%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO084-1 : 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 : 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 07:14:07 AM UTC 2026
% Result : Unsatisfiable 19.89s 8.93s
% Output : CNFRefutation 19.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of clauses : 25 ( 11 unt; 8 nHn; 23 RR)
% Number of literals : 46 ( 2 equ; 15 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(corollary_2_6_2_67,negated_conjecture,
'part$uof'(sk14,sk16) ).
cnf(corollary_2_6_2_68,negated_conjecture,
'part$uof'(sk15,sk16) ).
cnf(corollary_2_6_2_70,negated_conjecture,
~ 'part$uof'(sum(sk14,sk15),sk16) ).
cnf(part_of_defn_1,axiom,
( 'incident$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$uc'(X3,X0)
| X0 != sum(X1,X2) ) ).
cnf(c0,plain,
'part$uof'(sk14,sk16),
inference(clausification,[status(esa)],[corollary_2_6_2_67]) ).
cnf(c1,plain,
'part$uof'(sk15,sk16),
inference(clausification,[status(esa)],[corollary_2_6_2_68]) ).
cnf(c3,plain,
~ 'part$uof'(sum(sk14,sk15),sk16),
inference(clausification,[status(esa)],[corollary_2_6_2_70]) ).
cnf(c4,plain,
( 'incident$uc'(X0,X2)
| ~ 'part$uof'(X1,X2)
| ~ 'incident$uc'(X0,X1) ),
inference(clausification,[status(esa)],[part_of_defn_1]) ).
cnf(c5,plain,
( 'part$uof'(X0,X1)
| 'incident$uc'('ax0$usk1'(X0,X1),X0) ),
inference(clausification,[status(esa)],[part_of_defn_2]) ).
cnf(c6,plain,
( 'part$uof'(X0,X1)
| ~ 'incident$uc'('ax0$usk1'(X0,X1),X1) ),
inference(clausification,[status(esa)],[part_of_defn_3]) ).
cnf(c7,plain,
( 'incident$uc'(X0,X2)
| ~ 'incident$uc'(X0,X3)
| sum(X1,X2) != X3
| 'incident$uc'(X0,X1) ),
inference(clausification,[status(esa)],[sum_defn_4]) ).
cnf(d0,plain,
( ~ 'incident$uc'(X0,sk15)
| 'incident$uc'(X0,sk16) ),
inference(resolution,[status(thm)],[c4,c1]) ).
cnf(d1,plain,
( ~ 'incident$uc'(X0,sk14)
| 'incident$uc'(X0,sk16) ),
inference(resolution,[status(thm)],[c4,c0]) ).
cnf(d2,plain,
'incident$uc'('ax0$usk1'(sum(sk14,sk15),sk16),sum(sk14,sk15)),
inference(resolution,[status(thm)],[c5,c3]) ).
cnf(d3,plain,
( 'incident$uc'(X0,X1)
| 'incident$uc'(X0,X2)
| ~ 'incident$uc'(X0,sum(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c7]) ).
cnf(d4,plain,
( 'incident$uc'('ax0$usk1'(sum(sk14,sk15),sk16),sk14)
| 'incident$uc'('ax0$usk1'(sum(sk14,sk15),sk16),sk15) ),
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
( 'incident$uc'('ax0$usk1'(sum(sk14,sk15),sk16),sk16)
| 'incident$uc'('ax0$usk1'(sum(sk14,sk15),sk16),sk15) ),
inference(resolution,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
( 'part$uof'(sum(sk14,sk15),sk16)
| 'incident$uc'('ax0$usk1'(sum(sk14,sk15),sk16),sk15) ),
inference(resolution,[status(thm)],[d5,c6]) ).
cnf(d7,plain,
'incident$uc'('ax0$usk1'(sum(sk14,sk15),sk16),sk15),
inference(resolution,[status(thm)],[c3,d6]) ).
cnf(d8,plain,
'incident$uc'('ax0$usk1'(sum(sk14,sk15),sk16),sk16),
inference(resolution,[status(thm)],[d7,d0]) ).
cnf(d9,plain,
'part$uof'(sum(sk14,sk15),sk16),
inference(resolution,[status(thm)],[d8,c6]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[c3,d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO084-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/0.52 % Computer : n012.cluster.edu
% 0.04/0.52 % Model : x86_64 x86_64
% 0.04/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.52 % Memory : 8046.5625MB
% 0.04/0.52 % OS : Linux 6.8.0-71-generic
% 0.04/0.52 % CPULimit : 300
% 0.04/0.52 % WCLimit : 300
% 0.04/0.52 % DateTime : Fri Sep 25 12:41:06 UTC 2026
% 0.04/0.52 % CPUTime :
% 0.04/0.52 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.89/8.93 % SZS status Unsatisfiable for theBenchmark.p
% 19.89/8.93 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------