%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SYN015-1 : 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 : 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 09:20:41 AM UTC 2026
% Result : Unsatisfiable 14.27s 2.51s
% Output : CNFRefutation 14.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 86
% Number of leaves : 15
% Syntax : Number of clauses : 132 ( 4 unt; 124 nHn; 127 RR)
% Number of literals : 858 ( 724 equ; 102 neg)
% Maximal clause size : 17 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 46 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c_1,negated_conjecture,
m != n ).
cnf(c_2,negated_conjecture,
( element(X0,j)
| X0 != k
| X0 = j ) ).
cnf(c_3,negated_conjecture,
( ~ element(X0,j)
| X0 = k
| X0 = j ) ).
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,
( element(X0,j)
| X0 != k
| X0 = j ),
inference(clausification,[status(esa)],[c_2]) ).
cnf(c2,plain,
( ~ element(X0,j)
| X0 = k
| X0 = j ),
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,
( X1 = m
| ~ element(X0,X1)
| X1 = X0
| X0 = m
| ~ element(X1,X0)
| element(X0,m) ),
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(X0,n)
| X1 = X0
| ~ element(X1,X0)
| X0 = n
| ~ element(X0,X1) ),
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(n,k)
| n = k ),
inference(equality_resolution,[status(thm)],[c14]) ).
cnf(d2,plain,
( element(X0,n)
| X0 = n
| element(X0,m)
| ~ element(g(X0),X0)
| X0 = m
| g(X0) = m
| g(X0) = X0 ),
inference(resolution,[status(thm)],[c7,c10]) ).
cnf(d3,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)],[d2,c11]) ).
cnf(d4,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)],[d3,c7]) ).
cnf(d5,plain,
( n = k
| element(k,m)
| g(k) = m
| g(k) = k
| n = m
| n = k
| k = n
| k = m ),
inference(resolution,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
( element(k,n)
| k = n
| g(k) = k
| g(k) = n
| g(k) = m ),
inference(resolution,[status(thm)],[c15,c11]) ).
cnf(d7,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)],[d6,c12]) ).
cnf(d8,plain,
( g(k) = k
| g(k) = m
| k = n
| k = m
| n = k
| n = m
| ~ element(m,k)
| g(k) = k
| g(k) = n
| g(k) = m
| k = n
| m = k
| m = n ),
inference(resolution,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
( ~ element(m,k)
| g(k) = k
| g(k) = n
| g(k) = m
| k = n
| k = m
| n = k
| n = m
| m = k ),
inference(resolution,[status(thm)],[c0,d8]) ).
cnf(d10,plain,
( m = k
| g(k) = k
| g(k) = n
| g(k) = m
| k = n
| k = m
| n = k
| n = m
| m = k ),
inference(resolution,[status(thm)],[d9,d0]) ).
cnf(d11,plain,
( g(k) = n
| g(k) = m
| k = n
| k = m
| n = k
| n = m
| m = k
| element(k,n)
| k = n
| k != k ),
inference(superposition,[status(thm)],[d10,c9]) ).
cnf(d12,plain,
( element(k,n)
| g(k) = n
| g(k) = m
| k = n
| k = m
| n = k
| n = m
| m = k ),
inference(equality_resolution,[status(thm)],[d11]) ).
cnf(d13,plain,
( element(k,m)
| ~ element(n,k)
| k = m
| n = m
| n = k
| g(k) = n
| g(k) = m
| k = n
| k = m
| n = k
| n = m
| m = k ),
inference(resolution,[status(thm)],[d12,c7]) ).
cnf(d14,plain,
( n = k
| element(k,m)
| g(k) = n
| g(k) = m
| k = n
| k = m
| n = k
| n = m
| m = k ),
inference(resolution,[status(thm)],[d13,d1]) ).
cnf(d15,plain,
( ~ element(k,X0)
| ~ element(X0,k)
| k = n
| X0 = n
| X0 = k
| g(k) = n
| g(k) = m
| k = n
| k = m
| n = k
| n = m
| m = k ),
inference(resolution,[status(thm)],[d12,c12]) ).
cnf(d16,plain,
( g(k) = n
| g(k) = m
| k = n
| k = m
| n = k
| n = m
| m = k
| ~ element(m,k)
| g(k) = n
| g(k) = m
| k = n
| k = m
| n = k
| n = m
| m = k
| m = k
| m = n ),
inference(resolution,[status(thm)],[d15,d14]) ).
cnf(d17,plain,
( ~ element(m,k)
| g(k) = n
| g(k) = m
| k = n
| k = m
| n = k
| n = m
| m = k ),
inference(resolution,[status(thm)],[c0,d16]) ).
cnf(d18,plain,
( m = k
| g(k) = n
| g(k) = m
| k = n
| k = m
| n = k
| n = m
| m = k ),
inference(resolution,[status(thm)],[d17,d0]) ).
cnf(d19,plain,
( g(k) = m
| k = n
| k = m
| n = k
| n = m
| m = k
| element(k,n)
| k = n
| element(k,n) ),
inference(superposition,[status(thm)],[d18,c10]) ).
cnf(d20,plain,
( element(k,m)
| ~ element(n,k)
| k = m
| n = m
| n = k
| g(k) = m
| k = n
| k = m
| n = k
| n = m
| m = k ),
inference(resolution,[status(thm)],[d19,c7]) ).
cnf(d21,plain,
( n = k
| element(k,m)
| g(k) = m
| k = n
| k = m
| n = k
| n = m
| m = k ),
inference(resolution,[status(thm)],[d20,d1]) ).
cnf(d22,plain,
( ~ element(k,X0)
| ~ element(X0,k)
| k = n
| X0 = n
| X0 = k
| g(k) = m
| k = n
| k = m
| n = k
| n = m
| m = k ),
inference(resolution,[status(thm)],[d19,c12]) ).
cnf(d23,plain,
( g(k) = m
| k = n
| k = m
| n = k
| n = m
| m = k
| ~ element(m,k)
| g(k) = m
| k = n
| k = m
| n = k
| n = m
| m = k
| m = k
| m = n ),
inference(resolution,[status(thm)],[d22,d21]) ).
cnf(d24,plain,
( ~ element(m,k)
| g(k) = m
| k = n
| k = m
| n = k
| n = m
| m = k ),
inference(resolution,[status(thm)],[c0,d23]) ).
cnf(d25,plain,
( m = k
| g(k) = m
| k = n
| k = m
| n = k
| n = m
| m = k ),
inference(resolution,[status(thm)],[d24,d0]) ).
cnf(d26,plain,
( k = n
| k = m
| n = k
| n = m
| m = k
| element(k,n)
| k = n
| element(k,m) ),
inference(superposition,[status(thm)],[d25,c10]) ).
cnf(d27,plain,
( element(k,m)
| ~ element(n,k)
| k = m
| n = m
| n = k
| element(k,m)
| k = n
| k = m
| n = k
| n = m
| m = k ),
inference(resolution,[status(thm)],[d26,c7]) ).
cnf(d28,plain,
( n = k
| element(k,m)
| k = n
| k = m
| n = k
| n = m
| m = k ),
inference(resolution,[status(thm)],[d27,d1]) ).
cnf(d29,plain,
( ~ element(k,m)
| k = m
| f(k) = k
| f(k) = n
| f(k) = m ),
inference(resolution,[status(thm)],[c15,c6]) ).
cnf(d30,plain,
( f(k) = k
| f(k) = n
| f(k) = m
| k = m
| k = n
| k = m
| n = k
| n = m
| m = k ),
inference(resolution,[status(thm)],[d28,d29]) ).
cnf(d31,plain,
( f(k) = n
| f(k) = m
| k = n
| k = m
| n = k
| n = m
| m = k
| ~ element(k,m)
| k = m
| k != k ),
inference(superposition,[status(thm)],[d30,c4]) ).
cnf(d32,plain,
( ~ element(k,m)
| f(k) = n
| f(k) = m
| k = n
| k = m
| n = k
| n = m
| m = k ),
inference(equality_resolution,[status(thm)],[d31]) ).
cnf(d33,plain,
( k = n
| k = m
| n = k
| n = m
| m = k
| f(k) = n
| f(k) = m
| k = n
| k = m
| n = k
| n = m
| m = k ),
inference(resolution,[status(thm)],[d32,d28]) ).
cnf(d34,plain,
( f(k) = m
| k = n
| k = m
| n = k
| n = m
| m = k
| ~ element(k,m)
| k = m
| element(k,n) ),
inference(superposition,[status(thm)],[d33,c5]) ).
cnf(d35,plain,
( k = n
| k = m
| n = k
| n = m
| m = k
| element(k,n)
| f(k) = m
| k = n
| k = m
| n = k
| n = m
| m = k ),
inference(resolution,[status(thm)],[d34,d28]) ).
cnf(d36,plain,
( ~ element(k,X0)
| ~ element(X0,k)
| k = n
| X0 = n
| X0 = k
| f(k) = m
| k = n
| k = m
| n = k
| n = m
| m = k ),
inference(resolution,[status(thm)],[d35,c12]) ).
cnf(d37,plain,
( k = n
| k = m
| n = k
| n = m
| m = k
| ~ element(m,k)
| f(k) = m
| k = n
| k = m
| n = k
| n = m
| m = k
| m = k
| m = n ),
inference(resolution,[status(thm)],[d36,d28]) ).
cnf(d38,plain,
( ~ element(m,k)
| f(k) = m
| k = n
| k = m
| n = k
| n = m
| m = k ),
inference(resolution,[status(thm)],[c0,d37]) ).
cnf(d39,plain,
( m = k
| f(k) = m
| k = n
| k = m
| n = k
| n = m
| m = k ),
inference(resolution,[status(thm)],[d38,d0]) ).
cnf(d40,plain,
( k = n
| k = m
| n = k
| n = m
| m = k
| ~ element(k,m)
| k = m
| m != m ),
inference(superposition,[status(thm)],[d39,c3]) ).
cnf(d41,plain,
( ~ element(k,m)
| k = n
| k = m
| n = k
| n = m
| m = k ),
inference(equality_resolution,[status(thm)],[d40]) ).
cnf(d42,plain,
( k = n
| k = m
| n = k
| n = m
| m = k
| k = n
| k = m
| n = k
| n = m
| m = k ),
inference(resolution,[status(thm)],[d41,d28]) ).
cnf(d43,plain,
( k = n
| k = m
| n = m
| m = k
| n != n ),
inference(equality_factoring,[status(thm)],[d42]) ).
cnf(d44,plain,
( k = n
| k = m
| n = m
| m = k ),
inference(equality_resolution,[status(thm)],[d43]) ).
cnf(d45,plain,
( k = m
| n = m
| m = k
| m = k
| element(m,n) ),
inference(superposition,[status(thm)],[d44,d0]) ).
cnf(d46,plain,
( k = m
| n = m
| m = k
| X0 = k
| X0 = n
| X0 = m
| ~ element(X0,n) ),
inference(superposition,[status(thm)],[d44,c15]) ).
cnf(d47,plain,
( g(j) = j
| g(j) = k
| element(j,n)
| j = n ),
inference(resolution,[status(thm)],[c11,c2]) ).
cnf(d48,plain,
( g(j) = j
| g(j) = k
| j = n
| k = m
| n = m
| m = k
| j = k
| j = n
| j = m ),
inference(resolution,[status(thm)],[d46,d47]) ).
cnf(d49,plain,
( g(j) = k
| j = k
| j = n
| j = m
| k = m
| n = m
| m = k
| element(j,n)
| j = n
| j != j ),
inference(superposition,[status(thm)],[d48,c9]) ).
cnf(d50,plain,
( element(j,n)
| g(j) = k
| j = k
| j = n
| j = m
| k = m
| n = m
| m = k ),
inference(equality_resolution,[status(thm)],[d49]) ).
cnf(d51,plain,
( k = m
| n = m
| m = k
| j = k
| j = n
| j = m
| g(j) = k
| j = k
| j = n
| j = m
| k = m
| n = m
| m = k ),
inference(resolution,[status(thm)],[d50,d46]) ).
cnf(d52,plain,
( j = k
| j = n
| j = m
| k = m
| n = m
| m = k
| element(j,n)
| j = n
| element(j,k) ),
inference(superposition,[status(thm)],[d51,c10]) ).
cnf(d53,plain,
( j = k
| j = n
| j = m
| element(j,n)
| j = k
| j = n
| j = m
| k = m
| n = m
| m = k ),
inference(resolution,[status(thm)],[d52,c15]) ).
cnf(d54,plain,
( k = m
| n = m
| m = k
| j = k
| j = n
| j = m
| j = k
| j = n
| j = m
| k = m
| n = m
| m = k ),
inference(resolution,[status(thm)],[d53,d46]) ).
cnf(d55,plain,
( j = n
| j = m
| k = m
| n = m
| m = k
| X0 = j
| X0 = k
| ~ element(X0,k) ),
inference(superposition,[status(thm)],[d54,c2]) ).
cnf(d56,plain,
( m = k
| j = n
| j = m
| k = m
| n = m
| m = k
| m = j
| m = k ),
inference(resolution,[status(thm)],[d55,d0]) ).
cnf(d57,plain,
( j = m
| k = m
| n = m
| m = j
| m = k
| X0 = j
| X0 = k
| ~ element(X0,n) ),
inference(superposition,[status(thm)],[d56,c2]) ).
cnf(d58,plain,
( k = m
| n = m
| m = k
| j = m
| k = m
| n = m
| m = j
| m = k
| m = j
| m = k ),
inference(resolution,[status(thm)],[d57,d45]) ).
cnf(d59,plain,
( j = m
| k = m
| n = m
| m = k
| m != m ),
inference(equality_factoring,[status(thm)],[d58]) ).
cnf(d60,plain,
( j = m
| k = m
| n = m
| m = k ),
inference(equality_resolution,[status(thm)],[d59]) ).
cnf(d61,plain,
( element(k,j)
| k = j ),
inference(equality_resolution,[status(thm)],[c1]) ).
cnf(d62,plain,
( k = m
| n = m
| m = k
| k = j
| element(n,j) ),
inference(superposition,[status(thm)],[d44,d61]) ).
cnf(d63,plain,
( k = m
| n = m
| m = k
| k = j
| k = m
| n = m
| m = k
| element(n,m) ),
inference(superposition,[status(thm)],[d60,d62]) ).
cnf(d64,plain,
( k = m
| n = m
| m = k
| k = j
| element(k,m) ),
inference(superposition,[status(thm)],[d60,d61]) ).
cnf(d65,plain,
( f(k) = k
| f(k) = n
| f(k) = m
| k = m
| k = j
| k = m
| n = m
| m = k ),
inference(resolution,[status(thm)],[d64,d29]) ).
cnf(d66,plain,
( f(k) = n
| f(k) = m
| k = j
| k = m
| n = m
| m = k
| ~ element(k,m)
| k = m
| k != k ),
inference(superposition,[status(thm)],[d65,c4]) ).
cnf(d67,plain,
( ~ element(k,m)
| f(k) = n
| f(k) = m
| k = j
| k = m
| n = m
| m = k ),
inference(equality_resolution,[status(thm)],[d66]) ).
cnf(d68,plain,
( k = j
| k = m
| n = m
| m = k
| f(k) = n
| f(k) = m
| k = j
| k = m
| n = m
| m = k ),
inference(resolution,[status(thm)],[d67,d64]) ).
cnf(d69,plain,
( k = m
| n = m
| m = k
| f(k) = m
| k = j
| k = m
| n = m
| m = k
| f(n) = n ),
inference(superposition,[status(thm)],[d44,d68]) ).
cnf(d70,plain,
( f(n) = n
| k = j
| k = m
| n = m
| m = k
| ~ element(k,m)
| k = m
| m != m ),
inference(superposition,[status(thm)],[d69,c3]) ).
cnf(d71,plain,
( ~ element(k,m)
| f(n) = n
| k = j
| k = m
| n = m
| m = k ),
inference(equality_resolution,[status(thm)],[d70]) ).
cnf(d72,plain,
( k = j
| k = m
| n = m
| m = k
| f(n) = n
| k = j
| k = m
| n = m
| m = k ),
inference(resolution,[status(thm)],[d71,d64]) ).
cnf(d73,plain,
( k = j
| k = m
| n = m
| m = k
| ~ element(n,m)
| n = m
| n != n ),
inference(superposition,[status(thm)],[d72,c4]) ).
cnf(d74,plain,
( ~ element(n,m)
| k = j
| k = m
| n = m
| m = k ),
inference(equality_resolution,[status(thm)],[d73]) ).
cnf(d75,plain,
( k = j
| k = m
| n = m
| m = k
| k = j
| k = m
| n = m
| m = k ),
inference(resolution,[status(thm)],[d74,d63]) ).
cnf(d76,plain,
( k = m
| n = m
| m = k
| k = m
| n = m
| m = k
| k = m ),
inference(superposition,[status(thm)],[d75,d60]) ).
cnf(d77,plain,
( k = m
| n = m
| m != m ),
inference(equality_factoring,[status(thm)],[d76]) ).
cnf(d78,plain,
( k = m
| n = m ),
inference(equality_resolution,[status(thm)],[d77]) ).
cnf(d79,plain,
( n = m
| n = k
| element(n,m) ),
inference(superposition,[status(thm)],[d78,d1]) ).
cnf(d80,plain,
( ~ element(X0,m)
| X0 = m
| element(f(X0),m)
| ~ element(X0,f(X0))
| f(X0) = m
| X0 = m
| X0 = f(X0) ),
inference(resolution,[status(thm)],[c7,c6]) ).
cnf(d81,plain,
( ~ element(X0,m)
| X0 = m
| element(f(X0),m)
| ~ element(X0,m)
| f(X0) = m
| X0 = f(X0)
| X0 = m ),
inference(resolution,[status(thm)],[d80,c5]) ).
cnf(d82,plain,
( n = m
| X0 = k
| X0 = n
| X0 = m
| ~ element(X0,m) ),
inference(superposition,[status(thm)],[d78,c15]) ).
cnf(d83,plain,
( ~ element(X0,m)
| f(X0) = m
| X0 = f(X0)
| X0 = m
| n = m
| f(X0) = k
| f(X0) = n
| f(X0) = m ),
inference(resolution,[status(thm)],[d82,d81]) ).
cnf(d84,plain,
( n = k
| n = m
| f(n) = k
| f(n) = n
| f(n) = m
| n = m
| n = f(n)
| n = m ),
inference(resolution,[status(thm)],[d83,d79]) ).
cnf(d85,plain,
( f(n) = n
| f(n) = m
| n = f(n)
| n = k
| n = m
| ~ element(n,m)
| n = m
| k != m ),
inference(superposition,[status(thm)],[d84,c3]) ).
cnf(d86,plain,
( n = m
| m = k
| m != m ),
inference(equality_factoring,[status(thm)],[d76]) ).
cnf(d87,plain,
( n = m
| m = k ),
inference(equality_resolution,[status(thm)],[d86]) ).
cnf(d88,plain,
( n = m
| ~ element(n,m)
| f(n) = n
| f(n) = m
| n = f(n)
| n = k
| n = m
| m != m ),
inference(superposition,[status(thm)],[d87,d85]) ).
cnf(d89,plain,
( ~ element(n,m)
| f(n) = n
| f(n) = m
| n = f(n)
| n = k
| n = m ),
inference(equality_resolution,[status(thm)],[d88]) ).
cnf(d90,plain,
( n = k
| n = m
| f(n) = n
| f(n) = m
| n = f(n)
| n = k
| n = m ),
inference(resolution,[status(thm)],[d89,d79]) ).
cnf(d91,plain,
( f(n) = n
| f(n) = m
| n = k
| n = m
| n != n ),
inference(equality_factoring,[status(thm)],[d90]) ).
cnf(d92,plain,
( f(n) = n
| f(n) = m
| n = k
| n = m ),
inference(equality_resolution,[status(thm)],[d91]) ).
cnf(d93,plain,
( f(n) = m
| n = k
| n = m
| ~ element(n,m)
| n = m
| n != n ),
inference(superposition,[status(thm)],[d92,c4]) ).
cnf(d94,plain,
( ~ element(n,m)
| f(n) = m
| n = k
| n = m ),
inference(equality_resolution,[status(thm)],[d93]) ).
cnf(d95,plain,
( n = k
| n = m
| f(n) = m
| n = k
| n = m ),
inference(resolution,[status(thm)],[d94,d79]) ).
cnf(d96,plain,
( n = k
| n = m
| ~ element(n,m)
| n = m
| m != m ),
inference(superposition,[status(thm)],[d95,c3]) ).
cnf(d97,plain,
( ~ element(n,m)
| n = k
| n = m ),
inference(equality_resolution,[status(thm)],[d96]) ).
cnf(d98,plain,
( n = k
| n = m
| n = k
| n = m ),
inference(resolution,[status(thm)],[d97,d79]) ).
cnf(d99,plain,
( n = m
| n = m
| n = m ),
inference(superposition,[status(thm)],[d98,d78]) ).
cnf(d100,plain,
m != m,
inference(demodulation,[status(thm)],[c0,d99]) ).
cnf(d101,plain,
$false,
inference(equality_resolution,[status(thm)],[d100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN015-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n001.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sat Sep 26 17:10:15 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.27/2.51 % SZS status Unsatisfiable for theBenchmark.p
% 14.27/2.51 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------