%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP119-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 07:22:22 AM UTC 2026
% Result : Unsatisfiable 170.49s 26.58s
% Output : CNFRefutation 170.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 71
% Number of leaves : 3
% Syntax : Number of clauses : 164 ( 164 unt; 0 nHn; 6 RR)
% Number of literals : 164 ( 163 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 271 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),multiply(X1,X2))),multiply(X2,multiply(X2,X2)))) = X1 ).
cnf(single_axiom2,axiom,
multiply(identity,identity) = identity ).
cnf(prove_order4,negated_conjecture,
multiply(a,multiply(a,multiply(a,a))) != identity ).
cnf(c0,plain,
multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),multiply(X1,X2))),multiply(X2,multiply(X2,X2)))) = X1,
inference(clausification,[status(esa)],[single_axiom]) ).
cnf(c1,plain,
multiply(identity,identity) = identity,
inference(clausification,[status(esa)],[single_axiom2]) ).
cnf(c2,plain,
multiply(a,multiply(a,multiply(a,a))) != identity,
inference(clausification,[status(esa)],[prove_order4]) ).
cnf(d0,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X0,X1))),multiply(X1,multiply(X1,X1)))) = X0,
inference(superposition,[status(thm)],[c1,c0]) ).
cnf(d1,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X0,identity))),multiply(identity,identity))) = X0,
inference(superposition,[status(thm)],[c1,d0]) ).
cnf(d2,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X0,identity))),identity)) = X0,
inference(demodulation,[status(thm)],[d1,c1]) ).
cnf(d3,plain,
multiply(identity,multiply(multiply(identity,X0),identity)) = multiply(identity,multiply(identity,multiply(X0,identity))),
inference(superposition,[status(thm)],[d2,d2]) ).
cnf(d4,plain,
multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),multiply(X1,identity))),multiply(identity,identity))) = X1,
inference(superposition,[status(thm)],[c1,c0]) ).
cnf(d5,plain,
multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),multiply(X1,identity))),identity)) = X1,
inference(demodulation,[status(thm)],[d4,c1]) ).
cnf(d6,plain,
X0 = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,identity),multiply(X0,identity)),identity))),
inference(superposition,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
X0 = multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X0,identity)),identity))),
inference(demodulation,[status(thm)],[d6,c1]) ).
cnf(d8,plain,
X0 = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(X0,identity),identity)))),
inference(demodulation,[status(thm)],[d7,d3]) ).
cnf(d9,plain,
multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X0,identity)),identity))) = X0,
inference(demodulation,[status(thm)],[d2,d3]) ).
cnf(d10,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(multiply(X0,identity),identity)))) = X0,
inference(demodulation,[status(thm)],[d9,d3]) ).
cnf(d11,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X0,identity))),identity)) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,X0),identity),identity))),
inference(superposition,[status(thm)],[d3,d3]) ).
cnf(d12,plain,
multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X0,identity)),identity))) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,X0),identity),identity))),
inference(demodulation,[status(thm)],[d11,d3]) ).
cnf(d13,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(multiply(X0,identity),identity)))) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,X0),identity),identity))),
inference(demodulation,[status(thm)],[d12,d3]) ).
cnf(d14,plain,
X0 = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,X0),identity),identity))),
inference(demodulation,[status(thm)],[d13,d10]) ).
cnf(d15,plain,
multiply(identity,multiply(X0,multiply(identity,multiply(identity,identity)))) = multiply(multiply(identity,X0),identity),
inference(superposition,[status(thm)],[d14,d0]) ).
cnf(d16,plain,
multiply(identity,multiply(X0,multiply(identity,identity))) = multiply(multiply(identity,X0),identity),
inference(demodulation,[status(thm)],[d15,c1]) ).
cnf(d17,plain,
multiply(identity,multiply(X0,identity)) = multiply(multiply(identity,X0),identity),
inference(demodulation,[status(thm)],[d16,c1]) ).
cnf(d18,plain,
multiply(X0,multiply(multiply(X0,X1),identity)) = multiply(multiply(X0,X0),multiply(multiply(multiply(X0,X0),multiply(X0,X0)),multiply(X1,identity))),
inference(superposition,[status(thm)],[d5,d5]) ).
cnf(d19,plain,
multiply(multiply(X0,X0),multiply(multiply(X0,multiply(multiply(X0,X1),identity)),identity)) = X1,
inference(superposition,[status(thm)],[d18,d5]) ).
cnf(d20,plain,
multiply(X1,multiply(multiply(X1,multiply(multiply(X1,X1),multiply(identity,multiply(X0,identity)))),identity)) = multiply(identity,X0),
inference(superposition,[status(thm)],[d17,d5]) ).
cnf(d21,plain,
multiply(X1,multiply(multiply(X1,multiply(multiply(X1,X1),X0)),identity)) = multiply(identity,multiply(identity,multiply(multiply(identity,identity),multiply(X0,identity)))),
inference(superposition,[status(thm)],[d5,d20]) ).
cnf(d22,plain,
multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),X1)),identity)) = multiply(identity,multiply(identity,multiply(identity,multiply(X1,identity)))),
inference(demodulation,[status(thm)],[d21,c1]) ).
cnf(d23,plain,
multiply(multiply(X0,X0),multiply(multiply(X0,multiply(multiply(identity,multiply(identity,multiply(identity,multiply(X1,identity)))),identity)),identity)) = multiply(multiply(X0,multiply(multiply(X0,X0),X1)),identity),
inference(superposition,[status(thm)],[d22,d19]) ).
cnf(d24,plain,
multiply(multiply(X1,X1),multiply(multiply(X1,multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X0,identity))),identity))),identity)) = multiply(multiply(X1,multiply(multiply(X1,X1),X0)),identity),
inference(demodulation,[status(thm)],[d23,d17]) ).
cnf(d25,plain,
multiply(multiply(X1,X1),multiply(multiply(X1,multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X0,identity)),identity)))),identity)) = multiply(multiply(X1,multiply(multiply(X1,X1),X0)),identity),
inference(demodulation,[status(thm)],[d24,d17]) ).
cnf(d26,plain,
multiply(multiply(X1,X1),multiply(multiply(X1,multiply(identity,multiply(identity,multiply(identity,multiply(multiply(X0,identity),identity))))),identity)) = multiply(multiply(X1,multiply(multiply(X1,X1),X0)),identity),
inference(demodulation,[status(thm)],[d25,d17]) ).
cnf(d27,plain,
multiply(multiply(X1,X1),multiply(multiply(X1,X0),identity)) = multiply(multiply(X1,multiply(multiply(X1,X1),X0)),identity),
inference(demodulation,[status(thm)],[d26,d10]) ).
cnf(d28,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(X0,X0),multiply(multiply(X0,X1),identity)),identity)))) = multiply(X0,multiply(multiply(X0,X0),X1)),
inference(superposition,[status(thm)],[d27,d10]) ).
cnf(d29,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,multiply(identity,multiply(X0,identity)))),multiply(identity,multiply(identity,identity)))) = multiply(identity,X0),
inference(superposition,[status(thm)],[d3,d0]) ).
cnf(d30,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,multiply(identity,multiply(X0,identity)))),multiply(identity,identity))) = multiply(identity,X0),
inference(demodulation,[status(thm)],[d29,c1]) ).
cnf(d31,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,multiply(identity,multiply(X0,identity)))),identity)) = multiply(identity,X0),
inference(demodulation,[status(thm)],[d30,c1]) ).
cnf(d32,plain,
multiply(identity,multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X0,identity))),identity))) = multiply(identity,X0),
inference(demodulation,[status(thm)],[d31,d3]) ).
cnf(d33,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X0,identity)),identity)))) = multiply(identity,X0),
inference(demodulation,[status(thm)],[d32,d3]) ).
cnf(d34,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(multiply(X0,identity),identity))))) = multiply(identity,X0),
inference(demodulation,[status(thm)],[d33,d3]) ).
cnf(d35,plain,
multiply(identity,X0) = multiply(identity,X0),
inference(demodulation,[status(thm)],[d34,d10]) ).
cnf(d36,plain,
multiply(identity,multiply(identity,multiply(X0,identity))) = multiply(identity,multiply(multiply(identity,X0),identity)),
inference(superposition,[status(thm)],[d3,d35]) ).
cnf(d37,plain,
multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(multiply(identity,X0),identity),identity)),identity))) = multiply(identity,multiply(X0,identity)),
inference(superposition,[status(thm)],[d14,d36]) ).
cnf(d38,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(identity,X0),identity),identity),identity)))) = multiply(identity,multiply(X0,identity)),
inference(demodulation,[status(thm)],[d37,d17]) ).
cnf(d39,plain,
multiply(multiply(identity,X0),identity) = multiply(identity,multiply(X0,identity)),
inference(demodulation,[status(thm)],[d38,d10]) ).
cnf(d40,plain,
multiply(X0,multiply(multiply(X0,X1),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))))) = multiply(multiply(X0,X0),multiply(multiply(multiply(X0,X0),multiply(X0,X0)),multiply(X1,X2))),
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d41,plain,
multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(multiply(identity,multiply(X0,multiply(X1,multiply(X1,X1)))),X1))) = X0,
inference(superposition,[status(thm)],[d40,d0]) ).
cnf(d42,plain,
multiply(identity,multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(multiply(identity,multiply(X0,multiply(X1,multiply(X1,X1)))),X1))) = X0,
inference(demodulation,[status(thm)],[d41,c1]) ).
cnf(d43,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(multiply(identity,multiply(X0,multiply(X1,multiply(X1,X1)))),X1))) = X0,
inference(demodulation,[status(thm)],[d42,c1]) ).
cnf(d44,plain,
multiply(identity,multiply(multiply(identity,identity),multiply(multiply(identity,multiply(X0,multiply(X1,multiply(X1,X1)))),X1))) = X0,
inference(demodulation,[status(thm)],[d43,c1]) ).
cnf(d45,plain,
multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X0,multiply(X1,multiply(X1,X1)))),X1))) = X0,
inference(demodulation,[status(thm)],[d44,c1]) ).
cnf(d46,plain,
multiply(X0,identity) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(X0,multiply(X1,multiply(X1,X1)))),X1)),identity)),
inference(superposition,[status(thm)],[d45,d39]) ).
cnf(d47,plain,
multiply(X0,identity) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(X0,multiply(X1,multiply(X1,X1)))),X1),identity))),
inference(demodulation,[status(thm)],[d46,d17]) ).
cnf(d48,plain,
multiply(multiply(X0,identity),identity) = multiply(identity,multiply(multiply(identity,multiply(multiply(multiply(identity,multiply(X0,multiply(X1,multiply(X1,X1)))),X1),identity)),identity)),
inference(superposition,[status(thm)],[d47,d39]) ).
cnf(d49,plain,
multiply(multiply(X0,identity),identity) = multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(identity,multiply(X0,multiply(X1,multiply(X1,X1)))),X1),identity),identity))),
inference(demodulation,[status(thm)],[d48,d17]) ).
cnf(d50,plain,
multiply(identity,multiply(multiply(X0,identity),identity)) = multiply(multiply(identity,multiply(X0,multiply(X1,multiply(X1,X1)))),X1),
inference(superposition,[status(thm)],[d49,d10]) ).
cnf(d51,plain,
multiply(multiply(X0,X0),multiply(multiply(X0,multiply(X1,identity)),identity)) = multiply(multiply(X0,multiply(multiply(X0,X0),multiply(X1,X2))),multiply(X2,multiply(X2,X2))),
inference(superposition,[status(thm)],[c0,d19]) ).
cnf(d52,plain,
multiply(identity,multiply(multiply(multiply(X0,multiply(multiply(X0,X0),multiply(X1,X2))),identity),identity)) = multiply(multiply(identity,multiply(multiply(X0,X0),multiply(multiply(X0,multiply(X1,identity)),identity))),X2),
inference(superposition,[status(thm)],[d51,d50]) ).
cnf(d53,plain,
multiply(identity,multiply(multiply(multiply(X0,X0),multiply(multiply(X0,multiply(X1,X2)),identity)),identity)) = multiply(multiply(identity,multiply(multiply(X0,X0),multiply(multiply(X0,multiply(X1,identity)),identity))),X2),
inference(demodulation,[status(thm)],[d52,d27]) ).
cnf(d54,plain,
multiply(multiply(X0,X0),multiply(multiply(X0,multiply(X1,identity)),identity)) = multiply(multiply(X0,multiply(multiply(X0,X0),multiply(X1,identity))),identity),
inference(superposition,[status(thm)],[d5,d19]) ).
cnf(d55,plain,
multiply(X0,multiply(multiply(X0,X0),multiply(multiply(X0,multiply(X1,identity)),identity))) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(X1,identity),identity)))),
inference(superposition,[status(thm)],[d54,d22]) ).
cnf(d56,plain,
multiply(X1,multiply(multiply(X1,X1),multiply(multiply(X1,multiply(X0,identity)),identity))) = X0,
inference(demodulation,[status(thm)],[d55,d10]) ).
cnf(d57,plain,
multiply(multiply(X0,X0),multiply(multiply(multiply(X0,X0),multiply(X0,X0)),multiply(X1,identity))) = multiply(X0,multiply(multiply(X0,X1),identity)),
inference(superposition,[status(thm)],[d19,d56]) ).
cnf(d58,plain,
multiply(X1,multiply(multiply(X1,X1),multiply(multiply(X1,multiply(identity,multiply(X0,identity))),identity))) = multiply(identity,X0),
inference(superposition,[status(thm)],[d39,d56]) ).
cnf(d59,plain,
multiply(X1,multiply(multiply(X1,X1),multiply(multiply(X1,multiply(identity,multiply(identity,multiply(X0,identity)))),identity))) = multiply(identity,multiply(identity,X0)),
inference(superposition,[status(thm)],[d39,d58]) ).
cnf(d60,plain,
multiply(X1,multiply(multiply(X1,X1),multiply(multiply(X1,X0),identity))) = multiply(identity,multiply(identity,multiply(identity,multiply(X0,multiply(identity,multiply(identity,identity)))))),
inference(superposition,[status(thm)],[d45,d59]) ).
cnf(d61,plain,
multiply(X0,multiply(multiply(X0,X0),multiply(multiply(X0,X1),identity))) = multiply(identity,multiply(identity,multiply(identity,multiply(X1,multiply(identity,identity))))),
inference(demodulation,[status(thm)],[d60,c1]) ).
cnf(d62,plain,
multiply(X0,multiply(multiply(X0,X0),multiply(multiply(X0,X1),identity))) = multiply(identity,multiply(identity,multiply(identity,multiply(X1,identity)))),
inference(demodulation,[status(thm)],[d61,c1]) ).
cnf(d63,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(X1,identity)))) = multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),X1)),identity)),
inference(superposition,[status(thm)],[d62,d57]) ).
cnf(d64,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(multiply(X1,identity),identity)))) = multiply(multiply(X0,X0),multiply(multiply(X0,multiply(multiply(X0,X1),identity)),identity)),
inference(superposition,[status(thm)],[d57,d63]) ).
cnf(d65,plain,
X0 = multiply(multiply(X1,X1),multiply(multiply(X1,multiply(multiply(X1,X0),identity)),identity)),
inference(demodulation,[status(thm)],[d64,d10]) ).
cnf(d66,plain,
multiply(identity,multiply(multiply(multiply(X0,X0),multiply(multiply(X0,multiply(multiply(X0,X1),X2)),identity)),identity)) = multiply(multiply(identity,X1),X2),
inference(superposition,[status(thm)],[d65,d53]) ).
cnf(d67,plain,
multiply(identity,multiply(identity,multiply(multiply(identity,X1),X2))) = multiply(X0,multiply(multiply(X0,X0),multiply(multiply(X0,X1),X2))),
inference(superposition,[status(thm)],[d66,d28]) ).
cnf(d68,plain,
multiply(multiply(X0,X0),multiply(multiply(X0,multiply(multiply(X0,X1),X2)),identity)) = multiply(multiply(identity,multiply(identity,multiply(multiply(identity,X1),X2))),identity),
inference(superposition,[status(thm)],[d67,d27]) ).
cnf(d69,plain,
multiply(multiply(X2,X2),multiply(multiply(X2,multiply(multiply(X2,X0),X1)),identity)) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,X0),X1)),identity)),
inference(demodulation,[status(thm)],[d68,d17]) ).
cnf(d70,plain,
multiply(multiply(X2,X2),multiply(multiply(X2,multiply(multiply(X2,X0),X1)),identity)) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,X0),X1),identity))),
inference(demodulation,[status(thm)],[d69,d17]) ).
cnf(d71,plain,
multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(X0,X1),X2)),identity))) = multiply(X0,multiply(identity,multiply(identity,multiply(multiply(multiply(identity,X1),X2),identity)))),
inference(superposition,[status(thm)],[d70,d67]) ).
cnf(d72,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(X0,X1),X2),identity)))) = multiply(X0,multiply(identity,multiply(identity,multiply(multiply(multiply(identity,X1),X2),identity)))),
inference(demodulation,[status(thm)],[d71,d17]) ).
cnf(d73,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(X0,identity),X1),identity)))) = multiply(X0,multiply(identity,multiply(identity,multiply(multiply(identity,X1),identity)))),
inference(superposition,[status(thm)],[c1,d72]) ).
cnf(d74,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(X1,identity),X0),identity)))) = multiply(X1,multiply(identity,multiply(identity,multiply(identity,multiply(X0,identity))))),
inference(demodulation,[status(thm)],[d73,d17]) ).
cnf(d75,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(multiply(X0,identity),X1),identity))),identity)) = multiply(multiply(X0,multiply(identity,multiply(identity,multiply(identity,multiply(X1,identity))))),identity),
inference(superposition,[status(thm)],[d74,d17]) ).
cnf(d76,plain,
multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(multiply(X0,identity),X1),identity)),identity))) = multiply(multiply(X0,multiply(identity,multiply(identity,multiply(identity,multiply(X1,identity))))),identity),
inference(demodulation,[status(thm)],[d75,d17]) ).
cnf(d77,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(X0,identity),X1),identity),identity)))) = multiply(multiply(X0,multiply(identity,multiply(identity,multiply(identity,multiply(X1,identity))))),identity),
inference(demodulation,[status(thm)],[d76,d17]) ).
cnf(d78,plain,
multiply(multiply(X0,identity),X1) = multiply(multiply(X0,multiply(identity,multiply(identity,multiply(identity,multiply(X1,identity))))),identity),
inference(demodulation,[status(thm)],[d77,d10]) ).
cnf(d79,plain,
multiply(multiply(X1,identity),multiply(X0,identity)) = multiply(multiply(X1,X0),identity),
inference(superposition,[status(thm)],[d10,d78]) ).
cnf(d80,plain,
multiply(multiply(identity,multiply(X0,identity)),multiply(X1,identity)) = multiply(multiply(multiply(identity,X0),X1),identity),
inference(superposition,[status(thm)],[d39,d79]) ).
cnf(d81,plain,
multiply(multiply(identity,multiply(identity,multiply(X0,identity))),multiply(X1,identity)) = multiply(multiply(multiply(identity,multiply(identity,X0)),X1),identity),
inference(superposition,[status(thm)],[d39,d80]) ).
cnf(d82,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(X0,identity)))),multiply(X1,identity)) = multiply(multiply(multiply(identity,multiply(identity,multiply(identity,X0))),X1),identity),
inference(superposition,[status(thm)],[d39,d81]) ).
cnf(d83,plain,
multiply(X0,multiply(X1,identity)) = multiply(multiply(multiply(identity,multiply(identity,multiply(identity,multiply(X0,identity)))),X1),identity),
inference(superposition,[status(thm)],[d10,d82]) ).
cnf(d84,plain,
multiply(X0,multiply(multiply(X1,identity),identity)) = multiply(multiply(multiply(multiply(identity,multiply(identity,multiply(identity,X0))),X1),identity),identity),
inference(superposition,[status(thm)],[d82,d83]) ).
cnf(d85,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,X0))),X1) = multiply(identity,multiply(identity,multiply(identity,multiply(X0,multiply(multiply(X1,identity),identity))))),
inference(superposition,[status(thm)],[d84,d8]) ).
cnf(d86,plain,
multiply(multiply(identity,multiply(identity,multiply(X0,X1))),multiply(X1,multiply(X1,X1))) = multiply(identity,multiply(identity,multiply(multiply(X0,identity),identity))),
inference(superposition,[status(thm)],[d0,d14]) ).
cnf(d87,plain,
multiply(X0,multiply(multiply(multiply(X0,identity),identity),multiply(multiply(multiply(X0,identity),identity),multiply(multiply(X0,identity),identity)))) = multiply(identity,multiply(identity,multiply(multiply(identity,identity),identity))),
inference(superposition,[status(thm)],[d8,d86]) ).
cnf(d88,plain,
multiply(X0,multiply(multiply(multiply(X0,identity),identity),multiply(multiply(multiply(X0,identity),identity),multiply(multiply(X0,identity),identity)))) = multiply(identity,multiply(identity,multiply(identity,multiply(identity,identity)))),
inference(demodulation,[status(thm)],[d87,d17]) ).
cnf(d89,plain,
multiply(X0,multiply(multiply(multiply(X0,identity),identity),multiply(multiply(multiply(X0,identity),identity),multiply(multiply(X0,identity),identity)))) = multiply(identity,multiply(identity,multiply(identity,identity))),
inference(demodulation,[status(thm)],[d88,c1]) ).
cnf(d90,plain,
multiply(X0,multiply(multiply(multiply(X0,identity),identity),multiply(multiply(multiply(X0,identity),identity),multiply(multiply(X0,identity),identity)))) = multiply(identity,multiply(identity,identity)),
inference(demodulation,[status(thm)],[d89,c1]) ).
cnf(d91,plain,
multiply(X0,multiply(multiply(multiply(X0,identity),identity),multiply(multiply(multiply(X0,identity),identity),multiply(multiply(X0,identity),identity)))) = multiply(identity,identity),
inference(demodulation,[status(thm)],[d90,c1]) ).
cnf(d92,plain,
multiply(X0,multiply(multiply(multiply(X0,identity),identity),multiply(multiply(multiply(X0,identity),identity),multiply(multiply(X0,identity),identity)))) = identity,
inference(demodulation,[status(thm)],[d91,c1]) ).
cnf(d93,plain,
multiply(multiply(X0,X0),multiply(multiply(X0,multiply(identity,identity)),identity)) = multiply(multiply(multiply(X0,identity),identity),multiply(multiply(multiply(X0,identity),identity),multiply(multiply(X0,identity),identity))),
inference(superposition,[status(thm)],[d92,d19]) ).
cnf(d94,plain,
multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)) = multiply(multiply(multiply(X0,identity),identity),multiply(multiply(multiply(X0,identity),identity),multiply(multiply(X0,identity),identity))),
inference(demodulation,[status(thm)],[d93,c1]) ).
cnf(d95,plain,
multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)) = multiply(multiply(multiply(X0,identity),identity),multiply(multiply(multiply(X0,identity),multiply(X0,identity)),identity)),
inference(demodulation,[status(thm)],[d94,d79]) ).
cnf(d96,plain,
multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)) = multiply(multiply(multiply(X0,identity),multiply(multiply(X0,identity),multiply(X0,identity))),identity),
inference(demodulation,[status(thm)],[d95,d79]) ).
cnf(d97,plain,
multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)) = multiply(multiply(multiply(X0,identity),multiply(multiply(X0,X0),identity)),identity),
inference(demodulation,[status(thm)],[d96,d79]) ).
cnf(d98,plain,
multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)) = multiply(multiply(multiply(X0,multiply(X0,X0)),identity),identity),
inference(demodulation,[status(thm)],[d97,d79]) ).
cnf(d99,plain,
multiply(X0,multiply(X0,X0)) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity))))),
inference(superposition,[status(thm)],[d98,d8]) ).
cnf(d100,plain,
multiply(X0,multiply(X0,X0)) = multiply(multiply(identity,multiply(identity,multiply(identity,multiply(X0,X0)))),X0),
inference(demodulation,[status(thm)],[d99,d85]) ).
cnf(d101,plain,
multiply(X0,multiply(multiply(X0,X0),X1)) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(X0,X0),multiply(multiply(X0,X1),identity)),identity)))),
inference(superposition,[status(thm)],[d27,d8]) ).
cnf(d102,plain,
multiply(X0,multiply(multiply(X0,X0),multiply(multiply(X0,X1),X2))) = multiply(identity,multiply(identity,multiply(multiply(identity,X1),X2))),
inference(superposition,[status(thm)],[d66,d101]) ).
cnf(d103,plain,
multiply(X0,multiply(multiply(X0,multiply(identity,X1)),identity)) = multiply(multiply(X0,X0),multiply(multiply(multiply(X0,X0),multiply(X0,X0)),multiply(identity,multiply(X1,identity)))),
inference(superposition,[status(thm)],[d20,d5]) ).
cnf(d104,plain,
multiply(multiply(X0,X0),multiply(multiply(X0,multiply(multiply(X0,multiply(identity,X1)),identity)),multiply(multiply(X1,identity),multiply(multiply(X1,identity),multiply(X1,identity))))) = identity,
inference(superposition,[status(thm)],[d103,c0]) ).
cnf(d105,plain,
multiply(X0,identity) = multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(X0,multiply(identity,X1)),identity)),multiply(multiply(X1,identity),multiply(multiply(X1,identity),multiply(X1,identity)))))),
inference(superposition,[status(thm)],[d104,d102]) ).
cnf(d106,plain,
multiply(X1,identity) = multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(X1,multiply(identity,X0)),identity)),multiply(multiply(X0,identity),multiply(multiply(X0,X0),identity))))),
inference(demodulation,[status(thm)],[d105,d79]) ).
cnf(d107,plain,
multiply(X1,identity) = multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(X1,multiply(identity,X0)),identity)),multiply(multiply(X0,multiply(X0,X0)),identity)))),
inference(demodulation,[status(thm)],[d106,d79]) ).
cnf(d108,plain,
multiply(X0,identity) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(X0,multiply(identity,X1))),multiply(X1,multiply(X1,X1))),identity))),
inference(demodulation,[status(thm)],[d107,d80]) ).
cnf(d109,plain,
multiply(multiply(X2,identity),multiply(multiply(identity,multiply(X0,multiply(identity,X1))),multiply(X1,multiply(X1,X1)))) = multiply(multiply(X2,multiply(identity,multiply(X0,identity))),identity),
inference(superposition,[status(thm)],[d108,d78]) ).
cnf(d110,plain,
multiply(identity,multiply(multiply(identity,multiply(X0,multiply(identity,X1))),multiply(X1,multiply(X1,X1)))) = multiply(multiply(identity,multiply(identity,multiply(X0,identity))),identity),
inference(superposition,[status(thm)],[c1,d109]) ).
cnf(d111,plain,
multiply(identity,multiply(multiply(identity,multiply(X0,multiply(identity,X1))),multiply(X1,multiply(X1,X1)))) = multiply(identity,multiply(multiply(identity,multiply(X0,identity)),identity)),
inference(demodulation,[status(thm)],[d110,d17]) ).
cnf(d112,plain,
multiply(identity,multiply(multiply(identity,multiply(X0,multiply(identity,X1))),multiply(X1,multiply(X1,X1)))) = multiply(identity,multiply(identity,multiply(multiply(X0,identity),identity))),
inference(demodulation,[status(thm)],[d111,d17]) ).
cnf(d113,plain,
multiply(identity,multiply(multiply(multiply(identity,multiply(X0,multiply(identity,X1))),identity),identity)) = multiply(multiply(identity,multiply(identity,multiply(multiply(X0,identity),identity))),X1),
inference(superposition,[status(thm)],[d112,d50]) ).
cnf(d114,plain,
multiply(identity,multiply(multiply(identity,multiply(multiply(X0,multiply(identity,X1)),identity)),identity)) = multiply(multiply(identity,multiply(identity,multiply(multiply(X0,identity),identity))),X1),
inference(demodulation,[status(thm)],[d113,d17]) ).
cnf(d115,plain,
multiply(identity,multiply(identity,multiply(multiply(multiply(X0,multiply(identity,X1)),identity),identity))) = multiply(multiply(identity,multiply(identity,multiply(multiply(X0,identity),identity))),X1),
inference(demodulation,[status(thm)],[d114,d17]) ).
cnf(d116,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(X0,identity),identity))),X1)) = multiply(X0,multiply(identity,X1)),
inference(superposition,[status(thm)],[d115,d10]) ).
cnf(d117,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X0,identity)),identity))),X1)) = multiply(multiply(identity,X0),multiply(identity,X1)),
inference(superposition,[status(thm)],[d39,d116]) ).
cnf(d118,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(X0,identity),identity)))),X1)) = multiply(multiply(identity,X0),multiply(identity,X1)),
inference(demodulation,[status(thm)],[d117,d17]) ).
cnf(d119,plain,
multiply(identity,multiply(X0,X1)) = multiply(multiply(identity,X0),multiply(identity,X1)),
inference(demodulation,[status(thm)],[d118,d10]) ).
cnf(d120,plain,
multiply(identity,multiply(X1,multiply(identity,multiply(identity,multiply(multiply(X0,identity),identity))))) = multiply(multiply(identity,X1),X0),
inference(superposition,[status(thm)],[d10,d119]) ).
cnf(d121,plain,
multiply(identity,multiply(identity,multiply(X0,multiply(identity,multiply(multiply(X1,identity),identity))))) = multiply(multiply(identity,multiply(identity,X0)),X1),
inference(superposition,[status(thm)],[d119,d120]) ).
cnf(d122,plain,
multiply(identity,multiply(multiply(multiply(identity,multiply(identity,multiply(X0,identity))),X1),identity)) = multiply(X0,multiply(identity,multiply(X1,identity))),
inference(superposition,[status(thm)],[d81,d116]) ).
cnf(d123,plain,
multiply(identity,multiply(multiply(multiply(multiply(identity,multiply(identity,X0)),X1),identity),identity)) = multiply(X0,multiply(identity,multiply(multiply(X1,identity),identity))),
inference(superposition,[status(thm)],[d81,d122]) ).
cnf(d124,plain,
multiply(identity,multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(X0,X1))),identity)) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,X0),multiply(multiply(X1,multiply(X1,X1)),multiply(multiply(X1,multiply(X1,X1)),multiply(X1,multiply(X1,X1))))),identity))),
inference(superposition,[status(thm)],[d40,d3]) ).
cnf(d125,plain,
multiply(identity,multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(multiply(multiply(identity,identity),multiply(X0,X1)),identity))) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,X0),multiply(multiply(X1,multiply(X1,X1)),multiply(multiply(X1,multiply(X1,X1)),multiply(X1,multiply(X1,X1))))),identity))),
inference(demodulation,[status(thm)],[d124,d27]) ).
cnf(d126,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(multiply(multiply(identity,identity),multiply(X0,X1)),identity))) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,X0),multiply(multiply(X1,multiply(X1,X1)),multiply(multiply(X1,multiply(X1,X1)),multiply(X1,multiply(X1,X1))))),identity))),
inference(demodulation,[status(thm)],[d125,c1]) ).
cnf(d127,plain,
multiply(identity,multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(X0,X1)),identity))) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,X0),multiply(multiply(X1,multiply(X1,X1)),multiply(multiply(X1,multiply(X1,X1)),multiply(X1,multiply(X1,X1))))),identity))),
inference(demodulation,[status(thm)],[d126,c1]) ).
cnf(d128,plain,
multiply(identity,multiply(identity,multiply(multiply(multiply(identity,identity),multiply(X0,X1)),identity))) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,X0),multiply(multiply(X1,multiply(X1,X1)),multiply(multiply(X1,multiply(X1,X1)),multiply(X1,multiply(X1,X1))))),identity))),
inference(demodulation,[status(thm)],[d127,c1]) ).
cnf(d129,plain,
multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X0,X1)),identity))) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,X0),multiply(multiply(X1,multiply(X1,X1)),multiply(multiply(X1,multiply(X1,X1)),multiply(X1,multiply(X1,X1))))),identity))),
inference(demodulation,[status(thm)],[d128,c1]) ).
cnf(d130,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(multiply(X0,X1),identity)))) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,X0),multiply(multiply(X1,multiply(X1,X1)),multiply(multiply(X1,multiply(X1,X1)),multiply(X1,multiply(X1,X1))))),identity))),
inference(demodulation,[status(thm)],[d129,d17]) ).
cnf(d131,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(X0,multiply(identity,multiply(X1,multiply(X1,X1)))),X1),identity)))) = multiply(X0,identity),
inference(superposition,[status(thm)],[d108,d130]) ).
cnf(d132,plain,
multiply(multiply(multiply(X0,multiply(identity,multiply(X1,multiply(X1,X1)))),X1),multiply(X2,identity)) = multiply(multiply(multiply(X0,identity),X2),identity),
inference(superposition,[status(thm)],[d131,d83]) ).
cnf(d133,plain,
multiply(multiply(multiply(X0,multiply(identity,multiply(X1,multiply(X1,X1)))),X1),identity) = multiply(multiply(multiply(X0,identity),identity),identity),
inference(superposition,[status(thm)],[c1,d132]) ).
cnf(d134,plain,
multiply(identity,multiply(multiply(multiply(multiply(identity,identity),identity),identity),identity)) = multiply(multiply(X0,multiply(X0,X0)),multiply(identity,multiply(multiply(X0,identity),identity))),
inference(superposition,[status(thm)],[d133,d123]) ).
cnf(d135,plain,
multiply(identity,multiply(multiply(multiply(identity,multiply(identity,identity)),identity),identity)) = multiply(multiply(X0,multiply(X0,X0)),multiply(identity,multiply(multiply(X0,identity),identity))),
inference(demodulation,[status(thm)],[d134,d17]) ).
cnf(d136,plain,
multiply(identity,multiply(multiply(identity,multiply(multiply(identity,identity),identity)),identity)) = multiply(multiply(X0,multiply(X0,X0)),multiply(identity,multiply(multiply(X0,identity),identity))),
inference(demodulation,[status(thm)],[d135,d17]) ).
cnf(d137,plain,
multiply(identity,multiply(identity,multiply(multiply(multiply(identity,identity),identity),identity))) = multiply(multiply(X0,multiply(X0,X0)),multiply(identity,multiply(multiply(X0,identity),identity))),
inference(demodulation,[status(thm)],[d136,d17]) ).
cnf(d138,plain,
multiply(identity,multiply(identity,multiply(multiply(identity,multiply(identity,identity)),identity))) = multiply(multiply(X0,multiply(X0,X0)),multiply(identity,multiply(multiply(X0,identity),identity))),
inference(demodulation,[status(thm)],[d137,d17]) ).
cnf(d139,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(multiply(identity,identity),identity)))) = multiply(multiply(X0,multiply(X0,X0)),multiply(identity,multiply(multiply(X0,identity),identity))),
inference(demodulation,[status(thm)],[d138,d17]) ).
cnf(d140,plain,
identity = multiply(multiply(X0,multiply(X0,X0)),multiply(identity,multiply(multiply(X0,identity),identity))),
inference(demodulation,[status(thm)],[d139,d10]) ).
cnf(d141,plain,
multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X0,X0)),multiply(identity,multiply(multiply(X0,identity),identity))))) = multiply(X0,multiply(multiply(X0,X0),identity)),
inference(superposition,[status(thm)],[d140,d67]) ).
cnf(d142,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(X0,X0)))),X0) = multiply(X0,multiply(multiply(X0,X0),identity)),
inference(demodulation,[status(thm)],[d141,d121]) ).
cnf(d143,plain,
multiply(X0,multiply(X0,X0)) = multiply(X0,multiply(multiply(X0,X0),identity)),
inference(demodulation,[status(thm)],[d142,d100]) ).
cnf(d144,plain,
multiply(multiply(X0,multiply(X0,X0)),identity) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),identity)))),
inference(superposition,[status(thm)],[d98,d8]) ).
cnf(d145,plain,
multiply(multiply(X0,multiply(X0,X0)),identity) = multiply(X0,multiply(multiply(X0,X0),identity)),
inference(demodulation,[status(thm)],[d144,d28]) ).
cnf(d146,plain,
multiply(multiply(X0,multiply(X0,X0)),identity) = multiply(X0,multiply(X0,X0)),
inference(demodulation,[status(thm)],[d145,d143]) ).
cnf(d147,plain,
multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)) = multiply(multiply(X0,multiply(X0,X0)),identity),
inference(superposition,[status(thm)],[d143,d27]) ).
cnf(d148,plain,
multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)) = multiply(X0,multiply(X0,X0)),
inference(demodulation,[status(thm)],[d147,d146]) ).
cnf(d149,plain,
multiply(identity,multiply(identity,multiply(multiply(identity,identity),identity))) = multiply(X0,multiply(X0,multiply(X0,X0))),
inference(superposition,[status(thm)],[d148,d67]) ).
cnf(d150,plain,
multiply(identity,multiply(identity,multiply(identity,identity))) = multiply(X0,multiply(X0,multiply(X0,X0))),
inference(demodulation,[status(thm)],[d149,d143]) ).
cnf(d151,plain,
multiply(identity,multiply(identity,identity)) = multiply(X0,multiply(X0,multiply(X0,X0))),
inference(demodulation,[status(thm)],[d150,c1]) ).
cnf(d152,plain,
multiply(identity,identity) = multiply(X0,multiply(X0,multiply(X0,X0))),
inference(demodulation,[status(thm)],[d151,c1]) ).
cnf(d153,plain,
identity = multiply(X0,multiply(X0,multiply(X0,X0))),
inference(demodulation,[status(thm)],[d152,c1]) ).
cnf(d154,plain,
identity != identity,
inference(demodulation,[status(thm)],[c2,d153]) ).
cnf(d155,plain,
X0 = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,identity),multiply(X0,X1))),multiply(X1,multiply(X1,X1)))),
inference(superposition,[status(thm)],[c0,d35]) ).
cnf(d156,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d155,c0]) ).
cnf(d157,plain,
$false,
inference(resolution,[status(thm)],[d156,d154]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP119-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 14:23:18 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 170.49/26.58 % SZS status Unsatisfiable for theBenchmark.p
% 170.49/26.58 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------