TSTP Solution File: GRP052-1 by SNARK---20120808r022
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- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP052-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n025.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 1.88s 2.04s
% Output : Refutation 1.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 2
% Syntax : Number of clauses : 123 ( 119 unt; 0 nHn; 6 RR)
% Number of literals : 129 ( 128 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 12 ( 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 : 427 ( 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,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,
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(552,plain,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(inverse(X),X),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference('PARAMODULATE',[status(thm)],[prove_these_axioms,541,theory(equality)]) ).
cnf(566,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(567,plain,
( multiply(multiply(inverse(X),X),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference('REWRITE',[status(thm)],[552,566,theory(equality)]) ).
cnf(577,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(598,plain,
inverse(multiply(inverse(X),X)) = inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,Z))),
inference('PARAMODULATE',[status(thm)],[355,566,theory(equality)]) ).
cnf(599,plain,
multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z)) = multiply(inverse(multiply(U,Y)),multiply(U,X)),
inference('PARAMODULATE',[status(thm)],[52,566,theory(equality)]) ).
cnf(600,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z)) = multiply(inverse(multiply(U,Y)),multiply(U,Z)),
inference('PARAMODULATE',[status(thm)],[52,566,theory(equality)]) ).
cnf(606,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)],[542,566,theory(equality)]) ).
cnf(628,plain,
inverse(multiply(inverse(X),X)) = inverse(multiply(inverse(Y),Y)),
inference('PARAMODULATE',[status(thm)],[598,598,theory(equality)]) ).
cnf(629,plain,
multiply(inverse(X),X) = multiply(inverse(multiply(inverse(Y),Y)),multiply(inverse(Z),Z)),
inference('PARAMODULATE',[status(thm)],[566,628,theory(equality)]) ).
cnf(630,plain,
inverse(multiply(inverse(X),X)) = inverse(multiply(inverse(multiply(inverse(Y),Y)),multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[628,628,theory(equality)]) ).
cnf(663,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)],[123,629,theory(equality)]) ).
cnf(664,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)],[123,629,theory(equality)]) ).
cnf(702,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)],[599,566,theory(equality)]) ).
cnf(703,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)],[599,541,theory(equality)]) ).
cnf(887,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)],[600,630,theory(equality)]) ).
cnf(902,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(910,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(911,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)],[543,629,theory(equality)]) ).
cnf(916,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)],[543,629,theory(equality)]) ).
cnf(950,plain,
multiply(multiply(multiply(inverse(X),X),inverse(multiply(inverse(Y),Y))),Z) = Z,
inference('PARAMODULATE',[status(thm)],[544,566,theory(equality)]) ).
cnf(972,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)],[599,544,theory(equality)]) ).
cnf(984,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)],[544,630,theory(equality)]) ).
cnf(1006,plain,
multiply(inverse(X),Y) = multiply(inverse(multiply(Z,X)),multiply(Z,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[52,950,theory(equality)]),950,theory(equality)]) ).
cnf(1009,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)],[887,1006,theory(equality)]) ).
cnf(1041,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)],[664,1006,theory(equality)]) ).
cnf(1043,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)],[663,1006,theory(equality)]) ).
cnf(1045,plain,
multiply(inverse(inverse(X)),inverse(multiply(multiply(multiply(inverse(Y),Y),inverse(Z)),X))) = Z,
inference('REWRITE',[status(thm)],[916,1043,theory(equality)]) ).
cnf(1046,plain,
multiply(inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y))),Z) = Z,
inference('REWRITE',[status(thm)],[911,1045,theory(equality)]) ).
cnf(1047,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(multiply(inverse(Y),Y)),Z)) = Z,
inference('REWRITE',[status(thm)],[1009,1046,theory(equality)]) ).
cnf(1049,plain,
X = multiply(inverse(multiply(inverse(Y),Y)),X),
inference('REWRITE',[status(thm)],[1041,1047,theory(equality)]) ).
cnf(1057,plain,
multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z)) = multiply(inverse(Y),X),
inference('REWRITE',[status(thm)],[702,1049,theory(equality)]) ).
cnf(1059,plain,
multiply(multiply(inverse(X),X),inverse(multiply(inverse(inverse(Y)),inverse(multiply(Z,Y))))) = Z,
inference('REWRITE',[status(thm)],[606,1057,theory(equality)]) ).
cnf(1060,plain,
multiply(inverse(X),Y) = multiply(inverse(multiply(multiply(inverse(Z),Z),X)),multiply(multiply(inverse(U),U),Y)),
inference('REWRITE',[status(thm)],[703,1057,theory(equality)]) ).
cnf(1094,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)],[984,1057,1006,theory(equality)]) ).
cnf(1104,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)],[353,1006,theory(equality)]) ).
cnf(1114,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)],[476,1006,theory(equality)]) ).
cnf(1131,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)],[972,1057,1006,theory(equality)]) ).
cnf(1132,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)],[1114,1131,theory(equality)]) ).
cnf(1134,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)],[1104,1132,theory(equality)]) ).
cnf(1154,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)],[910,1006,theory(equality)]) ).
cnf(1155,plain,
inverse(multiply(inverse(inverse(X)),inverse(multiply(multiply(multiply(inverse(Y),Y),Z),X)))) = Z,
inference('REWRITE',[status(thm)],[546,1006,theory(equality)]) ).
cnf(1166,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)],[577,1006,theory(equality)]) ).
cnf(1185,plain,
inverse(multiply(multiply(multiply(inverse(X),X),inverse(multiply(inverse(inverse(Y)),Z))),Y)) = Z,
inference('REWRITE',[status(thm)],[545,1006,theory(equality)]) ).
cnf(1203,plain,
multiply(inverse(inverse(X)),inverse(multiply(Y,X))) = multiply(inverse(inverse(Z)),inverse(multiply(Y,Z))),
inference('REWRITE',[status(thm)],[902,1006,theory(equality)]) ).
cnf(1418,plain,
multiply(inverse(inverse(X)),inverse(multiply(inverse(Y),Y))) = multiply(inverse(inverse(Z)),inverse(multiply(inverse(X),Z))),
inference('PARAMODULATE',[status(thm)],[1203,566,theory(equality)]) ).
cnf(1425,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)],[1057,1203,theory(equality)]),1057,theory(equality)]) ).
cnf(1426,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)],[1203,1057,theory(equality)]) ).
cnf(1432,plain,
inverse(multiply(inverse(inverse(X)),inverse(multiply(Y,X)))) = inverse(multiply(inverse(inverse(Z)),inverse(multiply(Y,Z)))),
inference('PARAMODULATE',[status(thm)],[1155,1059,theory(equality)]) ).
cnf(1442,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)],[1057,1155,theory(equality)]) ).
cnf(1471,plain,
multiply(inverse(X),inverse(multiply(inverse(Y),Y))) = multiply(inverse(inverse(Z)),inverse(multiply(X,Z))),
inference('PARAMODULATE',[status(thm)],[1418,1185,theory(equality)]) ).
cnf(1472,plain,
multiply(inverse(X),inverse(multiply(inverse(Y),Y))) = multiply(inverse(X),inverse(multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[1471,1471,theory(equality)]) ).
cnf(1473,plain,
multiply(multiply(inverse(X),X),inverse(multiply(inverse(Y),inverse(multiply(inverse(Z),Z))))) = Y,
inference('PARAMODULATE',[status(thm)],[1059,1471,theory(equality)]) ).
cnf(1474,plain,
inverse(multiply(inverse(multiply(multiply(inverse(X),X),Y)),inverse(multiply(inverse(Z),Z)))) = Y,
inference('PARAMODULATE',[status(thm)],[1155,1471,theory(equality)]) ).
cnf(1489,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)],[1203,1471,theory(equality)]) ).
cnf(1490,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)],[1471,1471,theory(equality)]) ).
cnf(1508,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)],[1471,1425,theory(equality)]) ).
cnf(1514,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)],[1425,1203,theory(equality)]) ).
cnf(1534,plain,
multiply(X,inverse(multiply(inverse(Y),Y))) = multiply(X,inverse(multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[1472,1185,theory(equality)]) ).
cnf(1556,plain,
inverse(multiply(inverse(inverse(X)),inverse(multiply(multiply(multiply(inverse(inverse(multiply(inverse(Y),Y))),inverse(multiply(inverse(Z),Z))),U),X)))) = U,
inference('PARAMODULATE',[status(thm)],[1155,1534,theory(equality)]) ).
cnf(1560,plain,
( multiply(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(Y),Y))),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference('PARAMODULATE',[status(thm)],[567,1534,theory(equality)]) ).
cnf(1646,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)],[1432,628,theory(equality)]) ).
cnf(1674,plain,
multiply(multiply(inverse(X),X),inverse(multiply(inverse(Y),Y))) = inverse(multiply(inverse(Z),Z)),
inference('PARAMODULATE',[status(thm)],[1473,566,theory(equality)]) ).
cnf(1686,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)],[1473,1534,theory(equality)]) ).
cnf(1716,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)],[1059,1674,theory(equality)]) ).
cnf(1727,plain,
inverse(multiply(inverse(X),inverse(multiply(inverse(Y),Y)))) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1474,1674,theory(equality)]),1060,theory(equality)]) ).
cnf(1728,plain,
multiply(multiply(inverse(X),X),Y) = Y,
inference('REWRITE',[status(thm)],[1686,1727,theory(equality)]) ).
cnf(1731,plain,
inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(Y,multiply(inverse(Z),Z))))) = Y,
inference('REWRITE',[status(thm)],[1716,1728,theory(equality)]) ).
cnf(1732,plain,
X = inverse(multiply(inverse(inverse(Y)),inverse(multiply(X,Y)))),
inference('REWRITE',[status(thm)],[1646,1731,theory(equality)]) ).
cnf(1741,plain,
multiply(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(Y),Y))),Z) = Z,
inference('REWRITE',[status(thm)],[1556,1732,theory(equality)]) ).
cnf(1742,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference('REWRITE',[status(thm)],[1560,1741,theory(equality)]) ).
cnf(1744,plain,
multiply(inverse(inverse(X)),inverse(multiply(inverse(Y),X))) = multiply(inverse(inverse(inverse(multiply(inverse(Z),Z)))),Y),
inference('REWRITE',[status(thm)],[1489,1732,theory(equality)]) ).
cnf(1752,plain,
multiply(inverse(X),inverse(inverse(multiply(X,Y)))) = multiply(inverse(inverse(multiply(inverse(inverse(Y)),Z))),inverse(Z)),
inference('REWRITE',[status(thm)],[1514,1732,theory(equality)]) ).
cnf(1761,plain,
multiply(inverse(inverse(X)),inverse(multiply(inverse(Y),Y))) = multiply(inverse(inverse(inverse(multiply(inverse(Z),Z)))),X),
inference('REWRITE',[status(thm)],[1490,1732,theory(equality)]) ).
cnf(1788,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)],[1442,1728,theory(equality)]) ).
cnf(1840,plain,
inverse(multiply(inverse(inverse(X)),inverse(X))) = multiply(inverse(Y),Y),
inference('REWRITE',[status(thm)],[1166,1732,1728,theory(equality)]) ).
cnf(1842,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)],[1134,1728,theory(equality)]) ).
cnf(1847,plain,
multiply(inverse(inverse(X)),inverse(multiply(inverse(Y),Y))) = X,
inference('REWRITE',[status(thm)],[1094,1057,1728,theory(equality)]) ).
cnf(1851,plain,
X = multiply(inverse(inverse(inverse(multiply(inverse(Y),Y)))),X),
inference('REWRITE',[status(thm)],[1761,1847,theory(equality)]) ).
cnf(1852,plain,
multiply(inverse(inverse(X)),inverse(multiply(inverse(Y),X))) = Y,
inference('REWRITE',[status(thm)],[1744,1851,theory(equality)]) ).
cnf(1853,plain,
multiply(inverse(inverse(multiply(X,Y))),inverse(Y)) = multiply(X,multiply(inverse(Z),Z)),
inference('REWRITE',[status(thm)],[1508,1852,theory(equality)]) ).
cnf(1855,plain,
multiply(inverse(inverse(multiply(X,inverse(multiply(Y,Z))))),Y) = multiply(X,inverse(Z)),
inference('REWRITE',[status(thm)],[1842,1852,theory(equality)]) ).
cnf(1857,plain,
multiply(inverse(X),Y) = multiply(inverse(inverse(multiply(inverse(Z),Z))),inverse(multiply(inverse(Y),X))),
inference('REWRITE',[status(thm)],[1426,1852,theory(equality)]) ).
cnf(1911,plain,
multiply(inverse(X),inverse(multiply(inverse(Y),multiply(inverse(inverse(Z)),inverse(multiply(X,Z)))))) = Y,
inference('REWRITE',[status(thm)],[1154,1728,theory(equality)]) ).
cnf(1957,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)],[1855,1203,theory(equality)]),1732,theory(equality)]) ).
cnf(1975,plain,
inverse(multiply(inverse(X),X)) = multiply(inverse(Y),Y),
inference('PARAMODULATE',[status(thm)],[1840,566,theory(equality)]) ).
cnf(1976,plain,
X = multiply(inverse(inverse(multiply(inverse(Y),Y))),X),
inference('PARAMODULATE',[status(thm)],[1049,1975,theory(equality)]) ).
cnf(1977,plain,
multiply(inverse(X),Y) = inverse(multiply(inverse(Y),X)),
inference('REWRITE',[status(thm)],[1857,1976,theory(equality)]) ).
cnf(2002,plain,
multiply(inverse(X),inverse(inverse(multiply(X,Y)))) = inverse(inverse(Y)),
inference('REWRITE',[status(thm)],[1752,1852,1977,theory(equality)]) ).
cnf(2006,plain,
X = multiply(X,multiply(inverse(Y),Y)),
inference('REWRITE',[status(thm)],[1853,1732,1977,theory(equality)]) ).
cnf(2024,plain,
inverse(multiply(X,Y)) = multiply(inverse(Y),multiply(inverse(inverse(Z)),inverse(multiply(X,Z)))),
inference('REWRITE',[status(thm)],[1788,2006,theory(equality)]) ).
cnf(2026,plain,
inverse(inverse(X)) = X,
inference('REWRITE',[status(thm)],[1911,2002,2024,theory(equality)]) ).
cnf(2056,plain,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
inference('REWRITE',[status(thm)],[1957,2026,theory(equality)]) ).
cnf(2057,plain,
$false,
inference('REWRITE',[status(thm)],[1742,2056,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP052-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run-snark %s %d
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 04:29:08 EDT 2022
% 0.13/0.34 % 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 2022-06-13T04:29:08
% 0.20/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n025.cluster.edu at 2022-06-13T04:29:08
% 1.88/2.04
% 1.88/2.04
% 1.88/2.04 #||
% 1.88/2.04 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.88/2.04 % SZS output start Refutation
% See solution above
% 1.90/2.06 ||#
% 1.90/2.06
% 1.90/2.06 ; Summary of computation:
% 1.90/2.06 ; 8304 formulas have been input or derived (from 65 formulas).
% 1.90/2.06 ; 2057 (25%) were retained. Of these,
% 1.90/2.06 ; 1878 (91%) were simplified or subsumed later,
% 1.90/2.06 ; 179 ( 9%) are still being kept.
% 1.90/2.06 ;
% 1.90/2.06 ; Run time in seconds excluding printing time:
% 1.90/2.06 ; 0.002 0% Read assertion file (1 call)
% 1.90/2.06 ; 0.000 0% Assert (2 calls)
% 1.90/2.06 ; 0.354 23% Process new row (7,940 calls)
% 1.90/2.06 ; 0.005 0% Resolution (128 calls)
% 1.90/2.06 ; 0.192 12% Paramodulation (64 calls)
% 1.90/2.06 ; 0.002 0% Condensing (54 calls)
% 1.90/2.06 ; 0.001 0% Forward subsumption (54 calls)
% 1.90/2.06 ; 0.000 0% Backward subsumption (10 calls)
% 1.90/2.06 ; 0.001 0% Clause clause subsumption (57 calls)
% 1.90/2.06 ; 0.489 31% Forward simplification (6,377 calls)
% 1.90/2.06 ; 0.348 22% Backward simplification (2,057 calls)
% 1.90/2.06 ; 0.123 8% Ordering (20,459 calls)
% 1.90/2.06 ; 0.000 0% Sortal reasoning (32 calls)
% 1.90/2.06 ; 0.000 0% Purity testing (1 call)
% 1.90/2.06 ; 0.052 3% Other
% 1.90/2.06 ; 1.569 Total
% 1.90/2.06 ; 1.592 Real time
% 1.90/2.06 ;
% 1.90/2.06 ; Term-hash-array has 11,682 terms in all.
% 1.90/2.06 ; Feature-vector-row-index has 0 entries (6 at peak, 10 added, 10 deleted).
% 1.90/2.06 ; Feature-vector-row-index has 1 node (43 at peak, 110 added, 109 deleted).
% 1.90/2.06 ; Retrieved 70 possibly forward subsuming rows in 54 calls.
% 1.90/2.06 ; Retrieved 1 possibly backward subsumed row in 10 calls.
% 1.90/2.06 ; Path-index has 1,224 entries (6,155 at peak, 13,003 added, 11,779 deleted).
% 1.90/2.06 ; Path-index has 10,918 nodes (12,082 at peak, 17,998 added, 7,080 deleted).
% 1.90/2.06 ; Trie-index has 1,224 entries (6,155 at peak, 13,003 added, 11,779 deleted).
% 1.90/2.06 ; Trie-index has 4,827 nodes (39,954 at peak, 75,634 added, 70,807 deleted).
% 1.90/2.06 ; Retrieved 27,867 generalization terms in 85,233 calls.
% 1.90/2.06 ; Retrieved 17,332 instance terms in 2,421 calls.
% 1.90/2.06 ; Retrieved 70,964 unifiable terms in 799 calls.
% 1.90/2.06 ;
% 1.90/2.06 ; The agenda of backward simplifiable rows to process has 165 entries:
% 1.90/2.06 ; 165 with value 0
% 1.90/2.06 ; The agenda of rows to process has 92 entries:
% 1.90/2.06 ; 1 with value 33 6 with value 38 5 with value 43
% 1.90/2.06 ; 2 with value 34 15 with value 39 6 with value 44
% 1.90/2.06 ; 9 with value 35 11 with value 40 5 with value 45
% 1.90/2.06 ; 9 with value 36 6 with value 41 2 with value 48
% 1.90/2.06 ; 3 with value 37 10 with value 42 2 with value 50
% 1.90/2.06 ; The agenda of rows to give has 173 entries:
% 1.90/2.06 ; 1 with value (4 13) 1 with value (4 35) 4 with value (4 47)
% 1.90/2.06 ; 1 with value (4 15) 5 with value (4 36) 6 with value (4 48)
% 1.90/2.06 ; 1 with value (4 19) 2 with value (4 37) 16 with value (4 49)
% 1.90/2.06 ; 1 with value (4 24) 6 with value (4 38) 16 with value (4 50)
% 1.90/2.06 ; 1 with value (4 26) 6 with value (4 39) 11 with value (4 51)
% 1.90/2.06 ; 2 with value (4 27) 5 with value (4 40) 6 with value (4 52)
% 1.90/2.06 ; 1 with value (4 28) 5 with value (4 41) 5 with value (4 53)
% 1.90/2.06 ; 1 with value (4 30) 6 with value (4 42) 4 with value (4 54)
% 1.90/2.06 ; 9 with value (4 31) 6 with value (4 43) 4 with value (4 55)
% 1.90/2.06 ; 1 with value (4 32) 9 with value (4 44) 4 with value (4 56)
% 1.90/2.06 ; 4 with value (4 33) 10 with value (4 45) 2 with value (4 59)
% 1.90/2.06 ; 2 with value (4 34) 9 with value (4 46)
% 1.90/2.06 Evaluation took:
% 1.90/2.06 1.592 seconds of real time
% 1.90/2.06 1.484732 seconds of user run time
% 1.90/2.06 0.107102 seconds of system run time
% 1.90/2.06 [Run times include 0.176 seconds GC run time.]
% 1.90/2.06 0 calls to %EVAL
% 1.90/2.06 0 page faults and
% 1.90/2.06 135,812,632 bytes consed.
% 1.90/2.06 :PROOF-FOUND
% 1.90/2.06 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T04:29:10
% 1.90/2.06 :PROOF-FOUND
% 1.90/2.06 *
%------------------------------------------------------------------------------