%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LAT394-1 : TPTP v9.3.1. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 07:48:36 AM UTC 2026
% Result : Unsatisfiable 53.39s 8.79s
% Output : CNFRefutation 53.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of clauses : 90 ( 90 unt; 0 nHn; 5 RR)
% Number of literals : 90 ( 89 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 189 ( 29 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(sos,axiom,
f(f(f(f(X0,X1),f(X1,X2)),X3),f(X1,f(f(X1,f(f(X0,X0),X0)),X2))) = X1 ).
cnf(sos_001,axiom,
or(X0,X1) = f(f(X0,X0),f(X1,X1)) ).
cnf(sos_002,axiom,
and(X0,X1) = f(f(X0,X1),f(X0,X1)) ).
cnf(sos_003,axiom,
neg(X0) = f(X0,X0) ).
cnf(goals,negated_conjecture,
f(x0,f(x0,x0)) != f(x1,f(x1,x1)) ).
cnf(c0,plain,
f(f(f(f(X0,X1),f(X1,X2)),X3),f(X1,f(f(X1,f(f(X0,X0),X0)),X2))) = X1,
inference(clausification,[status(esa)],[sos]) ).
cnf(c1,plain,
or(X0,X1) = f(f(X0,X0),f(X1,X1)),
inference(clausification,[status(esa)],[sos_001]) ).
cnf(c2,plain,
and(X0,X1) = f(f(X0,X1),f(X0,X1)),
inference(clausification,[status(esa)],[sos_002]) ).
cnf(c3,plain,
neg(X0) = f(X0,X0),
inference(clausification,[status(esa)],[sos_003]) ).
cnf(c4,plain,
f(x0,f(x0,x0)) != f(x1,f(x1,x1)),
inference(clausification,[status(esa)],[goals]) ).
cnf(d0,plain,
f(x0,neg(x0)) != f(x1,f(x1,x1)),
inference(demodulation,[status(thm)],[c4,c3]) ).
cnf(d1,plain,
f(x0,neg(x0)) != f(x1,neg(x1)),
inference(demodulation,[status(thm)],[d0,c3]) ).
cnf(d2,plain,
or(X0,X1) = f(neg(X0),f(X1,X1)),
inference(demodulation,[status(thm)],[c1,c3]) ).
cnf(d3,plain,
or(X1,X0) = f(neg(X1),neg(X0)),
inference(demodulation,[status(thm)],[d2,c3]) ).
cnf(d4,plain,
f(f(f(f(X0,X1),f(X1,X2)),X3),f(X1,f(f(X1,f(neg(X0),X0)),X2))) = X1,
inference(demodulation,[status(thm)],[c0,c3]) ).
cnf(d5,plain,
and(X0,X1) = neg(f(X0,X1)),
inference(demodulation,[status(thm)],[c2,c3]) ).
cnf(d6,plain,
f(f(X1,X3),f(X1,f(f(X1,f(neg(f(f(X0,X1),f(X1,X2))),f(f(X0,X1),f(X1,X2)))),f(f(X1,f(neg(X0),X0)),X2)))) = X1,
inference(superposition,[status(thm)],[d4,d4]) ).
cnf(d7,plain,
f(f(X1,X3),f(X1,f(f(X1,f(and(f(X0,X1),f(X1,X2)),f(f(X0,X1),f(X1,X2)))),f(f(X1,f(neg(X0),X0)),X2)))) = X1,
inference(demodulation,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
f(f(f(f(X1,X0),f(X0,f(X0,f(f(X0,f(and(f(X2,X0),f(X0,X3)),f(f(X2,X0),f(X0,X3)))),f(f(X0,f(neg(X2),X2)),X3))))),X4),f(X0,X0)) = X0,
inference(superposition,[status(thm)],[d7,d4]) ).
cnf(d9,plain,
f(f(f(f(X1,X0),f(X0,f(X0,f(f(X0,f(and(f(X2,X0),f(X0,X3)),f(f(X2,X0),f(X0,X3)))),f(f(X0,f(neg(X2),X2)),X3))))),X4),neg(X0)) = X0,
inference(demodulation,[status(thm)],[d8,c3]) ).
cnf(d10,plain,
f(f(X0,X3),f(X0,f(f(X0,f(neg(X0),X0)),f(f(X0,f(and(f(X1,X0),f(X0,X2)),f(f(X1,X0),f(X0,X2)))),f(f(X0,f(neg(X1),X1)),X2))))) = X0,
inference(superposition,[status(thm)],[d7,d4]) ).
cnf(d11,plain,
f(f(X0,X1),neg(X1)) = X1,
inference(superposition,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
f(neg(X0),neg(X0)) = X0,
inference(superposition,[status(thm)],[c3,d11]) ).
cnf(d13,plain,
or(X0,X0) = X0,
inference(demodulation,[status(thm)],[d12,d3]) ).
cnf(d14,plain,
neg(neg(X0)) = or(X0,X0),
inference(superposition,[status(thm)],[d3,c3]) ).
cnf(d15,plain,
or(neg(X0),X1) = f(or(X0,X0),neg(X1)),
inference(superposition,[status(thm)],[d14,d3]) ).
cnf(d16,plain,
or(neg(X0),X1) = f(X0,neg(X1)),
inference(demodulation,[status(thm)],[d15,d13]) ).
cnf(d17,plain,
neg(neg(X0)) = X0,
inference(demodulation,[status(thm)],[d14,d13]) ).
cnf(d18,plain,
and(X0,X0) = neg(neg(X0)),
inference(superposition,[status(thm)],[c3,d5]) ).
cnf(d19,plain,
and(X0,X0) = or(X0,X0),
inference(superposition,[status(thm)],[d18,d14]) ).
cnf(d20,plain,
or(X1,neg(X0)) = f(neg(X1),or(X0,X0)),
inference(superposition,[status(thm)],[d14,d3]) ).
cnf(d21,plain,
or(neg(X0),neg(X1)) = f(and(X0,X0),or(X1,X1)),
inference(superposition,[status(thm)],[d18,d20]) ).
cnf(d22,plain,
or(neg(X0),neg(X1)) = f(or(X0,X0),or(X1,X1)),
inference(demodulation,[status(thm)],[d21,d19]) ).
cnf(d23,plain,
or(neg(X0),neg(X1)) = f(X0,or(X1,X1)),
inference(demodulation,[status(thm)],[d22,d13]) ).
cnf(d24,plain,
or(neg(X1),neg(X0)) = f(X1,X0),
inference(demodulation,[status(thm)],[d23,d13]) ).
cnf(d25,plain,
f(X0,neg(neg(X1))) = f(X0,X1),
inference(demodulation,[status(thm)],[d24,d16]) ).
cnf(d26,plain,
f(X1,X0) = f(X1,X0),
inference(demodulation,[status(thm)],[d25,d17]) ).
cnf(d27,plain,
X1 = f(f(X0,X1),neg(X1)),
inference(superposition,[status(thm)],[d11,d26]) ).
cnf(d28,plain,
neg(X0) = f(f(X1,neg(X0)),X0),
inference(superposition,[status(thm)],[d17,d27]) ).
cnf(d29,plain,
f(X1,f(f(X1,X2),f(f(f(X1,X2),f(neg(f(X0,X1)),f(X0,X1))),X3))) = f(X1,X2),
inference(superposition,[status(thm)],[d4,d4]) ).
cnf(d30,plain,
f(X1,f(f(X1,X2),f(f(f(X1,X2),f(and(X0,X1),f(X0,X1))),X3))) = f(X1,X2),
inference(demodulation,[status(thm)],[d29,d5]) ).
cnf(d31,plain,
f(f(f(f(X1,X0),f(X0,f(f(f(X0,f(neg(X1),X1)),f(and(X2,X0),f(X2,X0))),X3))),X4),f(X0,f(neg(X1),X1))) = X0,
inference(superposition,[status(thm)],[d30,d4]) ).
cnf(d32,plain,
neg(f(X1,f(neg(X0),X0))) = X1,
inference(superposition,[status(thm)],[d31,d28]) ).
cnf(d33,plain,
and(X0,f(neg(X1),X1)) = X0,
inference(demodulation,[status(thm)],[d32,d5]) ).
cnf(d34,plain,
or(X0,X0) = neg(neg(X0)),
inference(superposition,[status(thm)],[c3,d3]) ).
cnf(d35,plain,
or(neg(X0),X1) = f(neg(neg(X0)),neg(X1)),
inference(superposition,[status(thm)],[d34,d15]) ).
cnf(d36,plain,
or(neg(X0),X1) = or(neg(X0),X1),
inference(demodulation,[status(thm)],[d35,d3]) ).
cnf(d37,plain,
or(neg(neg(X0)),X1) = or(and(X0,X0),X1),
inference(superposition,[status(thm)],[d18,d36]) ).
cnf(d38,plain,
or(neg(neg(X0)),X1) = or(or(X0,X0),X1),
inference(demodulation,[status(thm)],[d37,d19]) ).
cnf(d39,plain,
or(neg(neg(X0)),X1) = or(X0,X1),
inference(demodulation,[status(thm)],[d38,d13]) ).
cnf(d40,plain,
f(neg(X0),neg(X1)) = or(X0,X1),
inference(demodulation,[status(thm)],[d39,d16]) ).
cnf(d41,plain,
and(X1,or(neg(X0),X0)) = X1,
inference(superposition,[status(thm)],[d40,d33]) ).
cnf(d42,plain,
and(X1,f(X0,neg(X0))) = X1,
inference(demodulation,[status(thm)],[d41,d16]) ).
cnf(d43,plain,
and(neg(X0),neg(X1)) = neg(or(X0,X1)),
inference(superposition,[status(thm)],[d3,d5]) ).
cnf(d44,plain,
neg(neg(neg(X0))) = neg(or(X0,X0)),
inference(superposition,[status(thm)],[d18,d43]) ).
cnf(d45,plain,
neg(neg(neg(X0))) = neg(X0),
inference(demodulation,[status(thm)],[d44,d13]) ).
cnf(d46,plain,
neg(X0) = neg(X0),
inference(demodulation,[status(thm)],[d45,d17]) ).
cnf(d47,plain,
neg(f(X0,X1)) = and(X0,X1),
inference(superposition,[status(thm)],[d5,d46]) ).
cnf(d48,plain,
f(f(X1,neg(X0)),X0) = neg(X0),
inference(superposition,[status(thm)],[d17,d11]) ).
cnf(d49,plain,
f(or(X0,X1),X1) = neg(X1),
inference(superposition,[status(thm)],[d40,d48]) ).
cnf(d50,plain,
neg(neg(X1)) = and(or(X0,X1),X1),
inference(superposition,[status(thm)],[d49,d47]) ).
cnf(d51,plain,
X0 = and(or(X1,X0),X0),
inference(demodulation,[status(thm)],[d50,d17]) ).
cnf(d52,plain,
f(X0,f(f(X0,X1),f(X0,X1))) = f(X0,X1),
inference(superposition,[status(thm)],[d7,d30]) ).
cnf(d53,plain,
f(X0,neg(f(X0,X1))) = f(X0,X1),
inference(demodulation,[status(thm)],[d52,c3]) ).
cnf(d54,plain,
f(X0,and(X0,X1)) = f(X0,X1),
inference(demodulation,[status(thm)],[d53,d5]) ).
cnf(d55,plain,
and(X0,and(X0,X1)) = neg(f(X0,X1)),
inference(superposition,[status(thm)],[d54,d5]) ).
cnf(d56,plain,
and(X0,and(X0,X1)) = and(X0,X1),
inference(demodulation,[status(thm)],[d55,d5]) ).
cnf(d57,plain,
and(neg(X2),and(X0,X1)) = neg(or(X2,f(X0,X1))),
inference(superposition,[status(thm)],[d5,d43]) ).
cnf(d58,plain,
or(X2,f(X0,X1)) = f(neg(X2),and(X0,X1)),
inference(superposition,[status(thm)],[d5,d3]) ).
cnf(d59,plain,
or(X0,f(neg(X0),X1)) = f(neg(X0),X1),
inference(superposition,[status(thm)],[d54,d58]) ).
cnf(d60,plain,
and(neg(X0),and(neg(X0),X1)) = neg(f(neg(X0),X1)),
inference(superposition,[status(thm)],[d59,d57]) ).
cnf(d61,plain,
and(neg(X0),X1) = neg(f(neg(X0),X1)),
inference(demodulation,[status(thm)],[d60,d56]) ).
cnf(d62,plain,
and(neg(X0),X1) = and(neg(X0),X1),
inference(demodulation,[status(thm)],[d61,d5]) ).
cnf(d63,plain,
and(neg(neg(X0)),X1) = and(and(X0,X0),X1),
inference(superposition,[status(thm)],[d18,d62]) ).
cnf(d64,plain,
and(neg(neg(X0)),X1) = and(or(X0,X0),X1),
inference(demodulation,[status(thm)],[d63,d19]) ).
cnf(d65,plain,
and(neg(neg(X0)),X1) = and(X0,X1),
inference(demodulation,[status(thm)],[d64,d13]) ).
cnf(d66,plain,
and(X0,X1) = and(X0,X1),
inference(demodulation,[status(thm)],[d65,d17]) ).
cnf(d67,plain,
f(f(f(f(X4,f(X0,X1)),X0),X5),f(f(X0,X1),f(f(f(X0,X1),f(neg(X4),X4)),f(X0,f(f(X0,f(and(f(X2,X0),f(X0,X3)),f(f(X2,X0),f(X0,X3)))),f(f(X0,f(neg(X2),X2)),X3)))))) = f(X0,X1),
inference(superposition,[status(thm)],[d7,d4]) ).
cnf(d68,plain,
f(f(X1,X2),neg(X1)) = X1,
inference(superposition,[status(thm)],[d67,d9]) ).
cnf(d69,plain,
f(f(neg(X0),X1),X0) = neg(X0),
inference(superposition,[status(thm)],[d17,d68]) ).
cnf(d70,plain,
f(or(X0,X1),X0) = neg(X0),
inference(superposition,[status(thm)],[d40,d69]) ).
cnf(d71,plain,
neg(neg(X0)) = and(or(X0,X1),X0),
inference(superposition,[status(thm)],[d70,d47]) ).
cnf(d72,plain,
X0 = and(or(X0,X1),X0),
inference(demodulation,[status(thm)],[d71,d17]) ).
cnf(d73,plain,
and(or(X0,X1),X0) = X0,
inference(superposition,[status(thm)],[d72,d66]) ).
cnf(d74,plain,
or(f(neg(X0),X0),X1) = f(neg(X0),X0),
inference(superposition,[status(thm)],[d33,d73]) ).
cnf(d75,plain,
X1 = and(f(neg(X0),X0),X1),
inference(superposition,[status(thm)],[d74,d51]) ).
cnf(d76,plain,
X1 = and(or(neg(X0),X0),X1),
inference(superposition,[status(thm)],[d40,d75]) ).
cnf(d77,plain,
X1 = and(f(X0,neg(X0)),X1),
inference(demodulation,[status(thm)],[d76,d16]) ).
cnf(d78,plain,
f(X1,neg(X1)) = f(X0,neg(X0)),
inference(superposition,[status(thm)],[d77,d42]) ).
cnf(d79,plain,
$false,
inference(resolution,[status(thm)],[d78,d1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT394-1 : TPTP v9.3.1. Released v5.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n011.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 21:40:43 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 53.39/8.79 % SZS status Unsatisfiable for theBenchmark.p
% 53.39/8.79 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------