TSTP Solution File: GRP019-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP019-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 10:32:17 EDT 2022
% Result : Unsatisfiable 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of clauses : 34 ( 19 unt; 0 nHn; 20 RR)
% Number of literals : 57 ( 29 equ; 25 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 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(prove_id_times_X_is_X,negated_conjecture,
multiply(identity,a) != a ).
cnf(refute_0_0,plain,
product(multiply(identity,identity),X_54,multiply(multiply(identity,identity),X_54)),
inference(subst,[],[total_function1:[bind(X,$fot(multiply(identity,identity))),bind(Y,$fot(X_54))]]) ).
cnf(refute_0_1,plain,
product(identity,identity,multiply(identity,identity)),
inference(subst,[],[total_function1:[bind(X,$fot(identity)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_2,plain,
product(identity,X_31,X_31),
inference(subst,[],[left_identity:[bind(X,$fot(X_31))]]) ).
cnf(refute_0_3,plain,
( ~ product(identity,X_31,X_31)
| ~ product(identity,identity,X_29)
| product(X_29,X_31,X_31) ),
inference(subst,[],[associativity2:[bind(U,$fot(X_29)),bind(V,$fot(X_31)),bind(W,$fot(X_31)),bind(X,$fot(identity)),bind(Y,$fot(identity)),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_4,plain,
( ~ product(identity,identity,X_29)
| product(X_29,X_31,X_31) ),
inference(resolve,[$cnf( product(identity,X_31,X_31) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ product(identity,identity,multiply(identity,identity))
| product(multiply(identity,identity),X_33,X_33) ),
inference(subst,[],[refute_0_4:[bind(X_29,$fot(multiply(identity,identity))),bind(X_31,$fot(X_33))]]) ).
cnf(refute_0_6,plain,
product(multiply(identity,identity),X_33,X_33),
inference(resolve,[$cnf( product(identity,identity,multiply(identity,identity)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
product(multiply(identity,identity),X_50,X_50),
inference(subst,[],[refute_0_6:[bind(X_33,$fot(X_50))]]) ).
cnf(refute_0_8,plain,
( ~ product(multiply(identity,identity),X_50,X_50)
| ~ product(multiply(identity,identity),X_50,X_53)
| X_53 = X_50 ),
inference(subst,[],[total_function2:[bind(W,$fot(X_50)),bind(X,$fot(multiply(identity,identity))),bind(Y,$fot(X_50)),bind(Z,$fot(X_53))]]) ).
cnf(refute_0_9,plain,
( ~ product(multiply(identity,identity),X_50,X_53)
| X_53 = X_50 ),
inference(resolve,[$cnf( product(multiply(identity,identity),X_50,X_50) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ product(multiply(identity,identity),X_54,multiply(multiply(identity,identity),X_54))
| multiply(multiply(identity,identity),X_54) = X_54 ),
inference(subst,[],[refute_0_9:[bind(X_50,$fot(X_54)),bind(X_53,$fot(multiply(multiply(identity,identity),X_54)))]]) ).
cnf(refute_0_11,plain,
multiply(multiply(identity,identity),X_54) = X_54,
inference(resolve,[$cnf( product(multiply(identity,identity),X_54,multiply(multiply(identity,identity),X_54)) )],[refute_0_0,refute_0_10]) ).
cnf(refute_0_12,plain,
product(multiply(identity,identity),identity,multiply(identity,identity)),
inference(subst,[],[right_identity:[bind(X,$fot(multiply(identity,identity)))]]) ).
cnf(refute_0_13,plain,
( ~ product(multiply(identity,identity),identity,multiply(identity,identity))
| multiply(identity,identity) = identity ),
inference(subst,[],[refute_0_9:[bind(X_50,$fot(identity)),bind(X_53,$fot(multiply(identity,identity)))]]) ).
cnf(refute_0_14,plain,
multiply(identity,identity) = identity,
inference(resolve,[$cnf( product(multiply(identity,identity),identity,multiply(identity,identity)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
multiply(multiply(identity,identity),X_54) = multiply(multiply(identity,identity),X_54),
introduced(tautology,[refl,[$fot(multiply(multiply(identity,identity),X_54))]]) ).
cnf(refute_0_16,plain,
( multiply(multiply(identity,identity),X_54) != multiply(multiply(identity,identity),X_54)
| multiply(identity,identity) != identity
| multiply(multiply(identity,identity),X_54) = multiply(identity,X_54) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(identity,identity),X_54),multiply(multiply(identity,identity),X_54)) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_17,plain,
( multiply(identity,identity) != identity
| multiply(multiply(identity,identity),X_54) = multiply(identity,X_54) ),
inference(resolve,[$cnf( $equal(multiply(multiply(identity,identity),X_54),multiply(multiply(identity,identity),X_54)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
multiply(multiply(identity,identity),X_54) = multiply(identity,X_54),
inference(resolve,[$cnf( $equal(multiply(identity,identity),identity) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
( multiply(multiply(identity,identity),X_54) != X_54
| multiply(multiply(identity,identity),X_54) != multiply(identity,X_54)
| multiply(identity,X_54) = X_54 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(identity,identity),X_54),X_54) ),[0],$fot(multiply(identity,X_54))]]) ).
cnf(refute_0_20,plain,
( multiply(multiply(identity,identity),X_54) != X_54
| multiply(identity,X_54) = X_54 ),
inference(resolve,[$cnf( $equal(multiply(multiply(identity,identity),X_54),multiply(identity,X_54)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
multiply(identity,X_54) = X_54,
inference(resolve,[$cnf( $equal(multiply(multiply(identity,identity),X_54),X_54) )],[refute_0_11,refute_0_20]) ).
cnf(refute_0_22,plain,
multiply(identity,a) = a,
inference(subst,[],[refute_0_21:[bind(X_54,$fot(a))]]) ).
cnf(refute_0_23,plain,
( multiply(identity,a) != a
| a != a
| multiply(identity,a) = a ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(identity,a),a) ),[0],$fot(a)]]) ).
cnf(refute_0_24,plain,
( a != a
| multiply(identity,a) = a ),
inference(resolve,[$cnf( $equal(multiply(identity,a),a) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
a != a,
inference(resolve,[$cnf( $equal(multiply(identity,a),a) )],[refute_0_24,prove_id_times_X_is_X]) ).
cnf(refute_0_26,plain,
a = a,
introduced(tautology,[refl,[$fot(a)]]) ).
cnf(refute_0_27,plain,
$false,
inference(resolve,[$cnf( $equal(a,a) )],[refute_0_26,refute_0_25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP019-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 20:53:33 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.39 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.39
% 0.12/0.39 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.39
%------------------------------------------------------------------------------