TSTP Solution File: GRP054-1 by SNARK---20120808r022
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP054-1 : 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 11:35:40 EDT 2022
% Result : Unsatisfiable 10.68s 10.89s
% Output : Refutation 10.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 58
% Number of leaves : 2
% Syntax : Number of clauses : 174 ( 171 unt; 0 nHn; 5 RR)
% Number of literals : 178 ( 177 equ; 8 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 21 ( 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 : 685 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z))) = Y,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(3,plain,
inverse(multiply(inverse(multiply(X,inverse(multiply(Y,inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z))) = multiply(inverse(multiply(U,inverse(multiply(inverse(Y),inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),multiply(U,V)),
inference('PARAMODULATE',[status(thm)],[single_axiom,single_axiom,theory(equality)]) ).
cnf(4,plain,
inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),inverse(multiply(multiply(inverse(multiply(Z,inverse(multiply(inverse(U),inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),multiply(Z,V)),inverse(multiply(U,multiply(inverse(multiply(Z,inverse(multiply(inverse(U),inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),multiply(Z,V)))))))))),multiply(X,multiply(inverse(multiply(Z,inverse(multiply(inverse(U),inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),multiply(Z,V))))) = Y,
inference('PARAMODULATE',[status(thm)],[single_axiom,single_axiom,theory(equality)]) ).
cnf(5,plain,
multiply(inverse(multiply(X,inverse(multiply(inverse(inverse(Y)),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z)) = Y,
inference('PARAMODULATE',[status(thm)],[single_axiom,3,theory(equality)]) ).
cnf(6,plain,
inverse(inverse(multiply(inverse(multiply(X,inverse(multiply(Y,inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z)))) = Y,
inference('PARAMODULATE',[status(thm)],[single_axiom,3,theory(equality)]) ).
cnf(15,plain,
inverse(multiply(inverse(multiply(X,inverse(multiply(Y,inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z))) = multiply(inverse(multiply(U,inverse(multiply(inverse(Y),inverse(multiply(multiply(inverse(multiply(V,inverse(multiply(inverse(W),inverse(multiply(X1,inverse(multiply(inverse(X1),X1)))))))),multiply(V,X1)),inverse(multiply(W,multiply(inverse(multiply(V,inverse(multiply(inverse(W),inverse(multiply(X1,inverse(multiply(inverse(X1),X1)))))))),multiply(V,X1)))))))))),multiply(U,multiply(inverse(multiply(V,inverse(multiply(inverse(W),inverse(multiply(X1,inverse(multiply(inverse(X1),X1)))))))),multiply(V,X1)))),
inference('PARAMODULATE',[status(thm)],[3,single_axiom,theory(equality)]) ).
cnf(19,plain,
multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(inverse(Y)),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),inverse(multiply(inverse(inverse(U)),inverse(multiply(multiply(X,Z),inverse(multiply(inverse(multiply(X,Z)),multiply(X,Z))))))))),Y) = U,
inference('PARAMODULATE',[status(thm)],[5,5,theory(equality)]) ).
cnf(20,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(inverse(Y)),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),inverse(multiply(inverse(U),inverse(multiply(multiply(X,Z),inverse(multiply(inverse(multiply(X,Z)),multiply(X,Z))))))))),Y)) = U,
inference('PARAMODULATE',[status(thm)],[single_axiom,5,theory(equality)]) ).
cnf(24,plain,
multiply(inverse(multiply(X,inverse(multiply(Y,inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z)) = multiply(inverse(multiply(U,inverse(multiply(Y,inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),multiply(U,V)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[5,3,theory(equality)]),single_axiom,theory(equality)]) ).
cnf(90,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))) = multiply(inverse(multiply(U,inverse(multiply(inverse(inverse(inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))),inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),inverse(multiply(inverse(Y),inverse(multiply(multiply(U,V),inverse(multiply(inverse(multiply(U,V)),multiply(U,V)))))))),
inference('PARAMODULATE',[status(thm)],[single_axiom,20,theory(equality)]) ).
cnf(163,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))) = inverse(multiply(inverse(multiply(U,Y)),multiply(U,Z))),
inference('PARAMODULATE',[status(thm)],[90,90,theory(equality)]) ).
cnf(164,plain,
multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z)))),inverse(multiply(Z,inverse(multiply(inverse(Z),Z))))) = Y,
inference('PARAMODULATE',[status(thm)],[19,90,theory(equality)]) ).
cnf(165,plain,
inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z)))),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))) = Y,
inference('PARAMODULATE',[status(thm)],[20,90,theory(equality)]) ).
cnf(265,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),V))) = inverse(multiply(inverse(multiply(W,multiply(U,Z))),multiply(W,V))),
inference('PARAMODULATE',[status(thm)],[163,163,theory(equality)]) ).
cnf(270,plain,
multiply(inverse(multiply(X,Y)),multiply(X,Z)) = multiply(inverse(multiply(U,Y)),multiply(U,Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[5,163,theory(equality)]),5,theory(equality)]) ).
cnf(292,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)],[270,270,theory(equality)]) ).
cnf(293,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)],[270,270,theory(equality)]) ).
cnf(294,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),multiply(inverse(multiply(U,Y)),multiply(U,V)))) = inverse(multiply(inverse(multiply(W,Z)),multiply(W,multiply(X,V)))),
inference('PARAMODULATE',[status(thm)],[163,270,theory(equality)]) ).
cnf(309,plain,
multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,multiply(Z,U))))),inverse(multiply(multiply(Z,U),inverse(multiply(inverse(multiply(V,U)),multiply(V,U)))))) = Y,
inference('PARAMODULATE',[status(thm)],[164,163,theory(equality)]) ).
cnf(327,plain,
multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(multiply(inverse(multiply(Z,inverse(multiply(U,inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),multiply(Z,V))))))),inverse(multiply(inverse(multiply(inverse(multiply(Z,inverse(multiply(U,inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),multiply(Z,V))),inverse(multiply(U,inverse(multiply(inverse(multiply(Z,inverse(multiply(U,inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),multiply(Z,V)))))))) = Y,
inference('PARAMODULATE',[status(thm)],[164,6,theory(equality)]) ).
cnf(330,plain,
inverse(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z)))) = inverse(inverse(multiply(inverse(multiply(U,Y)),multiply(U,Z)))),
inference('PARAMODULATE',[status(thm)],[6,165,theory(equality)]) ).
cnf(335,plain,
multiply(inverse(inverse(multiply(X,multiply(inverse(inverse(multiply(inverse(multiply(Y,X)),multiply(Y,Z)))),U)))),inverse(multiply(U,inverse(multiply(inverse(U),U))))) = multiply(Z,inverse(multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[164,165,theory(equality)]) ).
cnf(344,plain,
inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(Y,inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z))),multiply(inverse(multiply(U,inverse(multiply(Y,inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),W)))),inverse(multiply(W,inverse(multiply(inverse(W),W)))))) = multiply(U,V),
inference('PARAMODULATE',[status(thm)],[165,24,theory(equality)]) ).
cnf(464,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)],[292,293,theory(equality)]) ).
cnf(572,plain,
inverse(multiply(inverse(multiply(X,multiply(Y,Z))),multiply(X,multiply(Y,U)))) = inverse(multiply(inverse(multiply(V,multiply(W,Z))),multiply(V,multiply(W,U)))),
inference('PARAMODULATE',[status(thm)],[163,464,theory(equality)]) ).
cnf(589,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,multiply(Z,U)))),multiply(inverse(multiply(inverse(multiply(Z,V)),Y)),multiply(inverse(multiply(W,V)),X1))) = multiply(inverse(multiply(Y1,multiply(Z1,multiply(W,U)))),multiply(Y1,multiply(Z1,X1))),
inference('PARAMODULATE',[status(thm)],[464,292,theory(equality)]) ).
cnf(628,plain,
multiply(inverse(multiply(X,multiply(inverse(multiply(Y,inverse(multiply(Z,inverse(multiply(U,inverse(multiply(inverse(U),U)))))))),multiply(Y,U)))),multiply(X,multiply(inverse(multiply(V,inverse(multiply(Z,inverse(multiply(W,inverse(multiply(inverse(W),W)))))))),X1))) = multiply(inverse(multiply(Y1,multiply(Z1,multiply(V,W)))),multiply(Y1,multiply(Z1,X1))),
inference('PARAMODULATE',[status(thm)],[464,24,theory(equality)]) ).
cnf(744,plain,
inverse(multiply(inverse(multiply(X,multiply(inverse(multiply(Y,inverse(multiply(Z,inverse(multiply(U,inverse(multiply(inverse(U),U)))))))),multiply(Y,U)))),multiply(X,multiply(inverse(multiply(V,inverse(multiply(Z,inverse(multiply(W,inverse(multiply(inverse(W),W)))))))),X1)))) = inverse(multiply(inverse(multiply(Y1,multiply(Z1,multiply(V,W)))),multiply(Y1,multiply(Z1,X1)))),
inference('PARAMODULATE',[status(thm)],[572,24,theory(equality)]) ).
cnf(844,plain,
multiply(multiply(X,Y),inverse(multiply(inverse(multiply(X,Y)),multiply(X,Y)))) = multiply(multiply(X,Y),inverse(multiply(inverse(multiply(Z,Y)),multiply(Z,Y)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[164,309,theory(equality)]),335,theory(equality)]) ).
cnf(905,plain,
multiply(X,inverse(multiply(inverse(X),X))) = multiply(X,inverse(multiply(inverse(multiply(Y,multiply(Z,U))),multiply(Y,multiply(Z,U))))),
inference('PARAMODULATE',[status(thm)],[844,5,theory(equality)]) ).
cnf(907,plain,
multiply(X,inverse(multiply(inverse(X),X))) = multiply(X,inverse(multiply(inverse(Y),Y))),
inference('PARAMODULATE',[status(thm)],[905,5,theory(equality)]) ).
cnf(908,plain,
multiply(X,inverse(multiply(inverse(Y),Y))) = multiply(X,inverse(multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[907,907,theory(equality)]) ).
cnf(909,plain,
multiply(inverse(multiply(X,inverse(multiply(inverse(Y),Y)))),multiply(X,Z)) = multiply(Z,inverse(multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[5,908,theory(equality)]) ).
cnf(910,plain,
inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z)))),inverse(multiply(Z,inverse(multiply(inverse(U),U)))))) = Y,
inference('PARAMODULATE',[status(thm)],[165,908,theory(equality)]) ).
cnf(911,plain,
multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z)))),inverse(multiply(Z,inverse(multiply(inverse(U),U))))) = Y,
inference('PARAMODULATE',[status(thm)],[164,908,theory(equality)]) ).
cnf(950,plain,
multiply(inverse(multiply(X,inverse(multiply(inverse(Y),Y)))),multiply(X,Z)) = multiply(Z,inverse(multiply(inverse(U),U))),
inference('PARAMODULATE',[status(thm)],[908,909,theory(equality)]) ).
cnf(1066,plain,
inverse(multiply(inverse(X),X)) = inverse(multiply(inverse(Y),Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[910,908,theory(equality)]),911,theory(equality)]) ).
cnf(1072,plain,
inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),Y)))),multiply(X,inverse(inverse(multiply(inverse(multiply(Z,U)),multiply(Z,inverse(inverse(multiply(inverse(V),V)))))))))) = U,
inference('PARAMODULATE',[status(thm)],[910,950,theory(equality)]) ).
cnf(1110,plain,
inverse(inverse(multiply(inverse(X),X))) = inverse(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,Z)))),
inference('PARAMODULATE',[status(thm)],[330,1066,theory(equality)]) ).
cnf(1111,plain,
inverse(multiply(inverse(X),X)) = inverse(multiply(inverse(multiply(inverse(Y),Y)),multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[1066,1066,theory(equality)]) ).
cnf(1112,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z)) = multiply(inverse(multiply(U,Y)),multiply(U,Z)),
inference('PARAMODULATE',[status(thm)],[270,1066,theory(equality)]) ).
cnf(1114,plain,
inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(Y,inverse(multiply(inverse(Z),Z)))))) = Y,
inference('PARAMODULATE',[status(thm)],[910,1066,theory(equality)]) ).
cnf(1116,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z))) = inverse(multiply(inverse(multiply(U,Y)),multiply(U,Z))),
inference('PARAMODULATE',[status(thm)],[163,1066,theory(equality)]) ).
cnf(1123,plain,
inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z)))),inverse(multiply(Z,inverse(multiply(inverse(U),U)))))) = Y,
inference('PARAMODULATE',[status(thm)],[910,1066,theory(equality)]) ).
cnf(1147,plain,
inverse(inverse(multiply(inverse(X),X))) = inverse(inverse(multiply(inverse(Y),Y))),
inference('PARAMODULATE',[status(thm)],[1110,1110,theory(equality)]) ).
cnf(1198,plain,
multiply(inverse(X),X) = multiply(inverse(Y),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[910,1111,theory(equality)]),1123,theory(equality)]) ).
cnf(1199,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,1198,theory(equality)]) ).
cnf(1254,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y)) = multiply(inverse(Z),Z),
inference('PARAMODULATE',[status(thm)],[1198,1066,theory(equality)]) ).
cnf(1255,plain,
multiply(inverse(X),X) = multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[950,1198,theory(equality)]) ).
cnf(1256,plain,
multiply(inverse(X),X) = multiply(inverse(inverse(multiply(inverse(Y),Y))),inverse(multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[908,1198,theory(equality)]) ).
cnf(1257,plain,
multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z)) = multiply(inverse(multiply(U,Y)),multiply(U,X)),
inference('PARAMODULATE',[status(thm)],[270,1198,theory(equality)]) ).
cnf(1258,plain,
( multiply(multiply(inverse(X),X),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference('PARAMODULATE',[status(thm)],[1199,1198,theory(equality)]) ).
cnf(1276,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(U),U))) = inverse(multiply(inverse(multiply(V,multiply(W,Z))),multiply(V,multiply(W,Y)))),
inference('PARAMODULATE',[status(thm)],[265,1198,theory(equality)]) ).
cnf(1278,plain,
inverse(multiply(inverse(multiply(X,multiply(inverse(Y),Z))),multiply(X,multiply(inverse(U),U)))) = inverse(multiply(inverse(multiply(V,multiply(W,Z))),multiply(V,multiply(W,Y)))),
inference('PARAMODULATE',[status(thm)],[572,1198,theory(equality)]) ).
cnf(1357,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),multiply(inverse(V),V)))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(W),W)),multiply(U,Z))),multiply(inverse(X1),X1))),
inference('PARAMODULATE',[status(thm)],[265,1254,theory(equality)]) ).
cnf(1429,plain,
multiply(inverse(X),X) = inverse(multiply(inverse(Y),Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[910,1255,theory(equality)]),1123,theory(equality)]) ).
cnf(1476,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),inverse(multiply(inverse(V),V))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(W),W)),multiply(U,Z))),multiply(inverse(X1),X1))),
inference('PARAMODULATE',[status(thm)],[265,1255,theory(equality)]) ).
cnf(1506,plain,
multiply(inverse(X),X) = inverse(inverse(multiply(inverse(Y),Y))),
inference('PARAMODULATE',[status(thm)],[1429,1429,theory(equality)]) ).
cnf(1509,plain,
multiply(X,inverse(multiply(inverse(Y),Y))) = multiply(X,multiply(inverse(Z),Z)),
inference('PARAMODULATE',[status(thm)],[908,1429,theory(equality)]) ).
cnf(1512,plain,
multiply(inverse(X),X) = multiply(multiply(inverse(Y),Y),inverse(multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[1255,1429,theory(equality)]) ).
cnf(1514,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y)) = inverse(multiply(inverse(Z),Z)),
inference('PARAMODULATE',[status(thm)],[1254,1429,theory(equality)]) ).
cnf(1518,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),multiply(inverse(Y),Y)) = multiply(inverse(Z),Z),
inference('PARAMODULATE',[status(thm)],[1254,1429,theory(equality)]) ).
cnf(1521,plain,
multiply(inverse(X),X) = multiply(inverse(multiply(inverse(Y),Y)),inverse(inverse(multiply(inverse(Z),Z)))),
inference('PARAMODULATE',[status(thm)],[1255,1429,theory(equality)]) ).
cnf(1573,plain,
inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(X),Y)),inverse(multiply(inverse(Z),Z))))),inverse(multiply(X,inverse(multiply(inverse(U),U)))))) = Y,
inference('PARAMODULATE',[status(thm)],[910,1429,theory(equality)]) ).
cnf(1637,plain,
multiply(multiply(inverse(X),X),inverse(multiply(inverse(Y),Y))) = inverse(multiply(inverse(Z),Z)),
inference('PARAMODULATE',[status(thm)],[1429,1506,theory(equality)]) ).
cnf(1638,plain,
multiply(multiply(inverse(X),X),multiply(inverse(Y),Y)) = inverse(inverse(multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[1506,1429,theory(equality)]) ).
cnf(1639,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y)) = inverse(inverse(multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[1254,1506,theory(equality)]) ).
cnf(1640,plain,
inverse(inverse(multiply(inverse(X),X))) = inverse(inverse(inverse(inverse(multiply(inverse(Y),Y))))),
inference('PARAMODULATE',[status(thm)],[1147,1506,theory(equality)]) ).
cnf(1641,plain,
multiply(inverse(X),X) = inverse(multiply(multiply(inverse(Y),Y),inverse(multiply(inverse(Z),Z)))),
inference('PARAMODULATE',[status(thm)],[1429,1506,theory(equality)]) ).
cnf(1642,plain,
multiply(multiply(inverse(X),X),inverse(multiply(inverse(Y),Y))) = inverse(inverse(multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[1506,1506,theory(equality)]) ).
cnf(1930,plain,
multiply(X,multiply(inverse(Y),Y)) = multiply(X,multiply(inverse(Z),Z)),
inference('PARAMODULATE',[status(thm)],[1509,1509,theory(equality)]) ).
cnf(2325,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)],[1112,1112,theory(equality)]) ).
cnf(2381,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(multiply(Y,Z)),U)) = multiply(inverse(multiply(Z,inverse(multiply(inverse(V),V)))),multiply(inverse(multiply(Y,inverse(multiply(inverse(W),W)))),U)),
inference('PARAMODULATE',[status(thm)],[1112,950,theory(equality)]) ).
cnf(2850,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),inverse(multiply(inverse(V),V))))) = inverse(multiply(inverse(multiply(multiply(inverse(W),W),multiply(U,Z))),multiply(inverse(X1),X1))),
inference('PARAMODULATE',[status(thm)],[265,1512,theory(equality)]) ).
cnf(3353,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),inverse(multiply(inverse(V),V))))) = inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(W),W))),multiply(U,Z))),multiply(inverse(X1),X1))),
inference('PARAMODULATE',[status(thm)],[265,1256,theory(equality)]) ).
cnf(4302,plain,
multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z)) = multiply(inverse(inverse(multiply(inverse(U),U))),multiply(inverse(Y),X)),
inference('PARAMODULATE',[status(thm)],[1257,1429,theory(equality)]) ).
cnf(4403,plain,
multiply(inverse(multiply(X,Y)),multiply(inverse(Z),Z)) = multiply(inverse(multiply(U,Y)),multiply(U,multiply(inverse(inverse(multiply(inverse(V),V))),inverse(multiply(X,inverse(multiply(inverse(W),W))))))),
inference('PARAMODULATE',[status(thm)],[1257,1114,theory(equality)]) ).
cnf(4500,plain,
multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(multiply(inverse(multiply(Z,U)),multiply(Z,multiply(V,W)))),multiply(inverse(multiply(inverse(multiply(V,X1)),U)),multiply(inverse(multiply(Y1,X1)),multiply(Y1,W))))) = multiply(inverse(multiply(Z1,Y)),multiply(Z1,X)),
inference('PARAMODULATE',[status(thm)],[1257,294,theory(equality)]) ).
cnf(4944,plain,
multiply(inverse(multiply(X,multiply(Y,Z))),multiply(X,multiply(Y,U))) = multiply(inverse(multiply(inverse(inverse(multiply(inverse(V),V))),multiply(inverse(U),Z))),multiply(inverse(W),W)),
inference('PARAMODULATE',[status(thm)],[464,1518,theory(equality)]) ).
cnf(5597,plain,
inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,Y)),multiply(X,multiply(inverse(Z),Z))))),inverse(inverse(multiply(inverse(U),U))))) = Y,
inference('PARAMODULATE',[status(thm)],[910,1637,theory(equality)]) ).
cnf(6426,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),multiply(inverse(Z),Z)))) = inverse(multiply(inverse(multiply(U,Y)),multiply(U,multiply(inverse(V),V)))),
inference('PARAMODULATE',[status(thm)],[1116,1930,theory(equality)]) ).
cnf(6463,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(multiply(Y,Z)),multiply(Y,U)))) = inverse(multiply(inverse(multiply(V,multiply(inverse(U),Z))),multiply(V,multiply(inverse(W),W)))),
inference('PARAMODULATE',[status(thm)],[1116,1257,theory(equality)]) ).
cnf(6592,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(multiply(Y,inverse(multiply(inverse(Z),Z)))),multiply(Y,inverse(U))))) = inverse(multiply(inverse(multiply(V,U)),multiply(V,inverse(multiply(inverse(W),W))))),
inference('PARAMODULATE',[status(thm)],[1116,950,theory(equality)]) ).
cnf(6603,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),multiply(inverse(Z),Z)))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(U),V)),Y)),multiply(inverse(multiply(W,V)),multiply(W,U)))),
inference('PARAMODULATE',[status(thm)],[1116,1257,theory(equality)]) ).
cnf(6882,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(U),U))) = inverse(multiply(inverse(multiply(V,multiply(inverse(Y),Z))),multiply(V,inverse(inverse(multiply(inverse(W),W)))))),
inference('PARAMODULATE',[status(thm)],[265,1521,theory(equality)]) ).
cnf(7528,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(X),Y)),Z)),multiply(inverse(multiply(U,Y)),multiply(U,X)))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(V),V)),Z)),inverse(inverse(multiply(inverse(W),W))))),
inference('PARAMODULATE',[status(thm)],[294,1639,theory(equality)]) ).
cnf(7529,plain,
inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(X),X)),Y)),inverse(inverse(multiply(inverse(Z),Z)))))),inverse(multiply(multiply(inverse(U),U),inverse(multiply(inverse(V),V)))))) = Y,
inference('PARAMODULATE',[status(thm)],[910,1639,theory(equality)]) ).
cnf(7548,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),multiply(inverse(V),V)))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(W),W)),multiply(U,Z))),inverse(inverse(multiply(inverse(X1),X1))))),
inference('PARAMODULATE',[status(thm)],[265,1639,theory(equality)]) ).
cnf(8451,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),inverse(multiply(inverse(V),V))))) = inverse(multiply(inverse(multiply(multiply(inverse(W),W),multiply(U,Z))),inverse(inverse(multiply(inverse(X1),X1))))),
inference('PARAMODULATE',[status(thm)],[265,1642,theory(equality)]) ).
cnf(9563,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(Y,Z)) = multiply(inverse(multiply(inverse(U),U)),multiply(Y,Z)),
inference('PARAMODULATE',[status(thm)],[2325,910,theory(equality)]) ).
cnf(9982,plain,
multiply(inverse(multiply(inverse(X),X)),Y) = multiply(inverse(multiply(inverse(Z),Z)),Y),
inference('PARAMODULATE',[status(thm)],[9563,911,theory(equality)]) ).
cnf(9984,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(Y),inverse(multiply(inverse(Z),Z))))) = Y,
inference('PARAMODULATE',[status(thm)],[911,1066,theory(equality)]) ).
cnf(10005,plain,
multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,multiply(inverse(Z),Z))))),inverse(multiply(inverse(U),U))) = Y,
inference('PARAMODULATE',[status(thm)],[911,1512,theory(equality)]) ).
cnf(10006,plain,
multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,multiply(inverse(Z),Z))))),multiply(inverse(U),U)) = Y,
inference('PARAMODULATE',[status(thm)],[911,1641,theory(equality)]) ).
cnf(10019,plain,
multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(inverse(multiply(inverse(Z),Z))))))),multiply(inverse(U),U)) = Y,
inference('PARAMODULATE',[status(thm)],[911,1429,theory(equality)]) ).
cnf(10021,plain,
multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(multiply(inverse(Z),Z)))))),inverse(multiply(inverse(multiply(inverse(U),U)),inverse(multiply(inverse(V),V))))) = Y,
inference('PARAMODULATE',[status(thm)],[911,908,theory(equality)]) ).
cnf(10033,plain,
multiply(inverse(multiply(X,inverse(multiply(inverse(Y),Y)))),multiply(X,inverse(inverse(multiply(inverse(multiply(Z,inverse(U))),multiply(Z,inverse(inverse(multiply(inverse(V),V))))))))) = U,
inference('PARAMODULATE',[status(thm)],[950,911,theory(equality)]) ).
cnf(10131,plain,
multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(X),X)),inverse(Y))),inverse(multiply(inverse(Z),Z))))),inverse(multiply(multiply(inverse(U),U),inverse(multiply(inverse(V),V))))) = Y,
inference('PARAMODULATE',[status(thm)],[911,1514,theory(equality)]) ).
cnf(10133,plain,
multiply(inverse(inverse(multiply(inverse(multiply(multiply(inverse(X),X),inverse(Y))),inverse(inverse(multiply(inverse(Z),Z)))))),inverse(multiply(multiply(inverse(U),U),inverse(multiply(inverse(V),V))))) = Y,
inference('PARAMODULATE',[status(thm)],[911,1638,theory(equality)]) ).
cnf(10163,plain,
multiply(inverse(inverse(multiply(inverse(multiply(multiply(inverse(X),X),inverse(Y))),inverse(inverse(multiply(inverse(Z),Z)))))),inverse(multiply(inverse(multiply(inverse(U),U)),inverse(multiply(inverse(V),V))))) = Y,
inference('PARAMODULATE',[status(thm)],[911,1642,theory(equality)]) ).
cnf(10322,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),Y) = multiply(inverse(multiply(inverse(Z),Z)),Y),
inference('PARAMODULATE',[status(thm)],[9982,1429,theory(equality)]) ).
cnf(10386,plain,
multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(X),X)),inverse(Y))),multiply(inverse(multiply(inverse(Z),Z)),U)))),inverse(multiply(U,inverse(multiply(inverse(V),V))))) = Y,
inference('PARAMODULATE',[status(thm)],[911,9982,theory(equality)]) ).
cnf(10545,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(Y),multiply(inverse(Z),Z)))) = Y,
inference('PARAMODULATE',[status(thm)],[9984,1429,theory(equality)]) ).
cnf(10548,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(multiply(Y,inverse(multiply(inverse(Z),Z)))),multiply(Y,inverse(U))))) = U,
inference('PARAMODULATE',[status(thm)],[9984,950,theory(equality)]) ).
cnf(10671,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(Y),inverse(multiply(inverse(inverse(multiply(inverse(Z),Z))),inverse(inverse(inverse(multiply(inverse(U),U))))))))) = Y,
inference('PARAMODULATE',[status(thm)],[9984,1640,theory(equality)]) ).
cnf(10874,plain,
multiply(multiply(inverse(X),X),inverse(multiply(inverse(Y),multiply(inverse(Z),Z)))) = Y,
inference('PARAMODULATE',[status(thm)],[10545,1506,theory(equality)]) ).
cnf(10875,plain,
X = multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(X),multiply(inverse(Z),Z)))),
inference('PARAMODULATE',[status(thm)],[10322,10545,theory(equality)]) ).
cnf(10880,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,U)))) = multiply(inverse(U),Z),
inference('PARAMODULATE',[status(thm)],[10545,1257,theory(equality)]) ).
cnf(10881,plain,
multiply(inverse(inverse(X)),inverse(multiply(inverse(Y),Y))) = X,
inference('REWRITE',[status(thm)],[10548,10880,theory(equality)]) ).
cnf(10883,plain,
multiply(inverse(multiply(X,inverse(Y))),multiply(X,multiply(inverse(Z),Z))) = Y,
inference('REWRITE',[status(thm)],[10005,10881,theory(equality)]) ).
cnf(10884,plain,
multiply(inverse(inverse(X)),multiply(inverse(Y),Y)) = X,
inference('REWRITE',[status(thm)],[10006,10883,theory(equality)]) ).
cnf(10886,plain,
multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(inverse(multiply(inverse(Z),Z))))) = Y,
inference('REWRITE',[status(thm)],[10019,10884,theory(equality)]) ).
cnf(10887,plain,
multiply(inverse(multiply(X,inverse(multiply(inverse(Y),Y)))),multiply(X,inverse(inverse(Z)))) = Z,
inference('REWRITE',[status(thm)],[10033,10886,theory(equality)]) ).
cnf(10888,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(X,inverse(inverse(multiply(inverse(Z),Z)))))) = Y,
inference('REWRITE',[status(thm)],[1072,10887,theory(equality)]) ).
cnf(10890,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(U),U))) = multiply(inverse(Y),Z),
inference('REWRITE',[status(thm)],[6882,10888,theory(equality)]) ).
cnf(10891,plain,
multiply(inverse(X),Y) = inverse(multiply(inverse(multiply(Z,multiply(U,Y))),multiply(Z,multiply(U,X)))),
inference('REWRITE',[status(thm)],[1276,10890,theory(equality)]) ).
cnf(10920,plain,
inverse(multiply(inverse(multiply(X,multiply(inverse(multiply(Y,inverse(multiply(Z,inverse(multiply(U,inverse(multiply(inverse(U),U)))))))),multiply(Y,U)))),multiply(X,multiply(inverse(multiply(V,inverse(multiply(Z,inverse(multiply(W,inverse(multiply(inverse(W),W)))))))),X1)))) = multiply(inverse(X1),multiply(V,W)),
inference('REWRITE',[status(thm)],[744,10891,theory(equality)]) ).
cnf(10995,plain,
inverse(multiply(inverse(multiply(X,multiply(inverse(Y),Z))),multiply(X,multiply(inverse(U),U)))) = multiply(inverse(Y),Z),
inference('REWRITE',[status(thm)],[1278,10891,theory(equality)]) ).
cnf(10996,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(multiply(Y,Z)),multiply(Y,U)))) = multiply(inverse(U),Z),
inference('REWRITE',[status(thm)],[6463,10995,theory(equality)]) ).
cnf(10997,plain,
X = inverse(multiply(inverse(multiply(Y,X)),multiply(Y,inverse(multiply(inverse(Z),Z))))),
inference('REWRITE',[status(thm)],[6592,10881,10996,theory(equality)]) ).
cnf(10998,plain,
multiply(inverse(inverse(X)),inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(Z),Z))))) = X,
inference('REWRITE',[status(thm)],[10021,10997,theory(equality)]) ).
cnf(10999,plain,
multiply(inverse(multiply(multiply(inverse(X),X),inverse(Y))),inverse(inverse(multiply(inverse(Z),Z)))) = Y,
inference('REWRITE',[status(thm)],[10163,10998,theory(equality)]) ).
cnf(11000,plain,
multiply(inverse(inverse(X)),inverse(multiply(multiply(inverse(Y),Y),inverse(multiply(inverse(Z),Z))))) = X,
inference('REWRITE',[status(thm)],[10133,10999,theory(equality)]) ).
cnf(11004,plain,
multiply(inverse(multiply(inverse(multiply(inverse(X),X)),inverse(Y))),inverse(multiply(inverse(Z),Z))) = Y,
inference('REWRITE',[status(thm)],[10131,11000,theory(equality)]) ).
cnf(11008,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(X),X)),Y)),inverse(inverse(multiply(inverse(Z),Z))))) = Y,
inference('REWRITE',[status(thm)],[7529,11000,theory(equality)]) ).
cnf(11009,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),multiply(inverse(V),V)))) = multiply(U,Z),
inference('REWRITE',[status(thm)],[7548,11008,theory(equality)]) ).
cnf(11010,plain,
multiply(X,Y) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z),Z)),multiply(X,Y))),multiply(inverse(U),U))),
inference('REWRITE',[status(thm)],[1357,11009,theory(equality)]) ).
cnf(11011,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),inverse(multiply(inverse(V),V))))) = multiply(U,Z),
inference('REWRITE',[status(thm)],[1476,11010,theory(equality)]) ).
cnf(11015,plain,
multiply(X,Y) = inverse(multiply(inverse(multiply(multiply(inverse(Z),Z),multiply(X,Y))),multiply(inverse(U),U))),
inference('REWRITE',[status(thm)],[2850,11011,theory(equality)]) ).
cnf(11016,plain,
multiply(X,Y) = inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(Z),Z))),multiply(X,Y))),multiply(inverse(U),U))),
inference('REWRITE',[status(thm)],[3353,11011,theory(equality)]) ).
cnf(11019,plain,
multiply(X,Y) = inverse(multiply(inverse(multiply(multiply(inverse(Z),Z),multiply(X,Y))),inverse(inverse(multiply(inverse(U),U))))),
inference('REWRITE',[status(thm)],[8451,11011,theory(equality)]) ).
cnf(11021,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(X),Y)),Z)),multiply(inverse(multiply(U,Y)),multiply(U,X)))) = Z,
inference('REWRITE',[status(thm)],[7528,11008,theory(equality)]) ).
cnf(11022,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),multiply(inverse(Z),Z)))) = Y,
inference('REWRITE',[status(thm)],[6603,11021,theory(equality)]) ).
cnf(11023,plain,
X = inverse(multiply(inverse(multiply(Y,X)),multiply(Y,multiply(inverse(Z),Z)))),
inference('REWRITE',[status(thm)],[6426,11022,theory(equality)]) ).
cnf(11048,plain,
inverse(multiply(inverse(X),inverse(inverse(multiply(inverse(Y),Y))))) = X,
inference('REWRITE',[status(thm)],[5597,11023,theory(equality)]) ).
cnf(11049,plain,
multiply(X,Y) = multiply(multiply(inverse(Z),Z),multiply(X,Y)),
inference('REWRITE',[status(thm)],[11019,11048,theory(equality)]) ).
cnf(11050,plain,
multiply(X,Y) = inverse(multiply(inverse(multiply(X,Y)),multiply(inverse(Z),Z))),
inference('REWRITE',[status(thm)],[11015,11049,theory(equality)]) ).
cnf(11051,plain,
multiply(X,Y) = multiply(inverse(inverse(multiply(inverse(Z),Z))),multiply(X,Y)),
inference('REWRITE',[status(thm)],[11016,11050,theory(equality)]) ).
cnf(11057,plain,
multiply(inverse(multiply(X,multiply(Y,Z))),multiply(X,multiply(Y,U))) = multiply(inverse(multiply(inverse(U),Z)),multiply(inverse(V),V)),
inference('REWRITE',[status(thm)],[4944,11051,theory(equality)]) ).
cnf(11063,plain,
multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z)) = multiply(inverse(Y),X),
inference('REWRITE',[status(thm)],[4302,11051,theory(equality)]) ).
cnf(11064,plain,
multiply(inverse(multiply(X,multiply(Y,Z))),multiply(X,multiply(Y,U))) = multiply(inverse(Z),U),
inference('REWRITE',[status(thm)],[11057,11063,theory(equality)]) ).
cnf(11185,plain,
multiply(inverse(multiply(X,multiply(inverse(multiply(Y,inverse(multiply(Z,inverse(multiply(U,inverse(multiply(inverse(U),U)))))))),multiply(Y,U)))),multiply(X,multiply(inverse(multiply(V,inverse(multiply(Z,inverse(multiply(W,inverse(multiply(inverse(W),W)))))))),X1))) = multiply(inverse(multiply(V,W)),X1),
inference('REWRITE',[status(thm)],[628,11064,theory(equality)]) ).
cnf(11186,plain,
inverse(multiply(inverse(multiply(X,Y)),Z)) = multiply(inverse(Z),multiply(X,Y)),
inference('REWRITE',[status(thm)],[10920,11185,theory(equality)]) ).
cnf(11453,plain,
multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(inverse(multiply(inverse(multiply(Z,U)),multiply(Z,inverse(multiply(V,inverse(multiply(U,inverse(multiply(inverse(U),U)))))))))))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(Z,U)),multiply(Z,inverse(multiply(V,inverse(multiply(U,inverse(multiply(inverse(U),U)))))))))),inverse(multiply(V,inverse(inverse(multiply(inverse(multiply(Z,U)),multiply(Z,inverse(multiply(V,inverse(multiply(U,inverse(multiply(inverse(U),U))))))))))))))) = Y,
inference('REWRITE',[status(thm)],[327,11186,theory(equality)]) ).
cnf(11528,plain,
inverse(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,inverse(multiply(inverse(U),inverse(multiply(Z,inverse(multiply(inverse(Z),Z))))))))))),multiply(X,inverse(multiply(inverse(V),inverse(multiply(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,inverse(multiply(inverse(U),inverse(multiply(Z,inverse(multiply(inverse(Z),Z))))))))),inverse(multiply(U,inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,inverse(multiply(inverse(U),inverse(multiply(Z,inverse(multiply(inverse(Z),Z))))))))))))))))))) = V,
inference('REWRITE',[status(thm)],[4,11186,theory(equality)]) ).
cnf(11541,plain,
inverse(inverse(multiply(inverse(multiply(X,Y)),multiply(X,inverse(multiply(Z,inverse(multiply(Y,inverse(multiply(inverse(Y),Y)))))))))) = inverse(multiply(inverse(multiply(U,inverse(multiply(inverse(multiply(V,W)),multiply(V,inverse(multiply(inverse(X1),inverse(multiply(W,inverse(multiply(inverse(W),W))))))))))),multiply(U,inverse(multiply(inverse(Z),inverse(multiply(inverse(multiply(inverse(multiply(V,W)),multiply(V,inverse(multiply(inverse(X1),inverse(multiply(W,inverse(multiply(inverse(W),W))))))))),inverse(multiply(X1,inverse(multiply(inverse(multiply(V,W)),multiply(V,inverse(multiply(inverse(X1),inverse(multiply(W,inverse(multiply(inverse(W),W)))))))))))))))))),
inference('REWRITE',[status(thm)],[15,11186,theory(equality)]) ).
cnf(11562,plain,
inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,Y)),multiply(X,inverse(multiply(Z,inverse(multiply(Y,inverse(multiply(inverse(Y),Y)))))))))),multiply(inverse(multiply(U,inverse(multiply(Z,inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),W)))),inverse(multiply(W,inverse(multiply(inverse(W),W)))))) = multiply(U,V),
inference('REWRITE',[status(thm)],[344,11186,theory(equality)]) ).
cnf(11594,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,multiply(Z,U)))),multiply(inverse(multiply(inverse(multiply(Z,V)),Y)),multiply(inverse(multiply(W,V)),X1))) = multiply(inverse(multiply(W,U)),X1),
inference('REWRITE',[status(thm)],[589,11064,theory(equality)]) ).
cnf(11595,plain,
multiply(inverse(X),Y) = multiply(inverse(multiply(Z,X)),multiply(Z,Y)),
inference('REWRITE',[status(thm)],[4500,11063,11594,theory(equality)]) ).
cnf(11603,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),inverse(inverse(Y))) = Y,
inference('REWRITE',[status(thm)],[10887,11595,theory(equality)]) ).
cnf(11604,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),Y) = Y,
inference('REWRITE',[status(thm)],[10671,11048,11603,theory(equality)]) ).
cnf(11605,plain,
inverse(inverse(X)) = X,
inference('REWRITE',[status(thm)],[11603,11604,theory(equality)]) ).
cnf(11613,plain,
inverse(multiply(multiply(inverse(multiply(inverse(X),Y)),inverse(multiply(inverse(Z),Z))),inverse(multiply(X,inverse(multiply(inverse(U),U)))))) = Y,
inference('REWRITE',[status(thm)],[1573,11605,theory(equality)]) ).
cnf(11632,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(X),X)),inverse(Y))),multiply(inverse(multiply(inverse(Z),Z)),U)),inverse(multiply(U,inverse(multiply(inverse(V),V))))) = Y,
inference('REWRITE',[status(thm)],[10386,11605,theory(equality)]) ).
cnf(11655,plain,
multiply(multiply(inverse(X),X),Y) = Y,
inference('REWRITE',[status(thm)],[11604,11605,theory(equality)]) ).
cnf(11656,plain,
inverse(multiply(inverse(X),multiply(inverse(Y),Y))) = X,
inference('REWRITE',[status(thm)],[10874,11655,theory(equality)]) ).
cnf(11657,plain,
X = multiply(inverse(multiply(inverse(Y),Y)),X),
inference('REWRITE',[status(thm)],[10875,11656,theory(equality)]) ).
cnf(11660,plain,
multiply(X,inverse(multiply(inverse(Y),Y))) = X,
inference('REWRITE',[status(thm)],[11004,11605,11657,theory(equality)]) ).
cnf(11663,plain,
multiply(X,multiply(inverse(X),Y)) = Y,
inference('REWRITE',[status(thm)],[11613,11605,11186,11660,theory(equality)]) ).
cnf(11665,plain,
X = multiply(X,multiply(inverse(Y),Y)),
inference('REWRITE',[status(thm)],[1509,11660,theory(equality)]) ).
cnf(11666,plain,
inverse(multiply(inverse(X),Y)) = multiply(inverse(Y),X),
inference('REWRITE',[status(thm)],[11063,11665,theory(equality)]) ).
cnf(11673,plain,
multiply(inverse(multiply(X,Y)),Z) = multiply(inverse(Y),multiply(inverse(X),Z)),
inference('REWRITE',[status(thm)],[2381,11665,11666,11657,theory(equality)]) ).
cnf(11680,plain,
multiply(multiply(X,Y),inverse(Y)) = X,
inference('REWRITE',[status(thm)],[11632,11665,11605,11655,11666,11657,theory(equality)]) ).
cnf(11684,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference('REWRITE',[status(thm)],[1258,11655,theory(equality)]) ).
cnf(11690,plain,
multiply(multiply(inverse(X),inverse(multiply(inverse(Y),inverse(X)))),inverse(multiply(inverse(Z),inverse(multiply(inverse(multiply(inverse(X),inverse(multiply(inverse(Y),inverse(X))))),inverse(multiply(Y,inverse(multiply(inverse(X),inverse(multiply(inverse(Y),inverse(X)))))))))))) = Z,
inference('REWRITE',[status(thm)],[11528,11605,11663,11666,11595,theory(equality)]) ).
cnf(11695,plain,
inverse(multiply(multiply(multiply(inverse(X),inverse(multiply(Y,inverse(X)))),multiply(inverse(multiply(Z,inverse(multiply(Y,inverse(U))))),V)),inverse(V))) = multiply(Z,U),
inference('REWRITE',[status(thm)],[11562,11605,11663,11666,11595,theory(equality)]) ).
cnf(11697,plain,
multiply(multiply(X,multiply(inverse(Y),inverse(multiply(Z,inverse(Y))))),inverse(multiply(multiply(inverse(Y),inverse(multiply(Z,inverse(Y)))),inverse(multiply(Z,multiply(inverse(Y),inverse(multiply(Z,inverse(Y))))))))) = X,
inference('REWRITE',[status(thm)],[11453,11605,11663,11666,11595,theory(equality)]) ).
cnf(11704,plain,
multiply(inverse(X),inverse(multiply(Y,inverse(X)))) = inverse(Y),
inference('REWRITE',[status(thm)],[11541,11690,11605,11663,11666,11595,theory(equality)]) ).
cnf(11705,plain,
multiply(multiply(X,inverse(Y)),Y) = X,
inference('REWRITE',[status(thm)],[11697,11605,11704,theory(equality)]) ).
cnf(11709,plain,
multiply(multiply(X,inverse(multiply(Y,inverse(Z)))),Y) = multiply(X,Z),
inference('REWRITE',[status(thm)],[11695,11605,11680,11673,11704,theory(equality)]) ).
cnf(11713,plain,
inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)),
inference('REWRITE',[status(thm)],[4403,11655,11666,11665,11595,theory(equality)]) ).
cnf(12058,plain,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[11705,11709,theory(equality)]),11605,11713,theory(equality)]) ).
cnf(12059,plain,
$false,
inference('REWRITE',[status(thm)],[11684,12058,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP054-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : run-snark %s %d
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 20:57:57 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.45 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.46 *
% 0.20/0.46 *
% 0.20/0.47 #<PACKAGE "SNARK-USER">
% 0.20/0.47 *
% 0.20/0.47 SNARK-TPTP-OPTIONS
% 0.20/0.47 *
% 0.20/0.47 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.47 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.47 (USE-FACTORING :POS)
% 0.20/0.47 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.47 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.47 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.47 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.47 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.47 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.47 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.47 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.47 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.47 (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.47 *
% 0.20/0.47 "."
% 0.20/0.47 *
% 0.20/0.47 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T20:57:57
% 0.20/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n021.cluster.edu at 2022-06-13T20:57:57
% 10.68/10.89
% 10.68/10.89
% 10.68/10.89 #||
% 10.68/10.89 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.68/10.89 % SZS output start Refutation
% See solution above
% 10.75/10.96 ||#
% 10.75/10.96
% 10.75/10.96 ; Summary of computation:
% 10.75/10.96 ; 42461 formulas have been input or derived (from 98 formulas).
% 10.75/10.96 ; 12059 (28%) were retained. Of these,
% 10.75/10.96 ; 11822 (98%) were simplified or subsumed later,
% 10.75/10.96 ; 237 ( 2%) are still being kept.
% 10.75/10.96 ;
% 10.75/10.96 ; Run time in seconds excluding printing time:
% 10.75/10.96 ; 0.001 0% Read assertion file (1 call)
% 10.75/10.96 ; 0.000 0% Assert (2 calls)
% 10.75/10.96 ; 2.341 22% Process new row (41,924 calls)
% 10.75/10.96 ; 0.031 0% Resolution (194 calls)
% 10.75/10.96 ; 0.762 7% Paramodulation (97 calls)
% 10.75/10.96 ; 0.000 0% Condensing (3 calls)
% 10.75/10.96 ; 0.000 0% Forward subsumption (3 calls)
% 10.75/10.96 ; 0.000 0% Backward subsumption (3 calls)
% 10.75/10.96 ; 0.000 0% Clause clause subsumption (1 call)
% 10.75/10.96 ; 3.413 33% Forward simplification (39,586 calls)
% 10.75/10.96 ; 2.733 26% Backward simplification (12,059 calls)
% 10.75/10.96 ; 0.969 9% Ordering (235,655 calls)
% 10.75/10.96 ; 0.000 0% Sortal reasoning (32 calls)
% 10.75/10.96 ; 0.000 0% Purity testing (1 call)
% 10.75/10.96 ; 0.167 2% Other
% 10.75/10.96 ; 10.417 Total
% 10.75/10.96 ; 10.488 Real time
% 10.75/10.96 ;
% 10.75/10.96 ; Term-hash-array has 30,831 terms in all.
% 10.75/10.96 ; Feature-vector-row-index has 0 entries (1 at peak, 3 added, 3 deleted).
% 10.75/10.96 ; Feature-vector-row-index has 1 node (30 at peak, 71 added, 70 deleted).
% 10.75/10.96 ; Retrieved 0 possibly forward subsuming rows in 3 calls.
% 10.75/10.96 ; Retrieved 1 possibly backward subsumed row in 3 calls.
% 10.75/10.96 ; Path-index has 993 entries (23,724 at peak, 32,022 added, 31,029 deleted).
% 10.75/10.96 ; Path-index has 46,050 nodes (55,902 at peak, 69,318 added, 23,268 deleted).
% 10.75/10.96 ; Trie-index has 993 entries (23,724 at peak, 32,022 added, 31,029 deleted).
% 10.75/10.96 ; Trie-index has 4,998 nodes (234,196 at peak, 361,112 added, 356,114 deleted).
% 10.75/10.96 ; Retrieved 280,942 generalization terms in 527,672 calls.
% 10.75/10.96 ; Retrieved 64,444 instance terms in 12,372 calls.
% 10.75/10.96 ; Retrieved 267,976 unifiable terms in 1,304 calls.
% 10.75/10.96 ;
% 10.75/10.96 ; The agenda of backward simplifiable rows to process has 2 entries:
% 10.75/10.96 ; 2 with value 0
% 10.75/10.96 ; The agenda of rows to process has 19 entries:
% 10.75/10.96 ; 1 with value 26 2 with value 31 1 with value 34
% 10.75/10.96 ; 3 with value 28 3 with value 32 2 with value 35
% 10.75/10.96 ; 1 with value 29 2 with value 33 4 with value 36
% 10.75/10.96 ; The agenda of rows to give has 229 entries:
% 10.75/10.96 ; 1 with value (4 21) 7 with value (4 33) 13 with value (4 42)
% 10.75/10.96 ; 1 with value (4 25) 6 with value (4 34) 10 with value (4 43)
% 10.75/10.96 ; 6 with value (4 26) 12 with value (4 35) 8 with value (4 44)
% 10.75/10.96 ; 1 with value (4 27) 17 with value (4 36) 10 with value (4 45)
% 10.75/10.96 ; 7 with value (4 28) 15 with value (4 37) 8 with value (4 46)
% 10.75/10.96 ; 9 with value (4 29) 16 with value (4 38) 10 with value (4 47)
% 10.75/10.96 ; 4 with value (4 30) 12 with value (4 39) 6 with value (4 49)
% 10.75/10.96 ; 4 with value (4 31) 21 with value (4 40) 2 with value (4 50)
% 10.75/10.96 ; 7 with value (4 32) 14 with value (4 41) 2 with value (4 52)
% 10.75/10.96 Evaluation took:
% 10.75/10.96 10.489 seconds of real time
% 10.75/10.96 9.595918 seconds of user run time
% 10.75/10.96 0.892604 seconds of system run time
% 10.75/10.96 [Run times include 2.288 seconds GC run time.]
% 10.75/10.96 0 calls to %EVAL
% 10.75/10.96 0 page faults and
% 10.75/10.96 668,367,152 bytes consed.
% 10.75/10.96 :PROOF-FOUND
% 10.75/10.96 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T20:58:08
% 10.75/10.96 :PROOF-FOUND
% 10.75/10.96 *
%------------------------------------------------------------------------------