%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP002-4 : 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 : n026.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 64.25s 12.61s
% Output : CNFRefutation 64.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 8
% Syntax : Number of clauses : 117 ( 117 unt; 0 nHn; 5 RR)
% Number of literals : 117 ( 116 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 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 : 233 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(right_identity,axiom,
multiply(X0,identity) = X0 ).
cnf(right_inverse,axiom,
multiply(X0,inverse(X0)) = identity ).
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,
multiply(X0,identity) = X0,
inference(clausification,[status(esa)],[right_identity]) ).
cnf(c1,plain,
multiply(X0,inverse(X0)) = identity,
inference(clausification,[status(esa)],[right_inverse]) ).
cnf(c2,plain,
multiply(X0,multiply(X1,multiply(inverse(X0),inverse(X1)))) = commutator(X0,X1),
inference(clausification,[status(esa)],[commutator]) ).
cnf(c3,plain,
multiply(X0,multiply(X0,X0)) = identity,
inference(clausification,[status(esa)],[x_cubed_is_identity]) ).
cnf(c4,plain,
commutator(commutator(a,b),b) != identity,
inference(clausification,[status(esa)],[prove_commutator]) ).
cnf(c5,plain,
multiply(identity,X0) = X0,
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c6,plain,
multiply(inverse(X0),X0) = identity,
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c7,plain,
multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
inference(clausification,[status(esa)],[associativity]) ).
cnf(d0,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c5,c1]) ).
cnf(d1,plain,
multiply(X0,multiply(inverse(X0),X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c1,c7]) ).
cnf(d2,plain,
multiply(X1,multiply(inverse(X1),X0)) = X0,
inference(demodulation,[status(thm)],[d1,c5]) ).
cnf(d3,plain,
multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = identity,
inference(superposition,[status(thm)],[c7,c1]) ).
cnf(d4,plain,
multiply(X0,identity) = multiply(X1,inverse(multiply(inverse(X0),X1))),
inference(superposition,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
X0 = multiply(X1,inverse(multiply(inverse(X0),X1))),
inference(demodulation,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c6,c7]) ).
cnf(d7,plain,
multiply(inverse(X1),multiply(X1,X0)) = X0,
inference(demodulation,[status(thm)],[d6,c5]) ).
cnf(d8,plain,
multiply(inverse(X0),identity) = inverse(X0),
inference(superposition,[status(thm)],[c1,d7]) ).
cnf(d9,plain,
inverse(X0) = inverse(X0),
inference(demodulation,[status(thm)],[d8,c0]) ).
cnf(d10,plain,
multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c1,d2]) ).
cnf(d11,plain,
X0 = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[d10,c0]) ).
cnf(d12,plain,
inverse(inverse(X0)) = X0,
inference(superposition,[status(thm)],[d11,d9]) ).
cnf(d13,plain,
inverse(X0) = multiply(X1,inverse(multiply(X0,X1))),
inference(superposition,[status(thm)],[d12,d5]) ).
cnf(d14,plain,
multiply(X0,inverse(X1)) = inverse(multiply(X1,inverse(X0))),
inference(superposition,[status(thm)],[d13,d2]) ).
cnf(d15,plain,
multiply(inverse(X0),inverse(X1)) = inverse(multiply(X1,X0)),
inference(superposition,[status(thm)],[d13,d7]) ).
cnf(d16,plain,
multiply(X0,multiply(X1,identity)) = multiply(X0,X1),
inference(superposition,[status(thm)],[c7,c0]) ).
cnf(d17,plain,
multiply(X1,X0) = multiply(X1,X0),
inference(demodulation,[status(thm)],[d16,c0]) ).
cnf(d18,plain,
X1 = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[status(thm)],[d7,d17]) ).
cnf(d19,plain,
multiply(X0,multiply(multiply(X0,X0),X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c3,c7]) ).
cnf(d20,plain,
multiply(X0,multiply(X0,multiply(X0,X1))) = multiply(identity,X1),
inference(demodulation,[status(thm)],[d19,c7]) ).
cnf(d21,plain,
multiply(X1,multiply(X1,multiply(X1,X0))) = X0,
inference(demodulation,[status(thm)],[d20,c5]) ).
cnf(d22,plain,
multiply(X0,multiply(X0,X1)) = multiply(inverse(X0),X1),
inference(superposition,[status(thm)],[d2,d21]) ).
cnf(d23,plain,
multiply(X2,multiply(X0,multiply(X1,multiply(inverse(X2),inverse(multiply(X0,X1)))))) = commutator(X2,multiply(X0,X1)),
inference(superposition,[status(thm)],[c7,c2]) ).
cnf(d24,plain,
multiply(X2,multiply(X0,multiply(multiply(X0,multiply(X0,X1)),multiply(inverse(X2),inverse(X1))))) = commutator(X2,multiply(X0,multiply(X0,multiply(X0,X1)))),
inference(superposition,[status(thm)],[d21,d23]) ).
cnf(d25,plain,
multiply(X2,multiply(X0,multiply(X0,multiply(multiply(X0,X1),multiply(inverse(X2),inverse(X1)))))) = commutator(X2,multiply(X0,multiply(X0,multiply(X0,X1)))),
inference(demodulation,[status(thm)],[d24,c7]) ).
cnf(d26,plain,
multiply(X2,multiply(inverse(X0),multiply(multiply(X0,X1),multiply(inverse(X2),inverse(X1))))) = commutator(X2,multiply(X0,multiply(X0,multiply(X0,X1)))),
inference(demodulation,[status(thm)],[d25,d22]) ).
cnf(d27,plain,
multiply(X2,multiply(inverse(X0),multiply(X0,multiply(X1,multiply(inverse(X2),inverse(X1)))))) = commutator(X2,multiply(X0,multiply(X0,multiply(X0,X1)))),
inference(demodulation,[status(thm)],[d26,c7]) ).
cnf(d28,plain,
multiply(X2,multiply(X1,multiply(inverse(X2),inverse(X1)))) = commutator(X2,multiply(X0,multiply(X0,multiply(X0,X1)))),
inference(demodulation,[status(thm)],[d27,d18]) ).
cnf(d29,plain,
multiply(X0,multiply(X1,inverse(multiply(X1,X0)))) = commutator(X0,multiply(X2,multiply(X2,multiply(X2,X1)))),
inference(demodulation,[status(thm)],[d28,d15]) ).
cnf(d30,plain,
multiply(X2,multiply(X1,inverse(multiply(X1,X2)))) = commutator(X2,multiply(inverse(X0),multiply(X0,X1))),
inference(demodulation,[status(thm)],[d29,d22]) ).
cnf(d31,plain,
multiply(X2,multiply(X1,inverse(multiply(X1,X2)))) = commutator(X2,X1),
inference(demodulation,[status(thm)],[d30,d18]) ).
cnf(d32,plain,
multiply(X1,multiply(inverse(inverse(X0)),inverse(multiply(X0,X1)))) = commutator(inverse(X0),multiply(X0,X1)),
inference(superposition,[status(thm)],[d7,d23]) ).
cnf(d33,plain,
multiply(X1,inverse(multiply(multiply(X0,X1),inverse(X0)))) = commutator(inverse(X0),multiply(X0,X1)),
inference(demodulation,[status(thm)],[d32,d15]) ).
cnf(d34,plain,
multiply(X1,multiply(X0,inverse(multiply(X0,X1)))) = commutator(inverse(X0),multiply(X0,X1)),
inference(demodulation,[status(thm)],[d33,d14]) ).
cnf(d35,plain,
commutator(X0,X1) = commutator(inverse(X1),multiply(X1,X0)),
inference(demodulation,[status(thm)],[d34,d31]) ).
cnf(d36,plain,
commutator(inverse(X0),multiply(X0,X1)) = multiply(X1,multiply(inverse(inverse(X0)),inverse(multiply(X0,X1)))),
inference(superposition,[status(thm)],[d23,d7]) ).
cnf(d37,plain,
commutator(X1,X0) = multiply(X1,multiply(inverse(inverse(X0)),inverse(multiply(X0,X1)))),
inference(demodulation,[status(thm)],[d36,d35]) ).
cnf(d38,plain,
commutator(X1,X0) = multiply(X1,inverse(multiply(multiply(X0,X1),inverse(X0)))),
inference(demodulation,[status(thm)],[d37,d15]) ).
cnf(d39,plain,
commutator(X1,X0) = multiply(X1,multiply(X0,inverse(multiply(X0,X1)))),
inference(demodulation,[status(thm)],[d38,d14]) ).
cnf(d40,plain,
multiply(inverse(X0),X1) = inverse(multiply(inverse(X1),X0)),
inference(superposition,[status(thm)],[d5,d7]) ).
cnf(d41,plain,
multiply(X0,multiply(multiply(X1,multiply(inverse(X0),inverse(X1))),X2)) = multiply(commutator(X0,X1),X2),
inference(superposition,[status(thm)],[c2,c7]) ).
cnf(d42,plain,
multiply(X1,multiply(X0,multiply(multiply(inverse(X1),inverse(X0)),X2))) = multiply(commutator(X1,X0),X2),
inference(demodulation,[status(thm)],[d41,c7]) ).
cnf(d43,plain,
multiply(X0,multiply(X1,multiply(inverse(X0),multiply(inverse(X1),X2)))) = multiply(commutator(X0,X1),X2),
inference(demodulation,[status(thm)],[d42,c7]) ).
cnf(d44,plain,
multiply(X0,multiply(X1,identity)) = multiply(commutator(X0,X1),inverse(multiply(inverse(X0),inverse(X1)))),
inference(superposition,[status(thm)],[d3,d43]) ).
cnf(d45,plain,
multiply(X1,X0) = multiply(commutator(X1,X0),inverse(multiply(inverse(X1),inverse(X0)))),
inference(demodulation,[status(thm)],[d44,c0]) ).
cnf(d46,plain,
multiply(X0,X1) = multiply(commutator(X0,X1),multiply(inverse(inverse(X1)),X0)),
inference(demodulation,[status(thm)],[d45,d40]) ).
cnf(d47,plain,
multiply(X1,X0) = multiply(commutator(X1,X0),multiply(X0,X1)),
inference(demodulation,[status(thm)],[d46,d11]) ).
cnf(d48,plain,
inverse(commutator(X0,X1)) = multiply(multiply(X1,X0),inverse(multiply(X0,X1))),
inference(superposition,[status(thm)],[d47,d13]) ).
cnf(d49,plain,
inverse(commutator(X1,X0)) = multiply(X0,multiply(X1,inverse(multiply(X1,X0)))),
inference(demodulation,[status(thm)],[d48,c7]) ).
cnf(d50,plain,
inverse(commutator(X1,X0)) = commutator(X0,X1),
inference(demodulation,[status(thm)],[d49,d39]) ).
cnf(d51,plain,
multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2,
inference(superposition,[status(thm)],[c7,d7]) ).
cnf(d52,plain,
multiply(X2,multiply(X0,multiply(inverse(X2),X1))) = multiply(commutator(X2,X0),multiply(inverse(X0),multiply(inverse(X0),X1))),
inference(superposition,[status(thm)],[d21,d43]) ).
cnf(d53,plain,
multiply(X2,multiply(X0,multiply(inverse(X2),X1))) = multiply(commutator(X2,X0),multiply(inverse(inverse(X0)),X1)),
inference(demodulation,[status(thm)],[d52,d22]) ).
cnf(d54,plain,
multiply(X1,multiply(X0,multiply(inverse(X1),X2))) = multiply(commutator(X1,X0),multiply(X0,X2)),
inference(demodulation,[status(thm)],[d53,d11]) ).
cnf(d55,plain,
multiply(multiply(X0,X1),multiply(X0,multiply(X1,multiply(X0,X1)))) = identity,
inference(superposition,[status(thm)],[c7,c3]) ).
cnf(d56,plain,
multiply(X0,multiply(X1,multiply(X0,multiply(X1,multiply(X0,X1))))) = identity,
inference(demodulation,[status(thm)],[d55,c7]) ).
cnf(d57,plain,
multiply(X0,multiply(multiply(X1,multiply(X0,multiply(X1,multiply(X0,X1)))),X2)) = multiply(identity,X2),
inference(superposition,[status(thm)],[d56,c7]) ).
cnf(d58,plain,
multiply(X1,multiply(X0,multiply(multiply(X1,multiply(X0,multiply(X1,X0))),X2))) = multiply(identity,X2),
inference(demodulation,[status(thm)],[d57,c7]) ).
cnf(d59,plain,
multiply(X0,multiply(X1,multiply(X0,multiply(multiply(X1,multiply(X0,X1)),X2)))) = multiply(identity,X2),
inference(demodulation,[status(thm)],[d58,c7]) ).
cnf(d60,plain,
multiply(X1,multiply(X0,multiply(X1,multiply(X0,multiply(multiply(X1,X0),X2))))) = multiply(identity,X2),
inference(demodulation,[status(thm)],[d59,c7]) ).
cnf(d61,plain,
multiply(X0,multiply(X1,multiply(X0,multiply(X1,multiply(X0,multiply(X1,X2)))))) = multiply(identity,X2),
inference(demodulation,[status(thm)],[d60,c7]) ).
cnf(d62,plain,
multiply(X1,multiply(X2,multiply(X1,multiply(X2,multiply(X1,multiply(X2,X0)))))) = X0,
inference(demodulation,[status(thm)],[d61,c5]) ).
cnf(d63,plain,
multiply(X0,identity) = inverse(multiply(X0,X0)),
inference(superposition,[status(thm)],[d3,d21]) ).
cnf(d64,plain,
X0 = inverse(multiply(X0,X0)),
inference(demodulation,[status(thm)],[d63,c0]) ).
cnf(d65,plain,
multiply(X0,X0) = inverse(X0),
inference(superposition,[status(thm)],[d64,d11]) ).
cnf(d66,plain,
multiply(multiply(X0,X1),multiply(X0,multiply(multiply(X0,X1),multiply(X0,inverse(multiply(X0,X1)))))) = X1,
inference(superposition,[status(thm)],[d65,d62]) ).
cnf(d67,plain,
multiply(X0,multiply(X1,multiply(X0,multiply(multiply(X0,X1),multiply(X0,inverse(multiply(X0,X1))))))) = X1,
inference(demodulation,[status(thm)],[d66,c7]) ).
cnf(d68,plain,
multiply(X0,multiply(X1,multiply(X0,multiply(X0,multiply(X1,multiply(X0,inverse(multiply(X0,X1)))))))) = X1,
inference(demodulation,[status(thm)],[d67,c7]) ).
cnf(d69,plain,
multiply(X0,multiply(X1,multiply(inverse(X0),multiply(X1,multiply(X0,inverse(multiply(X0,X1))))))) = X1,
inference(demodulation,[status(thm)],[d68,d22]) ).
cnf(d70,plain,
multiply(X1,multiply(X0,multiply(inverse(X1),commutator(X0,X1)))) = X0,
inference(demodulation,[status(thm)],[d69,d39]) ).
cnf(d71,plain,
X1 = multiply(commutator(X0,X1),multiply(X1,commutator(X1,X0))),
inference(superposition,[status(thm)],[d70,d54]) ).
cnf(d72,plain,
multiply(inverse(multiply(commutator(X0,X1),X1)),X1) = commutator(X1,X0),
inference(superposition,[status(thm)],[d71,d51]) ).
cnf(d73,plain,
multiply(X1,multiply(inverse(X0),inverse(multiply(inverse(X0),X1)))) = commutator(X0,multiply(inverse(X0),X1)),
inference(superposition,[status(thm)],[d2,d23]) ).
cnf(d74,plain,
commutator(X0,inverse(X1)) = commutator(X1,multiply(inverse(X1),X0)),
inference(demodulation,[status(thm)],[d73,d31]) ).
cnf(d75,plain,
commutator(multiply(X0,X1),inverse(X0)) = commutator(X0,X1),
inference(superposition,[status(thm)],[d18,d74]) ).
cnf(d76,plain,
commutator(multiply(inverse(X0),X1),X0) = commutator(inverse(X0),X1),
inference(superposition,[status(thm)],[d12,d75]) ).
cnf(d77,plain,
multiply(X0,multiply(X1,multiply(X2,multiply(inverse(multiply(X0,X1)),inverse(X2))))) = commutator(multiply(X0,X1),X2),
inference(superposition,[status(thm)],[c7,c2]) ).
cnf(d78,plain,
multiply(X0,multiply(multiply(X1,multiply(X2,multiply(inverse(multiply(X0,X1)),inverse(X2)))),X3)) = multiply(commutator(multiply(X0,X1),X2),X3),
inference(superposition,[status(thm)],[d77,c7]) ).
cnf(d79,plain,
multiply(X2,multiply(X0,multiply(multiply(X1,multiply(inverse(multiply(X2,X0)),inverse(X1))),X3))) = multiply(commutator(multiply(X2,X0),X1),X3),
inference(demodulation,[status(thm)],[d78,c7]) ).
cnf(d80,plain,
multiply(X1,multiply(X2,multiply(X0,multiply(multiply(inverse(multiply(X1,X2)),inverse(X0)),X3)))) = multiply(commutator(multiply(X1,X2),X0),X3),
inference(demodulation,[status(thm)],[d79,c7]) ).
cnf(d81,plain,
multiply(X0,multiply(X1,multiply(X2,multiply(inverse(multiply(X0,X1)),multiply(inverse(X2),X3))))) = multiply(commutator(multiply(X0,X1),X2),X3),
inference(demodulation,[status(thm)],[d80,c7]) ).
cnf(d82,plain,
identity = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[c6,d17]) ).
cnf(d83,plain,
multiply(inverse(X0),multiply(X1,multiply(X0,identity))) = multiply(commutator(multiply(inverse(X0),X1),X0),X1),
inference(superposition,[status(thm)],[d82,d81]) ).
cnf(d84,plain,
multiply(inverse(X0),multiply(X1,X0)) = multiply(commutator(multiply(inverse(X0),X1),X0),X1),
inference(demodulation,[status(thm)],[d83,c0]) ).
cnf(d85,plain,
multiply(inverse(X0),multiply(X1,X0)) = multiply(commutator(inverse(X0),X1),X1),
inference(demodulation,[status(thm)],[d84,d76]) ).
cnf(d86,plain,
multiply(X1,commutator(X1,X0)) = multiply(inverse(commutator(X0,X1)),X1),
inference(superposition,[status(thm)],[d71,d18]) ).
cnf(d87,plain,
multiply(X1,commutator(X1,X0)) = multiply(commutator(X1,X0),X1),
inference(demodulation,[status(thm)],[d86,d50]) ).
cnf(d88,plain,
X0 = multiply(inverse(commutator(X0,X1)),multiply(X0,commutator(X0,X1))),
inference(superposition,[status(thm)],[d87,d18]) ).
cnf(d89,plain,
X0 = multiply(commutator(inverse(commutator(X0,X1)),X0),X0),
inference(demodulation,[status(thm)],[d88,d85]) ).
cnf(d90,plain,
X0 = multiply(commutator(commutator(X1,X0),X0),X0),
inference(demodulation,[status(thm)],[d89,d50]) ).
cnf(d91,plain,
multiply(inverse(X1),X1) = commutator(X1,commutator(X0,X1)),
inference(superposition,[status(thm)],[d90,d72]) ).
cnf(d92,plain,
identity = commutator(X0,commutator(X1,X0)),
inference(demodulation,[status(thm)],[d91,c6]) ).
cnf(d93,plain,
inverse(identity) = commutator(commutator(X1,X0),X0),
inference(superposition,[status(thm)],[d92,d50]) ).
cnf(d94,plain,
identity = commutator(commutator(X0,X1),X1),
inference(demodulation,[status(thm)],[d93,d0]) ).
cnf(d95,plain,
identity != identity,
inference(demodulation,[status(thm)],[c4,d94]) ).
cnf(d96,plain,
multiply(X0,identity) = multiply(X0,multiply(X0,multiply(X0,X0))),
inference(superposition,[status(thm)],[d56,d21]) ).
cnf(d97,plain,
X0 = multiply(X0,multiply(X0,multiply(X0,X0))),
inference(demodulation,[status(thm)],[d96,c0]) ).
cnf(d98,plain,
X0 = multiply(inverse(X0),multiply(X0,X0)),
inference(demodulation,[status(thm)],[d97,d22]) ).
cnf(d99,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d98,d18]) ).
cnf(d100,plain,
$false,
inference(resolution,[status(thm)],[d99,d95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP002-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 14:18:27 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 64.25/12.61 % SZS status Unsatisfiable for theBenchmark.p
% 64.25/12.61 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
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