TSTP Solution File: RNG001-4 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : RNG001-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 : Mon Jul 18 20:35:41 EDT 2022
% Result : Unsatisfiable 0.19s 0.49s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of clauses : 52 ( 26 unt; 0 nHn; 30 RR)
% Number of literals : 95 ( 23 equ; 44 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 77 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(additive_identity1,axiom,
sum(additive_identity,X,X) ).
cnf(additive_identity2,axiom,
sum(X,additive_identity,X) ).
cnf(closure_of_multiplication,axiom,
product(X,Y,multiply(X,Y)) ).
cnf(associativity_of_multiplication2,axiom,
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W)
| product(U,Z,W) ) ).
cnf(distributivity1,axiom,
( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ product(X,V3,V4)
| sum(V1,V2,V4) ) ).
cnf(distributivity3,axiom,
( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| sum(V1,V2,V4) ) ).
cnf(cancellation1,axiom,
( ~ sum(X,Y,Z)
| ~ sum(X,W,Z)
| Y = W ) ).
cnf(prove_a_times_additive_id_is_additive_id,negated_conjecture,
~ product(a,additive_identity,additive_identity) ).
cnf(refute_0_0,plain,
product(X,additive_identity,multiply(X,additive_identity)),
inference(subst,[],[closure_of_multiplication:[bind(Y,$fot(additive_identity))]]) ).
cnf(refute_0_1,plain,
product(X_62,X_62,multiply(X_62,X_62)),
inference(subst,[],[closure_of_multiplication:[bind(X,$fot(X_62)),bind(Y,$fot(X_62))]]) ).
cnf(refute_0_2,plain,
product(X_60,X_58,multiply(X_60,X_58)),
inference(subst,[],[closure_of_multiplication:[bind(X,$fot(X_60)),bind(Y,$fot(X_58))]]) ).
cnf(refute_0_3,plain,
( ~ product(X_60,X_58,multiply(X_60,X_58))
| ~ product(X_60,X_60,X_58)
| product(X_58,X_60,multiply(X_60,X_58)) ),
inference(subst,[],[associativity_of_multiplication2:[bind(U,$fot(X_58)),bind(V,$fot(X_58)),bind(W,$fot(multiply(X_60,X_58))),bind(X,$fot(X_60)),bind(Y,$fot(X_60)),bind(Z,$fot(X_60))]]) ).
cnf(refute_0_4,plain,
( ~ product(X_60,X_60,X_58)
| product(X_58,X_60,multiply(X_60,X_58)) ),
inference(resolve,[$cnf( product(X_60,X_58,multiply(X_60,X_58)) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ product(X_62,X_62,multiply(X_62,X_62))
| product(multiply(X_62,X_62),X_62,multiply(X_62,multiply(X_62,X_62))) ),
inference(subst,[],[refute_0_4:[bind(X_58,$fot(multiply(X_62,X_62))),bind(X_60,$fot(X_62))]]) ).
cnf(refute_0_6,plain,
product(multiply(X_62,X_62),X_62,multiply(X_62,multiply(X_62,X_62))),
inference(resolve,[$cnf( product(X_62,X_62,multiply(X_62,X_62)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
product(multiply(additive_identity,additive_identity),additive_identity,multiply(additive_identity,multiply(additive_identity,additive_identity))),
inference(subst,[],[refute_0_6:[bind(X_62,$fot(additive_identity))]]) ).
cnf(refute_0_8,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(subst,[],[additive_identity1:[bind(X,$fot(additive_identity))]]) ).
cnf(refute_0_9,plain,
( ~ product(X_67,additive_identity,X_66)
| ~ sum(additive_identity,additive_identity,additive_identity)
| sum(X_66,X_66,X_66) ),
inference(subst,[],[distributivity1:[bind(V1,$fot(X_66)),bind(V2,$fot(X_66)),bind(V3,$fot(additive_identity)),bind(V4,$fot(X_66)),bind(X,$fot(X_67)),bind(Y,$fot(additive_identity)),bind(Z,$fot(additive_identity))]]) ).
cnf(refute_0_10,plain,
( ~ product(X_67,additive_identity,X_66)
| sum(X_66,X_66,X_66) ),
inference(resolve,[$cnf( sum(additive_identity,additive_identity,additive_identity) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ product(multiply(additive_identity,additive_identity),additive_identity,multiply(additive_identity,multiply(additive_identity,additive_identity)))
| sum(multiply(additive_identity,multiply(additive_identity,additive_identity)),multiply(additive_identity,multiply(additive_identity,additive_identity)),multiply(additive_identity,multiply(additive_identity,additive_identity))) ),
inference(subst,[],[refute_0_10:[bind(X_66,$fot(multiply(additive_identity,multiply(additive_identity,additive_identity)))),bind(X_67,$fot(multiply(additive_identity,additive_identity)))]]) ).
cnf(refute_0_12,plain,
sum(multiply(additive_identity,multiply(additive_identity,additive_identity)),multiply(additive_identity,multiply(additive_identity,additive_identity)),multiply(additive_identity,multiply(additive_identity,additive_identity))),
inference(resolve,[$cnf( product(multiply(additive_identity,additive_identity),additive_identity,multiply(additive_identity,multiply(additive_identity,additive_identity))) )],[refute_0_7,refute_0_11]) ).
cnf(refute_0_13,plain,
product(X_67,X_68,multiply(X_67,X_68)),
inference(subst,[],[closure_of_multiplication:[bind(X,$fot(X_67)),bind(Y,$fot(X_68))]]) ).
cnf(refute_0_14,plain,
( ~ product(X_67,X_68,multiply(X_67,X_68))
| ~ sum(X_68,X_68,X_68)
| sum(multiply(X_67,X_68),multiply(X_67,X_68),multiply(X_67,X_68)) ),
inference(subst,[],[distributivity1:[bind(V1,$fot(multiply(X_67,X_68))),bind(V2,$fot(multiply(X_67,X_68))),bind(V3,$fot(X_68)),bind(V4,$fot(multiply(X_67,X_68))),bind(X,$fot(X_67)),bind(Y,$fot(X_68)),bind(Z,$fot(X_68))]]) ).
cnf(refute_0_15,plain,
( ~ sum(X_68,X_68,X_68)
| sum(multiply(X_67,X_68),multiply(X_67,X_68),multiply(X_67,X_68)) ),
inference(resolve,[$cnf( product(X_67,X_68,multiply(X_67,X_68)) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ sum(multiply(additive_identity,multiply(additive_identity,additive_identity)),multiply(additive_identity,multiply(additive_identity,additive_identity)),multiply(additive_identity,multiply(additive_identity,additive_identity)))
| sum(multiply(X_82,multiply(additive_identity,multiply(additive_identity,additive_identity))),multiply(X_82,multiply(additive_identity,multiply(additive_identity,additive_identity))),multiply(X_82,multiply(additive_identity,multiply(additive_identity,additive_identity)))) ),
inference(subst,[],[refute_0_15:[bind(X_67,$fot(X_82)),bind(X_68,$fot(multiply(additive_identity,multiply(additive_identity,additive_identity))))]]) ).
cnf(refute_0_17,plain,
sum(multiply(X_82,multiply(additive_identity,multiply(additive_identity,additive_identity))),multiply(X_82,multiply(additive_identity,multiply(additive_identity,additive_identity))),multiply(X_82,multiply(additive_identity,multiply(additive_identity,additive_identity)))),
inference(resolve,[$cnf( sum(multiply(additive_identity,multiply(additive_identity,additive_identity)),multiply(additive_identity,multiply(additive_identity,additive_identity)),multiply(additive_identity,multiply(additive_identity,additive_identity))) )],[refute_0_12,refute_0_16]) ).
cnf(refute_0_18,plain,
sum(X_208,additive_identity,X_208),
inference(subst,[],[additive_identity2:[bind(X,$fot(X_208))]]) ).
cnf(refute_0_19,plain,
( ~ sum(X_208,X_207,X_208)
| ~ sum(X_208,additive_identity,X_208)
| X_207 = additive_identity ),
inference(subst,[],[cancellation1:[bind(W,$fot(additive_identity)),bind(X,$fot(X_208)),bind(Y,$fot(X_207)),bind(Z,$fot(X_208))]]) ).
cnf(refute_0_20,plain,
( ~ sum(X_208,X_207,X_208)
| X_207 = additive_identity ),
inference(resolve,[$cnf( sum(X_208,additive_identity,X_208) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ sum(multiply(X_82,multiply(additive_identity,multiply(additive_identity,additive_identity))),multiply(X_82,multiply(additive_identity,multiply(additive_identity,additive_identity))),multiply(X_82,multiply(additive_identity,multiply(additive_identity,additive_identity))))
| multiply(X_82,multiply(additive_identity,multiply(additive_identity,additive_identity))) = additive_identity ),
inference(subst,[],[refute_0_20:[bind(X_207,$fot(multiply(X_82,multiply(additive_identity,multiply(additive_identity,additive_identity))))),bind(X_208,$fot(multiply(X_82,multiply(additive_identity,multiply(additive_identity,additive_identity)))))]]) ).
cnf(refute_0_22,plain,
multiply(X_82,multiply(additive_identity,multiply(additive_identity,additive_identity))) = additive_identity,
inference(resolve,[$cnf( sum(multiply(X_82,multiply(additive_identity,multiply(additive_identity,additive_identity))),multiply(X_82,multiply(additive_identity,multiply(additive_identity,additive_identity))),multiply(X_82,multiply(additive_identity,multiply(additive_identity,additive_identity)))) )],[refute_0_17,refute_0_21]) ).
cnf(refute_0_23,plain,
product(additive_identity,X_102,multiply(additive_identity,X_102)),
inference(subst,[],[closure_of_multiplication:[bind(X,$fot(additive_identity)),bind(Y,$fot(X_102))]]) ).
cnf(refute_0_24,plain,
( ~ product(additive_identity,X_99,X_98)
| ~ sum(additive_identity,additive_identity,additive_identity)
| sum(X_98,X_98,X_98) ),
inference(subst,[],[distributivity3:[bind(V1,$fot(X_98)),bind(V2,$fot(X_98)),bind(V3,$fot(additive_identity)),bind(V4,$fot(X_98)),bind(X,$fot(X_99)),bind(Y,$fot(additive_identity)),bind(Z,$fot(additive_identity))]]) ).
cnf(refute_0_25,plain,
( ~ product(additive_identity,X_99,X_98)
| sum(X_98,X_98,X_98) ),
inference(resolve,[$cnf( sum(additive_identity,additive_identity,additive_identity) )],[refute_0_8,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ product(additive_identity,X_102,multiply(additive_identity,X_102))
| sum(multiply(additive_identity,X_102),multiply(additive_identity,X_102),multiply(additive_identity,X_102)) ),
inference(subst,[],[refute_0_25:[bind(X_98,$fot(multiply(additive_identity,X_102))),bind(X_99,$fot(X_102))]]) ).
cnf(refute_0_27,plain,
sum(multiply(additive_identity,X_102),multiply(additive_identity,X_102),multiply(additive_identity,X_102)),
inference(resolve,[$cnf( product(additive_identity,X_102,multiply(additive_identity,X_102)) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ sum(multiply(additive_identity,X_102),multiply(additive_identity,X_102),multiply(additive_identity,X_102))
| multiply(additive_identity,X_102) = additive_identity ),
inference(subst,[],[refute_0_20:[bind(X_207,$fot(multiply(additive_identity,X_102))),bind(X_208,$fot(multiply(additive_identity,X_102)))]]) ).
cnf(refute_0_29,plain,
multiply(additive_identity,X_102) = additive_identity,
inference(resolve,[$cnf( sum(multiply(additive_identity,X_102),multiply(additive_identity,X_102),multiply(additive_identity,X_102)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
multiply(additive_identity,multiply(additive_identity,additive_identity)) = additive_identity,
inference(subst,[],[refute_0_29:[bind(X_102,$fot(multiply(additive_identity,additive_identity)))]]) ).
cnf(refute_0_31,plain,
multiply(X_82,multiply(additive_identity,multiply(additive_identity,additive_identity))) = multiply(X_82,multiply(additive_identity,multiply(additive_identity,additive_identity))),
introduced(tautology,[refl,[$fot(multiply(X_82,multiply(additive_identity,multiply(additive_identity,additive_identity))))]]) ).
cnf(refute_0_32,plain,
( multiply(X_82,multiply(additive_identity,multiply(additive_identity,additive_identity))) != multiply(X_82,multiply(additive_identity,multiply(additive_identity,additive_identity)))
| multiply(additive_identity,multiply(additive_identity,additive_identity)) != additive_identity
| multiply(X_82,multiply(additive_identity,multiply(additive_identity,additive_identity))) = multiply(X_82,additive_identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_82,multiply(additive_identity,multiply(additive_identity,additive_identity))),multiply(X_82,multiply(additive_identity,multiply(additive_identity,additive_identity)))) ),[1,1],$fot(additive_identity)]]) ).
cnf(refute_0_33,plain,
( multiply(additive_identity,multiply(additive_identity,additive_identity)) != additive_identity
| multiply(X_82,multiply(additive_identity,multiply(additive_identity,additive_identity))) = multiply(X_82,additive_identity) ),
inference(resolve,[$cnf( $equal(multiply(X_82,multiply(additive_identity,multiply(additive_identity,additive_identity))),multiply(X_82,multiply(additive_identity,multiply(additive_identity,additive_identity)))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
multiply(X_82,multiply(additive_identity,multiply(additive_identity,additive_identity))) = multiply(X_82,additive_identity),
inference(resolve,[$cnf( $equal(multiply(additive_identity,multiply(additive_identity,additive_identity)),additive_identity) )],[refute_0_30,refute_0_33]) ).
cnf(refute_0_35,plain,
( multiply(X_82,multiply(additive_identity,multiply(additive_identity,additive_identity))) != multiply(X_82,additive_identity)
| multiply(X_82,multiply(additive_identity,multiply(additive_identity,additive_identity))) != additive_identity
| multiply(X_82,additive_identity) = additive_identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_82,multiply(additive_identity,multiply(additive_identity,additive_identity))),additive_identity) ),[0],$fot(multiply(X_82,additive_identity))]]) ).
cnf(refute_0_36,plain,
( multiply(X_82,multiply(additive_identity,multiply(additive_identity,additive_identity))) != additive_identity
| multiply(X_82,additive_identity) = additive_identity ),
inference(resolve,[$cnf( $equal(multiply(X_82,multiply(additive_identity,multiply(additive_identity,additive_identity))),multiply(X_82,additive_identity)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
multiply(X_82,additive_identity) = additive_identity,
inference(resolve,[$cnf( $equal(multiply(X_82,multiply(additive_identity,multiply(additive_identity,additive_identity))),additive_identity) )],[refute_0_22,refute_0_36]) ).
cnf(refute_0_38,plain,
multiply(X,additive_identity) = additive_identity,
inference(subst,[],[refute_0_37:[bind(X_82,$fot(X))]]) ).
cnf(refute_0_39,plain,
( multiply(X,additive_identity) != additive_identity
| ~ product(X,additive_identity,multiply(X,additive_identity))
| product(X,additive_identity,additive_identity) ),
introduced(tautology,[equality,[$cnf( product(X,additive_identity,multiply(X,additive_identity)) ),[2],$fot(additive_identity)]]) ).
cnf(refute_0_40,plain,
( ~ product(X,additive_identity,multiply(X,additive_identity))
| product(X,additive_identity,additive_identity) ),
inference(resolve,[$cnf( $equal(multiply(X,additive_identity),additive_identity) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
product(X,additive_identity,additive_identity),
inference(resolve,[$cnf( product(X,additive_identity,multiply(X,additive_identity)) )],[refute_0_0,refute_0_40]) ).
cnf(refute_0_42,plain,
product(a,additive_identity,additive_identity),
inference(subst,[],[refute_0_41:[bind(X,$fot(a))]]) ).
cnf(refute_0_43,plain,
$false,
inference(resolve,[$cnf( product(a,additive_identity,additive_identity) )],[refute_0_42,prove_a_times_additive_id_is_additive_id]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : RNG001-4 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon May 30 19:25:25 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.49 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.49
% 0.19/0.49 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.50
%------------------------------------------------------------------------------