),
inference(resolution,[status(thm)],[c49,c0]) ).
cnf(d1,plain,
'end$upoint'(sk16,'ax1$usk1'(sk18,sk17,sk16,sk15)),
inference(resolution,[status(thm)],[c47,c0]) ).
cnf(d2,plain,
'end$upoint'(sk18,'ax1$usk1'(sk18,sk17,sk16,sk15)),
inference(resolution,[status(thm)],[c48,c0]) ).
cnf(d3,plain,
'part$uof'('ax1$usk1'(sk18,sk17,sk16,sk15),sk15),
inference(resolution,[status(thm)],[c46,c0]) ).
cnf(d4,plain,
( ~ 'inner$upoint'(X2,'ax1$usk1'(sk18,sk17,sk16,sk15))
| ~ 'end$upoint'(X0,'ax1$usk1'(sk18,sk17,sk16,sk15))
| ~ 'end$upoint'(X1,'ax1$usk1'(sk18,sk17,sk16,sk15))
| 'between$uc'(sk15,X1,X2,X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c50,d3]) ).
cnf(d5,plain,
( ~ 'inner$upoint'(X1,'ax1$usk1'(sk18,sk17,sk16,sk15))
| ~ 'end$upoint'(X0,'ax1$usk1'(sk18,sk17,sk16,sk15))
| 'between$uc'(sk15,sk18,X1,X0)
| X0 = sk18 ),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
( ~ 'inner$upoint'(X0,'ax1$usk1'(sk18,sk17,sk16,sk15))
| 'between$uc'(sk15,sk18,X0,sk16)
| sk16 = sk18 ),
inference(resolution,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
( 'between$uc'(sk15,sk18,sk17,sk16)
| sk16 = sk18 ),
inference(resolution,[status(thm)],[d6,d0]) ).
cnf(d8,plain,
sk16 = sk18,
inference(resolution,[status(thm)],[c1,d7]) ).
cnf(d9,plain,
'between$uc'(sk15,sk16,sk17,sk16),
inference(demodulation,[status(thm)],[c0,d8]) ).
cnf(d10,plain,
~ 'between$uc'(X0,X1,X2,X1),
inference(equality_resolution,[status(thm)],[c45]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[d10,d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO112-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n008.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 12:48:39 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 184.34/30.39 % SZS status Unsatisfiable for theBenchmark.p
% 184.34/30.39 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------