%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO093-1 : 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 : n002.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 07:14:09 AM UTC 2026
% Result : Unsatisfiable 34.60s 30.79s
% Output : CNFRefutation 34.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of clauses : 66 ( 16 unt; 30 nHn; 44 RR)
% Number of literals : 164 ( 45 equ; 53 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 135 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(proposition_2_14_2_67,negated_conjecture,
open(sk14) ).
cnf(proposition_2_14_2_68,negated_conjecture,
'part$uof'(sk15,sk14) ).
cnf(proposition_2_14_2_69,negated_conjecture,
'part$uof'(sk16,sk14) ).
cnf(proposition_2_14_2_71,negated_conjecture,
~ open(sum(sk15,sk16)) ).
cnf(part_of_defn_1,axiom,
( 'incident$uc'(X2,X1)
| ~ 'incident$uc'(X2,X0)
| ~ 'part$uof'(X0,X1) ) ).
cnf(part_of_defn_2,axiom,
( 'part$uof'(X0,X1)
| 'incident$uc'('ax0$usk1'(X0,X1),X0) ) ).
cnf(part_of_defn_3,axiom,
( 'part$uof'(X0,X1)
| ~ 'incident$uc'('ax0$usk1'(X0,X1),X1) ) ).
cnf(sum_defn_4,axiom,
( 'incident$uc'(X3,X2)
| 'incident$uc'(X3,X1)
| ~ 'incident$uc'(X3,X0)
| X0 != sum(X1,X2) ) ).
cnf(sum_defn_5,axiom,
( 'incident$uc'(X3,X0)
| ~ 'incident$uc'(X3,X1)
| X0 != sum(X1,X2) ) ).
cnf(sum_defn_6,axiom,
( 'incident$uc'(X3,X0)
| ~ 'incident$uc'(X3,X2)
| X0 != sum(X1,X2) ) ).
cnf(sum_defn_7,axiom,
( X2 = sum(X1,X0)
| 'incident$uc'('ax0$usk2'(X0,X1,X2),X0)
| 'incident$uc'('ax0$usk2'(X0,X1,X2),X1)
| 'incident$uc'('ax0$usk2'(X0,X1,X2),X2) ) ).
cnf(sum_defn_11,axiom,
( X2 = sum(X1,X0)
| ~ 'incident$uc'('ax0$usk2'(X0,X1,X2),X2)
| ~ 'incident$uc'('ax0$usk2'(X0,X1,X2),X1) ) ).
cnf(sum_defn_12,axiom,
( X2 = sum(X1,X0)
| ~ 'incident$uc'('ax0$usk2'(X0,X1,X2),X2)
| ~ 'incident$uc'('ax0$usk2'(X0,X1,X2),X0) ) ).
cnf(c1_35,axiom,
( open(X0)
| X0 = X1
| ~ 'part$uof'(X0,X1) ) ).
cnf(c9_45,axiom,
( X1 = X0
| 'incident$uc'('ax0$usk13'(X0,X1),X0)
| 'incident$uc'('ax0$usk13'(X0,X1),X1) ) ).
cnf(c9_48,axiom,
( X1 = X0
| ~ 'incident$uc'('ax0$usk13'(X0,X1),X1)
| ~ 'incident$uc'('ax0$usk13'(X0,X1),X0) ) ).
cnf(c0,plain,
open(sk14),
inference(clausification,[status(esa)],[proposition_2_14_2_67]) ).
cnf(c1,plain,
'part$uof'(sk15,sk14),
inference(clausification,[status(esa)],[proposition_2_14_2_68]) ).
cnf(c2,plain,
'part$uof'(sk16,sk14),
inference(clausification,[status(esa)],[proposition_2_14_2_69]) ).
cnf(c4,plain,
~ open(sum(sk15,sk16)),
inference(clausification,[status(esa)],[proposition_2_14_2_71]) ).
cnf(c5,plain,
( 'incident$uc'(X0,X2)
| ~ 'part$uof'(X1,X2)
| ~ 'incident$uc'(X0,X1) ),
inference(clausification,[status(esa)],[part_of_defn_1]) ).
cnf(c6,plain,
( 'part$uof'(X0,X1)
| 'incident$uc'('ax0$usk1'(X0,X1),X0) ),
inference(clausification,[status(esa)],[part_of_defn_2]) ).
cnf(c7,plain,
( 'part$uof'(X0,X1)
| ~ 'incident$uc'('ax0$usk1'(X0,X1),X1) ),
inference(clausification,[status(esa)],[part_of_defn_3]) ).
cnf(c8,plain,
( 'incident$uc'(X0,X2)
| ~ 'incident$uc'(X0,X3)
| sum(X1,X2) != X3
| 'incident$uc'(X0,X1) ),
inference(clausification,[status(esa)],[sum_defn_4]) ).
cnf(c9,plain,
( 'incident$uc'(X0,X3)
| sum(X1,X2) != X3
| ~ 'incident$uc'(X0,X1) ),
inference(clausification,[status(esa)],[sum_defn_5]) ).
cnf(c10,plain,
( 'incident$uc'(X0,X3)
| sum(X2,X1) != X3
| ~ 'incident$uc'(X0,X1) ),
inference(clausification,[status(esa)],[sum_defn_6]) ).
cnf(c11,plain,
( sum(X1,X0) = X2
| 'incident$uc'('ax0$usk2'(X0,X1,X2),X1)
| 'incident$uc'('ax0$usk2'(X0,X1,X2),X2)
| 'incident$uc'('ax0$usk2'(X0,X1,X2),X0) ),
inference(clausification,[status(esa)],[sum_defn_7]) ).
cnf(c12,plain,
( sum(X1,X0) = X2
| ~ 'incident$uc'('ax0$usk2'(X0,X1,X2),X1)
| ~ 'incident$uc'('ax0$usk2'(X0,X1,X2),X2) ),
inference(clausification,[status(esa)],[sum_defn_11]) ).
cnf(c13,plain,
( sum(X1,X0) = X2
| ~ 'incident$uc'('ax0$usk2'(X0,X1,X2),X0)
| ~ 'incident$uc'('ax0$usk2'(X0,X1,X2),X2) ),
inference(clausification,[status(esa)],[sum_defn_12]) ).
cnf(c36,plain,
( open(X1)
| ~ 'part$uof'(X1,X0)
| X0 = X1 ),
inference(clausification,[status(esa)],[c1_35]) ).
cnf(c46,plain,
( X0 = X1
| 'incident$uc'('ax0$usk13'(X0,X1),X1)
| 'incident$uc'('ax0$usk13'(X0,X1),X0) ),
inference(clausification,[status(esa)],[c9_45]) ).
cnf(c47,plain,
( X0 = X1
| ~ 'incident$uc'('ax0$usk13'(X0,X1),X0)
| ~ 'incident$uc'('ax0$usk13'(X0,X1),X1) ),
inference(clausification,[status(esa)],[c9_48]) ).
cnf(d0,plain,
( 'incident$uc'('ax0$usk2'(X1,X0,X2),X3)
| ~ 'part$uof'(X1,X3)
| 'incident$uc'('ax0$usk2'(X1,X0,X2),X0)
| 'incident$uc'('ax0$usk2'(X1,X0,X2),X2)
| sum(X0,X1) = X2 ),
inference(resolution,[status(thm)],[c11,c5]) ).
cnf(d1,plain,
( 'incident$uc'('ax0$usk2'(X1,X0,X2),X0)
| 'incident$uc'('ax0$usk2'(X1,X0,X2),X2)
| ~ 'part$uof'(X1,X2)
| sum(X0,X1) = X2 ),
inference(factoring,[status(thm)],[d0]) ).
cnf(d2,plain,
( 'incident$uc'('ax0$usk2'(X1,X0,X0),X0)
| ~ 'part$uof'(X1,X0)
| sum(X0,X1) = X0 ),
inference(factoring,[status(thm)],[d1]) ).
cnf(d3,plain,
( 'incident$uc'('ax0$usk2'(X1,X0,X0),X1)
| 'incident$uc'('ax0$usk2'(X1,X0,X0),X0)
| sum(X0,X1) = X0 ),
inference(factoring,[status(thm)],[c11]) ).
cnf(d4,plain,
( ~ 'incident$uc'('ax0$usk2'(X1,X0,X0),X0)
| sum(X0,X1) = X0
| 'incident$uc'('ax0$usk2'(X1,X0,X0),X1)
| sum(X0,X1) = X0 ),
inference(resolution,[status(thm)],[d3,c12]) ).
cnf(d5,plain,
( 'incident$uc'('ax0$usk2'(X1,X0,X0),X1)
| sum(X0,X1) = X0
| 'incident$uc'('ax0$usk2'(X1,X0,X0),X1)
| sum(X0,X1) = X0 ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( ~ 'incident$uc'('ax0$usk2'(X1,X0,X0),X0)
| sum(X0,X1) = X0
| sum(X0,X1) = X0 ),
inference(resolution,[status(thm)],[d5,c13]) ).
cnf(d7,plain,
( ~ 'part$uof'(X1,X0)
| sum(X0,X1) = X0
| sum(X0,X1) = X0 ),
inference(resolution,[status(thm)],[d6,d2]) ).
cnf(d8,plain,
sum(sk14,sk16) = sk14,
inference(resolution,[status(thm)],[d7,c2]) ).
cnf(d9,plain,
( ~ 'incident$uc'(X0,X2)
| 'incident$uc'(X0,sum(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c10]) ).
cnf(d10,plain,
( ~ 'incident$uc'(X0,X1)
| 'incident$uc'(X0,sum(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c9]) ).
cnf(d11,plain,
( 'part$uof'(X0,sum(X1,X2))
| ~ 'incident$uc'('ax0$usk1'(X0,sum(X1,X2)),X1) ),
inference(resolution,[status(thm)],[d10,c7]) ).
cnf(d12,plain,
( ~ 'incident$uc'('ax0$usk1'(X0,sum(sum(X1,X2),X3)),X2)
| 'part$uof'(X0,sum(sum(X1,X2),X3)) ),
inference(resolution,[status(thm)],[d11,d9]) ).
cnf(d13,plain,
( 'part$uof'(X0,sum(X1,X2))
| ~ 'incident$uc'('ax0$usk1'(X0,sum(X1,X2)),X2) ),
inference(resolution,[status(thm)],[d9,c7]) ).
cnf(d14,plain,
( 'incident$uc'(X0,X1)
| 'incident$uc'(X0,X2)
| ~ 'incident$uc'(X0,sum(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c8]) ).
cnf(d15,plain,
( 'part$uof'(sum(X0,X1),X2)
| 'incident$uc'('ax0$usk1'(sum(X0,X1),X2),X0)
| 'incident$uc'('ax0$usk1'(sum(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[d14,c6]) ).
cnf(d16,plain,
( 'part$uof'(sum(X0,X1),sum(X2,X1))
| 'incident$uc'('ax0$usk1'(sum(X0,X1),sum(X2,X1)),X0)
| 'part$uof'(sum(X0,X1),sum(X2,X1)) ),
inference(resolution,[status(thm)],[d15,d13]) ).
cnf(d17,plain,
( 'part$uof'(sum(X0,X1),sum(sum(X2,X0),X1))
| 'part$uof'(sum(X0,X1),sum(sum(X2,X0),X1)) ),
inference(resolution,[status(thm)],[d16,d12]) ).
cnf(d18,plain,
( 'part$uof'(X0,sum(X0,X1))
| 'part$uof'(X0,sum(X0,X1)) ),
inference(resolution,[status(thm)],[d11,c6]) ).
cnf(d19,plain,
( open(X0)
| sum(X0,X1) = X0 ),
inference(resolution,[status(thm)],[d18,c36]) ).
cnf(d20,plain,
sum(sum(sk15,sk16),X0) = sum(sk15,sk16),
inference(resolution,[status(thm)],[d19,c4]) ).
cnf(d21,plain,
( ~ 'incident$uc'(X1,X0)
| 'incident$uc'(X1,sum(sk15,sk16)) ),
inference(superposition,[status(thm)],[d20,d9]) ).
cnf(d22,plain,
( 'incident$uc'('ax0$usk13'(X0,X1),X0)
| X0 = X1
| 'incident$uc'('ax0$usk13'(X0,X1),sum(sk15,sk16)) ),
inference(resolution,[status(thm)],[d21,c46]) ).
cnf(d23,plain,
( 'incident$uc'('ax0$usk13'(X0,X1),sum(sk15,sk16))
| 'incident$uc'('ax0$usk13'(X0,X1),sum(sk15,sk16))
| X0 = X1 ),
inference(resolution,[status(thm)],[d22,d21]) ).
cnf(d24,plain,
( 'incident$uc'('ax0$usk13'(X0,X1),X2)
| ~ 'part$uof'(X1,X2)
| 'incident$uc'('ax0$usk13'(X0,X1),X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c46,c5]) ).
cnf(d25,plain,
( 'incident$uc'('ax0$usk13'(X0,X1),X0)
| ~ 'part$uof'(X1,X0)
| X0 = X1 ),
inference(factoring,[status(thm)],[d24]) ).
cnf(d26,plain,
( ~ 'incident$uc'('ax0$usk13'(X0,X1),X1)
| X0 = X1
| ~ 'part$uof'(X1,X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[d25,c47]) ).
cnf(d27,plain,
( X0 = sum(sk15,sk16)
| ~ 'part$uof'(sum(sk15,sk16),X0)
| X0 = sum(sk15,sk16) ),
inference(resolution,[status(thm)],[d26,d23]) ).
cnf(d28,plain,
sum(sum(X0,sk15),sk16) = sum(sk15,sk16),
inference(resolution,[status(thm)],[d27,d17]) ).
cnf(d29,plain,
sum(sk14,sk15) = sk14,
inference(resolution,[status(thm)],[d7,c1]) ).
cnf(d30,plain,
sum(sk14,sk16) = sum(sk15,sk16),
inference(superposition,[status(thm)],[d29,d28]) ).
cnf(d31,plain,
sk14 = sum(sk15,sk16),
inference(demodulation,[status(thm)],[d30,d8]) ).
cnf(d32,plain,
~ open(sk14),
inference(demodulation,[status(thm)],[c4,d31]) ).
cnf(d33,plain,
$false,
inference(resolution,[status(thm)],[c0,d32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO093-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n002.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 12:45:19 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 34.60/30.79 % SZS status Unsatisfiable for theBenchmark.p
% 34.60/30.79 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------