TSTP Solution File: GRP022-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP022-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n032.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 10:32:18 EDT 2022
% Result : Unsatisfiable 0.10s 0.31s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of clauses : 29 ( 19 unt; 0 nHn; 15 RR)
% Number of literals : 44 ( 43 equ; 17 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 31 ( 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_inverse_is_original,negated_conjecture,
inverse(inverse(a)) != 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( $equal(inverse(inverse(X_7)),multiply(X_7,identity)) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
inverse(inverse(a)) = a,
inference(subst,[],[refute_0_17:[bind(X_7,$fot(a))]]) ).
cnf(refute_0_19,plain,
( a != a
| inverse(inverse(a)) != a
| inverse(inverse(a)) = a ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(a)),a) ),[0,0,0],$fot(a)]]) ).
cnf(refute_0_20,plain,
( a != a
| inverse(inverse(a)) = a ),
inference(resolve,[$cnf( $equal(inverse(inverse(a)),a) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
a != a,
inference(resolve,[$cnf( $equal(inverse(inverse(a)),a) )],[refute_0_20,prove_inverse_of_inverse_is_original]) ).
cnf(refute_0_22,plain,
a = a,
introduced(tautology,[refl,[$fot(a)]]) ).
cnf(refute_0_23,plain,
$false,
inference(resolve,[$cnf( $equal(a,a) )],[refute_0_22,refute_0_21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP022-2 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.11 % Command : metis --show proof --show saturation %s
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 600
% 0.10/0.30 % DateTime : Tue Jun 14 13:59:28 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.10/0.31 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.10/0.31 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.31
% 0.10/0.31 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.15/0.32
%------------------------------------------------------------------------------