TSTP Solution File: GRP414-1 by SNARK---20120808r022
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- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP414-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n028.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 11:38:25 EDT 2022
% Result : Unsatisfiable 2.00s 2.21s
% Output : Refutation 2.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 2
% Syntax : Number of clauses : 117 ( 117 unt; 0 nHn; 2 RR)
% Number of literals : 117 ( 116 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 12 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 416 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(X,inverse(multiply(multiply(multiply(inverse(Y),Y),inverse(multiply(inverse(multiply(X,inverse(Y))),Z))),Y))) = Z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_3) ).
cnf(3,plain,
multiply(X,inverse(multiply(multiply(multiply(inverse(Y),Y),inverse(Z)),Y))) = inverse(multiply(multiply(multiply(inverse(U),U),inverse(multiply(inverse(multiply(inverse(multiply(X,inverse(Y))),inverse(U))),Z))),U)),
inference('PARAMODULATE',[status(thm)],[single_axiom,single_axiom,theory(equality)]) ).
cnf(5,plain,
multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(multiply(multiply(multiply(inverse(Y),Y),inverse(Z)),Y)))) = Z,
inference('PARAMODULATE',[status(thm)],[single_axiom,3,theory(equality)]) ).
cnf(6,plain,
inverse(multiply(multiply(multiply(inverse(X),X),inverse(multiply(inverse(multiply(inverse(multiply(Y,inverse(Z))),inverse(X))),multiply(inverse(multiply(Y,inverse(Z))),U)))),X)) = U,
inference('PARAMODULATE',[status(thm)],[single_axiom,3,theory(equality)]) ).
cnf(24,plain,
multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(multiply(Z,Y)))) = multiply(multiply(multiply(inverse(U),U),inverse(multiply(inverse(multiply(multiply(inverse(Y),Y),inverse(U))),Z))),U),
inference('PARAMODULATE',[status(thm)],[5,single_axiom,theory(equality)]) ).
cnf(32,plain,
inverse(multiply(multiply(multiply(inverse(X),X),inverse(multiply(inverse(multiply(Y,inverse(X))),multiply(Y,Z)))),X)) = Z,
inference('PARAMODULATE',[status(thm)],[6,6,theory(equality)]) ).
cnf(33,plain,
multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z)) = multiply(inverse(multiply(U,inverse(Y))),multiply(U,Z)),
inference('PARAMODULATE',[status(thm)],[5,32,theory(equality)]) ).
cnf(52,plain,
multiply(inverse(multiply(X,Y)),multiply(X,Z)) = multiply(inverse(multiply(U,Y)),multiply(U,Z)),
inference('PARAMODULATE',[status(thm)],[33,32,theory(equality)]) ).
cnf(53,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)],[52,52,theory(equality)]) ).
cnf(54,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)],[52,52,theory(equality)]) ).
cnf(123,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)],[53,54,theory(equality)]) ).
cnf(244,plain,
multiply(multiply(inverse(X),X),inverse(multiply(inverse(multiply(Y,inverse(X))),multiply(Y,inverse(multiply(Z,X)))))) = Z,
inference('PARAMODULATE',[status(thm)],[single_axiom,24,theory(equality)]) ).
cnf(245,plain,
inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(multiply(multiply(multiply(inverse(Y),Y),Z),Y))))) = Z,
inference('PARAMODULATE',[status(thm)],[32,24,theory(equality)]) ).
cnf(246,plain,
multiply(multiply(multiply(inverse(X),X),inverse(multiply(inverse(multiply(multiply(inverse(Y),Y),inverse(X))),multiply(multiply(inverse(Y),Y),inverse(Z))))),X) = Z,
inference('PARAMODULATE',[status(thm)],[5,24,theory(equality)]) ).
cnf(324,plain,
multiply(multiply(inverse(multiply(X,Y)),multiply(X,Y)),inverse(multiply(inverse(multiply(Z,inverse(multiply(U,Y)))),multiply(Z,inverse(multiply(V,multiply(U,Y))))))) = V,
inference('PARAMODULATE',[status(thm)],[244,52,theory(equality)]) ).
cnf(329,plain,
multiply(multiply(inverse(multiply(X,Y)),multiply(X,Y)),inverse(multiply(inverse(multiply(Z,inverse(multiply(X,Y)))),multiply(Z,inverse(multiply(inverse(multiply(U,V)),multiply(U,Y))))))) = inverse(multiply(X,V)),
inference('PARAMODULATE',[status(thm)],[244,52,theory(equality)]) ).
cnf(353,plain,
multiply(inverse(multiply(multiply(inverse(X),X),inverse(multiply(Y,inverse(multiply(Z,X)))))),Z) = multiply(multiply(multiply(inverse(U),U),inverse(multiply(inverse(multiply(multiply(inverse(multiply(Y,inverse(multiply(Z,X)))),multiply(Y,inverse(multiply(Z,X)))),inverse(U))),inverse(multiply(Y,inverse(X)))))),U),
inference('PARAMODULATE',[status(thm)],[24,244,theory(equality)]) ).
cnf(355,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)],[244,54,theory(equality)]),329,theory(equality)]) ).
cnf(446,plain,
multiply(multiply(multiply(inverse(X),X),inverse(multiply(inverse(multiply(Y,inverse(X))),multiply(Y,inverse(Z))))),X) = Z,
inference('PARAMODULATE',[status(thm)],[246,52,theory(equality)]) ).
cnf(476,plain,
multiply(inverse(multiply(multiply(multiply(inverse(inverse(multiply(X,Y))),inverse(multiply(X,Y))),inverse(multiply(inverse(multiply(Z,inverse(inverse(multiply(X,Y))))),multiply(Z,inverse(U))))),inverse(Y))),U) = multiply(multiply(multiply(inverse(V),V),inverse(multiply(inverse(multiply(multiply(inverse(Y),Y),inverse(V))),X))),V),
inference('PARAMODULATE',[status(thm)],[24,446,theory(equality)]) ).
cnf(538,plain,
multiply(multiply(inverse(multiply(X,Y)),multiply(X,Y)),Z) = multiply(multiply(inverse(multiply(U,Y)),multiply(U,Y)),Z),
inference('PARAMODULATE',[status(thm)],[324,245,theory(equality)]) ).
cnf(540,plain,
multiply(multiply(inverse(X),X),Y) = multiply(multiply(inverse(multiply(Z,U)),multiply(Z,U)),Y),
inference('PARAMODULATE',[status(thm)],[538,446,theory(equality)]) ).
cnf(541,plain,
multiply(multiply(inverse(X),X),Y) = multiply(multiply(inverse(Z),Z),Y),
inference('PARAMODULATE',[status(thm)],[540,540,theory(equality)]) ).
cnf(542,plain,
multiply(multiply(inverse(X),X),inverse(multiply(inverse(multiply(Y,inverse(Z))),multiply(Y,inverse(multiply(U,Z)))))) = U,
inference('PARAMODULATE',[status(thm)],[244,541,theory(equality)]) ).
cnf(543,plain,
multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(multiply(multiply(multiply(inverse(Z),Z),inverse(U)),Y)))) = U,
inference('PARAMODULATE',[status(thm)],[5,541,theory(equality)]) ).
cnf(544,plain,
multiply(multiply(multiply(inverse(X),X),inverse(multiply(inverse(multiply(Y,inverse(Z))),multiply(Y,inverse(U))))),Z) = U,
inference('PARAMODULATE',[status(thm)],[446,541,theory(equality)]) ).
cnf(545,plain,
inverse(multiply(multiply(multiply(inverse(X),X),inverse(multiply(inverse(multiply(Y,inverse(Z))),multiply(Y,U)))),Z)) = U,
inference('PARAMODULATE',[status(thm)],[32,541,theory(equality)]) ).
cnf(546,plain,
inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(multiply(multiply(multiply(inverse(Z),Z),U),Y))))) = U,
inference('PARAMODULATE',[status(thm)],[245,541,theory(equality)]) ).
cnf(565,plain,
multiply(inverse(X),X) = multiply(inverse(Y),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[542,541,theory(equality)]),542,theory(equality)]) ).
cnf(575,plain,
multiply(multiply(inverse(X),X),inverse(multiply(inverse(multiply(Y,inverse(inverse(multiply(inverse(multiply(Z,inverse(U))),multiply(Z,inverse(multiply(V,U)))))))),multiply(Y,inverse(V))))) = multiply(inverse(W),W),
inference('PARAMODULATE',[status(thm)],[542,542,theory(equality)]) ).
cnf(596,plain,
inverse(multiply(inverse(X),X)) = inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,Z))),
inference('PARAMODULATE',[status(thm)],[355,565,theory(equality)]) ).
cnf(597,plain,
multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z)) = multiply(inverse(multiply(U,Y)),multiply(U,X)),
inference('PARAMODULATE',[status(thm)],[52,565,theory(equality)]) ).
cnf(598,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z)) = multiply(inverse(multiply(U,Y)),multiply(U,Z)),
inference('PARAMODULATE',[status(thm)],[52,565,theory(equality)]) ).
cnf(604,plain,
multiply(multiply(inverse(X),X),inverse(multiply(inverse(multiply(inverse(inverse(multiply(Y,Z))),inverse(Z))),multiply(inverse(U),U)))) = Y,
inference('PARAMODULATE',[status(thm)],[542,565,theory(equality)]) ).
cnf(626,plain,
inverse(multiply(inverse(X),X)) = inverse(multiply(inverse(Y),Y)),
inference('PARAMODULATE',[status(thm)],[596,596,theory(equality)]) ).
cnf(627,plain,
multiply(inverse(X),X) = multiply(inverse(multiply(inverse(Y),Y)),multiply(inverse(Z),Z)),
inference('PARAMODULATE',[status(thm)],[565,626,theory(equality)]) ).
cnf(628,plain,
inverse(multiply(inverse(X),X)) = inverse(multiply(inverse(multiply(inverse(Y),Y)),multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[626,626,theory(equality)]) ).
cnf(661,plain,
multiply(inverse(multiply(X,multiply(inverse(Y),Z))),multiply(X,multiply(inverse(multiply(inverse(U),U)),multiply(inverse(V),V)))) = multiply(inverse(multiply(W,multiply(X1,Z))),multiply(W,multiply(X1,Y))),
inference('PARAMODULATE',[status(thm)],[123,627,theory(equality)]) ).
cnf(662,plain,
multiply(inverse(multiply(X,multiply(inverse(Y),Y))),multiply(X,multiply(inverse(multiply(inverse(Z),Z)),U))) = multiply(inverse(multiply(V,multiply(W,multiply(inverse(X1),X1)))),multiply(V,multiply(W,U))),
inference('PARAMODULATE',[status(thm)],[123,627,theory(equality)]) ).
cnf(697,plain,
multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z)) = multiply(inverse(multiply(inverse(U),U)),multiply(inverse(Y),X)),
inference('PARAMODULATE',[status(thm)],[597,565,theory(equality)]) ).
cnf(698,plain,
multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z)) = multiply(inverse(multiply(multiply(inverse(U),U),Y)),multiply(multiply(inverse(V),V),X)),
inference('PARAMODULATE',[status(thm)],[597,541,theory(equality)]) ).
cnf(882,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(multiply(inverse(Y),Y)),Z)) = multiply(inverse(multiply(U,multiply(inverse(multiply(inverse(V),V)),multiply(inverse(W),W)))),multiply(U,Z)),
inference('PARAMODULATE',[status(thm)],[598,628,theory(equality)]) ).
cnf(895,plain,
multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(multiply(Z,Y)))) = multiply(inverse(multiply(U,inverse(V))),multiply(U,inverse(multiply(Z,V)))),
inference('PARAMODULATE',[status(thm)],[543,542,theory(equality)]) ).
cnf(903,plain,
multiply(inverse(X),multiply(multiply(inverse(Y),Y),inverse(multiply(multiply(multiply(inverse(Z),Z),inverse(U)),multiply(inverse(multiply(V,inverse(W))),multiply(V,inverse(multiply(X,W)))))))) = U,
inference('PARAMODULATE',[status(thm)],[543,542,theory(equality)]) ).
cnf(904,plain,
multiply(inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y))),multiply(inverse(inverse(Z)),inverse(multiply(multiply(multiply(inverse(U),U),inverse(V)),Z)))) = V,
inference('PARAMODULATE',[status(thm)],[543,627,theory(equality)]) ).
cnf(909,plain,
multiply(inverse(multiply(inverse(inverse(multiply(multiply(multiply(inverse(X),X),inverse(Y)),Z))),inverse(Z))),multiply(inverse(multiply(inverse(U),U)),multiply(inverse(V),V))) = Y,
inference('PARAMODULATE',[status(thm)],[543,627,theory(equality)]) ).
cnf(943,plain,
multiply(multiply(multiply(inverse(X),X),inverse(multiply(inverse(Y),Y))),Z) = Z,
inference('PARAMODULATE',[status(thm)],[544,565,theory(equality)]) ).
cnf(965,plain,
multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z)) = multiply(inverse(multiply(multiply(multiply(inverse(U),U),inverse(multiply(inverse(multiply(V,inverse(X))),multiply(V,inverse(W))))),Y)),W),
inference('PARAMODULATE',[status(thm)],[597,544,theory(equality)]) ).
cnf(977,plain,
multiply(multiply(multiply(inverse(X),X),inverse(multiply(inverse(multiply(Y,inverse(multiply(inverse(multiply(inverse(Z),Z)),multiply(inverse(U),U))))),multiply(Y,inverse(V))))),multiply(inverse(W),W)) = V,
inference('PARAMODULATE',[status(thm)],[544,628,theory(equality)]) ).
cnf(999,plain,
multiply(inverse(X),Y) = multiply(inverse(multiply(Z,X)),multiply(Z,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[52,943,theory(equality)]),943,theory(equality)]) ).
cnf(1002,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(multiply(inverse(Y),Y)),Z)) = multiply(inverse(multiply(inverse(multiply(inverse(U),U)),multiply(inverse(V),V))),Z),
inference('REWRITE',[status(thm)],[882,999,theory(equality)]) ).
cnf(1034,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(multiply(inverse(Y),Y)),Z)) = multiply(inverse(multiply(inverse(U),U)),Z),
inference('REWRITE',[status(thm)],[662,999,theory(equality)]) ).
cnf(1036,plain,
multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(multiply(inverse(Z),Z)),multiply(inverse(U),U))) = multiply(inverse(Y),X),
inference('REWRITE',[status(thm)],[661,999,theory(equality)]) ).
cnf(1038,plain,
multiply(inverse(inverse(X)),inverse(multiply(multiply(multiply(inverse(Y),Y),inverse(Z)),X))) = Z,
inference('REWRITE',[status(thm)],[909,1036,theory(equality)]) ).
cnf(1039,plain,
multiply(inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y))),Z) = Z,
inference('REWRITE',[status(thm)],[904,1038,theory(equality)]) ).
cnf(1040,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(multiply(inverse(Y),Y)),Z)) = Z,
inference('REWRITE',[status(thm)],[1002,1039,theory(equality)]) ).
cnf(1042,plain,
X = multiply(inverse(multiply(inverse(Y),Y)),X),
inference('REWRITE',[status(thm)],[1034,1040,theory(equality)]) ).
cnf(1050,plain,
multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z)) = multiply(inverse(Y),X),
inference('REWRITE',[status(thm)],[697,1042,theory(equality)]) ).
cnf(1052,plain,
multiply(multiply(inverse(X),X),inverse(multiply(inverse(inverse(Y)),inverse(multiply(Z,Y))))) = Z,
inference('REWRITE',[status(thm)],[604,1050,theory(equality)]) ).
cnf(1053,plain,
multiply(inverse(X),Y) = multiply(inverse(multiply(multiply(inverse(Z),Z),X)),multiply(multiply(inverse(U),U),Y)),
inference('REWRITE',[status(thm)],[698,1050,theory(equality)]) ).
cnf(1087,plain,
multiply(multiply(multiply(inverse(X),X),inverse(multiply(inverse(inverse(multiply(inverse(Y),Y))),inverse(Z)))),multiply(inverse(U),U)) = Z,
inference('REWRITE',[status(thm)],[977,1050,999,theory(equality)]) ).
cnf(1097,plain,
multiply(inverse(multiply(multiply(inverse(X),X),inverse(multiply(Y,inverse(multiply(Z,X)))))),Z) = multiply(multiply(multiply(inverse(U),U),inverse(multiply(inverse(multiply(multiply(inverse(inverse(multiply(Z,X))),inverse(multiply(Z,X))),inverse(U))),inverse(multiply(Y,inverse(X)))))),U),
inference('REWRITE',[status(thm)],[353,999,theory(equality)]) ).
cnf(1107,plain,
multiply(inverse(multiply(multiply(multiply(inverse(inverse(multiply(X,Y))),inverse(multiply(X,Y))),inverse(multiply(inverse(inverse(inverse(multiply(X,Y)))),inverse(Z)))),inverse(Y))),Z) = multiply(multiply(multiply(inverse(U),U),inverse(multiply(inverse(multiply(multiply(inverse(Y),Y),inverse(U))),X))),U),
inference('REWRITE',[status(thm)],[476,999,theory(equality)]) ).
cnf(1124,plain,
multiply(inverse(X),Y) = multiply(inverse(multiply(multiply(multiply(inverse(Z),Z),inverse(multiply(inverse(inverse(Y)),inverse(U)))),X)),U),
inference('REWRITE',[status(thm)],[965,1050,999,theory(equality)]) ).
cnf(1125,plain,
multiply(inverse(inverse(X)),inverse(multiply(Y,X))) = multiply(multiply(multiply(inverse(Z),Z),inverse(multiply(inverse(multiply(multiply(inverse(X),X),inverse(Z))),Y))),Z),
inference('REWRITE',[status(thm)],[1107,1124,theory(equality)]) ).
cnf(1127,plain,
multiply(inverse(multiply(multiply(inverse(X),X),inverse(multiply(Y,inverse(multiply(Z,X)))))),Z) = multiply(inverse(inverse(inverse(multiply(Z,X)))),inverse(multiply(inverse(multiply(Y,inverse(X))),inverse(multiply(Z,X))))),
inference('REWRITE',[status(thm)],[1097,1125,theory(equality)]) ).
cnf(1147,plain,
multiply(inverse(X),multiply(multiply(inverse(Y),Y),inverse(multiply(multiply(multiply(inverse(Z),Z),inverse(U)),multiply(inverse(inverse(V)),inverse(multiply(X,V))))))) = U,
inference('REWRITE',[status(thm)],[903,999,theory(equality)]) ).
cnf(1148,plain,
inverse(multiply(inverse(inverse(X)),inverse(multiply(multiply(multiply(inverse(Y),Y),Z),X)))) = Z,
inference('REWRITE',[status(thm)],[546,999,theory(equality)]) ).
cnf(1159,plain,
multiply(multiply(inverse(X),X),inverse(multiply(inverse(inverse(inverse(multiply(inverse(inverse(Y)),inverse(multiply(Z,Y)))))),inverse(Z)))) = multiply(inverse(U),U),
inference('REWRITE',[status(thm)],[575,999,theory(equality)]) ).
cnf(1178,plain,
inverse(multiply(multiply(multiply(inverse(X),X),inverse(multiply(inverse(inverse(Y)),Z))),Y)) = Z,
inference('REWRITE',[status(thm)],[545,999,theory(equality)]) ).
cnf(1196,plain,
multiply(inverse(inverse(X)),inverse(multiply(Y,X))) = multiply(inverse(inverse(Z)),inverse(multiply(Y,Z))),
inference('REWRITE',[status(thm)],[895,999,theory(equality)]) ).
cnf(1411,plain,
multiply(inverse(inverse(X)),inverse(multiply(inverse(Y),Y))) = multiply(inverse(inverse(Z)),inverse(multiply(inverse(X),Z))),
inference('PARAMODULATE',[status(thm)],[1196,565,theory(equality)]) ).
cnf(1418,plain,
multiply(inverse(inverse(multiply(X,Y))),inverse(Y)) = multiply(inverse(inverse(multiply(X,Z))),inverse(Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1050,1196,theory(equality)]),1050,theory(equality)]) ).
cnf(1419,plain,
multiply(inverse(inverse(X)),inverse(multiply(inverse(multiply(inverse(Y),Z)),X))) = multiply(inverse(inverse(multiply(inverse(U),U))),inverse(multiply(inverse(Z),Y))),
inference('PARAMODULATE',[status(thm)],[1196,1050,theory(equality)]) ).
cnf(1425,plain,
inverse(multiply(inverse(inverse(X)),inverse(multiply(Y,X)))) = inverse(multiply(inverse(inverse(Z)),inverse(multiply(Y,Z)))),
inference('PARAMODULATE',[status(thm)],[1148,1052,theory(equality)]) ).
cnf(1435,plain,
multiply(inverse(multiply(X,Y)),multiply(inverse(Z),Z)) = multiply(inverse(Y),multiply(inverse(inverse(U)),inverse(multiply(multiply(multiply(inverse(V),V),X),U)))),
inference('PARAMODULATE',[status(thm)],[1050,1148,theory(equality)]) ).
cnf(1463,plain,
multiply(inverse(X),inverse(multiply(inverse(Y),Y))) = multiply(inverse(inverse(Z)),inverse(multiply(X,Z))),
inference('PARAMODULATE',[status(thm)],[1411,1178,theory(equality)]) ).
cnf(1464,plain,
multiply(inverse(X),inverse(multiply(inverse(Y),Y))) = multiply(inverse(X),inverse(multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[1463,1463,theory(equality)]) ).
cnf(1465,plain,
multiply(multiply(inverse(X),X),inverse(multiply(inverse(Y),inverse(multiply(inverse(Z),Z))))) = Y,
inference('PARAMODULATE',[status(thm)],[1052,1463,theory(equality)]) ).
cnf(1466,plain,
inverse(multiply(inverse(multiply(multiply(inverse(X),X),Y)),inverse(multiply(inverse(Z),Z)))) = Y,
inference('PARAMODULATE',[status(thm)],[1148,1463,theory(equality)]) ).
cnf(1481,plain,
multiply(inverse(inverse(X)),inverse(multiply(inverse(Y),X))) = multiply(inverse(inverse(inverse(multiply(inverse(Z),Z)))),inverse(multiply(inverse(inverse(U)),inverse(multiply(Y,U))))),
inference('PARAMODULATE',[status(thm)],[1196,1463,theory(equality)]) ).
cnf(1482,plain,
multiply(inverse(inverse(X)),inverse(multiply(inverse(Y),Y))) = multiply(inverse(inverse(inverse(multiply(inverse(Z),Z)))),inverse(multiply(inverse(inverse(U)),inverse(multiply(X,U))))),
inference('PARAMODULATE',[status(thm)],[1463,1463,theory(equality)]) ).
cnf(1500,plain,
multiply(inverse(inverse(multiply(X,Y))),inverse(Y)) = multiply(inverse(inverse(Z)),inverse(multiply(inverse(multiply(X,multiply(inverse(U),U))),Z))),
inference('PARAMODULATE',[status(thm)],[1463,1418,theory(equality)]) ).
cnf(1506,plain,
multiply(inverse(inverse(multiply(inverse(inverse(X)),inverse(multiply(Y,X))))),inverse(inverse(multiply(Y,Z)))) = multiply(inverse(inverse(multiply(inverse(inverse(Z)),U))),inverse(U)),
inference('PARAMODULATE',[status(thm)],[1418,1196,theory(equality)]) ).
cnf(1526,plain,
multiply(X,inverse(multiply(inverse(Y),Y))) = multiply(X,inverse(multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[1464,1178,theory(equality)]) ).
cnf(1637,plain,
inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(Y,multiply(inverse(Z),Z))))) = inverse(multiply(inverse(inverse(U)),inverse(multiply(Y,U)))),
inference('PARAMODULATE',[status(thm)],[1425,626,theory(equality)]) ).
cnf(1665,plain,
multiply(multiply(inverse(X),X),inverse(multiply(inverse(Y),Y))) = inverse(multiply(inverse(Z),Z)),
inference('PARAMODULATE',[status(thm)],[1465,565,theory(equality)]) ).
cnf(1677,plain,
multiply(multiply(inverse(X),X),inverse(multiply(inverse(Y),inverse(multiply(inverse(inverse(multiply(inverse(Z),Z))),inverse(multiply(inverse(U),U))))))) = Y,
inference('PARAMODULATE',[status(thm)],[1465,1526,theory(equality)]) ).
cnf(1707,plain,
multiply(multiply(inverse(X),X),inverse(multiply(inverse(multiply(multiply(inverse(Y),Y),inverse(multiply(inverse(Z),Z)))),inverse(multiply(U,multiply(inverse(V),V)))))) = U,
inference('PARAMODULATE',[status(thm)],[1052,1665,theory(equality)]) ).
cnf(1718,plain,
inverse(multiply(inverse(X),inverse(multiply(inverse(Y),Y)))) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1466,1665,theory(equality)]),1053,theory(equality)]) ).
cnf(1719,plain,
multiply(multiply(inverse(X),X),Y) = Y,
inference('REWRITE',[status(thm)],[1677,1718,theory(equality)]) ).
cnf(1722,plain,
inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(Y,multiply(inverse(Z),Z))))) = Y,
inference('REWRITE',[status(thm)],[1707,1719,theory(equality)]) ).
cnf(1723,plain,
X = inverse(multiply(inverse(inverse(Y)),inverse(multiply(X,Y)))),
inference('REWRITE',[status(thm)],[1637,1722,theory(equality)]) ).
cnf(1734,plain,
multiply(inverse(inverse(X)),inverse(multiply(inverse(Y),X))) = multiply(inverse(inverse(inverse(multiply(inverse(Z),Z)))),Y),
inference('REWRITE',[status(thm)],[1481,1723,theory(equality)]) ).
cnf(1742,plain,
multiply(inverse(X),inverse(inverse(multiply(X,Y)))) = multiply(inverse(inverse(multiply(inverse(inverse(Y)),Z))),inverse(Z)),
inference('REWRITE',[status(thm)],[1506,1723,theory(equality)]) ).
cnf(1751,plain,
multiply(inverse(inverse(X)),inverse(multiply(inverse(Y),Y))) = multiply(inverse(inverse(inverse(multiply(inverse(Z),Z)))),X),
inference('REWRITE',[status(thm)],[1482,1723,theory(equality)]) ).
cnf(1778,plain,
multiply(inverse(multiply(X,Y)),multiply(inverse(Z),Z)) = multiply(inverse(Y),multiply(inverse(inverse(U)),inverse(multiply(X,U)))),
inference('REWRITE',[status(thm)],[1435,1719,theory(equality)]) ).
cnf(1830,plain,
inverse(multiply(inverse(inverse(X)),inverse(X))) = multiply(inverse(Y),Y),
inference('REWRITE',[status(thm)],[1159,1723,1719,theory(equality)]) ).
cnf(1832,plain,
multiply(inverse(inverse(multiply(X,inverse(multiply(Y,Z))))),Y) = multiply(inverse(inverse(inverse(multiply(Y,Z)))),inverse(multiply(inverse(multiply(X,inverse(Z))),inverse(multiply(Y,Z))))),
inference('REWRITE',[status(thm)],[1127,1719,theory(equality)]) ).
cnf(1837,plain,
multiply(inverse(inverse(X)),inverse(multiply(inverse(Y),Y))) = X,
inference('REWRITE',[status(thm)],[1087,1050,1719,theory(equality)]) ).
cnf(1841,plain,
X = multiply(inverse(inverse(inverse(multiply(inverse(Y),Y)))),X),
inference('REWRITE',[status(thm)],[1751,1837,theory(equality)]) ).
cnf(1842,plain,
multiply(inverse(inverse(X)),inverse(multiply(inverse(Y),X))) = Y,
inference('REWRITE',[status(thm)],[1734,1841,theory(equality)]) ).
cnf(1843,plain,
multiply(inverse(inverse(multiply(X,Y))),inverse(Y)) = multiply(X,multiply(inverse(Z),Z)),
inference('REWRITE',[status(thm)],[1500,1842,theory(equality)]) ).
cnf(1845,plain,
multiply(inverse(inverse(multiply(X,inverse(multiply(Y,Z))))),Y) = multiply(X,inverse(Z)),
inference('REWRITE',[status(thm)],[1832,1842,theory(equality)]) ).
cnf(1847,plain,
multiply(inverse(X),Y) = multiply(inverse(inverse(multiply(inverse(Z),Z))),inverse(multiply(inverse(Y),X))),
inference('REWRITE',[status(thm)],[1419,1842,theory(equality)]) ).
cnf(1901,plain,
multiply(inverse(X),inverse(multiply(inverse(Y),multiply(inverse(inverse(Z)),inverse(multiply(X,Z)))))) = Y,
inference('REWRITE',[status(thm)],[1147,1719,theory(equality)]) ).
cnf(1947,plain,
multiply(inverse(inverse(multiply(X,Y))),inverse(inverse(Z))) = multiply(X,inverse(inverse(multiply(Y,Z)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1845,1196,theory(equality)]),1723,theory(equality)]) ).
cnf(1965,plain,
inverse(multiply(inverse(X),X)) = multiply(inverse(Y),Y),
inference('PARAMODULATE',[status(thm)],[1830,565,theory(equality)]) ).
cnf(1966,plain,
X = multiply(inverse(inverse(multiply(inverse(Y),Y))),X),
inference('PARAMODULATE',[status(thm)],[1042,1965,theory(equality)]) ).
cnf(1967,plain,
multiply(inverse(X),Y) = inverse(multiply(inverse(Y),X)),
inference('REWRITE',[status(thm)],[1847,1966,theory(equality)]) ).
cnf(1992,plain,
multiply(inverse(X),inverse(inverse(multiply(X,Y)))) = inverse(inverse(Y)),
inference('REWRITE',[status(thm)],[1742,1842,1967,theory(equality)]) ).
cnf(1996,plain,
X = multiply(X,multiply(inverse(Y),Y)),
inference('REWRITE',[status(thm)],[1843,1723,1967,theory(equality)]) ).
cnf(2014,plain,
inverse(multiply(X,Y)) = multiply(inverse(Y),multiply(inverse(inverse(Z)),inverse(multiply(X,Z)))),
inference('REWRITE',[status(thm)],[1778,1996,theory(equality)]) ).
cnf(2016,plain,
inverse(inverse(X)) = X,
inference('REWRITE',[status(thm)],[1901,1992,2014,theory(equality)]) ).
cnf(2046,plain,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
inference('REWRITE',[status(thm)],[1947,2016,theory(equality)]) ).
cnf(2047,plain,
$false,
inference('REWRITE',[status(thm)],[prove_these_axioms_3,2046,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP414-1 : TPTP v8.1.0. Released v2.6.0.
% 0.08/0.14 % Command : run-snark %s %d
% 0.15/0.35 % Computer : n028.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Tue Jun 14 13:28:39 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.21/0.48 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.49 *
% 0.21/0.49 *
% 0.21/0.50 #<PACKAGE "SNARK-USER">
% 0.21/0.50 *
% 0.21/0.50 SNARK-TPTP-OPTIONS
% 0.21/0.50 *
% 0.21/0.50 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.21/0.50 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.21/0.50 (USE-FACTORING :POS)
% 0.21/0.50 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.21/0.50 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.21/0.50 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.21/0.50 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.21/0.50 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.21/0.50 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.21/0.50 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.21/0.50 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.21/0.50 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.21/0.50 (DECLARE-TPTP-SYMBOLS2))
% 0.21/0.50 *
% 0.21/0.50 "."
% 0.21/0.50 *
% 0.21/0.50 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T13:28:39
% 0.21/0.50 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n028.cluster.edu at 2022-06-14T13:28:39
% 2.00/2.21
% 2.00/2.21
% 2.00/2.21 #||
% 2.00/2.21 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.00/2.21 % SZS output start Refutation
% See solution above
% 2.00/2.24 ||#
% 2.00/2.24
% 2.00/2.24 ; Summary of computation:
% 2.00/2.24 ; 8240 formulas have been input or derived (from 64 formulas).
% 2.00/2.24 ; 2047 (25%) were retained. Of these,
% 2.00/2.24 ; 1868 (91%) were simplified or subsumed later,
% 2.00/2.24 ; 179 ( 9%) are still being kept.
% 2.00/2.24 ;
% 2.00/2.24 ; Run time in seconds excluding printing time:
% 2.00/2.24 ; 0.001 0% Read assertion file (1 call)
% 2.00/2.24 ; 0.000 0% Assert (2 calls)
% 2.00/2.24 ; 0.431 25% Process new row (7,876 calls)
% 2.00/2.24 ; 0.004 0% Resolution (126 calls)
% 2.00/2.24 ; 0.189 11% Paramodulation (63 calls)
% 2.00/2.24 ; 0.506 30% Forward simplification (6,321 calls)
% 2.00/2.24 ; 0.390 23% Backward simplification (2,047 calls)
% 2.00/2.24 ; 0.139 8% Ordering (20,432 calls)
% 2.00/2.24 ; 0.000 0% Sortal reasoning (32 calls)
% 2.00/2.24 ; 0.000 0% Purity testing (1 call)
% 2.00/2.24 ; 0.055 3% Other
% 2.00/2.24 ; 1.715 Total
% 2.00/2.24 ; 1.738 Real time
% 2.00/2.24 ;
% 2.00/2.24 ; Term-hash-array has 11,657 terms in all.
% 2.00/2.24 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 2.00/2.24 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 2.00/2.24 ; Path-index has 1,223 entries (6,142 at peak, 12,938 added, 11,715 deleted).
% 2.00/2.24 ; Path-index has 10,917 nodes (12,078 at peak, 17,902 added, 6,985 deleted).
% 2.00/2.24 ; Trie-index has 1,223 entries (6,142 at peak, 12,938 added, 11,715 deleted).
% 2.00/2.24 ; Trie-index has 4,826 nodes (39,935 at peak, 75,501 added, 70,675 deleted).
% 2.00/2.24 ; Retrieved 27,829 generalization terms in 84,435 calls.
% 2.00/2.24 ; Retrieved 17,327 instance terms in 2,421 calls.
% 2.00/2.24 ; Retrieved 70,613 unifiable terms in 774 calls.
% 2.00/2.24 ;
% 2.00/2.24 ; The agenda of backward simplifiable rows to process has 165 entries:
% 2.00/2.24 ; 165 with value 0
% 2.00/2.24 ; The agenda of rows to process has 92 entries:
% 2.00/2.24 ; 1 with value 33 6 with value 38 5 with value 43
% 2.00/2.24 ; 2 with value 34 15 with value 39 6 with value 44
% 2.00/2.24 ; 9 with value 35 11 with value 40 5 with value 45
% 2.00/2.24 ; 9 with value 36 6 with value 41 2 with value 48
% 2.00/2.24 ; 3 with value 37 10 with value 42 2 with value 50
% 2.00/2.24 ; The agenda of rows to give has 173 entries:
% 2.00/2.24 ; 1 with value (4 13) 1 with value (4 35) 4 with value (4 47)
% 2.00/2.24 ; 1 with value (4 15) 5 with value (4 36) 6 with value (4 48)
% 2.00/2.24 ; 1 with value (4 19) 2 with value (4 37) 16 with value (4 49)
% 2.00/2.24 ; 1 with value (4 24) 6 with value (4 38) 16 with value (4 50)
% 2.00/2.24 ; 1 with value (4 26) 6 with value (4 39) 11 with value (4 51)
% 2.00/2.24 ; 2 with value (4 27) 5 with value (4 40) 6 with value (4 52)
% 2.00/2.24 ; 1 with value (4 28) 5 with value (4 41) 5 with value (4 53)
% 2.00/2.24 ; 1 with value (4 30) 6 with value (4 42) 4 with value (4 54)
% 2.00/2.24 ; 9 with value (4 31) 6 with value (4 43) 4 with value (4 55)
% 2.00/2.24 ; 1 with value (4 32) 9 with value (4 44) 4 with value (4 56)
% 2.00/2.24 ; 4 with value (4 33) 10 with value (4 45) 2 with value (4 59)
% 2.00/2.24 ; 2 with value (4 34) 9 with value (4 46)
% 2.00/2.24 Evaluation took:
% 2.00/2.24 1.739 seconds of real time
% 2.00/2.24 1.629701 seconds of user run time
% 2.00/2.24 0.109658 seconds of system run time
% 2.00/2.24 [Run times include 0.216 seconds GC run time.]
% 2.00/2.24 0 calls to %EVAL
% 2.00/2.24 0 page faults and
% 2.00/2.24 133,905,632 bytes consed.
% 2.00/2.24 :PROOF-FOUND
% 2.00/2.24 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T13:28:41
% 2.00/2.24 :PROOF-FOUND
% 2.00/2.24 *
%------------------------------------------------------------------------------