TSTP Solution File: GRP008-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP008-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% 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 10:32:13 EDT 2022
% Result : Unsatisfiable 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of clauses : 50 ( 19 unt; 4 nHn; 37 RR)
% Number of literals : 98 ( 26 equ; 42 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
product(identity,X,X) ).
cnf(right_identity,axiom,
product(X,identity,X) ).
cnf(total_function1,axiom,
product(X,Y,multiply(X,Y)) ).
cnf(total_function2,axiom,
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| Z = W ) ).
cnf(associativity2,axiom,
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W)
| product(U,Z,W) ) ).
cnf(unknown_meaning3,axiom,
( product(j(A),A,h(A))
| product(A,j(A),h(A))
| q(A) ) ).
cnf(unknown_meaning4,axiom,
( ~ product(j(A),A,h(A))
| ~ product(A,j(A),h(A))
| q(A) ) ).
cnf(prove_identity_is_q,negated_conjecture,
~ q(identity) ).
cnf(refute_0_0,plain,
( ~ product(identity,j(identity),h(identity))
| ~ product(j(identity),identity,h(identity))
| q(identity) ),
inference(subst,[],[unknown_meaning4:[bind(A,$fot(identity))]]) ).
cnf(refute_0_1,plain,
( product(identity,j(identity),h(identity))
| product(j(identity),identity,h(identity))
| q(identity) ),
inference(subst,[],[unknown_meaning3:[bind(A,$fot(identity))]]) ).
cnf(refute_0_2,plain,
product(X_61,identity,X_61),
inference(subst,[],[right_identity:[bind(X,$fot(X_61))]]) ).
cnf(refute_0_3,plain,
( ~ product(X_61,identity,X_61)
| ~ product(X_61,identity,X_64)
| X_64 = X_61 ),
inference(subst,[],[total_function2:[bind(W,$fot(X_61)),bind(X,$fot(X_61)),bind(Y,$fot(identity)),bind(Z,$fot(X_64))]]) ).
cnf(refute_0_4,plain,
( ~ product(X_61,identity,X_64)
| X_64 = X_61 ),
inference(resolve,[$cnf( product(X_61,identity,X_61) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ product(j(identity),identity,h(identity))
| h(identity) = j(identity) ),
inference(subst,[],[refute_0_4:[bind(X_61,$fot(j(identity))),bind(X_64,$fot(h(identity)))]]) ).
cnf(refute_0_6,plain,
( h(identity) = j(identity)
| product(identity,j(identity),h(identity))
| q(identity) ),
inference(resolve,[$cnf( product(j(identity),identity,h(identity)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( h(identity) = j(identity)
| product(identity,j(identity),h(identity)) ),
inference(resolve,[$cnf( q(identity) )],[refute_0_6,prove_identity_is_q]) ).
cnf(refute_0_8,plain,
product(identity,identity,multiply(identity,identity)),
inference(subst,[],[total_function1:[bind(X,$fot(identity)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_9,plain,
product(identity,X_41,X_41),
inference(subst,[],[left_identity:[bind(X,$fot(X_41))]]) ).
cnf(refute_0_10,plain,
( ~ product(identity,X_41,X_41)
| ~ product(identity,identity,X_39)
| product(X_39,X_41,X_41) ),
inference(subst,[],[associativity2:[bind(U,$fot(X_39)),bind(V,$fot(X_41)),bind(W,$fot(X_41)),bind(X,$fot(identity)),bind(Y,$fot(identity)),bind(Z,$fot(X_41))]]) ).
cnf(refute_0_11,plain,
( ~ product(identity,identity,X_39)
| product(X_39,X_41,X_41) ),
inference(resolve,[$cnf( product(identity,X_41,X_41) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ product(identity,identity,multiply(identity,identity))
| product(multiply(identity,identity),X_43,X_43) ),
inference(subst,[],[refute_0_11:[bind(X_39,$fot(multiply(identity,identity))),bind(X_41,$fot(X_43))]]) ).
cnf(refute_0_13,plain,
product(multiply(identity,identity),X_43,X_43),
inference(resolve,[$cnf( product(identity,identity,multiply(identity,identity)) )],[refute_0_8,refute_0_12]) ).
cnf(refute_0_14,plain,
product(multiply(identity,identity),X_61,X_61),
inference(subst,[],[refute_0_13:[bind(X_43,$fot(X_61))]]) ).
cnf(refute_0_15,plain,
( ~ product(multiply(identity,identity),X_61,X_61)
| ~ product(multiply(identity,identity),X_61,X_64)
| X_64 = X_61 ),
inference(subst,[],[total_function2:[bind(W,$fot(X_61)),bind(X,$fot(multiply(identity,identity))),bind(Y,$fot(X_61)),bind(Z,$fot(X_64))]]) ).
cnf(refute_0_16,plain,
( ~ product(multiply(identity,identity),X_61,X_64)
| X_64 = X_61 ),
inference(resolve,[$cnf( product(multiply(identity,identity),X_61,X_61) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
product(X_65,identity,multiply(X_65,identity)),
inference(subst,[],[total_function1:[bind(X,$fot(X_65)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_18,plain,
( ~ product(X_65,identity,multiply(X_65,identity))
| multiply(X_65,identity) = X_65 ),
inference(subst,[],[refute_0_4:[bind(X_61,$fot(X_65)),bind(X_64,$fot(multiply(X_65,identity)))]]) ).
cnf(refute_0_19,plain,
multiply(X_65,identity) = X_65,
inference(resolve,[$cnf( product(X_65,identity,multiply(X_65,identity)) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
multiply(identity,identity) = identity,
inference(subst,[],[refute_0_19:[bind(X_65,$fot(identity))]]) ).
cnf(refute_0_21,plain,
( multiply(identity,identity) != identity
| ~ product(identity,X_61,X_64)
| product(multiply(identity,identity),X_61,X_64) ),
introduced(tautology,[equality,[$cnf( ~ product(multiply(identity,identity),X_61,X_64) ),[0],$fot(identity)]]) ).
cnf(refute_0_22,plain,
( ~ product(identity,X_61,X_64)
| product(multiply(identity,identity),X_61,X_64) ),
inference(resolve,[$cnf( $equal(multiply(identity,identity),identity) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ product(identity,X_61,X_64)
| X_64 = X_61 ),
inference(resolve,[$cnf( product(multiply(identity,identity),X_61,X_64) )],[refute_0_22,refute_0_16]) ).
cnf(refute_0_24,plain,
( ~ product(identity,j(identity),h(identity))
| h(identity) = j(identity) ),
inference(subst,[],[refute_0_23:[bind(X_61,$fot(j(identity))),bind(X_64,$fot(h(identity)))]]) ).
cnf(refute_0_25,plain,
h(identity) = j(identity),
inference(resolve,[$cnf( product(identity,j(identity),h(identity)) )],[refute_0_7,refute_0_24]) ).
cnf(refute_0_26,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_27,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_28,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( h(identity) != j(identity)
| j(identity) = h(identity) ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(h(identity))),bind(Y0,$fot(j(identity)))]]) ).
cnf(refute_0_30,plain,
j(identity) = h(identity),
inference(resolve,[$cnf( $equal(h(identity),j(identity)) )],[refute_0_25,refute_0_29]) ).
cnf(refute_0_31,plain,
( j(identity) != h(identity)
| ~ product(h(identity),identity,h(identity))
| product(j(identity),identity,h(identity)) ),
introduced(tautology,[equality,[$cnf( ~ product(j(identity),identity,h(identity)) ),[0],$fot(h(identity))]]) ).
cnf(refute_0_32,plain,
( ~ product(h(identity),identity,h(identity))
| product(j(identity),identity,h(identity)) ),
inference(resolve,[$cnf( $equal(j(identity),h(identity)) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ product(h(identity),identity,h(identity))
| ~ product(identity,j(identity),h(identity))
| q(identity) ),
inference(resolve,[$cnf( product(j(identity),identity,h(identity)) )],[refute_0_32,refute_0_0]) ).
cnf(refute_0_34,plain,
( j(identity) != h(identity)
| ~ product(identity,h(identity),h(identity))
| product(identity,j(identity),h(identity)) ),
introduced(tautology,[equality,[$cnf( ~ product(identity,j(identity),h(identity)) ),[1],$fot(h(identity))]]) ).
cnf(refute_0_35,plain,
( ~ product(identity,h(identity),h(identity))
| product(identity,j(identity),h(identity)) ),
inference(resolve,[$cnf( $equal(j(identity),h(identity)) )],[refute_0_30,refute_0_34]) ).
cnf(refute_0_36,plain,
( ~ product(h(identity),identity,h(identity))
| ~ product(identity,h(identity),h(identity))
| q(identity) ),
inference(resolve,[$cnf( product(identity,j(identity),h(identity)) )],[refute_0_35,refute_0_33]) ).
cnf(refute_0_37,plain,
product(h(identity),identity,h(identity)),
inference(subst,[],[right_identity:[bind(X,$fot(h(identity)))]]) ).
cnf(refute_0_38,plain,
( ~ product(identity,h(identity),h(identity))
| q(identity) ),
inference(resolve,[$cnf( product(h(identity),identity,h(identity)) )],[refute_0_37,refute_0_36]) ).
cnf(refute_0_39,plain,
product(identity,h(identity),h(identity)),
inference(subst,[],[left_identity:[bind(X,$fot(h(identity)))]]) ).
cnf(refute_0_40,plain,
q(identity),
inference(resolve,[$cnf( product(identity,h(identity),h(identity)) )],[refute_0_39,refute_0_38]) ).
cnf(refute_0_41,plain,
$false,
inference(resolve,[$cnf( q(identity) )],[refute_0_40,prove_identity_is_q]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP008-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.14 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n025.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 18:04:24 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.40 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.40
% 0.13/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.40
%------------------------------------------------------------------------------