TSTP Solution File: GRP012-4 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP012-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 10:32:15 EDT 2022
% Result : Unsatisfiable 0.13s 0.36s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 18
% Syntax : Number of clauses : 58 ( 35 unt; 0 nHn; 28 RR)
% Number of literals : 92 ( 91 equ; 36 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 87 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X) = X ).
cnf(associativity,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ).
cnf(right_identity,axiom,
multiply(X,identity) = X ).
cnf(right_inverse,axiom,
multiply(X,inverse(X)) = identity ).
cnf(prove_inverse_of_product_is_product_of_inverses,negated_conjecture,
inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)) ).
cnf(refute_0_0,plain,
multiply(multiply(X_4,inverse(X_4)),X_6) = multiply(X_4,multiply(inverse(X_4),X_6)),
inference(subst,[],[associativity:[bind(X,$fot(X_4)),bind(Y,$fot(inverse(X_4))),bind(Z,$fot(X_6))]]) ).
cnf(refute_0_1,plain,
multiply(X_4,inverse(X_4)) = identity,
inference(subst,[],[right_inverse:[bind(X,$fot(X_4))]]) ).
cnf(refute_0_2,plain,
( multiply(X_4,inverse(X_4)) != identity
| multiply(multiply(X_4,inverse(X_4)),X_6) != multiply(X_4,multiply(inverse(X_4),X_6))
| multiply(identity,X_6) = multiply(X_4,multiply(inverse(X_4),X_6)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_4,inverse(X_4)),X_6),multiply(X_4,multiply(inverse(X_4),X_6))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_3,plain,
( multiply(multiply(X_4,inverse(X_4)),X_6) != multiply(X_4,multiply(inverse(X_4),X_6))
| multiply(identity,X_6) = multiply(X_4,multiply(inverse(X_4),X_6)) ),
inference(resolve,[$cnf( $equal(multiply(X_4,inverse(X_4)),identity) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
multiply(identity,X_6) = multiply(X_4,multiply(inverse(X_4),X_6)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_4,inverse(X_4)),X_6),multiply(X_4,multiply(inverse(X_4),X_6))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
multiply(identity,X_6) = X_6,
inference(subst,[],[left_identity:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_6,plain,
( multiply(identity,X_6) != X_6
| multiply(identity,X_6) != multiply(X_4,multiply(inverse(X_4),X_6))
| X_6 = multiply(X_4,multiply(inverse(X_4),X_6)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_6),multiply(X_4,multiply(inverse(X_4),X_6))) ),[0],$fot(X_6)]]) ).
cnf(refute_0_7,plain,
( multiply(identity,X_6) != multiply(X_4,multiply(inverse(X_4),X_6))
| X_6 = multiply(X_4,multiply(inverse(X_4),X_6)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_6),X_6) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
X_6 = multiply(X_4,multiply(inverse(X_4),X_6)),
inference(resolve,[$cnf( $equal(multiply(identity,X_6),multiply(X_4,multiply(inverse(X_4),X_6))) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
inverse(inverse(X_7)) = multiply(X_7,multiply(inverse(X_7),inverse(inverse(X_7)))),
inference(subst,[],[refute_0_8:[bind(X_4,$fot(X_7)),bind(X_6,$fot(inverse(inverse(X_7))))]]) ).
cnf(refute_0_10,plain,
multiply(inverse(X_7),inverse(inverse(X_7))) = identity,
inference(subst,[],[right_inverse:[bind(X,$fot(inverse(X_7)))]]) ).
cnf(refute_0_11,plain,
( multiply(inverse(X_7),inverse(inverse(X_7))) != identity
| inverse(inverse(X_7)) != multiply(X_7,multiply(inverse(X_7),inverse(inverse(X_7))))
| inverse(inverse(X_7)) = multiply(X_7,identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_7)),multiply(X_7,multiply(inverse(X_7),inverse(inverse(X_7))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_12,plain,
( inverse(inverse(X_7)) != multiply(X_7,multiply(inverse(X_7),inverse(inverse(X_7))))
| inverse(inverse(X_7)) = multiply(X_7,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_7),inverse(inverse(X_7))),identity) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
inverse(inverse(X_7)) = multiply(X_7,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(X_7)),multiply(X_7,multiply(inverse(X_7),inverse(inverse(X_7))))) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
multiply(X_7,identity) = X_7,
inference(subst,[],[right_identity:[bind(X,$fot(X_7))]]) ).
cnf(refute_0_15,plain,
( multiply(X_7,identity) != X_7
| inverse(inverse(X_7)) != multiply(X_7,identity)
| inverse(inverse(X_7)) = X_7 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_7)),multiply(X_7,identity)) ),[1],$fot(X_7)]]) ).
cnf(refute_0_16,plain,
( inverse(inverse(X_7)) != multiply(X_7,identity)
| inverse(inverse(X_7)) = X_7 ),
inference(resolve,[$cnf( $equal(multiply(X_7,identity),X_7) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
inverse(inverse(X_7)) = X_7,
inference(resolve,[$cnf( $equal(inverse(inverse(X_7)),multiply(X_7,identity)) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
inverse(inverse(multiply(inverse(X_16),inverse(X_17)))) = multiply(inverse(X_16),inverse(X_17)),
inference(subst,[],[refute_0_17:[bind(X_7,$fot(multiply(inverse(X_16),inverse(X_17))))]]) ).
cnf(refute_0_19,plain,
inverse(multiply(inverse(X_13),inverse(X_4))) = multiply(X_4,multiply(inverse(X_4),inverse(multiply(inverse(X_13),inverse(X_4))))),
inference(subst,[],[refute_0_8:[bind(X_6,$fot(inverse(multiply(inverse(X_13),inverse(X_4)))))]]) ).
cnf(refute_0_20,plain,
multiply(X_11,inverse(multiply(inverse(X_4),X_11))) = multiply(X_4,multiply(inverse(X_4),multiply(X_11,inverse(multiply(inverse(X_4),X_11))))),
inference(subst,[],[refute_0_8:[bind(X_6,$fot(multiply(X_11,inverse(multiply(inverse(X_4),X_11)))))]]) ).
cnf(refute_0_21,plain,
multiply(multiply(X_4,X_5),inverse(multiply(X_4,X_5))) = identity,
inference(subst,[],[right_inverse:[bind(X,$fot(multiply(X_4,X_5)))]]) ).
cnf(refute_0_22,plain,
multiply(multiply(X_4,X_5),inverse(multiply(X_4,X_5))) = multiply(X_4,multiply(X_5,inverse(multiply(X_4,X_5)))),
inference(subst,[],[associativity:[bind(X,$fot(X_4)),bind(Y,$fot(X_5)),bind(Z,$fot(inverse(multiply(X_4,X_5))))]]) ).
cnf(refute_0_23,plain,
( multiply(multiply(X_4,X_5),inverse(multiply(X_4,X_5))) != multiply(X_4,multiply(X_5,inverse(multiply(X_4,X_5))))
| multiply(multiply(X_4,X_5),inverse(multiply(X_4,X_5))) != identity
| multiply(X_4,multiply(X_5,inverse(multiply(X_4,X_5)))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_4,X_5),inverse(multiply(X_4,X_5))),identity) ),[0],$fot(multiply(X_4,multiply(X_5,inverse(multiply(X_4,X_5)))))]]) ).
cnf(refute_0_24,plain,
( multiply(multiply(X_4,X_5),inverse(multiply(X_4,X_5))) != identity
| multiply(X_4,multiply(X_5,inverse(multiply(X_4,X_5)))) = identity ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_4,X_5),inverse(multiply(X_4,X_5))),multiply(X_4,multiply(X_5,inverse(multiply(X_4,X_5))))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
multiply(X_4,multiply(X_5,inverse(multiply(X_4,X_5)))) = identity,
inference(resolve,[$cnf( $equal(multiply(multiply(X_4,X_5),inverse(multiply(X_4,X_5))),identity) )],[refute_0_21,refute_0_24]) ).
cnf(refute_0_26,plain,
multiply(inverse(X_4),multiply(X_11,inverse(multiply(inverse(X_4),X_11)))) = identity,
inference(subst,[],[refute_0_25:[bind(X_4,$fot(inverse(X_4))),bind(X_5,$fot(X_11))]]) ).
cnf(refute_0_27,plain,
( multiply(X_11,inverse(multiply(inverse(X_4),X_11))) != multiply(X_4,multiply(inverse(X_4),multiply(X_11,inverse(multiply(inverse(X_4),X_11)))))
| multiply(inverse(X_4),multiply(X_11,inverse(multiply(inverse(X_4),X_11)))) != identity
| multiply(X_11,inverse(multiply(inverse(X_4),X_11))) = multiply(X_4,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_11,inverse(multiply(inverse(X_4),X_11))),multiply(X_4,multiply(inverse(X_4),multiply(X_11,inverse(multiply(inverse(X_4),X_11)))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_28,plain,
( multiply(X_11,inverse(multiply(inverse(X_4),X_11))) != multiply(X_4,multiply(inverse(X_4),multiply(X_11,inverse(multiply(inverse(X_4),X_11)))))
| multiply(X_11,inverse(multiply(inverse(X_4),X_11))) = multiply(X_4,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_4),multiply(X_11,inverse(multiply(inverse(X_4),X_11)))),identity) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
multiply(X_11,inverse(multiply(inverse(X_4),X_11))) = multiply(X_4,identity),
inference(resolve,[$cnf( $equal(multiply(X_11,inverse(multiply(inverse(X_4),X_11))),multiply(X_4,multiply(inverse(X_4),multiply(X_11,inverse(multiply(inverse(X_4),X_11)))))) )],[refute_0_20,refute_0_28]) ).
cnf(refute_0_30,plain,
multiply(X_4,identity) = X_4,
inference(subst,[],[right_identity:[bind(X,$fot(X_4))]]) ).
cnf(refute_0_31,plain,
( multiply(X_11,inverse(multiply(inverse(X_4),X_11))) != multiply(X_4,identity)
| multiply(X_4,identity) != X_4
| multiply(X_11,inverse(multiply(inverse(X_4),X_11))) = X_4 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_11,inverse(multiply(inverse(X_4),X_11))),X_4) ),[0],$fot(multiply(X_4,identity))]]) ).
cnf(refute_0_32,plain,
( multiply(X_11,inverse(multiply(inverse(X_4),X_11))) != multiply(X_4,identity)
| multiply(X_11,inverse(multiply(inverse(X_4),X_11))) = X_4 ),
inference(resolve,[$cnf( $equal(multiply(X_4,identity),X_4) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
multiply(X_11,inverse(multiply(inverse(X_4),X_11))) = X_4,
inference(resolve,[$cnf( $equal(multiply(X_11,inverse(multiply(inverse(X_4),X_11))),multiply(X_4,identity)) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
multiply(inverse(X_4),inverse(multiply(inverse(X_13),inverse(X_4)))) = X_13,
inference(subst,[],[refute_0_33:[bind(X_11,$fot(inverse(X_4))),bind(X_4,$fot(X_13))]]) ).
cnf(refute_0_35,plain,
( multiply(inverse(X_4),inverse(multiply(inverse(X_13),inverse(X_4)))) != X_13
| inverse(multiply(inverse(X_13),inverse(X_4))) != multiply(X_4,multiply(inverse(X_4),inverse(multiply(inverse(X_13),inverse(X_4)))))
| inverse(multiply(inverse(X_13),inverse(X_4))) = multiply(X_4,X_13) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_13),inverse(X_4))),multiply(X_4,multiply(inverse(X_4),inverse(multiply(inverse(X_13),inverse(X_4)))))) ),[1,1],$fot(X_13)]]) ).
cnf(refute_0_36,plain,
( inverse(multiply(inverse(X_13),inverse(X_4))) != multiply(X_4,multiply(inverse(X_4),inverse(multiply(inverse(X_13),inverse(X_4)))))
| inverse(multiply(inverse(X_13),inverse(X_4))) = multiply(X_4,X_13) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_4),inverse(multiply(inverse(X_13),inverse(X_4)))),X_13) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
inverse(multiply(inverse(X_13),inverse(X_4))) = multiply(X_4,X_13),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_13),inverse(X_4))),multiply(X_4,multiply(inverse(X_4),inverse(multiply(inverse(X_13),inverse(X_4)))))) )],[refute_0_19,refute_0_36]) ).
cnf(refute_0_38,plain,
inverse(multiply(inverse(X_16),inverse(X_17))) = multiply(X_17,X_16),
inference(subst,[],[refute_0_37:[bind(X_13,$fot(X_16)),bind(X_4,$fot(X_17))]]) ).
cnf(refute_0_39,plain,
( inverse(multiply(inverse(X_16),inverse(X_17))) != multiply(X_17,X_16)
| inverse(inverse(multiply(inverse(X_16),inverse(X_17)))) != multiply(inverse(X_16),inverse(X_17))
| inverse(multiply(X_17,X_16)) = multiply(inverse(X_16),inverse(X_17)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(multiply(inverse(X_16),inverse(X_17)))),multiply(inverse(X_16),inverse(X_17))) ),[0,0],$fot(multiply(X_17,X_16))]]) ).
cnf(refute_0_40,plain,
( inverse(inverse(multiply(inverse(X_16),inverse(X_17)))) != multiply(inverse(X_16),inverse(X_17))
| inverse(multiply(X_17,X_16)) = multiply(inverse(X_16),inverse(X_17)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_16),inverse(X_17))),multiply(X_17,X_16)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
inverse(multiply(X_17,X_16)) = multiply(inverse(X_16),inverse(X_17)),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(inverse(X_16),inverse(X_17)))),multiply(inverse(X_16),inverse(X_17))) )],[refute_0_18,refute_0_40]) ).
cnf(refute_0_42,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_43,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_44,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
( inverse(multiply(X_17,X_16)) != multiply(inverse(X_16),inverse(X_17))
| multiply(inverse(X_16),inverse(X_17)) = inverse(multiply(X_17,X_16)) ),
inference(subst,[],[refute_0_44:[bind(X0,$fot(inverse(multiply(X_17,X_16)))),bind(Y0,$fot(multiply(inverse(X_16),inverse(X_17))))]]) ).
cnf(refute_0_46,plain,
multiply(inverse(X_16),inverse(X_17)) = inverse(multiply(X_17,X_16)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_17,X_16)),multiply(inverse(X_16),inverse(X_17))) )],[refute_0_41,refute_0_45]) ).
cnf(refute_0_47,plain,
multiply(inverse(b),inverse(a)) = inverse(multiply(a,b)),
inference(subst,[],[refute_0_46:[bind(X_16,$fot(b)),bind(X_17,$fot(a))]]) ).
cnf(refute_0_48,plain,
( multiply(inverse(b),inverse(a)) != inverse(multiply(a,b))
| inverse(multiply(a,b)) != inverse(multiply(a,b))
| inverse(multiply(a,b)) = multiply(inverse(b),inverse(a)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(inverse(multiply(a,b)),multiply(inverse(b),inverse(a))) ),[1],$fot(inverse(multiply(a,b)))]]) ).
cnf(refute_0_49,plain,
( inverse(multiply(a,b)) != inverse(multiply(a,b))
| inverse(multiply(a,b)) = multiply(inverse(b),inverse(a)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(b),inverse(a)),inverse(multiply(a,b))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
inverse(multiply(a,b)) != inverse(multiply(a,b)),
inference(resolve,[$cnf( $equal(inverse(multiply(a,b)),multiply(inverse(b),inverse(a))) )],[refute_0_49,prove_inverse_of_product_is_product_of_inverses]) ).
cnf(refute_0_51,plain,
inverse(multiply(a,b)) = inverse(multiply(a,b)),
introduced(tautology,[refl,[$fot(inverse(multiply(a,b)))]]) ).
cnf(refute_0_52,plain,
$false,
inference(resolve,[$cnf( $equal(inverse(multiply(a,b)),inverse(multiply(a,b))) )],[refute_0_51,refute_0_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP012-4 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n027.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 : Tue Jun 14 14:30:03 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36
% 0.13/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.37
%------------------------------------------------------------------------------