%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO111-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/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 5.79s 9.22s
% Output : CNFRefutation 5.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of clauses : 45 ( 9 unt; 8 nHn; 45 RR)
% Number of literals : 102 ( 23 equ; 51 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 100 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(theorem_3_8_1_77,negated_conjecture,
'between$uc'(sk15,sk16,sk17,sk18) ).
cnf(theorem_3_8_1_78,negated_conjecture,
( sk16 = sk18
| sk17 = sk18
| sk16 = sk17
| ~ 'incident$uc'(sk18,sk15)
| ~ 'incident$uc'(sk17,sk15)
| ~ 'incident$uc'(sk16,sk15) ) ).
cnf(part_of_defn_1,axiom,
( 'incident$uc'(X2,X1)
| ~ 'incident$uc'(X2,X0)
| ~ 'part$uof'(X0,X1) ) ).
cnf(end_point_defn_13,axiom,
( 'incident$uc'(X0,X1)
| ~ 'end$upoint'(X0,X1) ) ).
cnf(inner_point_defn_21,axiom,
( 'incident$uc'(X0,X1)
| ~ 'inner$upoint'(X0,X1) ) ).
cnf(inner_point_defn_22,axiom,
( ~ 'end$upoint'(X0,X1)
| ~ 'inner$upoint'(X0,X1) ) ).
cnf(between_c_defn_1,axiom,
( X1 != X3
| ~ 'between$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(c0,plain,
'between$uc'(sk15,sk16,sk17,sk18),
inference(clausification,[status(esa)],[theorem_3_8_1_77]) ).
cnf(c1,plain,
( sk17 = sk18
| ~ 'incident$uc'(sk18,sk15)
| sk16 = sk18
| sk16 = sk17
| ~ 'incident$uc'(sk17,sk15)
| ~ 'incident$uc'(sk16,sk15) ),
inference(clausification,[status(esa)],[theorem_3_8_1_78]) ).
cnf(c2,plain,
( 'incident$uc'(X2,X1)
| ~ 'incident$uc'(X2,X0)
| ~ 'part$uof'(X0,X1) ),
inference(clausification,[status(esa)],[part_of_defn_1]) ).
cnf(c14,plain,
( 'incident$uc'(X0,X1)
| ~ 'end$upoint'(X0,X1) ),
inference(clausification,[status(esa)],[end_point_defn_13]) ).
cnf(c22,plain,
( 'incident$uc'(X0,X1)
| ~ 'inner$upoint'(X0,X1) ),
inference(clausification,[status(esa)],[inner_point_defn_21]) ).
cnf(c23,plain,
( ~ 'end$upoint'(X0,X1)
| ~ 'inner$upoint'(X0,X1) ),
inference(clausification,[status(esa)],[inner_point_defn_22]) ).
cnf(c50,plain,
( X1 != X3
| ~ 'between$uc'(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[between_c_defn_1]) ).
cnf(c51,plain,
( 'part$uof'('ax1$usk1'(X3,X2,X1,X0),X0)
| ~ 'between$uc'(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[between_c_defn_2]) ).
cnf(c52,plain,
( 'end$upoint'(X1,'ax1$usk1'(X3,X2,X1,X0))
| ~ 'between$uc'(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[between_c_defn_3]) ).
cnf(c53,plain,
( 'end$upoint'(X3,'ax1$usk1'(X3,X2,X1,X0))
| ~ 'between$uc'(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[between_c_defn_4]) ).
cnf(c54,plain,
( 'inner$upoint'(X2,'ax1$usk1'(X3,X2,X1,X0))
| ~ 'between$uc'(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[between_c_defn_5]) ).
cnf(d0,plain,
( ~ 'incident$uc'(X4,'ax1$usk1'(X3,X2,X1,X0))
| 'incident$uc'(X4,X0)
| ~ 'between$uc'(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c51,c2]) ).
cnf(d1,plain,
( 'incident$uc'(X1,'ax1$usk1'(X3,X2,X1,X0))
| ~ 'between$uc'(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c52,c14]) ).
cnf(d2,plain,
( 'incident$uc'(X1,X0)
| ~ 'between$uc'(X0,X1,X2,X3)
| ~ 'between$uc'(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
'incident$uc'(sk16,sk15),
inference(resolution,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
( ~ 'incident$uc'(sk18,sk15)
| ~ 'incident$uc'(sk17,sk15)
| sk17 = sk18
| sk16 = sk18
| sk16 = sk17 ),
inference(resolution,[status(thm)],[d3,c1]) ).
cnf(d5,plain,
( 'incident$uc'(X3,'ax1$usk1'(X3,X2,X1,X0))
| ~ 'between$uc'(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c53,c14]) ).
cnf(d6,plain,
( 'incident$uc'(X3,X0)
| ~ 'between$uc'(X0,X1,X2,X3)
| ~ 'between$uc'(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
'incident$uc'(sk18,sk15),
inference(resolution,[status(thm)],[d6,c0]) ).
cnf(d8,plain,
( ~ 'incident$uc'(sk17,sk15)
| sk17 = sk18
| sk16 = sk18
| sk16 = sk17 ),
inference(resolution,[status(thm)],[d7,d4]) ).
cnf(d9,plain,
( 'incident$uc'(X2,'ax1$usk1'(X3,X2,X1,X0))
| ~ 'between$uc'(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c54,c22]) ).
cnf(d10,plain,
( 'incident$uc'(X2,X0)
| ~ 'between$uc'(X0,X1,X2,X3)
| ~ 'between$uc'(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[d9,d0]) ).
cnf(d11,plain,
'incident$uc'(sk17,sk15),
inference(resolution,[status(thm)],[d10,c0]) ).
cnf(d12,plain,
( sk17 = sk18
| sk16 = sk18
| sk16 = sk17 ),
inference(resolution,[status(thm)],[d11,d8]) ).
cnf(d13,plain,
( sk16 = sk18
| sk16 = sk17
| 'between$uc'(sk15,sk16,sk17,sk17) ),
inference(superposition,[status(thm)],[d12,c0]) ).
cnf(d14,plain,
( ~ 'end$upoint'(X2,'ax1$usk1'(X3,X2,X1,X0))
| ~ 'between$uc'(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c54,c23]) ).
cnf(d15,plain,
( ~ 'between$uc'(X0,X1,X2,X2)
| ~ 'between$uc'(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[d14,c53]) ).
cnf(d16,plain,
( sk16 = sk18
| sk16 = sk17 ),
inference(resolution,[status(thm)],[d15,d13]) ).
cnf(d17,plain,
( sk16 = sk17
| 'between$uc'(sk15,sk16,sk17,sk16) ),
inference(superposition,[status(thm)],[d16,c0]) ).
cnf(d18,plain,
~ 'between$uc'(X0,X1,X2,X1),
inference(equality_resolution,[status(thm)],[c50]) ).
cnf(d19,plain,
sk16 = sk17,
inference(resolution,[status(thm)],[d18,d17]) ).
cnf(d20,plain,
'between$uc'(sk15,sk16,sk16,sk18),
inference(demodulation,[status(thm)],[c0,d19]) ).
cnf(d21,plain,
( ~ 'between$uc'(X0,X1,X1,X2)
| ~ 'between$uc'(X0,X1,X1,X2) ),
inference(resolution,[status(thm)],[d14,c52]) ).
cnf(d22,plain,
$false,
inference(resolution,[status(thm)],[d21,d20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO111-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.36 % Computer : n008.cluster.edu
% 0.06/0.36 % Model : x86_64 x86_64
% 0.06/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.36 % Memory : 8046.5625MB
% 0.06/0.36 % OS : Linux 6.8.0-71-generic
% 0.06/0.36 % CPULimit : 300
% 0.06/0.37 % WCLimit : 300
% 0.06/0.37 % DateTime : Fri Sep 25 12:48:54 UTC 2026
% 0.06/0.37 % CPUTime :
% 0.06/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.79/9.22 % SZS status Unsatisfiable for theBenchmark.p
% 5.79/9.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------