%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO083-1 : 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 : n017.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 116.77s 20.17s
% Output : CNFRefutation 116.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of clauses : 42 ( 7 unt; 18 nHn; 28 RR)
% Number of literals : 111 ( 25 equ; 40 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 104 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(corollary_2_6_1_67,negated_conjecture,
'part$uof'(sk15,sk16) ).
cnf(corollary_2_6_1_70,negated_conjecture,
~ 'part$uof'(sum(sk14,sk15),sum(sk14,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(c0,plain,
'part$uof'(sk15,sk16),
inference(clausification,[status(esa)],[corollary_2_6_1_67]) ).
cnf(c3,plain,
~ 'part$uof'(sum(sk14,sk15),sum(sk14,sk16)),
inference(clausification,[status(esa)],[corollary_2_6_1_70]) ).
cnf(c4,plain,
( 'incident$uc'(X2,X1)
| ~ 'incident$uc'(X2,X0)
| ~ 'part$uof'(X0,X1) ),
inference(clausification,[status(esa)],[part_of_defn_1]) ).
cnf(c5,plain,
( 'part$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'(X3,X2)
| 'incident$uc'(X3,X1)
| ~ 'incident$uc'(X3,X0)
| X0 != sum(X1,X2) ),
inference(clausification,[status(esa)],[sum_defn_4]) ).
cnf(c8,plain,
( 'incident$uc'(X3,X0)
| ~ 'incident$uc'(X3,X1)
| X0 != sum(X1,X2) ),
inference(clausification,[status(esa)],[sum_defn_5]) ).
cnf(c9,plain,
( 'incident$uc'(X3,X0)
| ~ 'incident$uc'(X3,X2)
| X0 != sum(X1,X2) ),
inference(clausification,[status(esa)],[sum_defn_6]) ).
cnf(c10,plain,
( 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) ),
inference(clausification,[status(esa)],[sum_defn_7]) ).
cnf(c14,plain,
( X2 = sum(X1,X0)
| ~ 'incident$uc'('ax0$usk2'(X0,X1,X2),X2)
| ~ 'incident$uc'('ax0$usk2'(X0,X1,X2),X1) ),
inference(clausification,[status(esa)],[sum_defn_11]) ).
cnf(c15,plain,
( X2 = sum(X1,X0)
| ~ 'incident$uc'('ax0$usk2'(X0,X1,X2),X2)
| ~ 'incident$uc'('ax0$usk2'(X0,X1,X2),X0) ),
inference(clausification,[status(esa)],[sum_defn_12]) ).
cnf(d0,plain,
( ~ 'incident$uc'(X0,sum(X2,X1))
| 'incident$uc'(X0,X2)
| 'incident$uc'(X0,X1) ),
inference(equality_resolution,[status(thm)],[c7]) ).
cnf(d1,plain,
( 'part$uof'(sum(X0,X1),X2)
| 'incident$uc'('ax0$usk1'(sum(X0,X1),X2),X1)
| 'incident$uc'('ax0$usk1'(sum(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[d0,c5]) ).
cnf(d2,plain,
( ~ 'incident$uc'(X0,X1)
| 'incident$uc'(X0,sum(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c8]) ).
cnf(d3,plain,
( 'part$uof'(X0,sum(X1,X2))
| ~ 'incident$uc'('ax0$usk1'(X0,sum(X1,X2)),X1) ),
inference(resolution,[status(thm)],[d2,c6]) ).
cnf(d4,plain,
( 'incident$uc'('ax0$usk1'(sum(X0,X1),sum(X0,X2)),X1)
| 'part$uof'(sum(X0,X1),sum(X0,X2))
| 'part$uof'(sum(X0,X1),sum(X0,X2)) ),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( 'incident$uc'(X0,sum(X2,X1))
| ~ 'incident$uc'(X0,X1) ),
inference(equality_resolution,[status(thm)],[c9]) ).
cnf(d6,plain,
( 'part$uof'(X0,sum(X1,X2))
| ~ 'incident$uc'('ax0$usk1'(X0,sum(X1,X2)),X2) ),
inference(resolution,[status(thm)],[d5,c6]) ).
cnf(d7,plain,
( ~ 'incident$uc'('ax0$usk1'(X0,sum(X1,sum(X2,X3))),X3)
| 'part$uof'(X0,sum(X1,sum(X2,X3))) ),
inference(resolution,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
( 'part$uof'(sum(X0,X1),sum(X0,sum(X2,X1)))
| 'part$uof'(sum(X0,X1),sum(X0,sum(X2,X1))) ),
inference(resolution,[status(thm)],[d7,d4]) ).
cnf(d9,plain,
( 'incident$uc'('ax0$usk2'(X2,X1,X0),X3)
| ~ 'part$uof'(X2,X3)
| 'incident$uc'('ax0$usk2'(X2,X1,X0),X1)
| 'incident$uc'('ax0$usk2'(X2,X1,X0),X0)
| X0 = sum(X1,X2) ),
inference(resolution,[status(thm)],[c10,c4]) ).
cnf(d10,plain,
( 'incident$uc'('ax0$usk2'(X2,X1,X0),X0)
| 'incident$uc'('ax0$usk2'(X2,X1,X0),X1)
| ~ 'part$uof'(X2,X1)
| X0 = sum(X1,X2) ),
inference(factoring,[status(thm)],[d9]) ).
cnf(d11,plain,
( 'incident$uc'('ax0$usk2'(X1,X0,X0),X0)
| ~ 'part$uof'(X1,X0)
| X0 = sum(X0,X1) ),
inference(factoring,[status(thm)],[d10]) ).
cnf(d12,plain,
( 'incident$uc'('ax0$usk2'(X1,X0,X0),X1)
| 'incident$uc'('ax0$usk2'(X1,X0,X0),X0)
| X0 = sum(X0,X1) ),
inference(factoring,[status(thm)],[c10]) ).
cnf(d13,plain,
( ~ 'incident$uc'('ax0$usk2'(X1,X0,X0),X0)
| X0 = sum(X0,X1)
| 'incident$uc'('ax0$usk2'(X1,X0,X0),X1)
| X0 = sum(X0,X1) ),
inference(resolution,[status(thm)],[d12,c14]) ).
cnf(d14,plain,
( 'incident$uc'('ax0$usk2'(X1,X0,X0),X1)
| X0 = sum(X0,X1)
| 'incident$uc'('ax0$usk2'(X1,X0,X0),X1)
| X0 = sum(X0,X1) ),
inference(resolution,[status(thm)],[d13,d12]) ).
cnf(d15,plain,
( ~ 'incident$uc'('ax0$usk2'(X1,X0,X0),X0)
| X0 = sum(X0,X1)
| X0 = sum(X0,X1) ),
inference(resolution,[status(thm)],[d14,c15]) ).
cnf(d16,plain,
( ~ 'part$uof'(X1,X0)
| X0 = sum(X0,X1)
| X0 = sum(X0,X1) ),
inference(resolution,[status(thm)],[d15,d11]) ).
cnf(d17,plain,
sk16 = sum(sk16,sk15),
inference(resolution,[status(thm)],[d16,c0]) ).
cnf(d18,plain,
'part$uof'(sum(X0,sk15),sum(X0,sk16)),
inference(superposition,[status(thm)],[d17,d8]) ).
cnf(d19,plain,
$false,
inference(resolution,[status(thm)],[d18,c3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO083-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.57 % Computer : n017.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Fri Sep 25 12:35:35 UTC 2026
% 0.10/0.58 % CPUTime :
% 0.10/0.58 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 116.77/20.17 % SZS status Unsatisfiable for theBenchmark.p
% 116.77/20.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------