%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LDA001-1 : 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 08:00:12 AM UTC 2026
% Result : Unsatisfiable 11.82s 2.29s
% Output : CNFRefutation 11.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of clauses : 32 ( 32 unt; 0 nHn; 24 RR)
% Number of literals : 32 ( 31 equ; 7 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 12 ( 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(prove_equation,negated_conjecture,
f(f(n3,n2),u) != f(f(u,u),u) ).
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,
f(f(n3,n2),u) != f(f(u,u),u),
inference(clausification,[status(esa)],[prove_equation]) ).
cnf(d0,plain,
f(n2,f(X0,n2)) = f(f(n2,X0),u),
inference(superposition,[status(thm)],[c3,c0]) ).
cnf(d1,plain,
f(n1,f(X0,n1)) = f(f(n1,X0),n2),
inference(superposition,[status(thm)],[c1,c0]) ).
cnf(d2,plain,
f(n1,f(n1,X0)) = f(n2,f(n1,X0)),
inference(superposition,[status(thm)],[c1,c0]) ).
cnf(d3,plain,
f(n1,n2) = f(n2,f(n1,n1)),
inference(superposition,[status(thm)],[c1,d2]) ).
cnf(d4,plain,
f(n1,n2) = f(n2,n2),
inference(demodulation,[status(thm)],[d3,c1]) ).
cnf(d5,plain,
f(n1,n2) = u,
inference(demodulation,[status(thm)],[d4,c3]) ).
cnf(d6,plain,
f(n1,f(n2,n1)) = f(u,n2),
inference(superposition,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
f(n1,n3) = f(u,n2),
inference(demodulation,[status(thm)],[d6,c2]) ).
cnf(d8,plain,
f(n2,f(n1,X0)) = f(n3,f(n2,X0)),
inference(superposition,[status(thm)],[c2,c0]) ).
cnf(d9,plain,
f(n2,f(n1,n1)) = f(n3,n3),
inference(superposition,[status(thm)],[c2,d8]) ).
cnf(d10,plain,
f(n2,n2) = f(n3,n3),
inference(demodulation,[status(thm)],[d9,c1]) ).
cnf(d11,plain,
u = f(n3,n3),
inference(demodulation,[status(thm)],[d10,c3]) ).
cnf(d12,plain,
f(n3,f(X0,n3)) = f(f(n3,X0),u),
inference(superposition,[status(thm)],[d11,c0]) ).
cnf(d13,plain,
f(n2,f(n2,X0)) = f(u,f(n2,X0)),
inference(superposition,[status(thm)],[c3,c0]) ).
cnf(d14,plain,
f(n2,f(n2,n2)) = f(u,u),
inference(superposition,[status(thm)],[c3,d13]) ).
cnf(d15,plain,
f(n2,u) = f(u,u),
inference(demodulation,[status(thm)],[d14,c3]) ).
cnf(d16,plain,
f(f(n3,n2),u) != f(f(n2,u),u),
inference(demodulation,[status(thm)],[c4,d15]) ).
cnf(d17,plain,
f(n3,f(n2,n3)) != f(f(n2,u),u),
inference(demodulation,[status(thm)],[d16,d12]) ).
cnf(d18,plain,
f(n2,f(n1,n3)) != f(f(n2,u),u),
inference(demodulation,[status(thm)],[d17,d8]) ).
cnf(d19,plain,
f(n2,f(u,n2)) != f(f(n2,u),u),
inference(demodulation,[status(thm)],[d18,d7]) ).
cnf(d20,plain,
f(n2,f(u,n2)) != f(n2,f(u,n2)),
inference(demodulation,[status(thm)],[d19,d0]) ).
cnf(d21,plain,
$false,
inference(equality_resolution,[status(thm)],[d20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LDA001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.57 % Computer : n004.cluster.edu
% 0.11/0.57 % Model : x86_64 x86_64
% 0.11/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.57 % Memory : 8046.5625MB
% 0.11/0.57 % OS : Linux 6.8.0-71-generic
% 0.11/0.57 % CPULimit : 300
% 0.11/0.57 % WCLimit : 300
% 0.11/0.57 % DateTime : Fri Sep 25 23:54:52 UTC 2026
% 0.11/0.58 % CPUTime :
% 0.11/0.58 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.82/2.29 % SZS status Unsatisfiable for theBenchmark.p
% 11.82/2.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------