%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP002-3 : 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 : n002.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 07:22:03 AM UTC 2026
% Result : Unsatisfiable 73.15s 11.06s
% Output : CNFRefutation 73.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 6
% Syntax : Number of clauses : 143 ( 143 unt; 0 nHn; 11 RR)
% Number of literals : 143 ( 142 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 260 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(commutator,axiom,
commutator(X0,X1) = multiply(X0,multiply(X1,multiply(inverse(X0),inverse(X1)))) ).
cnf(x_cubed_is_identity,hypothesis,
multiply(X0,multiply(X0,X0)) = identity ).
cnf(prove_commutator,negated_conjecture,
commutator(commutator(a,b),b) != identity ).
cnf(left_identity,axiom,
multiply(identity,X0) = X0 ).
cnf(left_inverse,axiom,
multiply(inverse(X0),X0) = identity ).
cnf(associativity,axiom,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)) ).
cnf(c0,plain,
commutator(X0,X1) = multiply(X0,multiply(X1,multiply(inverse(X0),inverse(X1)))),
inference(clausification,[status(esa)],[commutator]) ).
cnf(c1,plain,
multiply(X0,multiply(X0,X0)) = identity,
inference(clausification,[status(esa)],[x_cubed_is_identity]) ).
cnf(c2,plain,
commutator(commutator(a,b),b) != identity,
inference(clausification,[status(esa)],[prove_commutator]) ).
cnf(c3,plain,
multiply(identity,X0) = X0,
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c4,plain,
multiply(inverse(X0),X0) = identity,
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c5,plain,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(clausification,[status(esa)],[associativity]) ).
cnf(d0,plain,
multiply(identity,X1) = multiply(X0,multiply(multiply(X0,X0),X1)),
inference(superposition,[status(thm)],[c1,c5]) ).
cnf(d1,plain,
X0 = multiply(X1,multiply(multiply(X1,X1),X0)),
inference(demodulation,[status(thm)],[d0,c3]) ).
cnf(d2,plain,
X1 = multiply(X0,multiply(X0,multiply(X0,X1))),
inference(demodulation,[status(thm)],[d1,c5]) ).
cnf(d3,plain,
X0 = multiply(X0,identity),
inference(superposition,[status(thm)],[c1,d2]) ).
cnf(d4,plain,
multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[status(thm)],[c4,c5]) ).
cnf(d5,plain,
X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(demodulation,[status(thm)],[d4,c3]) ).
cnf(d6,plain,
multiply(X0,X0) = multiply(inverse(X0),identity),
inference(superposition,[status(thm)],[c1,d5]) ).
cnf(d7,plain,
multiply(X0,multiply(inverse(X0),identity)) = identity,
inference(superposition,[status(thm)],[d6,c1]) ).
cnf(d8,plain,
multiply(X0,inverse(X0)) = identity,
inference(demodulation,[status(thm)],[d7,d3]) ).
cnf(d9,plain,
multiply(X0,X1) = multiply(identity,multiply(X0,X1)),
inference(superposition,[status(thm)],[c3,c5]) ).
cnf(d10,plain,
multiply(X0,X1) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d9,c3]) ).
cnf(d11,plain,
multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(superposition,[status(thm)],[d5,d10]) ).
cnf(d12,plain,
X0 = multiply(inverse(inverse(X0)),identity),
inference(superposition,[status(thm)],[c4,d5]) ).
cnf(d13,plain,
multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[d12,d10]) ).
cnf(d14,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d13,d3]) ).
cnf(d15,plain,
multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[d14,d11]) ).
cnf(d16,plain,
multiply(commutator(X0,X1),X2) = multiply(X0,multiply(multiply(X1,multiply(inverse(X0),inverse(X1))),X2)),
inference(superposition,[status(thm)],[c0,c5]) ).
cnf(d17,plain,
multiply(commutator(X1,X0),X2) = multiply(X1,multiply(X0,multiply(multiply(inverse(X1),inverse(X0)),X2))),
inference(demodulation,[status(thm)],[d16,c5]) ).
cnf(d18,plain,
multiply(commutator(X0,X1),X2) = multiply(X0,multiply(X1,multiply(inverse(X0),multiply(inverse(X1),X2)))),
inference(demodulation,[status(thm)],[d17,c5]) ).
cnf(d19,plain,
commutator(X1,inverse(X0)) = multiply(X1,multiply(inverse(X0),multiply(inverse(X1),X0))),
inference(superposition,[status(thm)],[d14,c0]) ).
cnf(d20,plain,
multiply(commutator(X1,X0),X1) = multiply(X1,commutator(X0,inverse(X1))),
inference(superposition,[status(thm)],[d19,d18]) ).
cnf(d21,plain,
commutator(X1,inverse(X0)) = multiply(inverse(X0),multiply(commutator(X0,X1),X0)),
inference(superposition,[status(thm)],[d20,d5]) ).
cnf(d22,plain,
X1 = multiply(X0,multiply(inverse(X0),X1)),
inference(superposition,[status(thm)],[d14,d5]) ).
cnf(d23,plain,
X0 = multiply(identity,X0),
inference(superposition,[status(thm)],[c3,d10]) ).
cnf(d24,plain,
X0 = multiply(inverse(identity),X0),
inference(superposition,[status(thm)],[d23,d5]) ).
cnf(d25,plain,
commutator(identity,X0) = multiply(X0,multiply(inverse(identity),inverse(X0))),
inference(superposition,[status(thm)],[c0,c3]) ).
cnf(d26,plain,
multiply(inverse(identity),inverse(identity)) = commutator(identity,identity),
inference(superposition,[status(thm)],[d25,d23]) ).
cnf(d27,plain,
multiply(inverse(identity),commutator(identity,identity)) = identity,
inference(superposition,[status(thm)],[d26,c1]) ).
cnf(d28,plain,
commutator(identity,identity) = identity,
inference(demodulation,[status(thm)],[d27,d24]) ).
cnf(d29,plain,
commutator(identity,identity) = multiply(inverse(identity),inverse(identity)),
inference(superposition,[status(thm)],[d25,c3]) ).
cnf(d30,plain,
commutator(identity,identity) = inverse(identity),
inference(demodulation,[status(thm)],[d29,d24]) ).
cnf(d31,plain,
identity = inverse(identity),
inference(demodulation,[status(thm)],[d30,d28]) ).
cnf(d32,plain,
commutator(identity,X0) = multiply(X0,inverse(X0)),
inference(demodulation,[status(thm)],[d25,d24]) ).
cnf(d33,plain,
commutator(identity,X0) = identity,
inference(demodulation,[status(thm)],[d32,d8]) ).
cnf(d34,plain,
commutator(identity,multiply(X0,X1)) = multiply(X0,multiply(X1,multiply(inverse(identity),inverse(multiply(X0,X1))))),
inference(superposition,[status(thm)],[d25,c5]) ).
cnf(d35,plain,
identity = multiply(X0,multiply(X1,multiply(inverse(identity),inverse(multiply(X0,X1))))),
inference(demodulation,[status(thm)],[d34,d33]) ).
cnf(d36,plain,
identity = multiply(X0,multiply(X1,multiply(identity,inverse(multiply(X0,X1))))),
inference(demodulation,[status(thm)],[d35,d31]) ).
cnf(d37,plain,
identity = multiply(X0,multiply(X1,inverse(multiply(X0,X1)))),
inference(demodulation,[status(thm)],[d36,c3]) ).
cnf(d38,plain,
multiply(inverse(X0),identity) = multiply(X1,inverse(multiply(X0,X1))),
inference(superposition,[status(thm)],[d37,d11]) ).
cnf(d39,plain,
inverse(X0) = multiply(X1,inverse(multiply(X0,X1))),
inference(demodulation,[status(thm)],[d38,d3]) ).
cnf(d40,plain,
multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(superposition,[status(thm)],[d39,d10]) ).
cnf(d41,plain,
multiply(inverse(X0),inverse(X1)) = inverse(multiply(X1,X0)),
inference(superposition,[status(thm)],[d39,d11]) ).
cnf(d42,plain,
multiply(X0,multiply(X1,multiply(inverse(X0),inverse(X1)))) = commutator(X0,X1),
inference(superposition,[status(thm)],[c0,d10]) ).
cnf(d43,plain,
multiply(X0,multiply(X1,inverse(multiply(X1,X0)))) = commutator(X0,X1),
inference(demodulation,[status(thm)],[d42,d41]) ).
cnf(d44,plain,
multiply(X0,inverse(X1)) = inverse(multiply(X1,inverse(X0))),
inference(superposition,[status(thm)],[d39,d15]) ).
cnf(d45,plain,
commutator(X2,multiply(X0,X1)) = multiply(X2,multiply(X0,multiply(X1,multiply(inverse(X2),inverse(multiply(X0,X1)))))),
inference(superposition,[status(thm)],[c5,c0]) ).
cnf(d46,plain,
commutator(inverse(X0),multiply(X0,X1)) = multiply(X1,multiply(inverse(inverse(X0)),inverse(multiply(X0,X1)))),
inference(superposition,[status(thm)],[d45,d11]) ).
cnf(d47,plain,
commutator(inverse(X0),multiply(X0,X1)) = multiply(X1,inverse(multiply(multiply(X0,X1),inverse(X0)))),
inference(demodulation,[status(thm)],[d46,d41]) ).
cnf(d48,plain,
commutator(inverse(X0),multiply(X0,X1)) = multiply(X1,multiply(X0,inverse(multiply(X0,X1)))),
inference(demodulation,[status(thm)],[d47,d44]) ).
cnf(d49,plain,
commutator(inverse(X1),multiply(X1,X0)) = commutator(X0,X1),
inference(demodulation,[status(thm)],[d48,d43]) ).
cnf(d50,plain,
X0 = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[d12,d3]) ).
cnf(d51,plain,
commutator(X0,multiply(inverse(X0),X1)) = commutator(X1,inverse(X0)),
inference(superposition,[status(thm)],[d50,d49]) ).
cnf(d52,plain,
commutator(X0,X1) = commutator(multiply(X0,X1),inverse(X0)),
inference(superposition,[status(thm)],[d11,d51]) ).
cnf(d53,plain,
commutator(X0,multiply(X1,inverse(inverse(X0)))) = multiply(X0,multiply(X1,inverse(multiply(X1,inverse(inverse(X0)))))),
inference(superposition,[status(thm)],[d11,d45]) ).
cnf(d54,plain,
commutator(X0,multiply(X1,X0)) = multiply(X0,multiply(X1,inverse(multiply(X1,inverse(inverse(X0)))))),
inference(demodulation,[status(thm)],[d53,d14]) ).
cnf(d55,plain,
commutator(X1,multiply(X0,X1)) = multiply(X1,multiply(X0,multiply(inverse(X1),inverse(X0)))),
inference(demodulation,[status(thm)],[d54,d44]) ).
cnf(d56,plain,
commutator(X0,multiply(X1,X0)) = multiply(X0,multiply(X1,inverse(multiply(X1,X0)))),
inference(demodulation,[status(thm)],[d55,d41]) ).
cnf(d57,plain,
commutator(X0,multiply(X1,X0)) = commutator(X0,X1),
inference(demodulation,[status(thm)],[d56,d43]) ).
cnf(d58,plain,
commutator(multiply(X0,X1),X1) = commutator(multiply(X0,X1),inverse(X0)),
inference(superposition,[status(thm)],[d11,d57]) ).
cnf(d59,plain,
commutator(multiply(X0,X1),X1) = commutator(X0,X1),
inference(demodulation,[status(thm)],[d58,d52]) ).
cnf(d60,plain,
multiply(inverse(X1),X0) = inverse(multiply(inverse(X0),X1)),
inference(superposition,[status(thm)],[d50,d41]) ).
cnf(d61,plain,
multiply(inverse(multiply(X0,X1)),X0) = inverse(X1),
inference(superposition,[status(thm)],[d11,d60]) ).
cnf(d62,plain,
commutator(inverse(X1),X0) = commutator(inverse(multiply(X0,X1)),X0),
inference(superposition,[status(thm)],[d61,d59]) ).
cnf(d63,plain,
commutator(inverse(inverse(X1)),X0) = commutator(multiply(X1,inverse(X0)),X0),
inference(superposition,[status(thm)],[d44,d62]) ).
cnf(d64,plain,
commutator(X0,X1) = commutator(multiply(X0,inverse(X1)),X1),
inference(demodulation,[status(thm)],[d63,d14]) ).
cnf(d65,plain,
commutator(multiply(X0,X1),X2) = multiply(X0,multiply(X1,multiply(X2,multiply(inverse(multiply(X0,X1)),inverse(X2))))),
inference(superposition,[status(thm)],[c5,c0]) ).
cnf(d66,plain,
commutator(multiply(X1,inverse(X0)),X0) = multiply(X1,multiply(inverse(multiply(X1,inverse(X0))),inverse(X0))),
inference(superposition,[status(thm)],[d11,d65]) ).
cnf(d67,plain,
commutator(multiply(X0,inverse(X1)),X1) = multiply(X0,inverse(multiply(X1,multiply(X0,inverse(X1))))),
inference(demodulation,[status(thm)],[d66,d41]) ).
cnf(d68,plain,
commutator(X0,X1) = multiply(X0,inverse(multiply(X1,multiply(X0,inverse(X1))))),
inference(demodulation,[status(thm)],[d67,d64]) ).
cnf(d69,plain,
multiply(commutator(X1,X0),X0) = multiply(X1,multiply(X0,multiply(inverse(X1),identity))),
inference(superposition,[status(thm)],[c4,d18]) ).
cnf(d70,plain,
multiply(commutator(X0,X1),X1) = multiply(X0,multiply(X1,inverse(X0))),
inference(demodulation,[status(thm)],[d69,d3]) ).
cnf(d71,plain,
commutator(X1,X0) = multiply(X1,inverse(multiply(commutator(X0,X1),X1))),
inference(superposition,[status(thm)],[d70,d68]) ).
cnf(d72,plain,
commutator(X0,X1) = inverse(commutator(X1,X0)),
inference(demodulation,[status(thm)],[d71,d40]) ).
cnf(d73,plain,
X2 = multiply(commutator(X0,X1),multiply(commutator(X1,X0),X2)),
inference(superposition,[status(thm)],[d72,d22]) ).
cnf(d74,plain,
multiply(commutator(X2,X0),multiply(X0,X1)) = multiply(X2,multiply(X0,multiply(inverse(X2),X1))),
inference(superposition,[status(thm)],[d11,d18]) ).
cnf(d75,plain,
multiply(inverse(X0),X1) = multiply(X0,multiply(X0,X1)),
inference(superposition,[status(thm)],[d2,d11]) ).
cnf(d76,plain,
multiply(multiply(X0,X1),multiply(X0,multiply(X1,multiply(X0,X1)))) = identity,
inference(superposition,[status(thm)],[c5,c1]) ).
cnf(d77,plain,
multiply(X0,multiply(X1,multiply(X0,multiply(X1,multiply(X0,X1))))) = identity,
inference(demodulation,[status(thm)],[d76,c5]) ).
cnf(d78,plain,
multiply(identity,X2) = multiply(X0,multiply(multiply(X1,multiply(X0,multiply(X1,multiply(X0,X1)))),X2)),
inference(superposition,[status(thm)],[d77,c5]) ).
cnf(d79,plain,
X0 = multiply(X1,multiply(multiply(X2,multiply(X1,multiply(X2,multiply(X1,X2)))),X0)),
inference(demodulation,[status(thm)],[d78,c3]) ).
cnf(d80,plain,
X2 = multiply(X1,multiply(X0,multiply(multiply(X1,multiply(X0,multiply(X1,X0))),X2))),
inference(demodulation,[status(thm)],[d79,c5]) ).
cnf(d81,plain,
X2 = multiply(X0,multiply(X1,multiply(X0,multiply(multiply(X1,multiply(X0,X1)),X2)))),
inference(demodulation,[status(thm)],[d80,c5]) ).
cnf(d82,plain,
X2 = multiply(X1,multiply(X0,multiply(X1,multiply(X0,multiply(multiply(X1,X0),X2))))),
inference(demodulation,[status(thm)],[d81,c5]) ).
cnf(d83,plain,
X2 = multiply(X0,multiply(X1,multiply(X0,multiply(X1,multiply(X0,multiply(X1,X2)))))),
inference(demodulation,[status(thm)],[d82,c5]) ).
cnf(d84,plain,
multiply(X0,X0) = inverse(X0),
inference(demodulation,[status(thm)],[d6,d3]) ).
cnf(d85,plain,
X0 = multiply(X1,multiply(X0,multiply(X1,multiply(X0,multiply(X1,inverse(X0)))))),
inference(superposition,[status(thm)],[d84,d83]) ).
cnf(d86,plain,
commutator(inverse(X0),X1) = multiply(inverse(X0),multiply(X1,multiply(X0,inverse(X1)))),
inference(superposition,[status(thm)],[d14,c0]) ).
cnf(d87,plain,
multiply(X1,multiply(X0,inverse(X1))) = multiply(X0,commutator(inverse(X0),X1)),
inference(superposition,[status(thm)],[d86,d22]) ).
cnf(d88,plain,
X0 = multiply(X1,multiply(X0,multiply(X1,multiply(X1,commutator(inverse(X1),X0))))),
inference(superposition,[status(thm)],[d87,d85]) ).
cnf(d89,plain,
X1 = multiply(X0,multiply(X1,multiply(inverse(X0),commutator(inverse(X0),X1)))),
inference(demodulation,[status(thm)],[d88,d75]) ).
cnf(d90,plain,
multiply(commutator(X0,X1),multiply(X1,commutator(inverse(X0),X1))) = X1,
inference(superposition,[status(thm)],[d89,d74]) ).
cnf(d91,plain,
multiply(X1,commutator(inverse(X0),X1)) = multiply(commutator(X1,X0),X1),
inference(superposition,[status(thm)],[d90,d73]) ).
cnf(d92,plain,
multiply(inverse(X0),multiply(commutator(X0,X1),X0)) = commutator(inverse(X1),X0),
inference(superposition,[status(thm)],[d91,d11]) ).
cnf(d93,plain,
commutator(X1,inverse(X0)) = commutator(inverse(X1),X0),
inference(demodulation,[status(thm)],[d92,d21]) ).
cnf(d94,plain,
multiply(X1,multiply(inverse(inverse(X0)),inverse(multiply(X0,X1)))) = commutator(inverse(X0),multiply(X0,X1)),
inference(superposition,[status(thm)],[d45,d5]) ).
cnf(d95,plain,
multiply(X1,inverse(multiply(multiply(X0,X1),inverse(X0)))) = commutator(inverse(X0),multiply(X0,X1)),
inference(demodulation,[status(thm)],[d94,d41]) ).
cnf(d96,plain,
multiply(X1,multiply(X0,inverse(multiply(X0,X1)))) = commutator(inverse(X0),multiply(X0,X1)),
inference(demodulation,[status(thm)],[d95,d44]) ).
cnf(d97,plain,
commutator(X0,X1) = commutator(inverse(X1),multiply(X1,X0)),
inference(demodulation,[status(thm)],[d96,d43]) ).
cnf(d98,plain,
commutator(X1,X0) = commutator(X0,inverse(multiply(X0,X1))),
inference(demodulation,[status(thm)],[d97,d93]) ).
cnf(d99,plain,
commutator(X0,inverse(X1)) = commutator(X0,inverse(multiply(X0,X1))),
inference(superposition,[status(thm)],[d61,d57]) ).
cnf(d100,plain,
commutator(X0,inverse(inverse(X1))) = commutator(X0,multiply(X1,inverse(X0))),
inference(superposition,[status(thm)],[d44,d99]) ).
cnf(d101,plain,
commutator(X1,X0) = commutator(X1,multiply(X0,inverse(X1))),
inference(demodulation,[status(thm)],[d100,d14]) ).
cnf(d102,plain,
multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
inference(superposition,[status(thm)],[c5,d10]) ).
cnf(d103,plain,
commutator(X2,multiply(X0,multiply(X1,X2))) = commutator(X2,multiply(X0,X1)),
inference(superposition,[status(thm)],[d102,d57]) ).
cnf(d104,plain,
commutator(X0,multiply(X1,inverse(X0))) = commutator(X0,multiply(X1,X0)),
inference(superposition,[status(thm)],[d84,d103]) ).
cnf(d105,plain,
commutator(X0,X1) = commutator(X0,multiply(X1,X0)),
inference(demodulation,[status(thm)],[d104,d101]) ).
cnf(d106,plain,
commutator(X0,inverse(multiply(X0,X1))) = commutator(X0,inverse(X1)),
inference(superposition,[status(thm)],[d61,d105]) ).
cnf(d107,plain,
commutator(X1,X0) = commutator(X0,inverse(X1)),
inference(demodulation,[status(thm)],[d106,d98]) ).
cnf(d108,plain,
inverse(commutator(X1,X0)) = commutator(X0,X1),
inference(superposition,[status(thm)],[d72,d14]) ).
cnf(d109,plain,
commutator(commutator(X0,X1),X2) = commutator(X2,commutator(X1,X0)),
inference(superposition,[status(thm)],[d108,d107]) ).
cnf(d110,plain,
multiply(inverse(X0),multiply(inverse(X1),X2)) = multiply(inverse(multiply(X1,X0)),X2),
inference(superposition,[status(thm)],[d41,d102]) ).
cnf(d111,plain,
multiply(X1,multiply(inverse(X0),inverse(X1))) = multiply(inverse(X0),commutator(X0,X1)),
inference(superposition,[status(thm)],[c0,d5]) ).
cnf(d112,plain,
multiply(inverse(X0),multiply(inverse(X1),X0)) = multiply(inverse(X1),commutator(X1,inverse(X0))),
inference(superposition,[status(thm)],[d50,d111]) ).
cnf(d113,plain,
multiply(inverse(multiply(X1,X0)),X0) = multiply(inverse(X1),commutator(X1,inverse(X0))),
inference(demodulation,[status(thm)],[d112,d110]) ).
cnf(d114,plain,
multiply(inverse(multiply(X0,X1)),X1) = multiply(inverse(X0),commutator(X1,X0)),
inference(demodulation,[status(thm)],[d113,d107]) ).
cnf(d115,plain,
inverse(X1) = multiply(inverse(multiply(X0,X1)),X0),
inference(superposition,[status(thm)],[d61,d10]) ).
cnf(d116,plain,
multiply(X1,commutator(X0,X1)) = multiply(commutator(X1,inverse(X0)),X1),
inference(superposition,[status(thm)],[d50,d91]) ).
cnf(d117,plain,
multiply(X0,commutator(X1,X0)) = multiply(commutator(X1,X0),X0),
inference(demodulation,[status(thm)],[d116,d107]) ).
cnf(d118,plain,
inverse(X1) = multiply(inverse(multiply(X1,commutator(X0,X1))),commutator(X0,X1)),
inference(superposition,[status(thm)],[d117,d115]) ).
cnf(d119,plain,
inverse(X0) = multiply(inverse(X0),commutator(commutator(X1,X0),X0)),
inference(demodulation,[status(thm)],[d118,d114]) ).
cnf(d120,plain,
inverse(X1) = multiply(inverse(X1),commutator(X1,commutator(X1,X0))),
inference(demodulation,[status(thm)],[d119,d109]) ).
cnf(d121,plain,
multiply(X0,inverse(X0)) = commutator(X0,commutator(X0,X1)),
inference(superposition,[status(thm)],[d120,d15]) ).
cnf(d122,plain,
identity = commutator(X0,commutator(X0,X1)),
inference(demodulation,[status(thm)],[d121,d8]) ).
cnf(d123,plain,
commutator(b,commutator(b,a)) != identity,
inference(demodulation,[status(thm)],[c2,d109]) ).
cnf(d124,plain,
identity != identity,
inference(demodulation,[status(thm)],[d123,d122]) ).
cnf(d125,plain,
multiply(X1,multiply(X0,multiply(X1,multiply(X0,X1)))) = multiply(inverse(X0),identity),
inference(superposition,[status(thm)],[d77,d5]) ).
cnf(d126,plain,
multiply(X1,multiply(X0,multiply(X1,multiply(X0,X1)))) = inverse(X0),
inference(demodulation,[status(thm)],[d125,d3]) ).
cnf(d127,plain,
inverse(inverse(X0)) = multiply(X0,multiply(inverse(X0),X0)),
inference(superposition,[status(thm)],[d126,d15]) ).
cnf(d128,plain,
X0 = multiply(X0,multiply(inverse(X0),X0)),
inference(demodulation,[status(thm)],[d127,d14]) ).
cnf(d129,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d128,d15]) ).
cnf(d130,plain,
$false,
inference(resolution,[status(thm)],[d129,d124]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP002-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 14:18:24 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 73.15/11.06 % SZS status Unsatisfiable for theBenchmark.p
% 73.15/11.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------