%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LDA002-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 08:00:12 AM UTC 2026
% Result : Unsatisfiable 47.14s 6.66s
% Output : CNFRefutation 47.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of clauses : 97 ( 97 unt; 0 nHn; 82 RR)
% Number of literals : 97 ( 96 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 11 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a1,axiom,
f(X0,f(X1,X2)) = f(f(X0,X1),f(X0,X2)) ).
cnf(clause_2,axiom,
n2 = f(n1,n1) ).
cnf(clause_3,axiom,
n3 = f(n2,n1) ).
cnf(clause_4,axiom,
u = f(n2,n2) ).
cnf(clause_5,axiom,
u1 = f(u,n1) ).
cnf(clause_6,axiom,
u2 = f(u,n2) ).
cnf(clause_7,axiom,
u3 = f(u,n3) ).
cnf(clause_8,axiom,
uu = f(u,u) ).
cnf(clause_9,axiom,
a = f(f(n3,n2),u2) ).
cnf(clause_10,axiom,
b = f(u1,u3) ).
cnf(clause_11,axiom,
v = f(uu,uu) ).
cnf(prove_equation,negated_conjecture,
f(a,v) != f(b,v) ).
cnf(c0,plain,
f(X0,f(X1,X2)) = f(f(X0,X1),f(X0,X2)),
inference(clausification,[status(esa)],[a1]) ).
cnf(c1,plain,
n2 = f(n1,n1),
inference(clausification,[status(esa)],[clause_2]) ).
cnf(c2,plain,
n3 = f(n2,n1),
inference(clausification,[status(esa)],[clause_3]) ).
cnf(c3,plain,
u = f(n2,n2),
inference(clausification,[status(esa)],[clause_4]) ).
cnf(c4,plain,
u1 = f(u,n1),
inference(clausification,[status(esa)],[clause_5]) ).
cnf(c5,plain,
u2 = f(u,n2),
inference(clausification,[status(esa)],[clause_6]) ).
cnf(c6,plain,
u3 = f(u,n3),
inference(clausification,[status(esa)],[clause_7]) ).
cnf(c7,plain,
uu = f(u,u),
inference(clausification,[status(esa)],[clause_8]) ).
cnf(c8,plain,
a = f(f(n3,n2),u2),
inference(clausification,[status(esa)],[clause_9]) ).
cnf(c9,plain,
b = f(u1,u3),
inference(clausification,[status(esa)],[clause_10]) ).
cnf(c10,plain,
v = f(uu,uu),
inference(clausification,[status(esa)],[clause_11]) ).
cnf(c11,plain,
f(a,v) != f(b,v),
inference(clausification,[status(esa)],[prove_equation]) ).
cnf(d0,plain,
f(n2,f(n2,X0)) = f(u,f(n2,X0)),
inference(superposition,[status(thm)],[c3,c0]) ).
cnf(d1,plain,
f(n2,f(n2,n2)) = f(u,u),
inference(superposition,[status(thm)],[c3,d0]) ).
cnf(d2,plain,
f(n2,u) = f(u,u),
inference(demodulation,[status(thm)],[d1,c3]) ).
cnf(d3,plain,
f(n2,u) = uu,
inference(demodulation,[status(thm)],[d2,c7]) ).
cnf(d4,plain,
f(n2,f(n2,u)) = f(u,uu),
inference(superposition,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
f(n2,uu) = f(u,uu),
inference(demodulation,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
f(u,f(u,X0)) = f(uu,f(u,X0)),
inference(superposition,[status(thm)],[c7,c0]) ).
cnf(d7,plain,
f(u,f(u,u)) = f(uu,uu),
inference(superposition,[status(thm)],[c7,d6]) ).
cnf(d8,plain,
f(u,uu) = f(uu,uu),
inference(demodulation,[status(thm)],[d7,c7]) ).
cnf(d9,plain,
f(n2,uu) = f(uu,uu),
inference(demodulation,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
f(n2,uu) = v,
inference(demodulation,[status(thm)],[d9,c10]) ).
cnf(d11,plain,
f(n1,f(n1,X0)) = f(n2,f(n1,X0)),
inference(superposition,[status(thm)],[c1,c0]) ).
cnf(d12,plain,
f(n1,n2) = f(n2,f(n1,n1)),
inference(superposition,[status(thm)],[c1,d11]) ).
cnf(d13,plain,
f(n1,n2) = f(n2,n2),
inference(demodulation,[status(thm)],[d12,c1]) ).
cnf(d14,plain,
f(n1,n2) = u,
inference(demodulation,[status(thm)],[d13,c3]) ).
cnf(d15,plain,
f(n1,u) = f(n2,f(n1,n2)),
inference(superposition,[status(thm)],[d14,d11]) ).
cnf(d16,plain,
f(n1,u) = f(n2,u),
inference(demodulation,[status(thm)],[d15,d14]) ).
cnf(d17,plain,
f(n1,u) = uu,
inference(demodulation,[status(thm)],[d16,d3]) ).
cnf(d18,plain,
f(n2,f(n1,X0)) = f(n3,f(n2,X0)),
inference(superposition,[status(thm)],[c2,c0]) ).
cnf(d19,plain,
f(n2,f(n1,n2)) = f(n3,u),
inference(superposition,[status(thm)],[c3,d18]) ).
cnf(d20,plain,
f(n2,u) = f(n3,u),
inference(demodulation,[status(thm)],[d19,d14]) ).
cnf(d21,plain,
uu = f(n3,u),
inference(demodulation,[status(thm)],[d20,d3]) ).
cnf(d22,plain,
f(n3,f(X0,u)) = f(f(n3,X0),uu),
inference(superposition,[status(thm)],[d21,c0]) ).
cnf(d23,plain,
f(n1,uu) = f(n2,f(n1,u)),
inference(superposition,[status(thm)],[d17,d11]) ).
cnf(d24,plain,
f(n1,uu) = f(n2,uu),
inference(demodulation,[status(thm)],[d23,d17]) ).
cnf(d25,plain,
f(n1,uu) = v,
inference(demodulation,[status(thm)],[d24,d10]) ).
cnf(d26,plain,
f(n2,f(n1,u)) = f(n3,uu),
inference(superposition,[status(thm)],[d3,d18]) ).
cnf(d27,plain,
f(n2,uu) = f(n3,uu),
inference(demodulation,[status(thm)],[d26,d17]) ).
cnf(d28,plain,
v = f(n3,uu),
inference(demodulation,[status(thm)],[d27,d10]) ).
cnf(d29,plain,
f(n3,f(X0,uu)) = f(f(n3,X0),v),
inference(superposition,[status(thm)],[d28,c0]) ).
cnf(d30,plain,
f(f(n3,n2),f(u2,X0)) = f(a,f(f(n3,n2),X0)),
inference(superposition,[status(thm)],[c8,c0]) ).
cnf(d31,plain,
f(u,f(n2,X0)) = f(u2,f(u,X0)),
inference(superposition,[status(thm)],[c5,c0]) ).
cnf(d32,plain,
f(n2,f(n2,X0)) = f(u2,f(u,X0)),
inference(demodulation,[status(thm)],[d31,d0]) ).
cnf(d33,plain,
f(n2,f(n2,u)) = f(u2,uu),
inference(superposition,[status(thm)],[c7,d32]) ).
cnf(d34,plain,
f(n2,uu) = f(u2,uu),
inference(demodulation,[status(thm)],[d33,d3]) ).
cnf(d35,plain,
v = f(u2,uu),
inference(demodulation,[status(thm)],[d34,d10]) ).
cnf(d36,plain,
f(f(n3,n2),v) = f(a,f(f(n3,n2),uu)),
inference(superposition,[status(thm)],[d35,d30]) ).
cnf(d37,plain,
f(n3,f(n2,uu)) = f(a,f(f(n3,n2),uu)),
inference(demodulation,[status(thm)],[d36,d29]) ).
cnf(d38,plain,
f(n2,f(n1,uu)) = f(a,f(f(n3,n2),uu)),
inference(demodulation,[status(thm)],[d37,d18]) ).
cnf(d39,plain,
f(n2,v) = f(a,f(f(n3,n2),uu)),
inference(demodulation,[status(thm)],[d38,d25]) ).
cnf(d40,plain,
f(n2,v) = f(a,f(n3,f(n2,u))),
inference(demodulation,[status(thm)],[d39,d22]) ).
cnf(d41,plain,
f(n2,v) = f(a,f(n2,f(n1,u))),
inference(demodulation,[status(thm)],[d40,d18]) ).
cnf(d42,plain,
f(n2,v) = f(a,f(n2,uu)),
inference(demodulation,[status(thm)],[d41,d17]) ).
cnf(d43,plain,
f(n2,v) = f(a,v),
inference(demodulation,[status(thm)],[d42,d10]) ).
cnf(d44,plain,
f(n2,f(n2,uu)) = f(u,v),
inference(superposition,[status(thm)],[d10,d0]) ).
cnf(d45,plain,
f(n2,v) = f(u,v),
inference(demodulation,[status(thm)],[d44,d10]) ).
cnf(d46,plain,
f(u,f(n1,X0)) = f(u1,f(u,X0)),
inference(superposition,[status(thm)],[c4,c0]) ).
cnf(d47,plain,
v = f(u,uu),
inference(demodulation,[status(thm)],[d5,d10]) ).
cnf(d48,plain,
f(u,f(n1,uu)) = f(u1,v),
inference(superposition,[status(thm)],[d47,d46]) ).
cnf(d49,plain,
f(u,v) = f(u1,v),
inference(demodulation,[status(thm)],[d48,d25]) ).
cnf(d50,plain,
f(n2,v) = f(u1,v),
inference(demodulation,[status(thm)],[d49,d45]) ).
cnf(d51,plain,
f(u,f(n3,X0)) = f(u3,f(u,X0)),
inference(superposition,[status(thm)],[c6,c0]) ).
cnf(d52,plain,
f(u,f(n3,u)) = f(u3,uu),
inference(superposition,[status(thm)],[c7,d51]) ).
cnf(d53,plain,
f(u,uu) = f(u3,uu),
inference(demodulation,[status(thm)],[d52,d21]) ).
cnf(d54,plain,
f(n2,uu) = f(u3,uu),
inference(demodulation,[status(thm)],[d53,d5]) ).
cnf(d55,plain,
v = f(u3,uu),
inference(demodulation,[status(thm)],[d54,d10]) ).
cnf(d56,plain,
f(u1,f(u3,X0)) = f(b,f(u1,X0)),
inference(superposition,[status(thm)],[c9,c0]) ).
cnf(d57,plain,
f(u,f(n1,u)) = f(u1,uu),
inference(superposition,[status(thm)],[c7,d46]) ).
cnf(d58,plain,
f(u,uu) = f(u1,uu),
inference(demodulation,[status(thm)],[d57,d17]) ).
cnf(d59,plain,
f(n2,uu) = f(u1,uu),
inference(demodulation,[status(thm)],[d58,d5]) ).
cnf(d60,plain,
v = f(u1,uu),
inference(demodulation,[status(thm)],[d59,d10]) ).
cnf(d61,plain,
f(u1,f(u3,uu)) = f(b,v),
inference(superposition,[status(thm)],[d60,d56]) ).
cnf(d62,plain,
f(u1,v) = f(b,v),
inference(demodulation,[status(thm)],[d61,d55]) ).
cnf(d63,plain,
f(n2,v) = f(b,v),
inference(demodulation,[status(thm)],[d62,d50]) ).
cnf(d64,plain,
f(a,v) != f(n2,v),
inference(demodulation,[status(thm)],[c11,d63]) ).
cnf(d65,plain,
f(n2,v) != f(n2,v),
inference(demodulation,[status(thm)],[d64,d43]) ).
cnf(d66,plain,
f(n1,f(n2,X0)) = f(u,f(n1,X0)),
inference(superposition,[status(thm)],[d14,c0]) ).
cnf(d67,plain,
f(n1,f(n2,uu)) = f(n2,f(n1,uu)),
inference(superposition,[status(thm)],[d24,d11]) ).
cnf(d68,plain,
f(u,f(n1,uu)) = f(n2,f(n1,uu)),
inference(demodulation,[status(thm)],[d67,d66]) ).
cnf(d69,plain,
f(u,v) = f(n2,f(n1,uu)),
inference(demodulation,[status(thm)],[d68,d25]) ).
cnf(d70,plain,
f(n2,v) = f(n2,f(n1,uu)),
inference(demodulation,[status(thm)],[d69,d45]) ).
cnf(d71,plain,
f(n2,v) = f(n2,v),
inference(demodulation,[status(thm)],[d70,d25]) ).
cnf(d72,plain,
$false,
inference(resolution,[status(thm)],[d71,d65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LDA002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.56 % Computer : n014.cluster.edu
% 0.10/0.56 % Model : x86_64 x86_64
% 0.10/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.56 % Memory : 8046.5625MB
% 0.10/0.56 % OS : Linux 6.8.0-71-generic
% 0.10/0.56 % CPULimit : 300
% 0.10/0.56 % WCLimit : 300
% 0.10/0.56 % DateTime : Fri Sep 25 23:54:32 UTC 2026
% 0.10/0.56 % CPUTime :
% 0.10/0.56 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 47.14/6.66 % SZS status Unsatisfiable for theBenchmark.p
% 47.14/6.66 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------