%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : RNG038-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 20:35:51 EDT 2022
% Result : Unsatisfiable 0.19s 0.51s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 15
% Syntax : Number of clauses : 70 ( 35 unt; 0 nHn; 38 RR)
% Number of literals : 121 ( 46 equ; 53 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 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 : 99 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(additive_identity2,axiom,
sum(X,additive_identity,X) ).
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(distributivity3,axiom,
( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| sum(V1,V2,V4) ) ).
cnf(addition_is_well_defined,axiom,
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| U = V ) ).
cnf(some_property,hypothesis,
( X != additive_identity
| product(X,h(X,Y),Y) ) ).
cnf(prove_b_is_additive_identity,negated_conjecture,
b != additive_identity ).
cnf(refute_0_0,plain,
sum(X_135,X_136,add(X_135,X_136)),
inference(subst,[],[closure_of_addition:[bind(X,$fot(X_135)),bind(Y,$fot(X_136))]]) ).
cnf(refute_0_1,plain,
( ~ sum(X_135,X_136,X_134)
| ~ sum(X_135,X_136,add(X_135,X_136))
| add(X_135,X_136) = X_134 ),
inference(subst,[],[addition_is_well_defined:[bind(U,$fot(add(X_135,X_136))),bind(V,$fot(X_134)),bind(X,$fot(X_135)),bind(Y,$fot(X_136))]]) ).
cnf(refute_0_2,plain,
( ~ sum(X_135,X_136,X_134)
| add(X_135,X_136) = X_134 ),
inference(resolve,[$cnf( sum(X_135,X_136,add(X_135,X_136)) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ sum(X_186,additive_identity,additive_identity)
| add(X_186,additive_identity) = additive_identity ),
inference(subst,[],[refute_0_2:[bind(X_134,$fot(additive_identity)),bind(X_135,$fot(X_186)),bind(X_136,$fot(additive_identity))]]) ).
cnf(refute_0_4,plain,
( additive_identity != additive_identity
| product(additive_identity,h(additive_identity,Y),Y) ),
inference(subst,[],[some_property:[bind(X,$fot(additive_identity))]]) ).
cnf(refute_0_5,plain,
additive_identity = additive_identity,
introduced(tautology,[refl,[$fot(additive_identity)]]) ).
cnf(refute_0_6,plain,
product(additive_identity,h(additive_identity,Y),Y),
inference(resolve,[$cnf( $equal(additive_identity,additive_identity) )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
product(additive_identity,h(additive_identity,X_105),X_105),
inference(subst,[],[refute_0_6:[bind(Y,$fot(X_105))]]) ).
cnf(refute_0_8,plain,
( ~ product(additive_identity,h(additive_identity,X_105),X_105)
| ~ sum(additive_identity,additive_identity,additive_identity)
| sum(X_105,X_105,X_105) ),
inference(subst,[],[distributivity3:[bind(V1,$fot(X_105)),bind(V2,$fot(X_105)),bind(V3,$fot(additive_identity)),bind(V4,$fot(X_105)),bind(X,$fot(h(additive_identity,X_105))),bind(Y,$fot(additive_identity)),bind(Z,$fot(additive_identity))]]) ).
cnf(refute_0_9,plain,
( ~ sum(additive_identity,additive_identity,additive_identity)
| sum(X_105,X_105,X_105) ),
inference(resolve,[$cnf( product(additive_identity,h(additive_identity,X_105),X_105) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(subst,[],[additive_identity2:[bind(X,$fot(additive_identity))]]) ).
cnf(refute_0_11,plain,
sum(X_105,X_105,X_105),
inference(resolve,[$cnf( sum(additive_identity,additive_identity,additive_identity) )],[refute_0_10,refute_0_9]) ).
cnf(refute_0_12,plain,
sum(X_185,X_185,X_185),
inference(subst,[],[refute_0_11:[bind(X_105,$fot(X_185))]]) ).
cnf(refute_0_13,plain,
sum(X_180,additive_inverse(X_180),additive_identity),
inference(subst,[],[right_inverse:[bind(X,$fot(X_180))]]) ).
cnf(refute_0_14,plain,
( ~ sum(X_179,X_180,X_180)
| ~ sum(X_180,additive_inverse(X_180),additive_identity)
| sum(X_179,additive_identity,additive_identity) ),
inference(subst,[],[associativity_of_addition1:[bind(U,$fot(X_180)),bind(V,$fot(additive_identity)),bind(W,$fot(additive_identity)),bind(X,$fot(X_179)),bind(Y,$fot(X_180)),bind(Z,$fot(additive_inverse(X_180)))]]) ).
cnf(refute_0_15,plain,
( ~ sum(X_179,X_180,X_180)
| sum(X_179,additive_identity,additive_identity) ),
inference(resolve,[$cnf( sum(X_180,additive_inverse(X_180),additive_identity) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ sum(X_185,X_185,X_185)
| sum(X_185,additive_identity,additive_identity) ),
inference(subst,[],[refute_0_15:[bind(X_179,$fot(X_185)),bind(X_180,$fot(X_185))]]) ).
cnf(refute_0_17,plain,
sum(X_185,additive_identity,additive_identity),
inference(resolve,[$cnf( sum(X_185,X_185,X_185) )],[refute_0_12,refute_0_16]) ).
cnf(refute_0_18,plain,
sum(X_186,additive_identity,additive_identity),
inference(subst,[],[refute_0_17:[bind(X_185,$fot(X_186))]]) ).
cnf(refute_0_19,plain,
add(X_186,additive_identity) = additive_identity,
inference(resolve,[$cnf( sum(X_186,additive_identity,additive_identity) )],[refute_0_18,refute_0_3]) ).
cnf(refute_0_20,plain,
sum(X_145,additive_identity,add(X_145,additive_identity)),
inference(subst,[],[closure_of_addition:[bind(X,$fot(X_145)),bind(Y,$fot(additive_identity))]]) ).
cnf(refute_0_21,plain,
sum(X_9,X_10,add(X_9,X_10)),
inference(subst,[],[closure_of_addition:[bind(X,$fot(X_9)),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_22,plain,
( ~ sum(X_9,X_10,add(X_9,X_10))
| sum(X_10,X_9,add(X_9,X_10)) ),
inference(subst,[],[commutativity_of_addition:[bind(X,$fot(X_9)),bind(Y,$fot(X_10)),bind(Z,$fot(add(X_9,X_10)))]]) ).
cnf(refute_0_23,plain,
sum(X_10,X_9,add(X_9,X_10)),
inference(resolve,[$cnf( sum(X_9,X_10,add(X_9,X_10)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
sum(additive_identity,additive_identity,add(additive_identity,additive_identity)),
inference(subst,[],[refute_0_23:[bind(X_10,$fot(additive_identity)),bind(X_9,$fot(additive_identity))]]) ).
cnf(refute_0_25,plain,
sum(X_25,additive_identity,X_25),
inference(subst,[],[additive_identity2:[bind(X,$fot(X_25))]]) ).
cnf(refute_0_26,plain,
( ~ sum(X_25,additive_identity,X_25)
| ~ sum(additive_identity,additive_identity,X_24)
| sum(X_25,X_24,X_25) ),
inference(subst,[],[associativity_of_addition1:[bind(U,$fot(X_25)),bind(V,$fot(X_24)),bind(W,$fot(X_25)),bind(X,$fot(X_25)),bind(Y,$fot(additive_identity)),bind(Z,$fot(additive_identity))]]) ).
cnf(refute_0_27,plain,
( ~ sum(additive_identity,additive_identity,X_24)
| sum(X_25,X_24,X_25) ),
inference(resolve,[$cnf( sum(X_25,additive_identity,X_25) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ sum(additive_identity,additive_identity,add(additive_identity,additive_identity))
| sum(X_29,add(additive_identity,additive_identity),X_29) ),
inference(subst,[],[refute_0_27:[bind(X_24,$fot(add(additive_identity,additive_identity))),bind(X_25,$fot(X_29))]]) ).
cnf(refute_0_29,plain,
sum(X_29,add(additive_identity,additive_identity),X_29),
inference(resolve,[$cnf( sum(additive_identity,additive_identity,add(additive_identity,additive_identity)) )],[refute_0_24,refute_0_28]) ).
cnf(refute_0_30,plain,
sum(X_133,add(additive_identity,additive_identity),X_133),
inference(subst,[],[refute_0_29:[bind(X_29,$fot(X_133))]]) ).
cnf(refute_0_31,plain,
( ~ sum(X_133,add(additive_identity,additive_identity),X_133)
| ~ sum(X_133,add(additive_identity,additive_identity),X_134)
| X_133 = X_134 ),
inference(subst,[],[addition_is_well_defined:[bind(U,$fot(X_133)),bind(V,$fot(X_134)),bind(X,$fot(X_133)),bind(Y,$fot(add(additive_identity,additive_identity)))]]) ).
cnf(refute_0_32,plain,
( ~ sum(X_133,add(additive_identity,additive_identity),X_134)
| X_133 = X_134 ),
inference(resolve,[$cnf( sum(X_133,add(additive_identity,additive_identity),X_133) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
sum(X_142,X_142,add(X_142,X_142)),
inference(subst,[],[refute_0_23:[bind(X_10,$fot(X_142)),bind(X_9,$fot(X_142))]]) ).
cnf(refute_0_34,plain,
sum(X_133,X_133,X_133),
inference(subst,[],[refute_0_11:[bind(X_105,$fot(X_133))]]) ).
cnf(refute_0_35,plain,
( ~ sum(X_133,X_133,X_133)
| ~ sum(X_133,X_133,X_134)
| X_133 = X_134 ),
inference(subst,[],[addition_is_well_defined:[bind(U,$fot(X_133)),bind(V,$fot(X_134)),bind(X,$fot(X_133)),bind(Y,$fot(X_133))]]) ).
cnf(refute_0_36,plain,
( ~ sum(X_133,X_133,X_134)
| X_133 = X_134 ),
inference(resolve,[$cnf( sum(X_133,X_133,X_133) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( ~ sum(X_142,X_142,add(X_142,X_142))
| X_142 = add(X_142,X_142) ),
inference(subst,[],[refute_0_36:[bind(X_133,$fot(X_142)),bind(X_134,$fot(add(X_142,X_142)))]]) ).
cnf(refute_0_38,plain,
X_142 = add(X_142,X_142),
inference(resolve,[$cnf( sum(X_142,X_142,add(X_142,X_142)) )],[refute_0_33,refute_0_37]) ).
cnf(refute_0_39,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_40,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_41,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( X_142 != add(X_142,X_142)
| add(X_142,X_142) = X_142 ),
inference(subst,[],[refute_0_41:[bind(X0,$fot(X_142)),bind(Y0,$fot(add(X_142,X_142)))]]) ).
cnf(refute_0_43,plain,
add(X_142,X_142) = X_142,
inference(resolve,[$cnf( $equal(X_142,add(X_142,X_142)) )],[refute_0_38,refute_0_42]) ).
cnf(refute_0_44,plain,
add(additive_identity,additive_identity) = additive_identity,
inference(subst,[],[refute_0_43:[bind(X_142,$fot(additive_identity))]]) ).
cnf(refute_0_45,plain,
( add(additive_identity,additive_identity) != additive_identity
| ~ sum(X_133,additive_identity,X_134)
| sum(X_133,add(additive_identity,additive_identity),X_134) ),
introduced(tautology,[equality,[$cnf( ~ sum(X_133,add(additive_identity,additive_identity),X_134) ),[1],$fot(additive_identity)]]) ).
cnf(refute_0_46,plain,
( ~ sum(X_133,additive_identity,X_134)
| sum(X_133,add(additive_identity,additive_identity),X_134) ),
inference(resolve,[$cnf( $equal(add(additive_identity,additive_identity),additive_identity) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
( ~ sum(X_133,additive_identity,X_134)
| X_133 = X_134 ),
inference(resolve,[$cnf( sum(X_133,add(additive_identity,additive_identity),X_134) )],[refute_0_46,refute_0_32]) ).
cnf(refute_0_48,plain,
( ~ sum(X_145,additive_identity,add(X_145,additive_identity))
| X_145 = add(X_145,additive_identity) ),
inference(subst,[],[refute_0_47:[bind(X_133,$fot(X_145)),bind(X_134,$fot(add(X_145,additive_identity)))]]) ).
cnf(refute_0_49,plain,
X_145 = add(X_145,additive_identity),
inference(resolve,[$cnf( sum(X_145,additive_identity,add(X_145,additive_identity)) )],[refute_0_20,refute_0_48]) ).
cnf(refute_0_50,plain,
( X_145 != add(X_145,additive_identity)
| add(X_145,additive_identity) = X_145 ),
inference(subst,[],[refute_0_41:[bind(X0,$fot(X_145)),bind(Y0,$fot(add(X_145,additive_identity)))]]) ).
cnf(refute_0_51,plain,
add(X_145,additive_identity) = X_145,
inference(resolve,[$cnf( $equal(X_145,add(X_145,additive_identity)) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
add(X_186,additive_identity) = X_186,
inference(subst,[],[refute_0_51:[bind(X_145,$fot(X_186))]]) ).
cnf(refute_0_53,plain,
( add(X_186,additive_identity) != X_186
| add(X_186,additive_identity) != additive_identity
| X_186 = additive_identity ),
introduced(tautology,[equality,[$cnf( $equal(add(X_186,additive_identity),additive_identity) ),[0],$fot(X_186)]]) ).
cnf(refute_0_54,plain,
( add(X_186,additive_identity) != additive_identity
| X_186 = additive_identity ),
inference(resolve,[$cnf( $equal(add(X_186,additive_identity),X_186) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
X_186 = additive_identity,
inference(resolve,[$cnf( $equal(add(X_186,additive_identity),additive_identity) )],[refute_0_19,refute_0_54]) ).
cnf(refute_0_56,plain,
b = additive_identity,
inference(subst,[],[refute_0_55:[bind(X_186,$fot(b))]]) ).
cnf(refute_0_57,plain,
( additive_identity != additive_identity
| b != additive_identity
| b = additive_identity ),
introduced(tautology,[equality,[$cnf( $equal(b,additive_identity) ),[1],$fot(additive_identity)]]) ).
cnf(refute_0_58,plain,
( additive_identity != additive_identity
| b = additive_identity ),
inference(resolve,[$cnf( $equal(b,additive_identity) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
additive_identity != additive_identity,
inference(resolve,[$cnf( $equal(b,additive_identity) )],[refute_0_58,prove_b_is_additive_identity]) ).
cnf(refute_0_60,plain,
$false,
inference(resolve,[$cnf( $equal(additive_identity,additive_identity) )],[refute_0_5,refute_0_59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG038-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n022.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 May 30 08:35:52 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.51 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.51
% 0.19/0.51 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.51
%------------------------------------------------------------------------------