%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SYN013-1 : 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 : n013.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 09:20:41 AM UTC 2026
% Result : Unsatisfiable 4.22s 3.49s
% Output : CNFRefutation 4.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 15
% Syntax : Number of clauses : 93 ( 10 unt; 78 nHn; 88 RR)
% Number of literals : 493 ( 379 equ; 81 neg)
% Maximal clause size : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 35 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c_1,negated_conjecture,
m != n ).
cnf(c_2,negated_conjecture,
n != k ).
cnf(c_3,negated_conjecture,
k != m ).
cnf(c_4,negated_conjecture,
( f(X0) != m
| ~ element(X0,m)
| X0 = m ) ).
cnf(c_5,negated_conjecture,
( f(X0) != X0
| ~ element(X0,m)
| X0 = m ) ).
cnf(c_6,negated_conjecture,
( element(X0,f(X0))
| ~ element(X0,m)
| X0 = m ) ).
cnf(c_7,negated_conjecture,
( element(f(X0),X0)
| ~ element(X0,m)
| X0 = m ) ).
cnf(c_8,negated_conjecture,
( ~ element(X1,X0)
| ~ element(X0,X1)
| X1 = X0
| X1 = m
| element(X0,m)
| X0 = m ) ).
cnf(c_10,negated_conjecture,
( g(X0) != X0
| element(X0,n)
| X0 = n ) ).
cnf(c_11,negated_conjecture,
( element(X0,g(X0))
| element(X0,n)
| X0 = n ) ).
cnf(c_12,negated_conjecture,
( element(g(X0),X0)
| element(X0,n)
| X0 = n ) ).
cnf(c_13,negated_conjecture,
( ~ element(X1,X0)
| ~ element(X0,X1)
| X1 = X0
| X1 = n
| ~ element(X0,n)
| X0 = n ) ).
cnf(c_14,negated_conjecture,
( element(X0,k)
| X0 != m
| X0 = k ) ).
cnf(c_15,negated_conjecture,
( element(X0,k)
| X0 != n
| X0 = k ) ).
cnf(c_16,negated_conjecture,
( ~ element(X0,k)
| X0 = n
| X0 = m
| X0 = k ) ).
cnf(c0,plain,
m != n,
inference(clausification,[status(esa)],[c_1]) ).
cnf(c1,plain,
n != k,
inference(clausification,[status(esa)],[c_2]) ).
cnf(c2,plain,
k != m,
inference(clausification,[status(esa)],[c_3]) ).
cnf(c3,plain,
( f(X0) != m
| ~ element(X0,m)
| X0 = m ),
inference(clausification,[status(esa)],[c_4]) ).
cnf(c4,plain,
( f(X0) != X0
| ~ element(X0,m)
| X0 = m ),
inference(clausification,[status(esa)],[c_5]) ).
cnf(c5,plain,
( element(X0,f(X0))
| ~ element(X0,m)
| X0 = m ),
inference(clausification,[status(esa)],[c_6]) ).
cnf(c6,plain,
( element(f(X0),X0)
| ~ element(X0,m)
| X0 = m ),
inference(clausification,[status(esa)],[c_7]) ).
cnf(c7,plain,
( ~ element(X1,X0)
| X1 = m
| element(X1,m)
| X0 = m
| ~ element(X0,X1)
| X0 = X1 ),
inference(clausification,[status(esa)],[c_8]) ).
cnf(c9,plain,
( g(X0) != X0
| element(X0,n)
| X0 = n ),
inference(clausification,[status(esa)],[c_10]) ).
cnf(c10,plain,
( element(X0,g(X0))
| element(X0,n)
| X0 = n ),
inference(clausification,[status(esa)],[c_11]) ).
cnf(c11,plain,
( element(g(X0),X0)
| element(X0,n)
| X0 = n ),
inference(clausification,[status(esa)],[c_12]) ).
cnf(c12,plain,
( X1 = n
| ~ element(X1,X0)
| ~ element(X0,n)
| X1 = X0
| ~ element(X0,X1)
| X0 = n ),
inference(clausification,[status(esa)],[c_13]) ).
cnf(c13,plain,
( element(X0,k)
| X0 != m
| X0 = k ),
inference(clausification,[status(esa)],[c_14]) ).
cnf(c14,plain,
( element(X0,k)
| X0 != n
| X0 = k ),
inference(clausification,[status(esa)],[c_15]) ).
cnf(c15,plain,
( ~ element(X0,k)
| X0 = n
| X0 = m
| X0 = k ),
inference(clausification,[status(esa)],[c_16]) ).
cnf(d0,plain,
( element(m,k)
| m = k ),
inference(equality_resolution,[status(thm)],[c13]) ).
cnf(d1,plain,
( element(k,n)
| k = n
| g(k) = k
| g(k) = n
| g(k) = m ),
inference(resolution,[status(thm)],[c15,c11]) ).
cnf(d2,plain,
( ~ element(k,X0)
| ~ element(X0,k)
| k = n
| X0 = n
| X0 = k
| g(k) = k
| g(k) = n
| g(k) = m
| k = n ),
inference(resolution,[status(thm)],[d1,c12]) ).
cnf(d3,plain,
( element(k,m)
| ~ element(n,k)
| k = m
| n = m
| n = k
| g(k) = k
| g(k) = n
| g(k) = m
| k = n ),
inference(resolution,[status(thm)],[d1,c7]) ).
cnf(d4,plain,
( element(k,m)
| ~ element(n,k)
| g(k) = k
| g(k) = n
| g(k) = m
| k = n
| k = m
| n = m ),
inference(resolution,[status(thm)],[c1,d3]) ).
cnf(d5,plain,
( element(k,m)
| ~ element(n,k)
| g(k) = k
| g(k) = n
| g(k) = m
| k = n
| n = m ),
inference(resolution,[status(thm)],[c2,d4]) ).
cnf(d6,plain,
( element(n,k)
| n = k ),
inference(equality_resolution,[status(thm)],[c14]) ).
cnf(d7,plain,
element(n,k),
inference(resolution,[status(thm)],[c1,d6]) ).
cnf(d8,plain,
( element(k,m)
| g(k) = k
| g(k) = n
| g(k) = m
| k = n
| n = m ),
inference(resolution,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
( ~ element(m,k)
| g(k) = k
| g(k) = n
| g(k) = m
| k = n
| m = k
| m = n
| g(k) = k
| g(k) = n
| g(k) = m
| k = n
| n = m ),
inference(resolution,[status(thm)],[d8,d2]) ).
cnf(d10,plain,
( ~ element(m,k)
| g(k) = k
| g(k) = n
| g(k) = m
| k = n
| n = m
| m = k ),
inference(resolution,[status(thm)],[c0,d9]) ).
cnf(d11,plain,
( m = k
| g(k) = k
| g(k) = n
| g(k) = m
| k = n
| n = m
| m = k ),
inference(resolution,[status(thm)],[d10,d0]) ).
cnf(d12,plain,
( g(k) = n
| g(k) = m
| k = n
| n = m
| m = k
| element(k,n)
| k = n
| k != k ),
inference(superposition,[status(thm)],[d11,c9]) ).
cnf(d13,plain,
( element(k,n)
| g(k) = n
| g(k) = m
| k = n
| n = m
| m = k ),
inference(equality_resolution,[status(thm)],[d12]) ).
cnf(d14,plain,
( ~ element(k,X0)
| ~ element(X0,k)
| k = n
| X0 = n
| X0 = k
| g(k) = n
| g(k) = m
| k = n
| n = m
| m = k ),
inference(resolution,[status(thm)],[d13,c12]) ).
cnf(d15,plain,
( element(k,m)
| ~ element(n,k)
| k = m
| n = m
| n = k
| g(k) = n
| g(k) = m
| k = n
| n = m
| m = k ),
inference(resolution,[status(thm)],[d13,c7]) ).
cnf(d16,plain,
( element(k,m)
| ~ element(n,k)
| g(k) = n
| g(k) = m
| k = n
| k = m
| n = m
| m = k ),
inference(resolution,[status(thm)],[c1,d15]) ).
cnf(d17,plain,
( element(k,m)
| ~ element(n,k)
| g(k) = n
| g(k) = m
| k = n
| n = m
| m = k ),
inference(resolution,[status(thm)],[c2,d16]) ).
cnf(d18,plain,
( element(k,m)
| g(k) = n
| g(k) = m
| k = n
| n = m
| m = k ),
inference(resolution,[status(thm)],[d7,d17]) ).
cnf(d19,plain,
( ~ element(m,k)
| g(k) = n
| g(k) = m
| k = n
| n = m
| m = k
| m = k
| m = n
| g(k) = n
| g(k) = m
| k = n
| n = m
| m = k ),
inference(resolution,[status(thm)],[d18,d14]) ).
cnf(d20,plain,
( ~ element(m,k)
| g(k) = n
| g(k) = m
| k = n
| n = m
| m = k ),
inference(resolution,[status(thm)],[c0,d19]) ).
cnf(d21,plain,
( m = k
| g(k) = n
| g(k) = m
| k = n
| n = m
| m = k ),
inference(resolution,[status(thm)],[d20,d0]) ).
cnf(d22,plain,
( element(X0,m)
| ~ element(g(X0),X0)
| X0 = m
| g(X0) = m
| g(X0) = X0
| element(X0,n)
| X0 = n ),
inference(resolution,[status(thm)],[c10,c7]) ).
cnf(d23,plain,
( element(X0,n)
| X0 = n
| element(X0,n)
| element(X0,m)
| g(X0) = m
| g(X0) = X0
| X0 = n
| X0 = m ),
inference(resolution,[status(thm)],[d22,c11]) ).
cnf(d24,plain,
( element(X0,m)
| ~ element(n,X0)
| X0 = m
| n = m
| n = X0
| element(X0,m)
| g(X0) = m
| g(X0) = X0
| X0 = n
| X0 = m ),
inference(resolution,[status(thm)],[d23,c7]) ).
cnf(d25,plain,
( element(k,m)
| g(k) = m
| g(k) = k
| n = m
| n = k
| k = n
| k = m ),
inference(resolution,[status(thm)],[d24,d7]) ).
cnf(d26,plain,
( element(k,m)
| g(k) = k
| g(k) = m
| k = n
| k = m
| n = m ),
inference(resolution,[status(thm)],[c1,d25]) ).
cnf(d27,plain,
( element(k,m)
| g(k) = k
| g(k) = m
| k = n
| n = m ),
inference(resolution,[status(thm)],[c2,d26]) ).
cnf(d28,plain,
( g(k) = m
| k = n
| n = m
| m = k
| element(k,n)
| k = n
| element(k,n) ),
inference(superposition,[status(thm)],[d21,c10]) ).
cnf(d29,plain,
( ~ element(k,X0)
| ~ element(X0,k)
| k = n
| X0 = n
| X0 = k
| g(k) = m
| k = n
| n = m
| m = k ),
inference(resolution,[status(thm)],[d28,c12]) ).
cnf(d30,plain,
( g(k) = k
| g(k) = m
| k = n
| n = m
| ~ element(m,k)
| g(k) = m
| k = n
| n = m
| m = k
| m = k
| m = n ),
inference(resolution,[status(thm)],[d29,d27]) ).
cnf(d31,plain,
( ~ element(m,k)
| g(k) = k
| g(k) = m
| k = n
| n = m
| m = k ),
inference(resolution,[status(thm)],[c0,d30]) ).
cnf(d32,plain,
( m = k
| g(k) = k
| g(k) = m
| k = n
| n = m
| m = k ),
inference(resolution,[status(thm)],[d31,d0]) ).
cnf(d33,plain,
( g(k) = m
| k = n
| n = m
| m = k
| g(k) = m
| k = n
| n = m
| m = k
| k = n ),
inference(superposition,[status(thm)],[d32,d21]) ).
cnf(d34,plain,
( k = n
| n = m
| m = k
| element(k,n)
| k = n
| element(k,m) ),
inference(superposition,[status(thm)],[d33,c10]) ).
cnf(d35,plain,
( element(k,m)
| ~ element(n,k)
| k = m
| n = m
| n = k
| element(k,m)
| k = n
| n = m
| m = k ),
inference(resolution,[status(thm)],[d34,c7]) ).
cnf(d36,plain,
( element(k,m)
| ~ element(n,k)
| k = n
| k = m
| n = m
| m = k ),
inference(resolution,[status(thm)],[c1,d35]) ).
cnf(d37,plain,
( element(k,m)
| ~ element(n,k)
| k = n
| n = m
| m = k ),
inference(resolution,[status(thm)],[c2,d36]) ).
cnf(d38,plain,
( element(k,m)
| k = n
| n = m
| m = k ),
inference(resolution,[status(thm)],[d7,d37]) ).
cnf(d39,plain,
( ~ element(k,m)
| k = m
| f(k) = k
| f(k) = n
| f(k) = m ),
inference(resolution,[status(thm)],[c15,c6]) ).
cnf(d40,plain,
( ~ element(k,m)
| f(k) = k
| f(k) = n
| f(k) = m ),
inference(resolution,[status(thm)],[c2,d39]) ).
cnf(d41,plain,
( f(k) = k
| f(k) = n
| f(k) = m
| k = n
| n = m
| m = k ),
inference(resolution,[status(thm)],[d38,d40]) ).
cnf(d42,plain,
( f(k) = n
| f(k) = m
| k = n
| n = m
| m = k
| ~ element(k,m)
| k = m
| k != k ),
inference(superposition,[status(thm)],[d41,c4]) ).
cnf(d43,plain,
( ~ element(k,m)
| f(k) = n
| f(k) = m
| k != k
| k = n
| n = m
| m = k ),
inference(resolution,[status(thm)],[c2,d42]) ).
cnf(d44,plain,
( ~ element(k,m)
| f(k) = n
| f(k) = m
| k = n
| n = m
| m = k ),
inference(equality_resolution,[status(thm)],[d43]) ).
cnf(d45,plain,
( k = n
| n = m
| m = k
| f(k) = n
| f(k) = m
| k = n
| n = m
| m = k ),
inference(resolution,[status(thm)],[d44,d38]) ).
cnf(d46,plain,
( f(k) = m
| k = n
| n = m
| m = k
| ~ element(k,m)
| k = m
| element(k,n) ),
inference(superposition,[status(thm)],[d45,c5]) ).
cnf(d47,plain,
( element(k,n)
| ~ element(k,m)
| f(k) = m
| k = n
| n = m
| m = k ),
inference(resolution,[status(thm)],[c2,d46]) ).
cnf(d48,plain,
( k = n
| n = m
| m = k
| element(k,n)
| f(k) = m
| k = n
| n = m
| m = k ),
inference(resolution,[status(thm)],[d47,d38]) ).
cnf(d49,plain,
( ~ element(k,X0)
| ~ element(X0,k)
| k = n
| X0 = n
| X0 = k
| f(k) = m
| k = n
| n = m
| m = k ),
inference(resolution,[status(thm)],[d48,c12]) ).
cnf(d50,plain,
( k = n
| n = m
| m = k
| ~ element(m,k)
| f(k) = m
| k = n
| n = m
| m = k
| m = k
| m = n ),
inference(resolution,[status(thm)],[d49,d38]) ).
cnf(d51,plain,
( ~ element(m,k)
| f(k) = m
| k = n
| n = m
| m = k ),
inference(resolution,[status(thm)],[c0,d50]) ).
cnf(d52,plain,
( m = k
| f(k) = m
| k = n
| n = m
| m = k ),
inference(resolution,[status(thm)],[d51,d0]) ).
cnf(d53,plain,
( k = n
| n = m
| m = k
| ~ element(k,m)
| k = m
| m != m ),
inference(superposition,[status(thm)],[d52,c3]) ).
cnf(d54,plain,
( ~ element(k,m)
| k = n
| n = m
| m = k
| m != m ),
inference(resolution,[status(thm)],[c2,d53]) ).
cnf(d55,plain,
( ~ element(k,m)
| k = n
| n = m
| m = k ),
inference(equality_resolution,[status(thm)],[d54]) ).
cnf(d56,plain,
( k = n
| n = m
| m = k
| k = n
| n = m
| m = k ),
inference(resolution,[status(thm)],[d55,d38]) ).
cnf(d57,plain,
( n = m
| m = k
| n != n ),
inference(superposition,[status(thm)],[d56,c1]) ).
cnf(d58,plain,
( n = m
| m = k ),
inference(equality_resolution,[status(thm)],[d57]) ).
cnf(d59,plain,
( n = m
| m != m ),
inference(superposition,[status(thm)],[d58,c2]) ).
cnf(d60,plain,
n = m,
inference(equality_resolution,[status(thm)],[d59]) ).
cnf(d61,plain,
m != m,
inference(demodulation,[status(thm)],[c0,d60]) ).
cnf(d62,plain,
$false,
inference(equality_resolution,[status(thm)],[d61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN013-1 : 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 : n013.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 17:03:37 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.22/3.49 % SZS status Unsatisfiable for theBenchmark.p
% 4.22/3.49 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------