%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SYN015-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 09:20:42 AM UTC 2026
% Result : Unsatisfiable 3.72s 4.67s
% Output : CNFRefutation 3.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of clauses : 50 ( 12 unt; 22 nHn; 48 RR)
% Number of literals : 143 ( 0 equ; 49 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 47 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(reflexivityish,axiom,
equalish(X0,X0) ).
cnf(symmetryish,axiom,
( equalish(X1,X0)
| ~ equalish(X0,X1) ) ).
cnf(transitivityish,axiom,
( equalish(X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ) ).
cnf(element_substitutionish1,axiom,
( element(X2,X1)
| ~ element(X2,X0)
| ~ equalish(X0,X1) ) ).
cnf(element_substitutionish2,axiom,
( element(X2,X1)
| ~ equalish(X0,X2)
| ~ element(X0,X1) ) ).
cnf(c_5,negated_conjecture,
( equalish(X0,m)
| ~ element(X0,m)
| ~ equalish(f(X0),m) ) ).
cnf(c_6,negated_conjecture,
( equalish(X0,m)
| ~ element(X0,m)
| ~ equalish(f(X0),X0) ) ).
cnf(c_7,negated_conjecture,
( equalish(X0,m)
| ~ element(X0,m)
| element(X0,f(X0)) ) ).
cnf(c_8,negated_conjecture,
( equalish(X0,m)
| ~ element(X0,m)
| element(f(X0),X0) ) ).
cnf(c_9,negated_conjecture,
( equalish(X1,m)
| element(X1,m)
| equalish(X0,m)
| equalish(X0,X1)
| ~ element(X1,X0)
| ~ element(X0,X1) ) ).
cnf(c_16,negated_conjecture,
( equalish(X0,k)
| element(X0,k)
| ~ equalish(X0,n) ) ).
cnf(c_17,negated_conjecture,
( equalish(X0,k)
| equalish(X0,m)
| equalish(X0,n)
| ~ element(X0,k) ) ).
cnf(c_20,negated_conjecture,
~ equalish(n,k) ).
cnf(c_23,negated_conjecture,
equalish(m,k) ).
cnf(c0,plain,
equalish(X0,X0),
inference(clausification,[status(esa)],[reflexivityish]) ).
cnf(c1,plain,
( equalish(X1,X0)
| ~ equalish(X0,X1) ),
inference(clausification,[status(esa)],[symmetryish]) ).
cnf(c2,plain,
( equalish(X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ),
inference(clausification,[status(esa)],[transitivityish]) ).
cnf(c3,plain,
( element(X2,X1)
| ~ element(X2,X0)
| ~ equalish(X0,X1) ),
inference(clausification,[status(esa)],[element_substitutionish1]) ).
cnf(c4,plain,
( element(X2,X1)
| ~ equalish(X0,X2)
| ~ element(X0,X1) ),
inference(clausification,[status(esa)],[element_substitutionish2]) ).
cnf(c7,plain,
( equalish(X0,m)
| ~ element(X0,m)
| ~ equalish(f(X0),m) ),
inference(clausification,[status(esa)],[c_5]) ).
cnf(c8,plain,
( equalish(X0,m)
| ~ element(X0,m)
| ~ equalish(f(X0),X0) ),
inference(clausification,[status(esa)],[c_6]) ).
cnf(c9,plain,
( equalish(X0,m)
| ~ element(X0,m)
| element(X0,f(X0)) ),
inference(clausification,[status(esa)],[c_7]) ).
cnf(c10,plain,
( equalish(X0,m)
| ~ element(X0,m)
| element(f(X0),X0) ),
inference(clausification,[status(esa)],[c_8]) ).
cnf(c11,plain,
( ~ element(X1,X0)
| ~ element(X0,X1)
| equalish(X1,X0)
| equalish(X1,m)
| equalish(X0,m)
| element(X0,m) ),
inference(clausification,[status(esa)],[c_9]) ).
cnf(c18,plain,
( equalish(X0,k)
| element(X0,k)
| ~ equalish(X0,n) ),
inference(clausification,[status(esa)],[c_16]) ).
cnf(c19,plain,
( equalish(X0,k)
| equalish(X0,m)
| equalish(X0,n)
| ~ element(X0,k) ),
inference(clausification,[status(esa)],[c_17]) ).
cnf(c22,plain,
~ equalish(n,k),
inference(clausification,[status(esa)],[c_20]) ).
cnf(c25,plain,
equalish(m,k),
inference(clausification,[status(esa)],[c_23]) ).
cnf(d0,plain,
( ~ equalish(X0,m)
| equalish(X0,k) ),
inference(resolution,[status(thm)],[c25,c2]) ).
cnf(d1,plain,
equalish(k,m),
inference(resolution,[status(thm)],[c25,c1]) ).
cnf(d2,plain,
( ~ equalish(X0,k)
| equalish(X0,m) ),
inference(resolution,[status(thm)],[d1,c2]) ).
cnf(d3,plain,
( element(n,k)
| equalish(n,k) ),
inference(resolution,[status(thm)],[c18,c0]) ).
cnf(d4,plain,
element(n,k),
inference(resolution,[status(thm)],[c22,d3]) ).
cnf(d5,plain,
( element(n,X0)
| ~ equalish(k,X0) ),
inference(resolution,[status(thm)],[d4,c3]) ).
cnf(d6,plain,
element(n,m),
inference(resolution,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
( element(X0,m)
| ~ equalish(n,X0) ),
inference(resolution,[status(thm)],[d6,c4]) ).
cnf(d8,plain,
( ~ element(X0,m)
| equalish(X0,m)
| element(f(X0),m)
| ~ element(f(X0),X0)
| equalish(X0,m)
| equalish(X0,f(X0))
| equalish(f(X0),m) ),
inference(resolution,[status(thm)],[c11,c9]) ).
cnf(d9,plain,
( ~ element(X0,m)
| equalish(X0,m)
| element(f(X0),m)
| ~ element(X0,m)
| equalish(f(X0),m)
| equalish(X0,m)
| equalish(X0,f(X0)) ),
inference(resolution,[status(thm)],[d8,c10]) ).
cnf(d10,plain,
( element(f(n),m)
| element(f(n),m)
| ~ element(n,m)
| equalish(f(n),m)
| equalish(n,m) ),
inference(resolution,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
( element(f(n),m)
| equalish(n,m)
| equalish(f(n),m) ),
inference(resolution,[status(thm)],[d6,d10]) ).
cnf(d12,plain,
( element(f(n),X0)
| ~ equalish(m,X0)
| equalish(n,m)
| equalish(f(n),m) ),
inference(resolution,[status(thm)],[d11,c3]) ).
cnf(d13,plain,
( equalish(f(n),n)
| equalish(f(n),m)
| equalish(f(n),k)
| equalish(n,m)
| ~ equalish(m,k)
| equalish(f(n),m) ),
inference(resolution,[status(thm)],[d12,c19]) ).
cnf(d14,plain,
( equalish(n,m)
| equalish(f(n),n)
| equalish(f(n),m)
| equalish(f(n),k) ),
inference(resolution,[status(thm)],[c25,d13]) ).
cnf(d15,plain,
( equalish(f(n),m)
| equalish(n,m)
| equalish(f(n),n)
| equalish(f(n),m) ),
inference(resolution,[status(thm)],[d14,d2]) ).
cnf(d16,plain,
( ~ element(n,m)
| equalish(n,m)
| equalish(n,m)
| equalish(f(n),m) ),
inference(resolution,[status(thm)],[d15,c8]) ).
cnf(d17,plain,
( equalish(n,m)
| equalish(f(n),m) ),
inference(resolution,[status(thm)],[d6,d16]) ).
cnf(d18,plain,
( ~ element(n,m)
| equalish(n,m)
| equalish(n,m) ),
inference(resolution,[status(thm)],[d17,c7]) ).
cnf(d19,plain,
equalish(n,m),
inference(resolution,[status(thm)],[d6,d18]) ).
cnf(d20,plain,
equalish(n,k),
inference(resolution,[status(thm)],[d19,d0]) ).
cnf(d21,plain,
$false,
inference(resolution,[status(thm)],[c22,d20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN015-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n018.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 17:06:37 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.72/4.67 % SZS status Unsatisfiable for theBenchmark.p
% 3.72/4.67 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------