TSTP Solution File: GRP049-1 by SNARK---20120808r022
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- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP049-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n021.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 : 600s
% DateTime : Sat Jul 16 11:35:29 EDT 2022
% Result : Unsatisfiable 4.44s 4.63s
% Output : Refutation 4.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 2
% Syntax : Number of clauses : 98 ( 94 unt; 0 nHn; 6 RR)
% Number of literals : 103 ( 102 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 10 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 335 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),inverse(multiply(Y,multiply(inverse(Y),Y)))))) = Z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(3,plain,
multiply(X,inverse(multiply(inverse(Y),inverse(multiply(Z,multiply(inverse(Z),Z)))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Z)),U)),Y)),inverse(multiply(U,multiply(inverse(U),U))))),
inference('PARAMODULATE',[status(thm)],[single_axiom,single_axiom,theory(equality)]) ).
cnf(5,plain,
multiply(inverse(multiply(X,Y)),multiply(X,inverse(multiply(inverse(Z),inverse(multiply(Y,multiply(inverse(Y),Y))))))) = Z,
inference('PARAMODULATE',[status(thm)],[single_axiom,3,theory(equality)]) ).
cnf(6,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),multiply(inverse(multiply(X,Y)),U))),inverse(multiply(Z,multiply(inverse(Z),Z))))) = U,
inference('PARAMODULATE',[status(thm)],[single_axiom,3,theory(equality)]) ).
cnf(35,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),inverse(multiply(Y,multiply(inverse(Y),Y))))) = Z,
inference('PARAMODULATE',[status(thm)],[6,6,theory(equality)]) ).
cnf(36,plain,
multiply(inverse(multiply(X,Y)),multiply(X,Z)) = multiply(inverse(multiply(U,Y)),multiply(U,Z)),
inference('PARAMODULATE',[status(thm)],[5,35,theory(equality)]) ).
cnf(37,plain,
multiply(inverse(multiply(X,Y)),inverse(multiply(Z,inverse(multiply(multiply(X,Z),multiply(inverse(multiply(X,Z)),multiply(X,Z))))))) = inverse(multiply(Y,multiply(inverse(Y),Y))),
inference('PARAMODULATE',[status(thm)],[single_axiom,35,theory(equality)]) ).
cnf(59,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),V)) = multiply(inverse(multiply(W,multiply(U,Z))),multiply(W,V)),
inference('PARAMODULATE',[status(thm)],[36,36,theory(equality)]) ).
cnf(60,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),multiply(inverse(multiply(U,Y)),multiply(U,V))) = multiply(inverse(multiply(W,Z)),multiply(W,multiply(X,V))),
inference('PARAMODULATE',[status(thm)],[36,36,theory(equality)]) ).
cnf(62,plain,
multiply(X,multiply(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,X))),U)) = multiply(inverse(multiply(V,inverse(multiply(Z,multiply(inverse(Z),Z))))),multiply(V,U)),
inference('PARAMODULATE',[status(thm)],[36,35,theory(equality)]) ).
cnf(143,plain,
multiply(inverse(multiply(X,multiply(Y,Z))),multiply(X,multiply(Y,U))) = multiply(inverse(multiply(V,multiply(W,Z))),multiply(V,multiply(W,U))),
inference('PARAMODULATE',[status(thm)],[59,60,theory(equality)]) ).
cnf(330,plain,
multiply(X,multiply(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,X))),U)) = multiply(V,multiply(inverse(multiply(inverse(multiply(W,Z)),multiply(W,V))),U)),
inference('PARAMODULATE',[status(thm)],[62,62,theory(equality)]) ).
cnf(499,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,inverse(Z)))),inverse(multiply(Y,multiply(inverse(Y),Y)))) = Z,
inference('PARAMODULATE',[status(thm)],[5,37,theory(equality)]) ).
cnf(501,plain,
multiply(inverse(X),X) = multiply(Y,multiply(inverse(multiply(inverse(multiply(Z,U)),multiply(Z,Y))),inverse(multiply(U,multiply(inverse(U),U))))),
inference('PARAMODULATE',[status(thm)],[330,499,theory(equality)]) ).
cnf(546,plain,
multiply(inverse(X),X) = multiply(inverse(Y),Y),
inference('PARAMODULATE',[status(thm)],[501,501,theory(equality)]) ).
cnf(547,plain,
( multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference('REWRITE',[status(thm)],[prove_these_axioms,546,theory(equality)]) ).
cnf(651,plain,
X = inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(X,multiply(inverse(X),X))))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3,501,theory(equality)]),single_axiom,499,theory(equality)]) ).
cnf(685,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z)) = multiply(inverse(multiply(U,Y)),multiply(U,Z)),
inference('PARAMODULATE',[status(thm)],[36,546,theory(equality)]) ).
cnf(686,plain,
multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z)) = multiply(inverse(multiply(U,Y)),multiply(U,X)),
inference('PARAMODULATE',[status(thm)],[36,546,theory(equality)]) ).
cnf(687,plain,
multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(Y),multiply(inverse(inverse(Y)),inverse(Y))))) = Y,
inference('PARAMODULATE',[status(thm)],[499,546,theory(equality)]) ).
cnf(688,plain,
( multiply(multiply(inverse(X),X),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference('PARAMODULATE',[status(thm)],[547,546,theory(equality)]) ).
cnf(689,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,inverse(Z)))),inverse(multiply(Y,multiply(inverse(U),U)))) = Z,
inference('PARAMODULATE',[status(thm)],[499,546,theory(equality)]) ).
cnf(690,plain,
multiply(inverse(multiply(X,Y)),multiply(X,inverse(multiply(inverse(Z),Z)))) = inverse(multiply(Y,multiply(inverse(Y),Y))),
inference('PARAMODULATE',[status(thm)],[5,546,theory(equality)]) ).
cnf(691,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),inverse(multiply(Y,multiply(inverse(U),U))))) = Z,
inference('PARAMODULATE',[status(thm)],[35,546,theory(equality)]) ).
cnf(693,plain,
multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),inverse(multiply(Y,multiply(inverse(U),U)))))) = Z,
inference('PARAMODULATE',[status(thm)],[single_axiom,546,theory(equality)]) ).
cnf(717,plain,
multiply(X,inverse(multiply(inverse(Y),inverse(multiply(Z,multiply(inverse(U),U)))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Z)),V)),Y)),inverse(multiply(V,multiply(inverse(V),V))))),
inference('PARAMODULATE',[status(thm)],[3,546,theory(equality)]) ).
cnf(718,plain,
X = inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(X,multiply(inverse(Z),Z))))),
inference('PARAMODULATE',[status(thm)],[651,546,theory(equality)]) ).
cnf(719,plain,
inverse(multiply(inverse(X),X)) = inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(Z),Z)))),
inference('PARAMODULATE',[status(thm)],[718,546,theory(equality)]) ).
cnf(721,plain,
inverse(multiply(inverse(X),Y)) = inverse(multiply(inverse(multiply(inverse(Z),Z)),inverse(multiply(inverse(multiply(U,Y)),multiply(U,X))))),
inference('PARAMODULATE',[status(thm)],[718,36,theory(equality)]) ).
cnf(726,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))) = inverse(multiply(inverse(multiply(U,Y)),multiply(U,Z))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[718,59,theory(equality)]),721,theory(equality)]) ).
cnf(738,plain,
multiply(inverse(X),X) = multiply(inverse(multiply(inverse(Y),Y)),multiply(inverse(Z),Z)),
inference('PARAMODULATE',[status(thm)],[546,685,theory(equality)]) ).
cnf(739,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z)) = multiply(inverse(multiply(inverse(U),U)),multiply(inverse(Y),Z)),
inference('PARAMODULATE',[status(thm)],[685,685,theory(equality)]) ).
cnf(872,plain,
multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z)) = multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(U),U)),
inference('PARAMODULATE',[status(thm)],[686,686,theory(equality)]) ).
cnf(955,plain,
multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(Y),multiply(inverse(Z),Z)))) = Y,
inference('PARAMODULATE',[status(thm)],[687,546,theory(equality)]) ).
cnf(956,plain,
multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(Y),Y))) = multiply(inverse(Z),Z),
inference('PARAMODULATE',[status(thm)],[955,738,theory(equality)]) ).
cnf(959,plain,
multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(multiply(inverse(Y),Y)),multiply(inverse(Z),U)))) = multiply(inverse(U),Z),
inference('PARAMODULATE',[status(thm)],[955,685,theory(equality)]) ).
cnf(1068,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),multiply(inverse(Y),Y)) = multiply(inverse(Z),Z),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[956,719,theory(equality)]),959,theory(equality)]) ).
cnf(1142,plain,
inverse(multiply(inverse(X),X)) = multiply(inverse(Y),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[956,1068,theory(equality)]),955,theory(equality)]) ).
cnf(1155,plain,
inverse(multiply(inverse(X),X)) = inverse(inverse(multiply(inverse(Y),Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[719,1068,theory(equality)]),955,theory(equality)]) ).
cnf(1218,plain,
inverse(inverse(multiply(inverse(X),X))) = multiply(inverse(Y),Y),
inference('PARAMODULATE',[status(thm)],[1142,1142,theory(equality)]) ).
cnf(1222,plain,
inverse(multiply(multiply(inverse(X),X),multiply(inverse(Y),Y))) = multiply(inverse(Z),Z),
inference('PARAMODULATE',[status(thm)],[1142,1142,theory(equality)]) ).
cnf(1223,plain,
multiply(multiply(inverse(X),X),inverse(multiply(inverse(Y),multiply(inverse(Z),Z)))) = Y,
inference('PARAMODULATE',[status(thm)],[955,1142,theory(equality)]) ).
cnf(1226,plain,
multiply(multiply(inverse(X),X),multiply(inverse(Y),Z)) = multiply(inverse(multiply(U,Y)),multiply(U,Z)),
inference('PARAMODULATE',[status(thm)],[685,1142,theory(equality)]) ).
cnf(1227,plain,
X = inverse(multiply(multiply(inverse(Y),Y),inverse(multiply(X,multiply(inverse(Z),Z))))),
inference('PARAMODULATE',[status(thm)],[718,1142,theory(equality)]) ).
cnf(1310,plain,
inverse(multiply(inverse(X),X)) = inverse(inverse(inverse(multiply(inverse(Y),Y)))),
inference('PARAMODULATE',[status(thm)],[1155,1155,theory(equality)]) ).
cnf(1326,plain,
inverse(inverse(inverse(multiply(inverse(X),X)))) = multiply(inverse(Y),Y),
inference('PARAMODULATE',[status(thm)],[1142,1218,theory(equality)]) ).
cnf(1635,plain,
inverse(inverse(inverse(multiply(inverse(X),X)))) = inverse(inverse(inverse(multiply(inverse(Y),Y)))),
inference('PARAMODULATE',[status(thm)],[1310,1310,theory(equality)]) ).
cnf(1696,plain,
multiply(inverse(multiply(inverse(inverse(inverse(multiply(inverse(X),X)))),multiply(inverse(Y),Y))),inverse(multiply(inverse(Z),multiply(inverse(U),U)))) = Z,
inference('PARAMODULATE',[status(thm)],[955,1310,theory(equality)]) ).
cnf(1958,plain,
multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(Y),inverse(multiply(multiply(inverse(Z),Z),multiply(inverse(U),U)))))) = Y,
inference('PARAMODULATE',[status(thm)],[955,1222,theory(equality)]) ).
cnf(2063,plain,
( multiply(inverse(inverse(inverse(multiply(inverse(X),X)))),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference('PARAMODULATE',[status(thm)],[688,1326,theory(equality)]) ).
cnf(2176,plain,
multiply(inverse(multiply(X,Y)),multiply(X,multiply(inverse(multiply(inverse(multiply(Z,U)),multiply(Z,inverse(Y)))),V))) = multiply(inverse(multiply(W,multiply(X1,inverse(multiply(U,multiply(inverse(Y1),Y1)))))),multiply(W,multiply(X1,V))),
inference('PARAMODULATE',[status(thm)],[143,689,theory(equality)]) ).
cnf(2195,plain,
multiply(inverse(multiply(X,Y)),multiply(X,inverse(multiply(inverse(Z),Z)))) = inverse(multiply(Y,multiply(inverse(U),U))),
inference('PARAMODULATE',[status(thm)],[690,546,theory(equality)]) ).
cnf(2496,plain,
multiply(multiply(inverse(inverse(inverse(multiply(inverse(X),X)))),multiply(inverse(Y),Y)),inverse(multiply(inverse(Z),multiply(inverse(U),U)))) = Z,
inference('PARAMODULATE',[status(thm)],[1223,1310,theory(equality)]) ).
cnf(3394,plain,
multiply(inverse(multiply(inverse(X),X)),Y) = multiply(inverse(multiply(inverse(Z),Z)),Y),
inference('PARAMODULATE',[status(thm)],[739,955,theory(equality)]) ).
cnf(3395,plain,
multiply(multiply(inverse(X),X),Y) = multiply(inverse(multiply(inverse(Z),Z)),Y),
inference('PARAMODULATE',[status(thm)],[3394,1142,theory(equality)]) ).
cnf(3396,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),Y) = multiply(inverse(multiply(inverse(Z),Z)),Y),
inference('PARAMODULATE',[status(thm)],[3394,1142,theory(equality)]) ).
cnf(3446,plain,
multiply(multiply(inverse(X),X),Y) = multiply(inverse(inverse(multiply(inverse(Z),Z))),Y),
inference('PARAMODULATE',[status(thm)],[3395,1142,theory(equality)]) ).
cnf(3754,plain,
multiply(X,multiply(inverse(Y),Y)) = multiply(X,multiply(inverse(Z),Z)),
inference('PARAMODULATE',[status(thm)],[872,718,theory(equality)]) ).
cnf(3755,plain,
multiply(X,inverse(multiply(inverse(Y),Y))) = multiply(X,multiply(inverse(Z),Z)),
inference('PARAMODULATE',[status(thm)],[3754,1142,theory(equality)]) ).
cnf(4274,plain,
multiply(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),multiply(U,Z))),multiply(inverse(V),W)) = multiply(inverse(multiply(X1,V)),multiply(X1,W)),
inference('PARAMODULATE',[status(thm)],[1226,726,theory(equality)]) ).
cnf(4428,plain,
inverse(multiply(inverse(multiply(X,multiply(multiply(inverse(Y),Y),Z))),inverse(multiply(inverse(multiply(X,multiply(inverse(U),U))),multiply(inverse(V),V))))) = Z,
inference('PARAMODULATE',[status(thm)],[691,1227,theory(equality)]) ).
cnf(4469,plain,
X = inverse(multiply(multiply(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,U))),multiply(inverse(multiply(V,Z)),multiply(V,U))),inverse(multiply(X,multiply(inverse(W),W))))),
inference('PARAMODULATE',[status(thm)],[1227,726,theory(equality)]) ).
cnf(5690,plain,
multiply(X,inverse(multiply(inverse(Y),Y))) = multiply(X,multiply(inverse(inverse(inverse(multiply(inverse(Z),Z)))),inverse(inverse(multiply(inverse(U),U))))),
inference('PARAMODULATE',[status(thm)],[3755,1635,theory(equality)]) ).
cnf(5798,plain,
inverse(multiply(X,multiply(inverse(Y),Y))) = inverse(multiply(X,multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[2195,2195,theory(equality)]) ).
cnf(5820,plain,
X = inverse(multiply(multiply(inverse(Y),Y),multiply(inverse(multiply(Z,X)),multiply(Z,inverse(multiply(inverse(U),U)))))),
inference('PARAMODULATE',[status(thm)],[1227,2195,theory(equality)]) ).
cnf(5909,plain,
multiply(inverse(inverse(multiply(X,multiply(inverse(Y),Y)))),multiply(inverse(Z),Z)) = multiply(inverse(multiply(U,multiply(V,inverse(multiply(inverse(W),W))))),multiply(U,multiply(V,X))),
inference('PARAMODULATE',[status(thm)],[686,2195,theory(equality)]) ).
cnf(5968,plain,
multiply(inverse(multiply(inverse(X),multiply(Y,inverse(multiply(inverse(Z),Z))))),multiply(inverse(U),U)) = multiply(inverse(inverse(multiply(V,multiply(inverse(W),W)))),multiply(inverse(multiply(Y,V)),X)),
inference('PARAMODULATE',[status(thm)],[686,2195,theory(equality)]) ).
cnf(6069,plain,
multiply(multiply(inverse(X),X),multiply(inverse(multiply(Y,inverse(multiply(inverse(Z),Z)))),U)) = multiply(inverse(inverse(multiply(V,multiply(inverse(W),W)))),multiply(inverse(multiply(Y,V)),U)),
inference('PARAMODULATE',[status(thm)],[1226,2195,theory(equality)]) ).
cnf(6195,plain,
inverse(multiply(X,inverse(multiply(inverse(Y),Y)))) = inverse(multiply(X,multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[5798,1142,theory(equality)]) ).
cnf(6532,plain,
multiply(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),multiply(U,Z))),V) = multiply(inverse(inverse(multiply(inverse(W),W))),V),
inference('PARAMODULATE',[status(thm)],[3446,726,theory(equality)]) ).
cnf(6797,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),Y) = multiply(inverse(multiply(inverse(multiply(Z,multiply(inverse(U),U))),multiply(Z,inverse(multiply(inverse(V),V))))),Y),
inference('PARAMODULATE',[status(thm)],[3396,6195,theory(equality)]) ).
cnf(6975,plain,
multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(multiply(Y,Z)),inverse(multiply(inverse(multiply(Y,multiply(inverse(U),U))),multiply(inverse(V),V)))))) = Z,
inference('PARAMODULATE',[status(thm)],[693,718,theory(equality)]) ).
cnf(6982,plain,
multiply(inverse(multiply(inverse(X),X)),Y) = Y,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[693,738,theory(equality)]),1958,theory(equality)]) ).
cnf(6983,plain,
inverse(multiply(inverse(multiply(X,Y)),inverse(multiply(inverse(multiply(X,multiply(inverse(Z),Z))),multiply(inverse(U),U))))) = Y,
inference('REWRITE',[status(thm)],[6975,6982,theory(equality)]) ).
cnf(6984,plain,
multiply(multiply(inverse(X),X),Y) = Y,
inference('REWRITE',[status(thm)],[4428,6983,theory(equality)]) ).
cnf(6999,plain,
multiply(inverse(multiply(X,inverse(multiply(inverse(Y),Y)))),Z) = multiply(inverse(inverse(multiply(U,multiply(inverse(V),V)))),multiply(inverse(multiply(X,U)),Z)),
inference('REWRITE',[status(thm)],[6069,6984,theory(equality)]) ).
cnf(7004,plain,
X = inverse(multiply(inverse(multiply(Y,X)),multiply(Y,inverse(multiply(inverse(Z),Z))))),
inference('REWRITE',[status(thm)],[5820,6984,theory(equality)]) ).
cnf(7005,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),Y) = Y,
inference('REWRITE',[status(thm)],[6797,6984,7004,theory(equality)]) ).
cnf(7007,plain,
multiply(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),multiply(U,Z))),V) = V,
inference('REWRITE',[status(thm)],[6532,7005,theory(equality)]) ).
cnf(7008,plain,
X = inverse(inverse(multiply(X,multiply(inverse(Y),Y)))),
inference('REWRITE',[status(thm)],[4469,7007,theory(equality)]) ).
cnf(7016,plain,
multiply(inverse(multiply(X,inverse(multiply(inverse(Y),Y)))),Z) = multiply(U,multiply(inverse(multiply(X,U)),Z)),
inference('REWRITE',[status(thm)],[6999,7008,theory(equality)]) ).
cnf(7018,plain,
multiply(inverse(multiply(inverse(X),multiply(Y,inverse(multiply(inverse(Z),Z))))),multiply(inverse(U),U)) = multiply(V,multiply(inverse(multiply(Y,V)),X)),
inference('REWRITE',[status(thm)],[5968,7008,theory(equality)]) ).
cnf(7025,plain,
multiply(X,multiply(inverse(Y),Y)) = multiply(inverse(multiply(Z,multiply(U,inverse(multiply(inverse(V),V))))),multiply(Z,multiply(U,X))),
inference('REWRITE',[status(thm)],[5909,7008,theory(equality)]) ).
cnf(7053,plain,
multiply(inverse(X),Y) = multiply(inverse(multiply(Z,X)),multiply(Z,Y)),
inference('REWRITE',[status(thm)],[4274,7007,theory(equality)]) ).
cnf(7066,plain,
multiply(X,multiply(inverse(Y),Y)) = X,
inference('REWRITE',[status(thm)],[7025,7005,7053,theory(equality)]) ).
cnf(7071,plain,
inverse(multiply(inverse(X),multiply(Y,inverse(multiply(inverse(Z),Z))))) = multiply(U,multiply(inverse(multiply(Y,U)),X)),
inference('REWRITE',[status(thm)],[7018,7066,theory(equality)]) ).
cnf(7078,plain,
multiply(inverse(inverse(inverse(inverse(multiply(inverse(X),X))))),inverse(inverse(Y))) = Y,
inference('REWRITE',[status(thm)],[1696,7066,theory(equality)]) ).
cnf(7079,plain,
multiply(inverse(inverse(inverse(multiply(inverse(X),X)))),inverse(inverse(Y))) = Y,
inference('REWRITE',[status(thm)],[2496,7066,theory(equality)]) ).
cnf(7080,plain,
multiply(X,inverse(multiply(inverse(Y),Y))) = X,
inference('REWRITE',[status(thm)],[5690,7066,7079,theory(equality)]) ).
cnf(7081,plain,
inverse(multiply(inverse(X),Y)) = multiply(Z,multiply(inverse(multiply(Y,Z)),X)),
inference('REWRITE',[status(thm)],[7071,7080,theory(equality)]) ).
cnf(7088,plain,
multiply(inverse(X),Y) = inverse(multiply(inverse(Y),X)),
inference('REWRITE',[status(thm)],[7016,7081,7080,theory(equality)]) ).
cnf(7090,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference('REWRITE',[status(thm)],[2063,6984,7088,theory(equality)]) ).
cnf(7091,plain,
inverse(inverse(X)) = X,
inference('REWRITE',[status(thm)],[7078,6984,7088,theory(equality)]) ).
cnf(7110,plain,
multiply(X,inverse(multiply(inverse(Y),inverse(Z)))) = inverse(multiply(inverse(Y),inverse(multiply(X,Z)))),
inference('REWRITE',[status(thm)],[717,7081,7091,7088,7066,theory(equality)]) ).
cnf(7187,plain,
inverse(multiply(inverse(X),inverse(Y))) = multiply(Y,X),
inference('REWRITE',[status(thm)],[2176,7091,7066,7081,7053,theory(equality)]) ).
cnf(7214,plain,
multiply(X,multiply(Y,Z)) = multiply(multiply(X,Y),Z),
inference('REWRITE',[status(thm)],[7110,7187,theory(equality)]) ).
cnf(7215,plain,
$false,
inference('REWRITE',[status(thm)],[7090,7214,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP049-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : run-snark %s %d
% 0.11/0.33 % Computer : n021.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 : 600
% 0.11/0.33 % DateTime : Tue Jun 14 12:31:58 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.19/0.44 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 *
% 0.19/0.45 *
% 0.19/0.46 #<PACKAGE "SNARK-USER">
% 0.19/0.46 *
% 0.19/0.46 SNARK-TPTP-OPTIONS
% 0.19/0.46 *
% 0.19/0.46 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.46 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.46 (USE-FACTORING :POS)
% 0.19/0.46 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.46 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.46 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.46 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.46 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.46 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.46 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.46 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.46 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.46 (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.46 *
% 0.19/0.46 "."
% 0.19/0.46 *
% 0.19/0.46 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-14T12:31:58
% 0.19/0.46 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n021.cluster.edu at 2022-06-14T12:31:58
% 4.44/4.63
% 4.44/4.63
% 4.44/4.63 #||
% 4.44/4.63 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.44/4.63 % SZS output start Refutation
% See solution above
% 4.48/4.67 ||#
% 4.48/4.67
% 4.48/4.67 ; Summary of computation:
% 4.48/4.67 ; 27857 formulas have been input or derived (from 77 formulas).
% 4.48/4.67 ; 7215 (26%) were retained. Of these,
% 4.48/4.67 ; 7134 (99%) were simplified or subsumed later,
% 4.48/4.67 ; 81 ( 1%) are still being kept.
% 4.48/4.67 ;
% 4.48/4.67 ; Run time in seconds excluding printing time:
% 4.48/4.67 ; 0.002 0% Read assertion file (1 call)
% 4.48/4.67 ; 0.000 0% Assert (2 calls)
% 4.48/4.67 ; 0.811 19% Process new row (21,154 calls)
% 4.48/4.67 ; 0.019 0% Resolution (152 calls)
% 4.48/4.67 ; 0.640 15% Paramodulation (76 calls)
% 4.48/4.67 ; 0.001 0% Condensing (100 calls)
% 4.48/4.67 ; 0.022 1% Forward subsumption (100 calls)
% 4.48/4.67 ; 0.001 0% Backward subsumption (50 calls)
% 4.48/4.67 ; 0.001 0% Clause clause subsumption (569 calls)
% 4.48/4.67 ; 1.292 31% Forward simplification (19,477 calls)
% 4.48/4.67 ; 1.163 28% Backward simplification (7,215 calls)
% 4.48/4.67 ; 0.119 3% Ordering (45,202 calls)
% 4.48/4.67 ; 0.000 0% Sortal reasoning (32 calls)
% 4.48/4.67 ; 0.000 0% Purity testing (1 call)
% 4.48/4.67 ; 0.096 2% Other
% 4.48/4.67 ; 4.167 Total
% 4.48/4.67 ; 4.205 Real time
% 4.48/4.67 ;
% 4.48/4.67 ; Term-hash-array has 19,960 terms in all.
% 4.48/4.67 ; Feature-vector-row-index has 0 entries (47 at peak, 50 added, 50 deleted).
% 4.48/4.67 ; Feature-vector-row-index has 1 node (158 at peak, 212 added, 211 deleted).
% 4.48/4.67 ; Retrieved 585 possibly forward subsuming rows in 100 calls.
% 4.48/4.67 ; Retrieved 127 possibly backward subsumed rows in 50 calls.
% 4.48/4.67 ; Path-index has 461 entries (18,063 at peak, 20,385 added, 19,924 deleted).
% 4.48/4.67 ; Path-index has 10,776 nodes (15,317 at peak, 16,983 added, 6,207 deleted).
% 4.48/4.67 ; Trie-index has 461 entries (18,063 at peak, 20,385 added, 19,924 deleted).
% 4.48/4.67 ; Trie-index has 1,851 nodes (122,483 at peak, 138,345 added, 136,494 deleted).
% 4.48/4.67 ; Retrieved 50,644 generalization terms in 178,802 calls.
% 4.48/4.67 ; Retrieved 33,451 instance terms in 7,318 calls.
% 4.48/4.67 ; Retrieved 240,653 unifiable terms in 965 calls.
% 4.48/4.67 ;
% 4.48/4.67 ; The agenda of backward simplifiable rows to process has 5979 entries:
% 4.48/4.67 ; 5979 with value 0
% 4.48/4.67 ; The agenda of rows to process has 305 entries:
% 4.48/4.67 ; 29 with value 48 23 with value 54 5 with value 59
% 4.48/4.67 ; 19 with value 49 22 with value 55 4 with value 60
% 4.48/4.67 ; 25 with value 50 27 with value 56 8 with value 61
% 4.48/4.67 ; 27 with value 51 14 with value 57 5 with value 62
% 4.48/4.67 ; 39 with value 52 14 with value 58 6 with value 63
% 4.48/4.67 ; 38 with value 53
% 4.48/4.67 ; The agenda of rows to give has 79 entries:
% 4.48/4.67 ; 1 with value (4 20) 6 with value (4 30) 3 with value (4 41)
% 4.48/4.67 ; 2 with value (4 21) 4 with value (4 31) 2 with value (4 42)
% 4.48/4.67 ; 2 with value (4 22) 2 with value (4 32) 3 with value (4 43)
% 4.48/4.67 ; 4 with value (4 23) 3 with value (4 33) 3 with value (4 44)
% 4.48/4.67 ; 3 with value (4 24) 1 with value (4 34) 2 with value (4 45)
% 4.48/4.67 ; 3 with value (4 25) 2 with value (4 35) 1 with value (4 46)
% 4.48/4.67 ; 2 with value (4 26) 7 with value (4 36) 2 with value (4 47)
% 4.48/4.67 ; 3 with value (4 27) 4 with value (4 37) 4 with value (4 48)
% 4.48/4.67 ; 1 with value (4 28) 1 with value (4 39) 1 with value (4 49)
% 4.48/4.67 ; 3 with value (4 29) 3 with value (4 40) 1 with value (4 50)
% 4.48/4.67 Evaluation took:
% 4.48/4.67 4.206 seconds of real time
% 4.48/4.67 3.926222 seconds of user run time
% 4.48/4.67 0.27904 seconds of system run time
% 4.48/4.67 [Run times include 0.701 seconds GC run time.]
% 4.48/4.67 0 calls to %EVAL
% 4.48/4.67 0 page faults and
% 4.48/4.67 300,505,224 bytes consed.
% 4.48/4.67 :PROOF-FOUND
% 4.48/4.67 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-14T12:32:02
% 4.48/4.67 :PROOF-FOUND
% 4.48/4.67 *
%------------------------------------------------------------------------------