%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SYN014-1 : 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 : n004.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 13.76s 3.87s
% Output : CNFRefutation 13.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 16
% Syntax : Number of clauses : 100 ( 5 unt; 89 nHn; 96 RR)
% Number of literals : 428 ( 337 equ; 77 neg)
% Maximal clause size : 9 ( 4 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 : 42 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c_1,negated_conjecture,
m != n ).
cnf(c_2,negated_conjecture,
( m = k
| n = k ) ).
cnf(c_3,negated_conjecture,
( element(X0,j)
| X0 != k
| X0 = j ) ).
cnf(c_4,negated_conjecture,
( ~ element(X0,j)
| X0 = k
| X0 = j ) ).
cnf(c_5,negated_conjecture,
( f(X0) != m
| ~ element(X0,m)
| X0 = m ) ).
cnf(c_6,negated_conjecture,
( f(X0) != X0
| ~ element(X0,m)
| X0 = m ) ).
cnf(c_7,negated_conjecture,
( element(X0,f(X0))
| ~ element(X0,m)
| X0 = m ) ).
cnf(c_8,negated_conjecture,
( element(f(X0),X0)
| ~ element(X0,m)
| X0 = m ) ).
cnf(c_9,negated_conjecture,
( ~ element(X1,X0)
| ~ element(X0,X1)
| X1 = X0
| X1 = m
| element(X0,m)
| X0 = m ) ).
cnf(c_11,negated_conjecture,
( g(X0) != X0
| element(X0,n)
| X0 = n ) ).
cnf(c_12,negated_conjecture,
( element(X0,g(X0))
| element(X0,n)
| X0 = n ) ).
cnf(c_13,negated_conjecture,
( element(g(X0),X0)
| element(X0,n)
| X0 = n ) ).
cnf(c_14,negated_conjecture,
( ~ element(X1,X0)
| ~ element(X0,X1)
| X1 = X0
| X1 = n
| ~ element(X0,n)
| X0 = n ) ).
cnf(c_15,negated_conjecture,
( element(X0,k)
| X0 != m
| X0 = k ) ).
cnf(c_16,negated_conjecture,
( element(X0,k)
| X0 != n
| X0 = k ) ).
cnf(c_17,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,
( m = k
| n = k ),
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,
( ~ element(X0,j)
| X0 = k
| X0 = j ),
inference(clausification,[status(esa)],[c_4]) ).
cnf(c4,plain,
( f(X0) != m
| ~ element(X0,m)
| X0 = m ),
inference(clausification,[status(esa)],[c_5]) ).
cnf(c5,plain,
( f(X0) != X0
| ~ element(X0,m)
| X0 = m ),
inference(clausification,[status(esa)],[c_6]) ).
cnf(c6,plain,
( element(X0,f(X0))
| ~ element(X0,m)
| X0 = m ),
inference(clausification,[status(esa)],[c_7]) ).
cnf(c7,plain,
( element(f(X0),X0)
| ~ element(X0,m)
| X0 = m ),
inference(clausification,[status(esa)],[c_8]) ).
cnf(c8,plain,
( X1 = m
| ~ element(X0,X1)
| X1 = X0
| X0 = m
| ~ element(X1,X0)
| element(X0,m) ),
inference(clausification,[status(esa)],[c_9]) ).
cnf(c10,plain,
( g(X0) != X0
| element(X0,n)
| X0 = n ),
inference(clausification,[status(esa)],[c_11]) ).
cnf(c11,plain,
( element(X0,g(X0))
| element(X0,n)
| X0 = n ),
inference(clausification,[status(esa)],[c_12]) ).
cnf(c12,plain,
( element(g(X0),X0)
| element(X0,n)
| X0 = n ),
inference(clausification,[status(esa)],[c_13]) ).
cnf(c13,plain,
( X1 = n
| ~ element(X0,n)
| X1 = X0
| ~ element(X1,X0)
| X0 = n
| ~ element(X0,X1) ),
inference(clausification,[status(esa)],[c_14]) ).
cnf(c14,plain,
( element(X0,k)
| X0 != m
| X0 = k ),
inference(clausification,[status(esa)],[c_15]) ).
cnf(c15,plain,
( element(X0,k)
| X0 != n
| X0 = k ),
inference(clausification,[status(esa)],[c_16]) ).
cnf(c16,plain,
( ~ element(X0,k)
| X0 = n
| X0 = m
| X0 = k ),
inference(clausification,[status(esa)],[c_17]) ).
cnf(d0,plain,
( element(m,k)
| m = k ),
inference(equality_resolution,[status(thm)],[c14]) ).
cnf(d1,plain,
( m = k
| m = k
| element(m,n) ),
inference(superposition,[status(thm)],[c1,d0]) ).
cnf(d2,plain,
( m = k
| X0 = k
| X0 = n
| X0 = m
| ~ element(X0,n) ),
inference(superposition,[status(thm)],[c1,c16]) ).
cnf(d3,plain,
( g(j) = j
| g(j) = k
| element(j,n)
| j = n ),
inference(resolution,[status(thm)],[c12,c3]) ).
cnf(d4,plain,
( g(j) = j
| g(j) = k
| j = n
| m = k
| j = k
| j = n
| j = m ),
inference(resolution,[status(thm)],[d2,d3]) ).
cnf(d5,plain,
( g(j) = k
| j = k
| j = n
| j = m
| m = k
| element(j,n)
| j = n
| j != j ),
inference(superposition,[status(thm)],[d4,c10]) ).
cnf(d6,plain,
( element(j,n)
| g(j) = k
| j = k
| j = n
| j = m
| m = k ),
inference(equality_resolution,[status(thm)],[d5]) ).
cnf(d7,plain,
( m = k
| j = k
| j = n
| j = m
| g(j) = k
| j = k
| j = n
| j = m
| m = k ),
inference(resolution,[status(thm)],[d6,d2]) ).
cnf(d8,plain,
( j = k
| j = n
| j = m
| m = k
| element(j,n)
| j = n
| element(j,k) ),
inference(superposition,[status(thm)],[d7,c11]) ).
cnf(d9,plain,
( j = k
| j = n
| j = m
| element(j,n)
| j = k
| j = n
| j = m
| m = k ),
inference(resolution,[status(thm)],[d8,c16]) ).
cnf(d10,plain,
( m = k
| j = k
| j = n
| j = m
| j = k
| j = n
| j = m
| m = k ),
inference(resolution,[status(thm)],[d9,d2]) ).
cnf(d11,plain,
( j = n
| j = m
| m = k
| X0 = j
| X0 = k
| ~ element(X0,k) ),
inference(superposition,[status(thm)],[d10,c3]) ).
cnf(d12,plain,
( m = k
| j = n
| j = m
| m = k
| m = j
| m = k ),
inference(resolution,[status(thm)],[d11,d0]) ).
cnf(d13,plain,
( j = m
| m = j
| m = k
| X0 = j
| X0 = k
| ~ element(X0,n) ),
inference(superposition,[status(thm)],[d12,c3]) ).
cnf(d14,plain,
( m = k
| j = m
| m = j
| m = k
| m = j
| m = k ),
inference(resolution,[status(thm)],[d13,d1]) ).
cnf(d15,plain,
( m = j
| m = k
| m != m ),
inference(equality_factoring,[status(thm)],[d14]) ).
cnf(d16,plain,
( m = j
| m = k ),
inference(equality_resolution,[status(thm)],[d15]) ).
cnf(d17,plain,
( element(k,j)
| k = j ),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(d18,plain,
( j = m
| m = k
| m != m ),
inference(equality_factoring,[status(thm)],[d14]) ).
cnf(d19,plain,
( j = m
| m = k ),
inference(equality_resolution,[status(thm)],[d18]) ).
cnf(d20,plain,
( m = k
| k = j
| element(k,m) ),
inference(superposition,[status(thm)],[d19,d17]) ).
cnf(d21,plain,
( ~ element(k,m)
| k = m
| f(k) = k
| f(k) = n
| f(k) = m ),
inference(resolution,[status(thm)],[c16,c7]) ).
cnf(d22,plain,
( m = k
| f(k) = k
| f(k) = n
| f(k) = m
| k = m
| ~ element(n,m) ),
inference(superposition,[status(thm)],[c1,d21]) ).
cnf(d23,plain,
( m = k
| k = j
| element(n,j) ),
inference(superposition,[status(thm)],[c1,d17]) ).
cnf(d24,plain,
( m = k
| k = j
| m = k
| element(n,m) ),
inference(superposition,[status(thm)],[d19,d23]) ).
cnf(d25,plain,
( f(k) = k
| f(k) = n
| f(k) = m
| k = m
| m = k
| k = j
| m = k ),
inference(resolution,[status(thm)],[d24,d22]) ).
cnf(d26,plain,
( f(k) = n
| f(k) = m
| k = j
| k = m
| m = k
| ~ element(k,m)
| k = m
| k != k ),
inference(superposition,[status(thm)],[d25,c5]) ).
cnf(d27,plain,
( ~ element(k,m)
| f(k) = n
| f(k) = m
| k = j
| k = m
| m = k ),
inference(equality_resolution,[status(thm)],[d26]) ).
cnf(d28,plain,
( k = j
| m = k
| f(k) = n
| f(k) = m
| k = j
| k = m
| m = k ),
inference(resolution,[status(thm)],[d27,d20]) ).
cnf(d29,plain,
( m = k
| ~ element(m,X0)
| ~ element(X0,m)
| m = n
| X0 = n
| X0 = m ),
inference(resolution,[status(thm)],[c13,d1]) ).
cnf(d30,plain,
( ~ element(m,X0)
| ~ element(X0,m)
| m = k
| X0 = n
| X0 = m ),
inference(resolution,[status(thm)],[c0,d29]) ).
cnf(d31,plain,
( m = k
| ~ element(k,m)
| m = k
| k = n
| k = m ),
inference(resolution,[status(thm)],[d30,d0]) ).
cnf(d32,plain,
( m = k
| k = n
| k = m
| m = k
| ~ element(n,m) ),
inference(superposition,[status(thm)],[c1,d31]) ).
cnf(d33,plain,
( k = n
| k = m
| m = k
| k = j
| m = k ),
inference(resolution,[status(thm)],[d24,d32]) ).
cnf(d34,plain,
( k = n
| k = m
| m = k
| m = k
| m = k ),
inference(superposition,[status(thm)],[d33,d16]) ).
cnf(d35,plain,
( k = m
| m = k
| f(k) = m
| k = j
| k = m
| m = k
| f(n) = n ),
inference(superposition,[status(thm)],[d34,d28]) ).
cnf(d36,plain,
( f(n) = n
| k = j
| k = m
| m = k
| ~ element(k,m)
| k = m
| m != m ),
inference(superposition,[status(thm)],[d35,c4]) ).
cnf(d37,plain,
( ~ element(k,m)
| f(n) = n
| k = j
| k = m
| m = k ),
inference(equality_resolution,[status(thm)],[d36]) ).
cnf(d38,plain,
( k = j
| m = k
| f(n) = n
| k = j
| k = m
| m = k ),
inference(resolution,[status(thm)],[d37,d20]) ).
cnf(d39,plain,
( f(k) = m
| k = j
| k = m
| m = k
| ~ element(k,m)
| k = m
| n != k ),
inference(superposition,[status(thm)],[d28,c5]) ).
cnf(d40,plain,
( k = m
| m = k
| ~ element(k,m)
| f(k) = m
| k = j
| k = m
| m = k
| n != n ),
inference(superposition,[status(thm)],[d34,d39]) ).
cnf(d41,plain,
( ~ element(k,m)
| f(k) = m
| k = j
| k = m
| m = k ),
inference(equality_resolution,[status(thm)],[d40]) ).
cnf(d42,plain,
( k = j
| m = k
| f(k) = m
| k = j
| k = m
| m = k ),
inference(resolution,[status(thm)],[d41,d20]) ).
cnf(d43,plain,
( k = m
| m = k
| k = j
| k = m
| m = k
| f(n) = m ),
inference(superposition,[status(thm)],[d34,d42]) ).
cnf(d44,plain,
( k = j
| k = m
| m = k
| k = j
| k = m
| m = k
| m = n ),
inference(superposition,[status(thm)],[d43,d38]) ).
cnf(d45,plain,
( k = j
| k = m
| m = k ),
inference(resolution,[status(thm)],[c0,d44]) ).
cnf(d46,plain,
( k = m
| m = k
| m = k
| m = k ),
inference(superposition,[status(thm)],[d45,d16]) ).
cnf(d47,plain,
( k = m
| m != m ),
inference(equality_factoring,[status(thm)],[d46]) ).
cnf(d48,plain,
k = m,
inference(equality_resolution,[status(thm)],[d47]) ).
cnf(d49,plain,
( element(n,k)
| n = k ),
inference(equality_resolution,[status(thm)],[c15]) ).
cnf(d50,plain,
( element(n,k)
| n = m ),
inference(demodulation,[status(thm)],[d49,d48]) ).
cnf(d51,plain,
( element(n,m)
| n = m ),
inference(demodulation,[status(thm)],[d50,d48]) ).
cnf(d52,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)],[c8,c7]) ).
cnf(d53,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)],[d52,c6]) ).
cnf(d54,plain,
( ~ element(X0,k)
| X0 = m
| X0 = n
| X0 = m ),
inference(demodulation,[status(thm)],[c16,d48]) ).
cnf(d55,plain,
( ~ element(X0,m)
| X0 = m
| X0 = n
| X0 = m ),
inference(demodulation,[status(thm)],[d54,d48]) ).
cnf(d56,plain,
( ~ element(X0,m)
| f(X0) = m
| X0 = f(X0)
| X0 = m
| f(X0) = n
| f(X0) = m ),
inference(resolution,[status(thm)],[d55,d53]) ).
cnf(d57,plain,
( n = m
| f(n) = n
| f(n) = m
| n = f(n)
| n = m ),
inference(resolution,[status(thm)],[d56,d51]) ).
cnf(d58,plain,
( f(n) = n
| f(n) = m
| n = m
| n != n ),
inference(equality_factoring,[status(thm)],[d57]) ).
cnf(d59,plain,
( f(n) = n
| f(n) = m
| n = m ),
inference(equality_resolution,[status(thm)],[d58]) ).
cnf(d60,plain,
( f(n) = m
| n = m
| ~ element(n,m)
| n = m
| n != n ),
inference(superposition,[status(thm)],[d59,c5]) ).
cnf(d61,plain,
( ~ element(n,m)
| f(n) = m
| n = m ),
inference(equality_resolution,[status(thm)],[d60]) ).
cnf(d62,plain,
( n = m
| f(n) = m
| n = m ),
inference(resolution,[status(thm)],[d61,d51]) ).
cnf(d63,plain,
( n = m
| ~ element(n,m)
| n = m
| m != m ),
inference(superposition,[status(thm)],[d62,c4]) ).
cnf(d64,plain,
( ~ element(n,m)
| n = m ),
inference(equality_resolution,[status(thm)],[d63]) ).
cnf(d65,plain,
( n = m
| n = m ),
inference(resolution,[status(thm)],[d64,d51]) ).
cnf(d66,plain,
m != m,
inference(demodulation,[status(thm)],[c0,d65]) ).
cnf(d67,plain,
$false,
inference(equality_resolution,[status(thm)],[d66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYN014-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.41 % Computer : n004.cluster.edu
% 0.18/0.41 % Model : x86_64 x86_64
% 0.18/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.41 % Memory : 8046.5625MB
% 0.18/0.41 % OS : Linux 6.8.0-71-generic
% 0.18/0.41 % CPULimit : 300
% 0.18/0.41 % WCLimit : 300
% 0.18/0.41 % DateTime : Sat Sep 26 17:04:06 UTC 2026
% 0.18/0.41 % CPUTime :
% 0.18/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.76/3.87 % SZS status Unsatisfiable for theBenchmark.p
% 13.76/3.87 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------