TSTP Solution File: GRP002-4 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GRP002-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 05:52:15 EDT 2024
% Result : Unsatisfiable 2.22s 0.65s
% Output : Refutation 2.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 8
% Syntax : Number of formulae : 163 ( 163 unt; 0 def)
% Number of atoms : 163 ( 162 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 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 : 320 ( 320 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8742,plain,
$false,
inference(trivial_inequality_removal,[],[f8741]) ).
fof(f8741,plain,
identity != identity,
inference(superposition,[],[f8,f8350]) ).
fof(f8350,plain,
! [X0,X1] : identity = commutator(commutator(X0,X1),X1),
inference(backward_demodulation,[],[f7768,f8349]) ).
fof(f8349,plain,
! [X0,X1] : identity = multiply(multiply(inverse(multiply(X1,X0)),X0),multiply(X1,commutator(X1,X0))),
inference(forward_demodulation,[],[f8348,f399]) ).
fof(f399,plain,
! [X2,X0,X1] : multiply(inverse(multiply(X1,X0)),X2) = multiply(inverse(X0),multiply(inverse(X1),X2)),
inference(superposition,[],[f3,f222]) ).
fof(f222,plain,
! [X0,X1] : multiply(inverse(X0),inverse(X1)) = inverse(multiply(X1,X0)),
inference(superposition,[],[f37,f200]) ).
fof(f200,plain,
! [X0,X1] : inverse(X0) = multiply(X1,inverse(multiply(X0,X1))),
inference(forward_demodulation,[],[f173,f4]) ).
fof(f4,axiom,
! [X0] : multiply(X0,identity) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
fof(f173,plain,
! [X0,X1] : multiply(X1,inverse(multiply(X0,X1))) = multiply(inverse(X0),identity),
inference(superposition,[],[f37,f26]) ).
fof(f26,plain,
! [X0,X1] : identity = multiply(X0,multiply(X1,inverse(multiply(X0,X1)))),
inference(superposition,[],[f3,f5]) ).
fof(f5,axiom,
! [X0] : identity = multiply(X0,inverse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
fof(f37,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f24,f1]) ).
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f24,plain,
! [X0,X1] : multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[],[f3,f2]) ).
fof(f2,axiom,
! [X0] : identity = multiply(inverse(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f8348,plain,
! [X0,X1] : identity = multiply(multiply(inverse(X0),multiply(inverse(X1),X0)),multiply(X1,commutator(X1,X0))),
inference(forward_demodulation,[],[f8347,f116]) ).
fof(f116,plain,
! [X0,X1] : multiply(inverse(X0),X1) = multiply(X0,multiply(X0,X1)),
inference(superposition,[],[f3,f104]) ).
fof(f104,plain,
! [X0] : inverse(X0) = multiply(X0,X0),
inference(superposition,[],[f53,f52]) ).
fof(f52,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f43,f4]) ).
fof(f43,plain,
! [X0] : multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[],[f32,f5]) ).
fof(f32,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(forward_demodulation,[],[f20,f1]) ).
fof(f20,plain,
! [X0,X1] : multiply(identity,X1) = multiply(X0,multiply(inverse(X0),X1)),
inference(superposition,[],[f3,f5]) ).
fof(f53,plain,
! [X0] : multiply(inverse(X0),inverse(X0)) = X0,
inference(forward_demodulation,[],[f44,f4]) ).
fof(f44,plain,
! [X0] : multiply(X0,identity) = multiply(inverse(X0),inverse(X0)),
inference(superposition,[],[f32,f7]) ).
fof(f7,axiom,
! [X0] : identity = multiply(X0,multiply(X0,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_cubed_is_identity) ).
fof(f8347,plain,
! [X0,X1] : identity = multiply(multiply(inverse(X0),multiply(X1,multiply(X1,X0))),multiply(X1,commutator(X1,X0))),
inference(forward_demodulation,[],[f8346,f52]) ).
fof(f8346,plain,
! [X0,X1] : identity = multiply(multiply(inverse(X0),multiply(X1,inverse(inverse(multiply(X1,X0))))),multiply(X1,commutator(X1,X0))),
inference(forward_demodulation,[],[f8345,f3]) ).
fof(f8345,plain,
! [X0,X1] : identity = multiply(multiply(multiply(inverse(X0),X1),inverse(inverse(multiply(X1,X0)))),multiply(X1,commutator(X1,X0))),
inference(forward_demodulation,[],[f8344,f7631]) ).
fof(f7631,plain,
! [X0,X1] : commutator(inverse(X0),X1) = commutator(X1,X0),
inference(backward_demodulation,[],[f62,f7630]) ).
fof(f7630,plain,
! [X0,X1] : commutator(X0,X1) = multiply(inverse(X1),multiply(X0,multiply(X1,inverse(X0)))),
inference(forward_demodulation,[],[f7617,f4]) ).
fof(f7617,plain,
! [X0,X1] : commutator(X0,X1) = multiply(multiply(inverse(X1),identity),multiply(X0,multiply(X1,inverse(X0)))),
inference(backward_demodulation,[],[f7021,f7612]) ).
fof(f7612,plain,
! [X0,X1] : identity = commutator(X1,commutator(X0,X1)),
inference(forward_demodulation,[],[f7611,f4]) ).
fof(f7611,plain,
! [X0,X1] : multiply(identity,identity) = commutator(X1,commutator(X0,X1)),
inference(forward_demodulation,[],[f7587,f7601]) ).
fof(f7601,plain,
! [X0,X1] : identity = commutator(multiply(X1,commutator(X0,X1)),multiply(X0,inverse(multiply(X0,X1)))),
inference(forward_demodulation,[],[f7574,f82]) ).
fof(f82,plain,
! [X0] : identity = commutator(X0,identity),
inference(forward_demodulation,[],[f81,f32]) ).
fof(f81,plain,
! [X0] : multiply(X0,multiply(inverse(X0),identity)) = commutator(X0,identity),
inference(forward_demodulation,[],[f63,f1]) ).
fof(f63,plain,
! [X0] : commutator(X0,identity) = multiply(X0,multiply(identity,multiply(inverse(X0),identity))),
inference(superposition,[],[f6,f9]) ).
fof(f9,plain,
identity = inverse(identity),
inference(superposition,[],[f2,f4]) ).
fof(f6,axiom,
! [X0,X1] : commutator(X0,X1) = multiply(X0,multiply(X1,multiply(inverse(X0),inverse(X1)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutator) ).
fof(f7574,plain,
! [X0,X1] : commutator(multiply(X1,commutator(X0,X1)),multiply(X0,inverse(multiply(X0,X1)))) = commutator(multiply(X1,commutator(X0,X1)),identity),
inference(backward_demodulation,[],[f5051,f7568]) ).
fof(f7568,plain,
! [X0,X1] : identity = commutator(inverse(X0),commutator(X0,X1)),
inference(forward_demodulation,[],[f7443,f1350]) ).
fof(f1350,plain,
! [X0,X1] : identity = multiply(commutator(X1,X0),commutator(X0,X1)),
inference(superposition,[],[f2,f1320]) ).
fof(f1320,plain,
! [X0,X1] : commutator(X1,X0) = inverse(commutator(X0,X1)),
inference(backward_demodulation,[],[f1261,f1263]) ).
fof(f1263,plain,
! [X0,X1] : commutator(X0,X1) = multiply(multiply(X0,X1),inverse(multiply(X1,X0))),
inference(superposition,[],[f237,f1145]) ).
fof(f1145,plain,
! [X0,X1] : multiply(X1,X0) = multiply(commutator(X1,X0),multiply(X0,X1)),
inference(forward_demodulation,[],[f1061,f4]) ).
fof(f1061,plain,
! [X0,X1] : multiply(commutator(X1,X0),multiply(X0,X1)) = multiply(X1,multiply(X0,identity)),
inference(superposition,[],[f419,f2]) ).
fof(f419,plain,
! [X2,X0,X1] : multiply(commutator(X0,X1),X2) = multiply(X0,multiply(X1,multiply(inverse(multiply(X1,X0)),X2))),
inference(backward_demodulation,[],[f94,f399]) ).
fof(f94,plain,
! [X2,X0,X1] : multiply(commutator(X0,X1),X2) = multiply(X0,multiply(X1,multiply(inverse(X0),multiply(inverse(X1),X2)))),
inference(forward_demodulation,[],[f93,f3]) ).
fof(f93,plain,
! [X2,X0,X1] : multiply(commutator(X0,X1),X2) = multiply(X0,multiply(X1,multiply(multiply(inverse(X0),inverse(X1)),X2))),
inference(forward_demodulation,[],[f74,f3]) ).
fof(f74,plain,
! [X2,X0,X1] : multiply(X0,multiply(multiply(X1,multiply(inverse(X0),inverse(X1))),X2)) = multiply(commutator(X0,X1),X2),
inference(superposition,[],[f3,f6]) ).
fof(f237,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(X1)) = X0,
inference(forward_demodulation,[],[f219,f52]) ).
fof(f219,plain,
! [X0,X1] : inverse(inverse(X0)) = multiply(multiply(X0,X1),inverse(X1)),
inference(superposition,[],[f200,f37]) ).
fof(f1261,plain,
! [X0,X1] : inverse(commutator(X0,X1)) = multiply(multiply(X1,X0),inverse(multiply(X0,X1))),
inference(superposition,[],[f200,f1145]) ).
fof(f7443,plain,
! [X0,X1] : multiply(commutator(X0,X1),commutator(X1,X0)) = commutator(inverse(X0),commutator(X0,X1)),
inference(backward_demodulation,[],[f1867,f7432]) ).
fof(f7432,plain,
! [X0,X1] : commutator(X0,X1) = commutator(X1,inverse(X0)),
inference(forward_demodulation,[],[f7409,f37]) ).
fof(f7409,plain,
! [X0,X1] : commutator(X1,inverse(X0)) = multiply(inverse(X0),multiply(X0,commutator(X0,X1))),
inference(backward_demodulation,[],[f6032,f7384]) ).
fof(f7384,plain,
! [X0,X1] : multiply(X0,commutator(X0,X1)) = multiply(commutator(X0,X1),X0),
inference(backward_demodulation,[],[f6021,f7377]) ).
fof(f7377,plain,
! [X0,X1] : commutator(X0,X1) = commutator(X0,multiply(X0,X1)),
inference(backward_demodulation,[],[f7362,f7376]) ).
fof(f7376,plain,
! [X0,X1] : commutator(X0,X1) = commutator(X0,inverse(multiply(X1,multiply(X0,X1)))),
inference(forward_demodulation,[],[f7375,f1331]) ).
fof(f1331,plain,
! [X0,X1] : commutator(X1,X0) = commutator(multiply(X1,X0),X0),
inference(backward_demodulation,[],[f1315,f1320]) ).
fof(f1315,plain,
! [X0,X1] : inverse(commutator(X0,X1)) = commutator(multiply(X1,X0),X0),
inference(backward_demodulation,[],[f472,f1312]) ).
fof(f1312,plain,
! [X0,X1] : inverse(commutator(X1,X0)) = commutator(multiply(X0,X1),inverse(X0)),
inference(backward_demodulation,[],[f550,f1261]) ).
fof(f550,plain,
! [X0,X1] : commutator(multiply(X0,X1),inverse(X0)) = multiply(multiply(X0,X1),inverse(multiply(X1,X0))),
inference(forward_demodulation,[],[f507,f222]) ).
fof(f507,plain,
! [X0,X1] : commutator(multiply(X0,X1),inverse(X0)) = multiply(multiply(X0,X1),multiply(inverse(X0),inverse(X1))),
inference(superposition,[],[f241,f37]) ).
fof(f241,plain,
! [X0,X1] : commutator(X0,X1) = multiply(X0,multiply(X1,inverse(multiply(X1,X0)))),
inference(backward_demodulation,[],[f6,f222]) ).
fof(f472,plain,
! [X0,X1] : commutator(multiply(X1,X0),X0) = commutator(multiply(X1,X0),inverse(X1)),
inference(superposition,[],[f252,f200]) ).
fof(f252,plain,
! [X0,X1] : commutator(X0,X1) = commutator(X0,multiply(X1,inverse(X0))),
inference(forward_demodulation,[],[f251,f241]) ).
fof(f251,plain,
! [X0,X1] : commutator(X0,multiply(X1,inverse(X0))) = multiply(X0,multiply(X1,inverse(multiply(X1,X0)))),
inference(forward_demodulation,[],[f250,f222]) ).
fof(f250,plain,
! [X0,X1] : multiply(X0,multiply(X1,multiply(inverse(X0),inverse(X1)))) = commutator(X0,multiply(X1,inverse(X0))),
inference(forward_demodulation,[],[f226,f3]) ).
fof(f226,plain,
! [X0,X1] : commutator(X0,multiply(X1,inverse(X0))) = multiply(X0,multiply(multiply(X1,inverse(X0)),inverse(X1))),
inference(superposition,[],[f6,f200]) ).
fof(f7375,plain,
! [X0,X1] : commutator(multiply(X0,X1),X1) = commutator(X0,inverse(multiply(X1,multiply(X0,X1)))),
inference(forward_demodulation,[],[f7176,f7314]) ).
fof(f7314,plain,
! [X0,X1] : commutator(X1,X0) = commutator(inverse(X1),inverse(multiply(X0,X1))),
inference(backward_demodulation,[],[f4576,f7312]) ).
fof(f7312,plain,
! [X0,X1] : commutator(X0,X1) = commutator(multiply(X0,inverse(X1)),X0),
inference(forward_demodulation,[],[f7310,f241]) ).
fof(f7310,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(multiply(X1,X0)))) = commutator(multiply(X0,inverse(X1)),X0),
inference(backward_demodulation,[],[f5544,f7157]) ).
fof(f7157,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X0,X1))) = multiply(inverse(X0),multiply(X1,multiply(X0,X1))),
inference(superposition,[],[f116,f114]) ).
fof(f114,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(X0,multiply(X1,multiply(X0,X1))),
inference(superposition,[],[f104,f3]) ).
fof(f5544,plain,
! [X0,X1] : commutator(multiply(X0,inverse(X1)),X0) = multiply(X0,multiply(inverse(X1),multiply(X0,multiply(X1,X0)))),
inference(forward_demodulation,[],[f5443,f52]) ).
fof(f5443,plain,
! [X0,X1] : commutator(multiply(X0,inverse(X1)),X0) = multiply(X0,multiply(inverse(X1),multiply(X0,inverse(inverse(multiply(X1,X0)))))),
inference(superposition,[],[f244,f3846]) ).
fof(f3846,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(X1,multiply(X1,inverse(X0))),
inference(forward_demodulation,[],[f3769,f227]) ).
fof(f227,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = inverse(multiply(X1,inverse(X0))),
inference(superposition,[],[f32,f200]) ).
fof(f3769,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(X1,inverse(multiply(X0,inverse(X1)))),
inference(superposition,[],[f200,f3204]) ).
fof(f3204,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = multiply(multiply(X0,X1),X1),
inference(forward_demodulation,[],[f3147,f227]) ).
fof(f3147,plain,
! [X0,X1] : inverse(multiply(X1,inverse(X0))) = multiply(multiply(X0,X1),X1),
inference(superposition,[],[f709,f52]) ).
fof(f709,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(multiply(inverse(X1),X0),X0),
inference(forward_demodulation,[],[f682,f321]) ).
fof(f321,plain,
! [X0,X1] : multiply(inverse(X0),X1) = inverse(multiply(inverse(X1),X0)),
inference(superposition,[],[f37,f208]) ).
fof(f208,plain,
! [X0,X1] : multiply(X1,inverse(multiply(inverse(X0),X1))) = X0,
inference(forward_demodulation,[],[f178,f4]) ).
fof(f178,plain,
! [X0,X1] : multiply(X0,identity) = multiply(X1,inverse(multiply(inverse(X0),X1))),
inference(superposition,[],[f32,f26]) ).
fof(f682,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(multiply(inverse(X0),X1)),X0),
inference(superposition,[],[f230,f116]) ).
fof(f230,plain,
! [X0,X1] : inverse(X0) = multiply(inverse(multiply(X1,X0)),X1),
inference(forward_demodulation,[],[f214,f52]) ).
fof(f214,plain,
! [X0,X1] : inverse(X0) = multiply(inverse(multiply(X1,X0)),inverse(inverse(X1))),
inference(superposition,[],[f200,f200]) ).
fof(f244,plain,
! [X2,X0,X1] : commutator(multiply(X0,X1),X2) = multiply(X0,multiply(X1,multiply(X2,inverse(multiply(X2,multiply(X0,X1)))))),
inference(backward_demodulation,[],[f72,f222]) ).
fof(f72,plain,
! [X2,X0,X1] : multiply(X0,multiply(X1,multiply(X2,multiply(inverse(multiply(X0,X1)),inverse(X2))))) = commutator(multiply(X0,X1),X2),
inference(superposition,[],[f6,f3]) ).
fof(f4576,plain,
! [X0,X1] : commutator(inverse(X1),inverse(multiply(X0,X1))) = commutator(multiply(X1,inverse(X0)),X1),
inference(forward_demodulation,[],[f4575,f4561]) ).
fof(f4561,plain,
! [X0,X1] : commutator(multiply(X1,inverse(X0)),inverse(multiply(X0,X1))) = commutator(multiply(X1,inverse(X0)),X1),
inference(forward_demodulation,[],[f4375,f227]) ).
fof(f4375,plain,
! [X0,X1] : commutator(inverse(multiply(X0,inverse(X1))),inverse(multiply(X0,X1))) = commutator(inverse(multiply(X0,inverse(X1))),X1),
inference(superposition,[],[f469,f2798]) ).
fof(f2798,plain,
! [X0,X1] : multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X0))) = X0,
inference(forward_demodulation,[],[f2718,f227]) ).
fof(f2718,plain,
! [X0,X1] : multiply(inverse(multiply(X1,X0)),inverse(multiply(X0,inverse(X1)))) = X0,
inference(superposition,[],[f683,f222]) ).
fof(f683,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X1),inverse(multiply(X0,X1))) = X0,
inference(superposition,[],[f237,f116]) ).
fof(f469,plain,
! [X0,X1] : commutator(inverse(X0),X1) = commutator(inverse(X0),multiply(X1,X0)),
inference(superposition,[],[f252,f52]) ).
fof(f4575,plain,
! [X0,X1] : commutator(inverse(X1),inverse(multiply(X0,X1))) = commutator(multiply(X1,inverse(X0)),inverse(multiply(X0,X1))),
inference(forward_demodulation,[],[f4383,f227]) ).
fof(f4383,plain,
! [X0,X1] : commutator(inverse(multiply(X0,inverse(X1))),inverse(multiply(X0,X1))) = commutator(inverse(X1),inverse(multiply(X0,X1))),
inference(superposition,[],[f1375,f2798]) ).
fof(f1375,plain,
! [X0,X1] : commutator(inverse(X1),X0) = commutator(inverse(multiply(X0,X1)),X0),
inference(forward_demodulation,[],[f1345,f1320]) ).
fof(f1345,plain,
! [X0,X1] : commutator(inverse(multiply(X0,X1)),X0) = inverse(commutator(X0,inverse(X1))),
inference(superposition,[],[f1320,f479]) ).
fof(f479,plain,
! [X0,X1] : commutator(X1,inverse(X0)) = commutator(X1,inverse(multiply(X1,X0))),
inference(superposition,[],[f252,f222]) ).
fof(f7176,plain,
! [X0,X1] : commutator(X0,inverse(multiply(X1,multiply(X0,X1)))) = commutator(inverse(multiply(X0,X1)),inverse(multiply(X1,multiply(X0,X1)))),
inference(superposition,[],[f1380,f114]) ).
fof(f1380,plain,
! [X0,X1] : commutator(X1,inverse(X0)) = commutator(multiply(X1,X0),inverse(X0)),
inference(forward_demodulation,[],[f1349,f1320]) ).
fof(f1349,plain,
! [X0,X1] : inverse(commutator(inverse(X0),X1)) = commutator(multiply(X1,X0),inverse(X0)),
inference(superposition,[],[f1320,f469]) ).
fof(f7362,plain,
! [X0,X1] : commutator(X0,multiply(X0,X1)) = commutator(X0,inverse(multiply(X1,multiply(X0,X1)))),
inference(forward_demodulation,[],[f7169,f52]) ).
fof(f7169,plain,
! [X0,X1] : commutator(X0,inverse(inverse(multiply(X0,X1)))) = commutator(X0,inverse(multiply(X1,multiply(X0,X1)))),
inference(superposition,[],[f479,f114]) ).
fof(f6021,plain,
! [X0,X1] : multiply(X0,commutator(X0,X1)) = multiply(commutator(X0,multiply(X0,X1)),X0),
inference(superposition,[],[f1171,f1328]) ).
fof(f1328,plain,
! [X0,X1] : commutator(X0,X1) = commutator(multiply(X0,X1),inverse(X0)),
inference(backward_demodulation,[],[f1312,f1320]) ).
fof(f1171,plain,
! [X0,X1] : multiply(X1,commutator(X0,inverse(X1))) = multiply(commutator(X1,X0),X1),
inference(forward_demodulation,[],[f1170,f37]) ).
fof(f1170,plain,
! [X0,X1] : multiply(X1,commutator(X0,inverse(X1))) = multiply(commutator(X1,X0),multiply(inverse(X0),multiply(X0,X1))),
inference(forward_demodulation,[],[f1169,f321]) ).
fof(f1169,plain,
! [X0,X1] : multiply(commutator(X1,X0),inverse(multiply(inverse(multiply(X0,X1)),X0))) = multiply(X1,commutator(X0,inverse(X1))),
inference(forward_demodulation,[],[f1074,f479]) ).
fof(f1074,plain,
! [X0,X1] : multiply(commutator(X1,X0),inverse(multiply(inverse(multiply(X0,X1)),X0))) = multiply(X1,commutator(X0,inverse(multiply(X0,X1)))),
inference(superposition,[],[f419,f241]) ).
fof(f6032,plain,
! [X0,X1] : commutator(X1,inverse(X0)) = multiply(inverse(X0),multiply(commutator(X0,X1),X0)),
inference(superposition,[],[f37,f1171]) ).
fof(f1867,plain,
! [X0,X1] : commutator(inverse(X0),commutator(X0,X1)) = multiply(commutator(X1,inverse(X0)),commutator(X1,X0)),
inference(forward_demodulation,[],[f1866,f1673]) ).
fof(f1673,plain,
! [X0,X1] : commutator(multiply(X1,inverse(multiply(X1,X0))),X0) = commutator(inverse(X0),commutator(X0,X1)),
inference(superposition,[],[f1428,f241]) ).
fof(f1428,plain,
! [X0,X1] : commutator(X1,X0) = commutator(inverse(X0),multiply(X0,X1)),
inference(forward_demodulation,[],[f1404,f475]) ).
fof(f475,plain,
! [X0,X1] : commutator(X1,X0) = commutator(X1,multiply(X0,X1)),
inference(superposition,[],[f252,f237]) ).
fof(f1404,plain,
! [X0,X1] : commutator(X1,multiply(X0,X1)) = commutator(inverse(X0),multiply(X0,X1)),
inference(superposition,[],[f1331,f37]) ).
fof(f1866,plain,
! [X0,X1] : commutator(multiply(X1,inverse(multiply(X1,X0))),X0) = multiply(commutator(X1,inverse(X0)),commutator(X1,X0)),
inference(forward_demodulation,[],[f1865,f1141]) ).
fof(f1141,plain,
! [X2,X0,X1] : multiply(X0,multiply(inverse(multiply(X0,X1)),multiply(X1,X2))) = multiply(commutator(X0,inverse(X1)),X2),
inference(forward_demodulation,[],[f1140,f479]) ).
fof(f1140,plain,
! [X2,X0,X1] : multiply(commutator(X0,inverse(multiply(X0,X1))),X2) = multiply(X0,multiply(inverse(multiply(X0,X1)),multiply(X1,X2))),
inference(forward_demodulation,[],[f1139,f3]) ).
fof(f1139,plain,
! [X2,X0,X1] : multiply(commutator(X0,inverse(multiply(X0,X1))),X2) = multiply(X0,multiply(multiply(inverse(multiply(X0,X1)),X1),X2)),
inference(forward_demodulation,[],[f1138,f321]) ).
fof(f1138,plain,
! [X2,X0,X1] : multiply(commutator(X0,inverse(multiply(X0,X1))),X2) = multiply(X0,multiply(inverse(multiply(inverse(X1),multiply(X0,X1))),X2)),
inference(forward_demodulation,[],[f1057,f399]) ).
fof(f1057,plain,
! [X2,X0,X1] : multiply(commutator(X0,inverse(multiply(X0,X1))),X2) = multiply(X0,multiply(inverse(multiply(X0,X1)),multiply(inverse(inverse(X1)),X2))),
inference(superposition,[],[f419,f230]) ).
fof(f1865,plain,
! [X0,X1] : commutator(multiply(X1,inverse(multiply(X1,X0))),X0) = multiply(X1,multiply(inverse(multiply(X1,X0)),multiply(X0,commutator(X1,X0)))),
inference(forward_demodulation,[],[f1768,f1320]) ).
fof(f1768,plain,
! [X0,X1] : commutator(multiply(X1,inverse(multiply(X1,X0))),X0) = multiply(X1,multiply(inverse(multiply(X1,X0)),multiply(X0,inverse(commutator(X0,X1))))),
inference(superposition,[],[f244,f241]) ).
fof(f5051,plain,
! [X0,X1] : commutator(multiply(X1,commutator(X0,X1)),multiply(X0,inverse(multiply(X0,X1)))) = commutator(multiply(X1,commutator(X0,X1)),commutator(inverse(X1),commutator(X1,X0))),
inference(superposition,[],[f475,f1707]) ).
fof(f1707,plain,
! [X0,X1] : multiply(multiply(X1,inverse(multiply(X1,X0))),multiply(X0,commutator(X1,X0))) = commutator(inverse(X0),commutator(X0,X1)),
inference(backward_demodulation,[],[f1322,f1673]) ).
fof(f1322,plain,
! [X0,X1] : commutator(multiply(X1,inverse(multiply(X1,X0))),X0) = multiply(multiply(X1,inverse(multiply(X1,X0))),multiply(X0,commutator(X1,X0))),
inference(backward_demodulation,[],[f497,f1320]) ).
fof(f497,plain,
! [X0,X1] : commutator(multiply(X1,inverse(multiply(X1,X0))),X0) = multiply(multiply(X1,inverse(multiply(X1,X0))),multiply(X0,inverse(commutator(X0,X1)))),
inference(superposition,[],[f241,f241]) ).
fof(f7587,plain,
! [X0,X1] : commutator(X1,commutator(X0,X1)) = multiply(commutator(multiply(X1,commutator(X0,X1)),multiply(X0,inverse(multiply(X0,X1)))),identity),
inference(backward_demodulation,[],[f6380,f7568]) ).
fof(f6380,plain,
! [X0,X1] : multiply(commutator(multiply(X1,commutator(X0,X1)),multiply(X0,inverse(multiply(X0,X1)))),commutator(inverse(X1),commutator(X1,X0))) = commutator(X1,commutator(X0,X1)),
inference(backward_demodulation,[],[f5396,f6379]) ).
fof(f6379,plain,
! [X0,X1] : multiply(X1,multiply(commutator(X0,X1),multiply(X0,inverse(multiply(X0,X1))))) = commutator(X1,commutator(X0,X1)),
inference(forward_demodulation,[],[f6225,f227]) ).
fof(f6225,plain,
! [X0,X1] : commutator(X1,commutator(X0,X1)) = multiply(X1,multiply(commutator(X0,X1),inverse(multiply(multiply(X0,X1),inverse(X0))))),
inference(superposition,[],[f241,f1618]) ).
fof(f1618,plain,
! [X0,X1] : multiply(commutator(X0,X1),X1) = multiply(multiply(X0,X1),inverse(X0)),
inference(forward_demodulation,[],[f1587,f37]) ).
fof(f1587,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(X0)) = multiply(commutator(X0,X1),multiply(inverse(X0),multiply(X0,X1))),
inference(superposition,[],[f1145,f1328]) ).
fof(f5396,plain,
! [X0,X1] : multiply(commutator(multiply(X1,commutator(X0,X1)),multiply(X0,inverse(multiply(X0,X1)))),commutator(inverse(X1),commutator(X1,X0))) = multiply(X1,multiply(commutator(X0,X1),multiply(X0,inverse(multiply(X0,X1))))),
inference(forward_demodulation,[],[f5055,f3]) ).
fof(f5055,plain,
! [X0,X1] : multiply(multiply(X1,commutator(X0,X1)),multiply(X0,inverse(multiply(X0,X1)))) = multiply(commutator(multiply(X1,commutator(X0,X1)),multiply(X0,inverse(multiply(X0,X1)))),commutator(inverse(X1),commutator(X1,X0))),
inference(superposition,[],[f1145,f1707]) ).
fof(f7021,plain,
! [X0,X1] : commutator(X0,X1) = multiply(multiply(inverse(X1),commutator(X1,commutator(X0,X1))),multiply(X0,multiply(X1,inverse(X0)))),
inference(forward_demodulation,[],[f6786,f3]) ).
fof(f6786,plain,
! [X0,X1] : commutator(X0,X1) = multiply(multiply(inverse(X1),commutator(X1,commutator(X0,X1))),multiply(multiply(X0,X1),inverse(X0))),
inference(superposition,[],[f5935,f1618]) ).
fof(f5935,plain,
! [X0,X1] : multiply(multiply(inverse(X1),commutator(X1,X0)),multiply(X0,X1)) = X0,
inference(forward_demodulation,[],[f5725,f1360]) ).
fof(f1360,plain,
! [X2,X0,X1] : inverse(multiply(commutator(X0,X1),X2)) = multiply(inverse(X2),commutator(X1,X0)),
inference(superposition,[],[f222,f1320]) ).
fof(f5725,plain,
! [X0,X1] : multiply(inverse(multiply(commutator(X0,X1),X1)),multiply(X0,X1)) = X0,
inference(superposition,[],[f137,f1145]) ).
fof(f137,plain,
! [X2,X0,X1] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2,
inference(superposition,[],[f37,f3]) ).
fof(f62,plain,
! [X0,X1] : commutator(inverse(X0),X1) = multiply(inverse(X0),multiply(X1,multiply(X0,inverse(X1)))),
inference(superposition,[],[f6,f52]) ).
fof(f8344,plain,
! [X0,X1] : identity = multiply(multiply(multiply(inverse(X0),X1),inverse(inverse(multiply(X1,X0)))),multiply(X1,commutator(inverse(X0),X1))),
inference(forward_demodulation,[],[f8167,f1331]) ).
fof(f8167,plain,
! [X0,X1] : identity = multiply(multiply(multiply(inverse(X0),X1),inverse(inverse(multiply(X1,X0)))),multiply(X1,commutator(multiply(inverse(X0),X1),X1))),
inference(superposition,[],[f7571,f709]) ).
fof(f7571,plain,
! [X0,X1] : identity = multiply(multiply(X1,inverse(multiply(X1,X0))),multiply(X0,commutator(X1,X0))),
inference(backward_demodulation,[],[f1707,f7568]) ).
fof(f7768,plain,
! [X0,X1] : commutator(commutator(X0,X1),X1) = multiply(multiply(inverse(multiply(X1,X0)),X0),multiply(X1,commutator(X1,X0))),
inference(forward_demodulation,[],[f7767,f7631]) ).
fof(f7767,plain,
! [X0,X1] : commutator(commutator(X0,X1),X1) = multiply(multiply(inverse(multiply(X1,X0)),X0),multiply(X1,commutator(inverse(X0),X1))),
inference(forward_demodulation,[],[f7455,f7631]) ).
fof(f7455,plain,
! [X0,X1] : multiply(multiply(inverse(multiply(X1,X0)),X0),multiply(X1,commutator(inverse(X0),X1))) = commutator(inverse(X1),commutator(X0,X1)),
inference(backward_demodulation,[],[f5197,f7432]) ).
fof(f5197,plain,
! [X0,X1] : commutator(inverse(X1),commutator(X1,inverse(X0))) = multiply(multiply(inverse(multiply(X1,X0)),X0),multiply(X1,commutator(inverse(X0),X1))),
inference(forward_demodulation,[],[f5196,f475]) ).
fof(f5196,plain,
! [X0,X1] : commutator(inverse(X1),commutator(X1,multiply(inverse(X0),X1))) = multiply(multiply(inverse(multiply(X1,X0)),X0),multiply(X1,commutator(inverse(X0),X1))),
inference(forward_demodulation,[],[f5195,f399]) ).
fof(f5195,plain,
! [X0,X1] : commutator(inverse(X1),commutator(X1,multiply(inverse(X0),X1))) = multiply(multiply(inverse(X0),multiply(inverse(X1),X0)),multiply(X1,commutator(inverse(X0),X1))),
inference(forward_demodulation,[],[f5194,f116]) ).
fof(f5194,plain,
! [X0,X1] : commutator(inverse(X1),commutator(X1,multiply(inverse(X0),X1))) = multiply(multiply(inverse(X0),multiply(X1,multiply(X1,X0))),multiply(X1,commutator(inverse(X0),X1))),
inference(forward_demodulation,[],[f5193,f52]) ).
fof(f5193,plain,
! [X0,X1] : commutator(inverse(X1),commutator(X1,multiply(inverse(X0),X1))) = multiply(multiply(inverse(X0),multiply(X1,inverse(inverse(multiply(X1,X0))))),multiply(X1,commutator(inverse(X0),X1))),
inference(forward_demodulation,[],[f5192,f3]) ).
fof(f5192,plain,
! [X0,X1] : commutator(inverse(X1),commutator(X1,multiply(inverse(X0),X1))) = multiply(multiply(multiply(inverse(X0),X1),inverse(inverse(multiply(X1,X0)))),multiply(X1,commutator(inverse(X0),X1))),
inference(forward_demodulation,[],[f4996,f1331]) ).
fof(f4996,plain,
! [X0,X1] : commutator(inverse(X1),commutator(X1,multiply(inverse(X0),X1))) = multiply(multiply(multiply(inverse(X0),X1),inverse(inverse(multiply(X1,X0)))),multiply(X1,commutator(multiply(inverse(X0),X1),X1))),
inference(superposition,[],[f1707,f709]) ).
fof(f8,axiom,
identity != commutator(commutator(a,b),b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutator) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP002-4 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri May 3 20:43:22 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % (15227)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.34 % (15230)WARNING: value z3 for option sas not known
% 0.11/0.35 % (15231)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.35 % (15232)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.11/0.35 % (15228)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.35 % (15229)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.35 % (15233)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.11/0.35 % (15234)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.11/0.35 % (15230)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.11/0.35 TRYING [1]
% 0.11/0.35 TRYING [2]
% 0.11/0.35 TRYING [3]
% 0.11/0.35 TRYING [1]
% 0.11/0.35 TRYING [2]
% 0.11/0.35 TRYING [4]
% 0.11/0.35 TRYING [3]
% 0.11/0.36 TRYING [5]
% 0.11/0.36 TRYING [4]
% 0.18/0.38 TRYING [6]
% 0.18/0.40 TRYING [5]
% 0.18/0.43 TRYING [7]
% 1.50/0.54 TRYING [8]
% 1.65/0.56 TRYING [6]
% 2.22/0.64 % (15233)First to succeed.
% 2.22/0.64 % (15233)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-15227"
% 2.22/0.65 % (15233)Refutation found. Thanks to Tanya!
% 2.22/0.65 % SZS status Unsatisfiable for theBenchmark
% 2.22/0.65 % SZS output start Proof for theBenchmark
% See solution above
% 2.22/0.65 % (15233)------------------------------
% 2.22/0.65 % (15233)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 2.22/0.65 % (15233)Termination reason: Refutation
% 2.22/0.65
% 2.22/0.65 % (15233)Memory used [KB]: 4279
% 2.22/0.65 % (15233)Time elapsed: 0.299 s
% 2.22/0.65 % (15233)Instructions burned: 557 (million)
% 2.22/0.65 % (15227)Success in time 0.297 s
%------------------------------------------------------------------------------