%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP507-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Jul 15 06:44:12 AM UTC 2025
% Result : Unsatisfiable 280.53s 280.56s
% Output : CNFRefutation 280.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 2
% Syntax : Number of clauses : 150 ( 150 unt; 0 nHn; 3 RR)
% Number of literals : 150 ( 149 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 11 ( 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 : 650 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('theBenchmark.p',prove_these_axioms_3) ).
cnf(c1,axiom,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(multiply(Z,W)),multiply(Z,inverse(multiply(multiply(V,inverse(U)),inverse(W))))))),U) = V,
file('theBenchmark.p',single_axiom) ).
cnf(c2,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(multiply(Z,W)),multiply(Z,inverse(multiply(V,inverse(W))))))),U) = inverse(multiply(inverse(multiply(inverse(multiply(U2,U3)),multiply(U3,U2))),multiply(inverse(multiply(U4,U5)),multiply(U4,inverse(multiply(multiply(V,inverse(inverse(U))),inverse(U5))))))),
inference(equational,[status(thm)],[c1]) ).
cnf(c3,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(multiply(Z,W)),multiply(Z,inverse(multiply(V,inverse(W))))))),U),inverse(U)) = V,
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c4,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(multiply(Z,inverse(W))),multiply(Z,inverse(V))))),W) = inverse(multiply(inverse(multiply(inverse(multiply(U,U2)),multiply(U2,U))),multiply(inverse(multiply(U3,U4)),multiply(U3,inverse(multiply(V,inverse(U4))))))),
inference(equational,[status(thm)],[c1,c3]) ).
cnf(c6,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(multiply(Z,inverse(W))),multiply(Z,inverse(multiply(V,inverse(U))))))),W),U) = V,
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c7,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(multiply(Z,inverse(W))),multiply(Z,inverse(V))))),W),U),inverse(U)) = V,
inference(equational,[status(thm)],[c3,c4]) ).
cnf(c8,plain,
multiply(multiply(X,Y),inverse(Y)) = multiply(multiply(X,inverse(Z)),inverse(inverse(Z))),
inference(equational,[status(thm)],[c1,c7]) ).
cnf(c9,plain,
multiply(multiply(multiply(X,Y),inverse(Y)),inverse(inverse(inverse(Z)))) = multiply(multiply(multiply(X,inverse(Z)),W),inverse(W)),
inference(equational,[status(thm)],[c8]) ).
cnf(c10,plain,
multiply(multiply(multiply(X,inverse(Y)),Z),inverse(Z)) = multiply(multiply(multiply(X,inverse(Y)),W),inverse(W)),
inference(equational,[status(thm)],[c8,c9]) ).
cnf(c11,plain,
multiply(multiply(X,Y),inverse(Y)) = multiply(multiply(X,Z),inverse(Z)),
inference(equational,[status(thm)],[c1,c10]) ).
cnf(c12,plain,
multiply(multiply(multiply(X,Y),inverse(Y)),inverse(inverse(Z))) = multiply(multiply(multiply(X,Z),W),inverse(W)),
inference(equational,[status(thm)],[c11]) ).
cnf(c13,plain,
multiply(multiply(multiply(X,Y),inverse(Y)),inverse(inverse(Z))) = multiply(multiply(multiply(X,W),inverse(W)),inverse(inverse(Z))),
inference(equational,[status(thm)],[c11,c12]) ).
cnf(c14,plain,
multiply(multiply(multiply(multiply(X,Y),inverse(Y)),Z),inverse(Z)) = multiply(multiply(multiply(multiply(X,W),inverse(W)),V),inverse(V)),
inference(equational,[status(thm)],[c10,c11]) ).
cnf(c15,plain,
multiply(multiply(multiply(multiply(X,Y),Z),inverse(Z)),inverse(inverse(inverse(Y)))) = multiply(multiply(multiply(multiply(X,W),inverse(W)),V),inverse(V)),
inference(equational,[status(thm)],[c10,c12]) ).
cnf(c16,plain,
multiply(multiply(multiply(multiply(X,Y),inverse(Y)),inverse(inverse(inverse(Z)))),inverse(inverse(W))) = multiply(multiply(multiply(multiply(X,inverse(Z)),W),V),inverse(V)),
inference(equational,[status(thm)],[c8,c9]) ).
cnf(c17,plain,
multiply(multiply(multiply(multiply(X,Y),Z),inverse(Z)),inverse(inverse(inverse(Y)))) = multiply(multiply(multiply(multiply(X,W),V),inverse(V)),inverse(inverse(inverse(W)))),
inference(equational,[status(thm)],[c12]) ).
cnf(c18,plain,
multiply(multiply(multiply(multiply(X,Y),inverse(Y)),inverse(inverse(Z))),inverse(inverse(W))) = multiply(multiply(multiply(multiply(X,Z),W),V),inverse(V)),
inference(equational,[status(thm)],[c12]) ).
cnf(c20,plain,
multiply(multiply(multiply(multiply(multiply(X,Y),inverse(Y)),inverse(inverse(Z))),W),inverse(W)) = multiply(multiply(multiply(multiply(multiply(X,Z),V),inverse(V)),U),inverse(U)),
inference(equational,[status(thm)],[c10,c12]) ).
cnf(c21,plain,
multiply(multiply(multiply(multiply(multiply(X,Y),inverse(Y)),Z),W),inverse(W)) = multiply(multiply(multiply(multiply(multiply(X,V),inverse(V)),Z),U),inverse(U)),
inference(equational,[status(thm)],[c12,c14,c16]) ).
cnf(c22,plain,
multiply(multiply(multiply(multiply(multiply(X,Y),inverse(Y)),Z),inverse(Z)),inverse(inverse(W))) = multiply(multiply(multiply(multiply(multiply(X,V),inverse(V)),W),U),inverse(U)),
inference(equational,[status(thm)],[c12,c14]) ).
cnf(c26,plain,
multiply(multiply(multiply(multiply(multiply(X,inverse(Y)),Z),inverse(Z)),W),inverse(W)) = multiply(multiply(multiply(multiply(multiply(X,V),inverse(V)),U),inverse(U)),inverse(inverse(inverse(inverse(inverse(Y)))))),
inference(equational,[status(thm)],[c9]) ).
cnf(c29,plain,
multiply(multiply(multiply(multiply(multiply(X,Y),Z),inverse(Z)),inverse(inverse(inverse(Y)))),inverse(inverse(W))) = multiply(multiply(multiply(multiply(multiply(X,V),inverse(V)),W),U),inverse(U)),
inference(equational,[status(thm)],[c12]) ).
cnf(c31,plain,
multiply(multiply(multiply(multiply(multiply(X,Y),inverse(Y)),inverse(inverse(Z))),inverse(inverse(W))),inverse(inverse(V))) = multiply(multiply(multiply(multiply(multiply(X,Z),W),V),U),inverse(U)),
inference(equational,[status(thm)],[c12]) ).
cnf(c35,plain,
multiply(multiply(multiply(multiply(multiply(multiply(X,inverse(Y)),Z),inverse(Z)),W),inverse(W)),inverse(inverse(V))) = multiply(multiply(multiply(multiply(multiply(multiply(X,U),inverse(U)),inverse(inverse(inverse(Y)))),V),U2),inverse(U2)),
inference(equational,[status(thm)],[c16,c26]) ).
cnf(c46,plain,
multiply(multiply(multiply(multiply(multiply(multiply(X,Y),inverse(Y)),Z),inverse(Z)),inverse(inverse(W))),inverse(inverse(V))) = multiply(multiply(multiply(multiply(multiply(multiply(X,U),inverse(U)),W),V),U2),inverse(U2)),
inference(equational,[status(thm)],[c12,c14]) ).
cnf(c51,plain,
multiply(multiply(multiply(multiply(multiply(multiply(X,Y),Z),inverse(Z)),inverse(inverse(inverse(Y)))),W),inverse(W)) = multiply(multiply(multiply(multiply(multiply(multiply(X,V),U),inverse(U)),inverse(inverse(inverse(V)))),U2),inverse(U2)),
inference(equational,[status(thm)],[c15,c20]) ).
cnf(c55,plain,
multiply(multiply(multiply(multiply(multiply(multiply(X,inverse(Y)),inverse(inverse(Y))),Z),inverse(Z)),W),inverse(W)) = multiply(multiply(multiply(multiply(multiply(multiply(X,V),U),inverse(U)),U2),inverse(U2)),inverse(inverse(inverse(inverse(inverse(V)))))),
inference(equational,[status(thm)],[c16,c26]) ).
cnf(c57,plain,
multiply(multiply(multiply(multiply(multiply(multiply(X,Y),inverse(Y)),Z),inverse(Z)),W),inverse(W)) = multiply(multiply(multiply(multiply(multiply(multiply(X,V),U),inverse(U)),U2),inverse(U2)),inverse(inverse(inverse(inverse(inverse(V)))))),
inference(equational,[status(thm)],[c11,c26]) ).
cnf(c59,plain,
multiply(multiply(multiply(multiply(multiply(multiply(multiply(X,Y),inverse(Y)),Z),W),V),inverse(V)),inverse(inverse(U))) = multiply(multiply(multiply(multiply(multiply(multiply(multiply(X,U2),inverse(U2)),Z),W),U),U3),inverse(U3)),
inference(equational,[status(thm)],[c31,c46]) ).
cnf(c66,plain,
multiply(multiply(multiply(multiply(multiply(multiply(X,Y),Z),inverse(Z)),inverse(inverse(inverse(Y)))),W),inverse(W)) = multiply(multiply(multiply(multiply(multiply(multiply(X,V),U),inverse(U)),U2),inverse(U2)),inverse(inverse(inverse(inverse(inverse(V)))))),
inference(equational,[status(thm)],[c9,c17,c26]) ).
cnf(c70,plain,
multiply(multiply(multiply(multiply(multiply(multiply(multiply(X,Y),inverse(Y)),Z),inverse(Z)),W),inverse(W)),inverse(inverse(V))) = multiply(multiply(multiply(multiply(multiply(multiply(multiply(X,U),inverse(U)),U2),inverse(U2)),V),U3),inverse(U3)),
inference(equational,[status(thm)],[c9,c11,c35]) ).
cnf(c82,plain,
multiply(multiply(multiply(multiply(multiply(multiply(X,inverse(Y)),Z),W),inverse(W)),V),inverse(V)) = multiply(multiply(multiply(multiply(multiply(multiply(X,U),inverse(U)),inverse(inverse(inverse(Y)))),U2),inverse(U2)),inverse(inverse(inverse(inverse(Z))))),
inference(equational,[status(thm)],[c9,c16]) ).
cnf(c89,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(multiply(Z,W)),multiply(Z,inverse(multiply(multiply(multiply(V,inverse(U)),inverse(inverse(U))),inverse(W))))))) = V,
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c90,plain,
multiply(multiply(multiply(X,Y),inverse(Y)),inverse(Z)) = multiply(multiply(multiply(X,W),inverse(W)),inverse(Z)),
inference(equational,[status(thm)],[c13,c89]) ).
cnf(c91,plain,
multiply(multiply(multiply(X,Y),inverse(Y)),Z) = multiply(multiply(multiply(X,W),inverse(W)),Z),
inference(equational,[status(thm)],[c89,c90]) ).
cnf(c92,plain,
multiply(multiply(multiply(multiply(X,Y),inverse(Y)),inverse(inverse(Z))),W) = multiply(multiply(multiply(multiply(X,Z),V),inverse(V)),W),
inference(equational,[status(thm)],[c91]) ).
cnf(c110,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(multiply(Z,W)),multiply(Z,inverse(multiply(multiply(multiply(V,U),inverse(U)),inverse(W))))))) = V,
inference(equational,[status(thm)],[c89]) ).
cnf(c111,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(multiply(Z,inverse(W))),multiply(Z,inverse(V))))) = inverse(multiply(inverse(multiply(inverse(multiply(U,U2)),multiply(U2,U))),multiply(inverse(multiply(U3,inverse(W))),multiply(U3,inverse(V))))),
inference(equational,[status(thm)],[c7,c110]) ).
cnf(c112,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(multiply(Z,inverse(W))),multiply(Z,inverse(V)))) = multiply(inverse(multiply(inverse(multiply(U,U2)),multiply(U2,U))),multiply(inverse(multiply(U3,inverse(W))),multiply(U3,inverse(V)))),
inference(equational,[status(thm)],[c7,c111]) ).
cnf(c113,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(multiply(Z,W)),multiply(Z,inverse(V)))) = multiply(inverse(multiply(inverse(multiply(U,U2)),multiply(U2,U))),multiply(inverse(multiply(U3,W)),multiply(U3,inverse(V)))),
inference(equational,[status(thm)],[c110,c112]) ).
cnf(c114,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(multiply(Z,W)),multiply(Z,V))) = multiply(inverse(multiply(inverse(multiply(U,U2)),multiply(U2,U))),multiply(inverse(multiply(U3,W)),multiply(U3,V))),
inference(equational,[status(thm)],[c110,c113]) ).
cnf(c115,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(multiply(Z,W)),multiply(Z,inverse(V))))) = inverse(multiply(inverse(multiply(inverse(multiply(U,U2)),multiply(U2,U))),multiply(inverse(multiply(U3,W)),multiply(U3,inverse(V))))),
inference(equational,[status(thm)],[c110,c111]) ).
cnf(c120,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(multiply(Z,inverse(W))),multiply(Z,inverse(multiply(multiply(V,U),inverse(U))))))),W) = V,
inference(equational,[status(thm)],[c4,c110]) ).
cnf(c125,plain,
multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(X,Y),inverse(Y)),Z),W),V),U),inverse(U)),U2) = multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(X,U3),inverse(U3)),Z),W),V),U4),inverse(U4)),U2),
inference(equational,[status(thm)],[c59,c91]) ).
cnf(c126,plain,
multiply(multiply(multiply(multiply(multiply(multiply(X,Y),inverse(Y)),Z),W),V),U) = multiply(multiply(multiply(multiply(multiply(multiply(X,U2),inverse(U2)),Z),W),V),U),
inference(equational,[status(thm)],[c1,c110,c125]) ).
cnf(c127,plain,
multiply(multiply(multiply(multiply(multiply(multiply(X,Y),Z),inverse(Z)),W),V),U) = multiply(multiply(multiply(multiply(multiply(multiply(X,U2),inverse(U2)),inverse(inverse(Y))),W),V),U),
inference(equational,[status(thm)],[c92,c126]) ).
cnf(c139,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(multiply(Z,inverse(W))),multiply(Z,inverse(multiply(multiply(multiply(V,W),U),inverse(U))))))) = V,
inference(equational,[status(thm)],[c8,c110]) ).
cnf(c154,plain,
multiply(multiply(multiply(multiply(multiply(multiply(multiply(X,Y),Z),inverse(Z)),inverse(inverse(inverse(Y)))),W),inverse(W)),inverse(inverse(V))) = multiply(multiply(multiply(multiply(multiply(multiply(multiply(X,U),U2),inverse(U2)),inverse(inverse(inverse(U)))),V),U3),inverse(U3)),
inference(equational,[status(thm)],[c35,c66]) ).
cnf(c158,plain,
multiply(multiply(multiply(multiply(multiply(multiply(multiply(X,Y),inverse(Y)),Z),inverse(Z)),inverse(inverse(inverse(inverse(W))))),V),inverse(V)) = multiply(multiply(multiply(multiply(multiply(multiply(multiply(X,W),U),inverse(U)),U2),inverse(U2)),U3),inverse(U3)),
inference(equational,[status(thm)],[c57,c70]) ).
cnf(c166,plain,
multiply(multiply(multiply(multiply(multiply(multiply(multiply(X,Y),inverse(Y)),Z),W),inverse(W)),V),U) = multiply(multiply(multiply(multiply(multiply(multiply(multiply(X,U2),inverse(U2)),U3),inverse(U3)),inverse(inverse(Z))),V),U),
inference(equational,[status(thm)],[c22,c127]) ).
cnf(c173,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(multiply(multiply(Z,W),inverse(W))),multiply(multiply(Z,V),U))) = multiply(inverse(multiply(inverse(multiply(U2,U3)),multiply(U3,U2))),multiply(inverse(multiply(U4,inverse(V))),multiply(U4,U))),
inference(equational,[status(thm)],[c11,c114]) ).
cnf(c174,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(Z),Z)) = multiply(inverse(multiply(inverse(multiply(W,V)),multiply(V,W))),multiply(inverse(multiply(U,inverse(U2))),multiply(U,inverse(U2)))),
inference(equational,[status(thm)],[c3,c173]) ).
cnf(c175,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(Z),Z)) = multiply(inverse(multiply(inverse(multiply(W,V)),multiply(V,W))),multiply(inverse(U),U)),
inference(equational,[status(thm)],[c120,c174]) ).
cnf(c176,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(Z),Z))),W),V),inverse(V)) = W,
inference(equational,[status(thm)],[c7,c174]) ).
cnf(c177,plain,
multiply(X,inverse(inverse(inverse(X)))) = multiply(Y,inverse(inverse(inverse(Y)))),
inference(equational,[status(thm)],[c15,c176]) ).
cnf(c179,plain,
multiply(multiply(X,Y),inverse(Y)) = multiply(multiply(Z,inverse(inverse(inverse(Z)))),inverse(inverse(inverse(inverse(X))))),
inference(equational,[status(thm)],[c29,c176]) ).
cnf(c180,plain,
multiply(multiply(multiply(X,inverse(inverse(inverse(X)))),Y),inverse(Y)) = multiply(multiply(multiply(Z,inverse(inverse(inverse(Z)))),W),inverse(W)),
inference(equational,[status(thm)],[c51,c176]) ).
cnf(c183,plain,
multiply(X,inverse(inverse(inverse(X)))) = multiply(multiply(multiply(Y,inverse(multiply(multiply(Y,Z),inverse(Z)))),W),inverse(W)),
inference(equational,[status(thm)],[c9,c177]) ).
cnf(c184,plain,
multiply(multiply(X,inverse(multiply(multiply(X,Y),inverse(Y)))),inverse(inverse(Z))) = Z,
inference(equational,[status(thm)],[c6,c120,c183]) ).
cnf(c185,plain,
inverse(multiply(X,inverse(multiply(multiply(X,Y),inverse(Y))))) = multiply(Z,inverse(inverse(inverse(Z)))),
inference(equational,[status(thm)],[c177,c184]) ).
cnf(c191,plain,
multiply(multiply(X,inverse(inverse(inverse(X)))),inverse(inverse(inverse(inverse(multiply(Y,Z)))))) = multiply(multiply(multiply(Y,W),inverse(W)),inverse(inverse(Z))),
inference(equational,[status(thm)],[c12,c179]) ).
cnf(c196,plain,
multiply(multiply(multiply(multiply(X,inverse(inverse(inverse(X)))),Y),Z),inverse(Z)) = multiply(multiply(multiply(multiply(W,inverse(inverse(inverse(W)))),V),inverse(V)),inverse(inverse(Y))),
inference(equational,[status(thm)],[c154,c176]) ).
cnf(c197,plain,
multiply(multiply(multiply(X,inverse(multiply(multiply(X,Y),inverse(Y)))),Z),inverse(Z)) = multiply(multiply(multiply(W,inverse(multiply(multiply(W,V),inverse(V)))),U),inverse(U)),
inference(equational,[status(thm)],[c9,c183]) ).
cnf(c198,plain,
multiply(X,inverse(multiply(multiply(X,Y),inverse(Y)))) = multiply(Z,inverse(multiply(multiply(Z,W),inverse(W)))),
inference(equational,[status(thm)],[c120,c197]) ).
cnf(c199,plain,
multiply(multiply(X,inverse(multiply(multiply(X,Y),inverse(Y)))),Z) = multiply(multiply(W,inverse(multiply(multiply(W,V),inverse(V)))),Z),
inference(equational,[status(thm)],[c6,c120,c197]) ).
cnf(c211,plain,
inverse(multiply(multiply(X,Y),inverse(multiply(multiply(multiply(X,Z),inverse(Z)),inverse(inverse(Y)))))) = multiply(W,inverse(inverse(inverse(W)))),
inference(equational,[status(thm)],[c91,c185]) ).
cnf(c212,plain,
multiply(multiply(multiply(multiply(X,inverse(inverse(inverse(X)))),inverse(inverse(inverse(inverse(Y))))),Z),inverse(Z)) = multiply(multiply(multiply(multiply(Y,W),inverse(W)),V),inverse(V)),
inference(equational,[status(thm)],[c158,c176]) ).
cnf(c215,plain,
inverse(multiply(X,inverse(multiply(multiply(Y,inverse(inverse(inverse(Y)))),inverse(inverse(inverse(inverse(X)))))))) = multiply(Z,inverse(inverse(inverse(Z)))),
inference(equational,[status(thm)],[c177,c185]) ).
cnf(c230,plain,
multiply(multiply(multiply(X,Y),inverse(multiply(multiply(multiply(X,Z),inverse(Z)),inverse(inverse(Y))))),inverse(inverse(W))) = W,
inference(equational,[status(thm)],[c12,c184]) ).
cnf(c237,plain,
multiply(multiply(X,inverse(multiply(multiply(Y,inverse(inverse(inverse(Y)))),inverse(inverse(inverse(inverse(X))))))),inverse(inverse(Z))) = Z,
inference(equational,[status(thm)],[c177,c184]) ).
cnf(c241,plain,
multiply(multiply(multiply(X,inverse(inverse(inverse(X)))),Y),inverse(Y)) = inverse(inverse(inverse(inverse(multiply(inverse(multiply(inverse(multiply(Z,W)),multiply(W,Z))),multiply(inverse(V),V)))))),
inference(equational,[status(thm)],[c176,c180]) ).
cnf(c243,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(Z),Z))),multiply(multiply(W,V),inverse(V))) = W,
inference(equational,[status(thm)],[c120,c174]) ).
cnf(c252,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(Z),Z))),multiply(W,inverse(V))),V) = W,
inference(equational,[status(thm)],[c6,c174]) ).
cnf(c264,plain,
multiply(multiply(multiply(X,Y),inverse(Y)),inverse(multiply(Z,inverse(inverse(inverse(Z)))))) = multiply(multiply(multiply(X,multiply(W,inverse(multiply(multiply(W,V),inverse(V))))),U),inverse(U)),
inference(equational,[status(thm)],[c12,c185]) ).
cnf(c265,plain,
multiply(X,inverse(inverse(multiply(Y,inverse(multiply(multiply(Y,Z),inverse(Z))))))) = multiply(X,inverse(multiply(W,inverse(inverse(inverse(W)))))),
inference(equational,[status(thm)],[c3,c264]) ).
cnf(c266,plain,
multiply(X,inverse(multiply(Y,inverse(inverse(inverse(Y)))))) = multiply(X,inverse(multiply(Z,inverse(inverse(inverse(Z)))))),
inference(equational,[status(thm)],[c215,c265]) ).
cnf(c273,plain,
multiply(multiply(multiply(X,inverse(multiply(Y,inverse(inverse(inverse(Y)))))),Z),inverse(Z)) = multiply(multiply(multiply(X,inverse(multiply(W,inverse(inverse(inverse(W)))))),V),inverse(V)),
inference(equational,[status(thm)],[c10,c266]) ).
cnf(c274,plain,
multiply(multiply(X,inverse(multiply(Y,inverse(inverse(inverse(Y)))))),Z) = multiply(multiply(X,inverse(multiply(W,inverse(inverse(inverse(W)))))),Z),
inference(equational,[status(thm)],[c243,c252,c273]) ).
cnf(c301,plain,
multiply(multiply(X,inverse(inverse(inverse(X)))),inverse(inverse(inverse(inverse(multiply(multiply(Y,Z),inverse(Z))))))) = multiply(multiply(multiply(multiply(W,inverse(inverse(inverse(W)))),inverse(inverse(inverse(inverse(Y))))),V),inverse(V)),
inference(equational,[status(thm)],[c177,c212]) ).
cnf(c306,plain,
multiply(multiply(X,inverse(multiply(multiply(Y,inverse(inverse(inverse(Y)))),inverse(inverse(inverse(inverse(X))))))),Z) = multiply(multiply(W,inverse(multiply(multiply(W,V),inverse(V)))),Z),
inference(equational,[status(thm)],[c177,c199]) ).
cnf(c314,plain,
multiply(multiply(multiply(X,multiply(Y,inverse(inverse(inverse(Y))))),Z),inverse(Z)) = multiply(multiply(multiply(X,inverse(multiply(W,inverse(multiply(multiply(W,V),inverse(V)))))),U),inverse(U)),
inference(equational,[status(thm)],[c10,c185]) ).
cnf(c315,plain,
multiply(multiply(multiply(X,multiply(Y,inverse(inverse(inverse(Y))))),Z),inverse(Z)) = multiply(multiply(multiply(X,multiply(W,inverse(inverse(inverse(W))))),V),inverse(V)),
inference(equational,[status(thm)],[c215,c314]) ).
cnf(c319,plain,
multiply(multiply(multiply(X,multiply(Y,inverse(inverse(inverse(Y))))),Z),inverse(Z)) = multiply(multiply(multiply(X,W),inverse(W)),inverse(inverse(multiply(V,inverse(inverse(inverse(V))))))),
inference(equational,[status(thm)],[c191,c315]) ).
cnf(c320,plain,
multiply(X,inverse(inverse(multiply(Y,inverse(inverse(inverse(Y))))))) = multiply(X,inverse(inverse(multiply(Z,inverse(inverse(inverse(Z))))))),
inference(equational,[status(thm)],[c3,c319]) ).
cnf(c321,plain,
inverse(inverse(multiply(X,inverse(inverse(inverse(X)))))) = inverse(inverse(multiply(Y,inverse(inverse(inverse(Y)))))),
inference(equational,[status(thm)],[c176,c320]) ).
cnf(c322,plain,
inverse(inverse(inverse(multiply(X,inverse(multiply(multiply(X,Y),inverse(Y))))))) = inverse(inverse(multiply(Z,inverse(inverse(inverse(Z)))))),
inference(equational,[status(thm)],[c237,c306,c321]) ).
cnf(c330,plain,
multiply(multiply(multiply(multiply(X,inverse(inverse(inverse(X)))),Y),inverse(Y)),inverse(inverse(inverse(inverse(inverse(inverse(Z))))))) = multiply(multiply(multiply(multiply(Z,W),inverse(W)),V),inverse(V)),
inference(equational,[status(thm)],[c18,c196]) ).
cnf(c364,plain,
multiply(multiply(X,inverse(inverse(multiply(Y,inverse(multiply(multiply(Y,Z),inverse(Z))))))),W) = multiply(multiply(X,inverse(multiply(V,inverse(inverse(inverse(V)))))),W),
inference(equational,[status(thm)],[c237,c274,c306]) ).
cnf(c365,plain,
inverse(inverse(inverse(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X)))),multiply(inverse(Z),Z)))))) = multiply(multiply(multiply(W,inverse(inverse(inverse(W)))),V),inverse(V)),
inference(equational,[status(thm)],[c241,c243]) ).
cnf(c369,plain,
multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X)))),multiply(inverse(Z),Z))),multiply(multiply(W,V),inverse(V))) = W,
inference(equational,[status(thm)],[c243]) ).
cnf(c379,plain,
multiply(multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X)))),multiply(inverse(Z),Z))),multiply(W,inverse(V))),V) = W,
inference(equational,[status(thm)],[c243,c252]) ).
cnf(c398,plain,
multiply(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(Z),Z)),inverse(multiply(inverse(W),W))) = multiply(multiply(inverse(multiply(inverse(multiply(V,U)),multiply(U,V))),U2),inverse(U2)),
inference(equational,[status(thm)],[c11,c175]) ).
cnf(c399,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))) = inverse(multiply(inverse(multiply(Z,W)),multiply(W,Z))),
inference(equational,[status(thm)],[c369,c398]) ).
cnf(c400,plain,
multiply(inverse(multiply(X,Y)),multiply(Y,X)) = multiply(inverse(multiply(Z,W)),multiply(W,Z)),
inference(equational,[status(thm)],[c7,c399]) ).
cnf(c401,plain,
multiply(inverse(multiply(X,Y)),multiply(Y,X)) = inverse(multiply(inverse(multiply(Z,W)),multiply(W,Z))),
inference(equational,[status(thm)],[c243,c400]) ).
cnf(c403,plain,
multiply(inverse(multiply(X,Y)),multiply(Y,X)) = inverse(inverse(multiply(inverse(multiply(Z,W)),multiply(W,Z)))),
inference(equational,[status(thm)],[c369,c400]) ).
cnf(c407,plain,
multiply(multiply(inverse(multiply(X,Y)),multiply(Y,X)),inverse(multiply(Z,W))) = multiply(multiply(inverse(multiply(W,Z)),V),inverse(V)),
inference(equational,[status(thm)],[c11,c400]) ).
cnf(c409,plain,
multiply(multiply(inverse(multiply(multiply(X,Y),inverse(multiply(Y,X)))),Z),inverse(Z)) = multiply(inverse(W),W),
inference(equational,[status(thm)],[c379,c407]) ).
cnf(c410,plain,
multiply(inverse(multiply(multiply(X,Y),inverse(multiply(Y,X)))),Z) = inverse(inverse(Z)),
inference(equational,[status(thm)],[c369,c379,c409]) ).
cnf(c411,plain,
multiply(inverse(inverse(X)),inverse(X)) = multiply(inverse(Y),Y),
inference(equational,[status(thm)],[c409,c410]) ).
cnf(c412,plain,
multiply(inverse(X),X) = multiply(inverse(Y),Y),
inference(equational,[status(thm)],[c139,c411]) ).
cnf(c413,plain,
multiply(multiply(inverse(X),X),inverse(Y)) = multiply(multiply(inverse(Y),Z),inverse(Z)),
inference(equational,[status(thm)],[c11,c412]) ).
cnf(c414,plain,
multiply(multiply(inverse(X),X),Y) = multiply(multiply(Y,Z),inverse(Z)),
inference(equational,[status(thm)],[c139,c413]) ).
cnf(c418,plain,
multiply(inverse(X),X) = multiply(inverse(multiply(Y,Z)),multiply(Z,Y)),
inference(equational,[status(thm)],[c400,c412]) ).
cnf(c419,plain,
inverse(inverse(multiply(inverse(X),X))) = multiply(inverse(Y),Y),
inference(equational,[status(thm)],[c410,c418]) ).
cnf(c421,plain,
inverse(inverse(inverse(multiply(inverse(X),X)))) = multiply(inverse(multiply(Y,Z)),multiply(Z,Y)),
inference(equational,[status(thm)],[c401,c411,c419]) ).
cnf(c422,plain,
inverse(inverse(inverse(multiply(inverse(X),X)))) = multiply(inverse(Y),Y),
inference(equational,[status(thm)],[c412,c421]) ).
cnf(c423,plain,
inverse(multiply(inverse(X),X)) = multiply(inverse(Y),Y),
inference(equational,[status(thm)],[c419,c422]) ).
cnf(c426,plain,
inverse(multiply(inverse(X),X)) = multiply(inverse(multiply(Y,Z)),multiply(Z,Y)),
inference(equational,[status(thm)],[c401,c412]) ).
cnf(c428,plain,
inverse(inverse(multiply(inverse(X),X))) = multiply(inverse(multiply(Y,Z)),multiply(Z,Y)),
inference(equational,[status(thm)],[c403,c412]) ).
cnf(c437,plain,
inverse(inverse(inverse(multiply(inverse(X),X)))) = multiply(Y,inverse(multiply(multiply(Y,Z),inverse(Z)))),
inference(equational,[status(thm)],[c198,c410,c411]) ).
cnf(c438,plain,
inverse(inverse(inverse(inverse(multiply(inverse(X),X))))) = multiply(Y,inverse(inverse(inverse(Y)))),
inference(equational,[status(thm)],[c211,c437]) ).
cnf(c439,plain,
inverse(multiply(inverse(X),X)) = multiply(Y,inverse(inverse(inverse(Y)))),
inference(equational,[status(thm)],[c422,c438]) ).
cnf(c440,plain,
multiply(X,inverse(inverse(inverse(X)))) = multiply(inverse(Y),Y),
inference(equational,[status(thm)],[c184,c322,c423,c439]) ).
cnf(c442,plain,
multiply(X,inverse(inverse(inverse(X)))) = inverse(inverse(multiply(inverse(Y),Y))),
inference(equational,[status(thm)],[c428,c440]) ).
cnf(c443,plain,
multiply(multiply(inverse(X),X),inverse(inverse(Y))) = Y,
inference(equational,[status(thm)],[c184,c230,c439]) ).
cnf(c444,plain,
inverse(inverse(multiply(inverse(X),X))) = inverse(inverse(inverse(inverse(multiply(inverse(Y),Y))))),
inference(equational,[status(thm)],[c365,c369,c438,c442]) ).
cnf(c447,plain,
inverse(inverse(inverse(multiply(inverse(X),X)))) = inverse(inverse(multiply(inverse(Y),Y))),
inference(equational,[status(thm)],[c177,c442,c443,c444]) ).
cnf(c448,plain,
multiply(multiply(X,Y),inverse(Y)) = inverse(inverse(X)),
inference(equational,[status(thm)],[c179,c443,c447]) ).
cnf(c449,plain,
inverse(inverse(inverse(inverse(X)))) = X,
inference(equational,[status(thm)],[c443,c448]) ).
cnf(c450,plain,
multiply(multiply(inverse(X),X),Y) = inverse(inverse(Y)),
inference(equational,[status(thm)],[c414,c448]) ).
cnf(c451,plain,
multiply(multiply(X,inverse(X)),Y) = inverse(inverse(Y)),
inference(equational,[status(thm)],[c410,c449,c450]) ).
cnf(c452,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c448,c449,c451]) ).
cnf(c454,plain,
multiply(inverse(X),X) = multiply(Y,inverse(Y)),
inference(equational,[status(thm)],[c438,c452]) ).
cnf(c455,plain,
inverse(multiply(X,inverse(X))) = multiply(Y,inverse(Y)),
inference(equational,[status(thm)],[c438,c449,c451,c454]) ).
cnf(c456,plain,
inverse(multiply(X,Y)) = inverse(multiply(Y,X)),
inference(equational,[status(thm)],[c407,c448,c450,c451,c452,c455]) ).
cnf(c457,plain,
multiply(X,Y) = multiply(Y,X),
inference(equational,[status(thm)],[c452,c456]) ).
cnf(c461,plain,
multiply(X,inverse(X)) = multiply(multiply(Y,Z),inverse(multiply(Z,Y))),
inference(equational,[status(thm)],[c184,c426,c437,c454,c455,c457]) ).
cnf(c462,plain,
multiply(inverse(X),multiply(Y,X)) = Y,
inference(equational,[status(thm)],[c66,c448,c451,c452,c461]) ).
cnf(c463,plain,
multiply(X,multiply(Y,inverse(Y))) = X,
inference(equational,[status(thm)],[c301,c448,c451,c452,c461]) ).
cnf(c464,plain,
multiply(X,multiply(Y,inverse(X))) = Y,
inference(equational,[status(thm)],[c55,c448,c451,c452,c461]) ).
cnf(c465,plain,
multiply(X,inverse(multiply(X,Y))) = inverse(Y),
inference(equational,[status(thm)],[c330,c448,c451,c452,c462]) ).
cnf(c467,plain,
inverse(multiply(X,inverse(Y))) = multiply(Y,inverse(X)),
inference(equational,[status(thm)],[c464,c465]) ).
cnf(c468,plain,
multiply(inverse(X),inverse(Y)) = inverse(multiply(Y,X)),
inference(equational,[status(thm)],[c462,c465]) ).
cnf(c469,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference(equational,[status(thm)],[c14,c448,c452,c457,c465]) ).
cnf(c471,plain,
inverse(multiply(inverse(X),Y)) = multiply(inverse(Y),X),
inference(equational,[status(thm)],[c449,c452,c468]) ).
cnf(c473,plain,
multiply(multiply(multiply(X,Y),inverse(multiply(Y,X))),Z) = Z,
inference(equational,[status(thm)],[c166,c448,c451,c452,c461]) ).
cnf(c474,plain,
multiply(multiply(X,Y),inverse(multiply(Y,X))) = multiply(multiply(Z,W),inverse(multiply(W,Z))),
inference(equational,[status(thm)],[c399,c457,c469,c471,c473]) ).
cnf(c475,plain,
multiply(inverse(X),multiply(Y,inverse(Z))) = inverse(multiply(multiply(Z,inverse(Y)),X)),
inference(equational,[status(thm)],[c82,c448,c452,c467]) ).
cnf(c476,plain,
multiply(multiply(X,inverse(Y)),inverse(Z)) = inverse(multiply(Z,multiply(Y,inverse(X)))),
inference(equational,[status(thm)],[c467,c468]) ).
cnf(c477,plain,
multiply(X,inverse(X)) = multiply(multiply(Y,inverse(Z)),multiply(inverse(Y),Z)),
inference(equational,[status(thm)],[c82,c448,c451,c452,c467,c471,c473]) ).
cnf(c478,plain,
multiply(multiply(inverse(X),Y),inverse(Z)) = inverse(multiply(Z,multiply(X,inverse(Y)))),
inference(equational,[status(thm)],[c26,c448,c451,c452,c471,c476,c477]) ).
cnf(c479,plain,
multiply(X,multiply(multiply(Y,Z),inverse(multiply(Z,Y)))) = X,
inference(equational,[status(thm)],[c3,c448,c452,c457,c467,c469,c471,c473]) ).
cnf(c480,plain,
multiply(multiply(X,inverse(Y)),multiply(Y,Z)) = multiply(multiply(X,inverse(W)),multiply(W,Z)),
inference(equational,[status(thm)],[c115,c452,c463,c471,c473,c475,c478,c479]) ).
cnf(c481,plain,
multiply(multiply(X,inverse(Y)),multiply(Y,Z)) = multiply(X,Z),
inference(equational,[status(thm)],[c364,c448,c451,c452,c463,c467,c480]) ).
cnf(c482,plain,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
inference(equational,[status(thm)],[c21,c448,c452,c481]) ).
cnf(c483,plain,
multiply(X,multiply(Y,Z)) = multiply(Y,multiply(X,Z)),
inference(equational,[status(thm)],[c473,c474,c481,c482]) ).
cnf(g1,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(equational,[status(thm)],[c457,c483]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP507-1 : TPTP v9.0.0. Released v2.6.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.13/0.33 % Computer : n003.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Jul 14 08:30:34 EDT 2025
% 0.13/0.33 % CPUTime :
% 280.53/280.56 % SZS status Unsatisfiable
% 280.53/280.56 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------