%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG011-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 06:47:03 AM UTC 2026
% Result : Unsatisfiable 10.06s 1.69s
% Output : CNFRefutation 10.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of clauses : 26 ( 8 unt; 2 nHn; 22 RR)
% Number of literals : 63 ( 2 equ; 43 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 43 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(f_is_associative,axiom,
f(X0,f(X1,X2)) = f(f(X0,X1),X2) ).
cnf(partitions_union,axiom,
( d(X0)
| c(X0) ) ).
cnf(partitions_exclusive,hypothesis,
( ~ d(X0)
| ~ c(X0) ) ).
cnf(partition_c_not_empty,hypothesis,
c(a1) ).
cnf(partition_d_not_empty,hypothesis,
d(a2) ).
cnf(conjecture_1,negated_conjecture,
( ~ c(X1)
| ~ c(X0)
| d(f(X0,X1)) ) ).
cnf(conjecture_2,negated_conjecture,
( ~ d(X1)
| ~ d(X0)
| c(f(X0,X1)) ) ).
cnf(c0,plain,
f(X0,f(X1,X2)) = f(f(X0,X1),X2),
inference(clausification,[status(esa)],[f_is_associative]) ).
cnf(c1,plain,
( d(X0)
| c(X0) ),
inference(clausification,[status(esa)],[partitions_union]) ).
cnf(c2,plain,
( ~ d(X0)
| ~ c(X0) ),
inference(clausification,[status(esa)],[partitions_exclusive]) ).
cnf(c3,plain,
c(a1),
inference(clausification,[status(esa)],[partition_c_not_empty]) ).
cnf(c4,plain,
d(a2),
inference(clausification,[status(esa)],[partition_d_not_empty]) ).
cnf(c5,plain,
( ~ c(X1)
| ~ c(X0)
| d(f(X0,X1)) ),
inference(clausification,[status(esa)],[conjecture_1]) ).
cnf(c6,plain,
( ~ d(X1)
| ~ d(X0)
| c(f(X0,X1)) ),
inference(clausification,[status(esa)],[conjecture_2]) ).
cnf(d0,plain,
( ~ d(f(X0,X1))
| ~ d(X1)
| ~ d(X0) ),
inference(resolution,[status(thm)],[c6,c2]) ).
cnf(d1,plain,
( ~ c(X2)
| ~ c(f(X0,X1))
| d(f(X0,f(X1,X2))) ),
inference(superposition,[status(thm)],[c0,c5]) ).
cnf(d2,plain,
( ~ d(X1)
| ~ d(f(X2,X0))
| ~ c(f(X1,X2))
| ~ c(X0) ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( ~ d(X1)
| ~ d(X0)
| ~ c(X2)
| ~ d(f(X1,X2))
| ~ d(X0) ),
inference(resolution,[status(thm)],[d2,c6]) ).
cnf(d4,plain,
( d(f(X0,X1))
| ~ c(X2)
| ~ d(f(X1,X2))
| ~ d(X0) ),
inference(resolution,[status(thm)],[d2,c1]) ).
cnf(d5,plain,
( ~ c(X2)
| ~ c(X1)
| ~ c(X2)
| d(f(X0,X1))
| ~ d(X0) ),
inference(resolution,[status(thm)],[d4,c5]) ).
cnf(d6,plain,
( ~ c(X1)
| d(f(X0,a1))
| ~ d(X0) ),
inference(resolution,[status(thm)],[d5,c3]) ).
cnf(d7,plain,
( d(f(X0,a1))
| ~ d(X0) ),
inference(resolution,[status(thm)],[d6,c3]) ).
cnf(d8,plain,
( ~ c(a1)
| ~ d(X1)
| ~ d(X0)
| ~ d(X0) ),
inference(resolution,[status(thm)],[d7,d3]) ).
cnf(d9,plain,
( ~ d(X1)
| ~ d(X0) ),
inference(resolution,[status(thm)],[c3,d8]) ).
cnf(d10,plain,
~ d(X0),
inference(resolution,[status(thm)],[d9,c4]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[d10,c4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG011-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n001.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sat Sep 26 21:04:15 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.06/1.69 % SZS status Unsatisfiable for theBenchmark.p
% 10.06/1.69 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------