TSTP Solution File: RNG001-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : RNG001-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 0.20s 0.45s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of clauses : 65 ( 33 unt; 0 nHn; 36 RR)
% Number of literals : 114 ( 47 equ; 50 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 109 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(additive_identity1,axiom,
sum(additive_identity,X,X) ).
cnf(closure_of_multiplication,axiom,
product(X,Y,multiply(X,Y)) ).
cnf(closure_of_addition,axiom,
sum(X,Y,add(X,Y)) ).
cnf(right_inverse,axiom,
sum(X,additive_inverse(X),additive_identity) ).
cnf(associativity_of_addition1,axiom,
( ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(U,Z,W)
| sum(X,V,W) ) ).
cnf(commutativity_of_addition,axiom,
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ) ).
cnf(distributivity1,axiom,
( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ product(X,V3,V4)
| sum(V1,V2,V4) ) ).
cnf(addition_is_well_defined,axiom,
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| U = V ) ).
cnf(prove_a_times_0_is_0,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,$fot(additive_identity))]]) ).
cnf(refute_0_1,plain,
sum(X_15,X_16,add(X_15,X_16)),
inference(subst,[],[closure_of_addition:[bind(X,$fot(X_15)),bind(Y,$fot(X_16))]]) ).
cnf(refute_0_2,plain,
( ~ sum(X_15,X_16,X_14)
| ~ sum(X_15,X_16,add(X_15,X_16))
| add(X_15,X_16) = X_14 ),
inference(subst,[],[addition_is_well_defined:[bind(U,$fot(add(X_15,X_16))),bind(V,$fot(X_14)),bind(X,$fot(X_15)),bind(Y,$fot(X_16))]]) ).
cnf(refute_0_3,plain,
( ~ sum(X_15,X_16,X_14)
| add(X_15,X_16) = X_14 ),
inference(resolve,[$cnf( sum(X_15,X_16,add(X_15,X_16)) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ sum(multiply(X_180,additive_identity),additive_identity,additive_identity)
| add(multiply(X_180,additive_identity),additive_identity) = additive_identity ),
inference(subst,[],[refute_0_3:[bind(X_14,$fot(additive_identity)),bind(X_15,$fot(multiply(X_180,additive_identity))),bind(X_16,$fot(additive_identity))]]) ).
cnf(refute_0_5,plain,
product(X_82,additive_identity,multiply(X_82,additive_identity)),
inference(subst,[],[closure_of_multiplication:[bind(X,$fot(X_82)),bind(Y,$fot(additive_identity))]]) ).
cnf(refute_0_6,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(subst,[],[additive_identity1:[bind(X,$fot(additive_identity))]]) ).
cnf(refute_0_7,plain,
( ~ product(X_79,additive_identity,X_78)
| ~ sum(additive_identity,additive_identity,additive_identity)
| sum(X_78,X_78,X_78) ),
inference(subst,[],[distributivity1:[bind(V1,$fot(X_78)),bind(V2,$fot(X_78)),bind(V3,$fot(additive_identity)),bind(V4,$fot(X_78)),bind(X,$fot(X_79)),bind(Y,$fot(additive_identity)),bind(Z,$fot(additive_identity))]]) ).
cnf(refute_0_8,plain,
( ~ product(X_79,additive_identity,X_78)
| sum(X_78,X_78,X_78) ),
inference(resolve,[$cnf( sum(additive_identity,additive_identity,additive_identity) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ product(X_82,additive_identity,multiply(X_82,additive_identity))
| sum(multiply(X_82,additive_identity),multiply(X_82,additive_identity),multiply(X_82,additive_identity)) ),
inference(subst,[],[refute_0_8:[bind(X_78,$fot(multiply(X_82,additive_identity))),bind(X_79,$fot(X_82))]]) ).
cnf(refute_0_10,plain,
sum(multiply(X_82,additive_identity),multiply(X_82,additive_identity),multiply(X_82,additive_identity)),
inference(resolve,[$cnf( product(X_82,additive_identity,multiply(X_82,additive_identity)) )],[refute_0_5,refute_0_9]) ).
cnf(refute_0_11,plain,
sum(X_171,additive_inverse(X_171),additive_identity),
inference(subst,[],[right_inverse:[bind(X,$fot(X_171))]]) ).
cnf(refute_0_12,plain,
( ~ sum(X_170,X_171,X_171)
| ~ sum(X_171,additive_inverse(X_171),additive_identity)
| sum(X_170,additive_identity,additive_identity) ),
inference(subst,[],[associativity_of_addition1:[bind(U,$fot(X_171)),bind(V,$fot(additive_identity)),bind(W,$fot(additive_identity)),bind(X,$fot(X_170)),bind(Y,$fot(X_171)),bind(Z,$fot(additive_inverse(X_171)))]]) ).
cnf(refute_0_13,plain,
( ~ sum(X_170,X_171,X_171)
| sum(X_170,additive_identity,additive_identity) ),
inference(resolve,[$cnf( sum(X_171,additive_inverse(X_171),additive_identity) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ sum(multiply(X_82,additive_identity),multiply(X_82,additive_identity),multiply(X_82,additive_identity))
| sum(multiply(X_82,additive_identity),additive_identity,additive_identity) ),
inference(subst,[],[refute_0_13:[bind(X_170,$fot(multiply(X_82,additive_identity))),bind(X_171,$fot(multiply(X_82,additive_identity)))]]) ).
cnf(refute_0_15,plain,
sum(multiply(X_82,additive_identity),additive_identity,additive_identity),
inference(resolve,[$cnf( sum(multiply(X_82,additive_identity),multiply(X_82,additive_identity),multiply(X_82,additive_identity)) )],[refute_0_10,refute_0_14]) ).
cnf(refute_0_16,plain,
sum(multiply(X_180,additive_identity),additive_identity,additive_identity),
inference(subst,[],[refute_0_15:[bind(X_82,$fot(X_180))]]) ).
cnf(refute_0_17,plain,
add(multiply(X_180,additive_identity),additive_identity) = additive_identity,
inference(resolve,[$cnf( sum(multiply(X_180,additive_identity),additive_identity,additive_identity) )],[refute_0_16,refute_0_4]) ).
cnf(refute_0_18,plain,
sum(additive_identity,X_17,add(additive_identity,X_17)),
inference(subst,[],[closure_of_addition:[bind(X,$fot(additive_identity)),bind(Y,$fot(X_17))]]) ).
cnf(refute_0_19,plain,
sum(additive_identity,X_13,X_13),
inference(subst,[],[additive_identity1:[bind(X,$fot(X_13))]]) ).
cnf(refute_0_20,plain,
( ~ sum(additive_identity,X_13,X_13)
| ~ sum(additive_identity,X_13,X_14)
| X_13 = X_14 ),
inference(subst,[],[addition_is_well_defined:[bind(U,$fot(X_13)),bind(V,$fot(X_14)),bind(X,$fot(additive_identity)),bind(Y,$fot(X_13))]]) ).
cnf(refute_0_21,plain,
( ~ sum(additive_identity,X_13,X_14)
| X_13 = X_14 ),
inference(resolve,[$cnf( sum(additive_identity,X_13,X_13) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ sum(additive_identity,X_17,add(additive_identity,X_17))
| X_17 = add(additive_identity,X_17) ),
inference(subst,[],[refute_0_21:[bind(X_13,$fot(X_17)),bind(X_14,$fot(add(additive_identity,X_17)))]]) ).
cnf(refute_0_23,plain,
X_17 = add(additive_identity,X_17),
inference(resolve,[$cnf( sum(additive_identity,X_17,add(additive_identity,X_17)) )],[refute_0_18,refute_0_22]) ).
cnf(refute_0_24,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_25,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_26,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
( X_17 != add(additive_identity,X_17)
| add(additive_identity,X_17) = X_17 ),
inference(subst,[],[refute_0_26:[bind(X0,$fot(X_17)),bind(Y0,$fot(add(additive_identity,X_17)))]]) ).
cnf(refute_0_28,plain,
add(additive_identity,X_17) = X_17,
inference(resolve,[$cnf( $equal(X_17,add(additive_identity,X_17)) )],[refute_0_23,refute_0_27]) ).
cnf(refute_0_29,plain,
add(additive_identity,multiply(X_180,additive_identity)) = multiply(X_180,additive_identity),
inference(subst,[],[refute_0_28:[bind(X_17,$fot(multiply(X_180,additive_identity)))]]) ).
cnf(refute_0_30,plain,
sum(X_30,X_31,add(X_30,X_31)),
inference(subst,[],[closure_of_addition:[bind(X,$fot(X_30)),bind(Y,$fot(X_31))]]) ).
cnf(refute_0_31,plain,
sum(X_8,X_9,add(X_8,X_9)),
inference(subst,[],[closure_of_addition:[bind(X,$fot(X_8)),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_32,plain,
( ~ sum(X_8,X_9,add(X_8,X_9))
| sum(X_9,X_8,add(X_8,X_9)) ),
inference(subst,[],[commutativity_of_addition:[bind(X,$fot(X_8)),bind(Y,$fot(X_9)),bind(Z,$fot(add(X_8,X_9)))]]) ).
cnf(refute_0_33,plain,
sum(X_9,X_8,add(X_8,X_9)),
inference(resolve,[$cnf( sum(X_8,X_9,add(X_8,X_9)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
sum(X_15,X_16,add(X_16,X_15)),
inference(subst,[],[refute_0_33:[bind(X_8,$fot(X_16)),bind(X_9,$fot(X_15))]]) ).
cnf(refute_0_35,plain,
( ~ sum(X_15,X_16,X_14)
| ~ sum(X_15,X_16,add(X_16,X_15))
| add(X_16,X_15) = X_14 ),
inference(subst,[],[addition_is_well_defined:[bind(U,$fot(add(X_16,X_15))),bind(V,$fot(X_14)),bind(X,$fot(X_15)),bind(Y,$fot(X_16))]]) ).
cnf(refute_0_36,plain,
( ~ sum(X_15,X_16,X_14)
| add(X_16,X_15) = X_14 ),
inference(resolve,[$cnf( sum(X_15,X_16,add(X_16,X_15)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( ~ sum(X_30,X_31,add(X_30,X_31))
| add(X_31,X_30) = add(X_30,X_31) ),
inference(subst,[],[refute_0_36:[bind(X_14,$fot(add(X_30,X_31))),bind(X_15,$fot(X_30)),bind(X_16,$fot(X_31))]]) ).
cnf(refute_0_38,plain,
add(X_31,X_30) = add(X_30,X_31),
inference(resolve,[$cnf( sum(X_30,X_31,add(X_30,X_31)) )],[refute_0_30,refute_0_37]) ).
cnf(refute_0_39,plain,
( add(X_31,X_30) != add(X_30,X_31)
| add(X_30,X_31) = add(X_31,X_30) ),
inference(subst,[],[refute_0_26:[bind(X0,$fot(add(X_31,X_30))),bind(Y0,$fot(add(X_30,X_31)))]]) ).
cnf(refute_0_40,plain,
add(X_30,X_31) = add(X_31,X_30),
inference(resolve,[$cnf( $equal(add(X_31,X_30),add(X_30,X_31)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
add(multiply(X_180,additive_identity),additive_identity) = add(additive_identity,multiply(X_180,additive_identity)),
inference(subst,[],[refute_0_40:[bind(X_30,$fot(multiply(X_180,additive_identity))),bind(X_31,$fot(additive_identity))]]) ).
cnf(refute_0_42,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_43,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_26,refute_0_42]) ).
cnf(refute_0_44,plain,
( add(multiply(X_180,additive_identity),additive_identity) != add(additive_identity,multiply(X_180,additive_identity))
| add(additive_identity,multiply(X_180,additive_identity)) != multiply(X_180,additive_identity)
| add(multiply(X_180,additive_identity),additive_identity) = multiply(X_180,additive_identity) ),
inference(subst,[],[refute_0_43:[bind(X0,$fot(add(multiply(X_180,additive_identity),additive_identity))),bind(Y0,$fot(add(additive_identity,multiply(X_180,additive_identity)))),bind(Z0,$fot(multiply(X_180,additive_identity)))]]) ).
cnf(refute_0_45,plain,
( add(additive_identity,multiply(X_180,additive_identity)) != multiply(X_180,additive_identity)
| add(multiply(X_180,additive_identity),additive_identity) = multiply(X_180,additive_identity) ),
inference(resolve,[$cnf( $equal(add(multiply(X_180,additive_identity),additive_identity),add(additive_identity,multiply(X_180,additive_identity))) )],[refute_0_41,refute_0_44]) ).
cnf(refute_0_46,plain,
add(multiply(X_180,additive_identity),additive_identity) = multiply(X_180,additive_identity),
inference(resolve,[$cnf( $equal(add(additive_identity,multiply(X_180,additive_identity)),multiply(X_180,additive_identity)) )],[refute_0_29,refute_0_45]) ).
cnf(refute_0_47,plain,
( add(multiply(X_180,additive_identity),additive_identity) != multiply(X_180,additive_identity)
| add(multiply(X_180,additive_identity),additive_identity) != additive_identity
| multiply(X_180,additive_identity) = additive_identity ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_180,additive_identity),additive_identity),additive_identity) ),[0],$fot(multiply(X_180,additive_identity))]]) ).
cnf(refute_0_48,plain,
( add(multiply(X_180,additive_identity),additive_identity) != additive_identity
| multiply(X_180,additive_identity) = additive_identity ),
inference(resolve,[$cnf( $equal(add(multiply(X_180,additive_identity),additive_identity),multiply(X_180,additive_identity)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
multiply(X_180,additive_identity) = additive_identity,
inference(resolve,[$cnf( $equal(add(multiply(X_180,additive_identity),additive_identity),additive_identity) )],[refute_0_17,refute_0_48]) ).
cnf(refute_0_50,plain,
multiply(X,additive_identity) = additive_identity,
inference(subst,[],[refute_0_49:[bind(X_180,$fot(X))]]) ).
cnf(refute_0_51,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_52,plain,
( ~ product(X,additive_identity,multiply(X,additive_identity))
| product(X,additive_identity,additive_identity) ),
inference(resolve,[$cnf( $equal(multiply(X,additive_identity),additive_identity) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
product(X,additive_identity,additive_identity),
inference(resolve,[$cnf( product(X,additive_identity,multiply(X,additive_identity)) )],[refute_0_0,refute_0_52]) ).
cnf(refute_0_54,plain,
product(a,additive_identity,additive_identity),
inference(subst,[],[refute_0_53:[bind(X,$fot(a))]]) ).
cnf(refute_0_55,plain,
$false,
inference(resolve,[$cnf( product(a,additive_identity,additive_identity) )],[refute_0_54,prove_a_times_0_is_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG001-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n021.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 : Mon May 30 15:57:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.45 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45
% 0.20/0.45 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.46
%------------------------------------------------------------------------------