TSTP Solution File: RNG039-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : RNG039-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 0.18s 0.44s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 32
% Syntax : Number of clauses : 117 ( 59 unt; 0 nHn; 84 RR)
% Number of literals : 200 ( 120 equ; 85 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 : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 129 ( 7 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(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(multiplication_is_well_defined,axiom,
( ~ product(X,Y,U)
| ~ product(X,Y,V)
| U = V ) ).
cnf(absorbtion1,axiom,
sum(A,add(A,B),B) ).
cnf(clause34,axiom,
add(A,A) = additive_identity ).
cnf(clause35,axiom,
multiply(A,A) = A ).
cnf(clause36,axiom,
multiply(a,b) = c ).
cnf(clause37,axiom,
multiply(b,a) = d ).
cnf(clause43,axiom,
product(A,multiply(A,B),multiply(A,B)) ).
cnf(clause44,axiom,
product(a,multiply(b,A),multiply(B,A)) ).
cnf(prove_c_equals_d,negated_conjecture,
c != d ).
cnf(refute_0_0,plain,
product(a,b,multiply(a,b)),
inference(subst,[],[closure_of_multiplication:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).
cnf(refute_0_1,plain,
product(a,multiply(b,b),multiply(X_25,b)),
inference(subst,[],[clause44:[bind(A,$fot(b)),bind(B,$fot(X_25))]]) ).
cnf(refute_0_2,plain,
multiply(b,b) = b,
inference(subst,[],[clause35:[bind(A,$fot(b))]]) ).
cnf(refute_0_3,plain,
( multiply(b,b) != b
| ~ product(a,multiply(b,b),multiply(X_25,b))
| product(a,b,multiply(X_25,b)) ),
introduced(tautology,[equality,[$cnf( product(a,multiply(b,b),multiply(X_25,b)) ),[1],$fot(b)]]) ).
cnf(refute_0_4,plain,
( ~ product(a,multiply(b,b),multiply(X_25,b))
| product(a,b,multiply(X_25,b)) ),
inference(resolve,[$cnf( $equal(multiply(b,b),b) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
product(a,b,multiply(X_25,b)),
inference(resolve,[$cnf( product(a,multiply(b,b),multiply(X_25,b)) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
product(a,b,multiply(additive_identity,b)),
inference(subst,[],[refute_0_5:[bind(X_25,$fot(additive_identity))]]) ).
cnf(refute_0_7,plain,
sum(X_40,add(X_40,X_38),X_38),
inference(subst,[],[absorbtion1:[bind(A,$fot(X_40)),bind(B,$fot(X_38))]]) ).
cnf(refute_0_8,plain,
( ~ sum(X_40,add(X_40,X_38),X_38)
| ~ sum(X_40,add(X_40,X_38),X_39)
| X_38 = X_39 ),
inference(subst,[],[addition_is_well_defined:[bind(U,$fot(X_38)),bind(V,$fot(X_39)),bind(X,$fot(X_40)),bind(Y,$fot(add(X_40,X_38)))]]) ).
cnf(refute_0_9,plain,
( ~ sum(X_40,add(X_40,X_38),X_39)
| X_38 = X_39 ),
inference(resolve,[$cnf( sum(X_40,add(X_40,X_38),X_38) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ sum(X_74,add(X_74,add(X_55,X_74)),X_73)
| add(X_55,X_74) = X_73 ),
inference(subst,[],[refute_0_9:[bind(X_38,$fot(add(X_55,X_74))),bind(X_39,$fot(X_73)),bind(X_40,$fot(X_74))]]) ).
cnf(refute_0_11,plain,
sum(add(X_57,X_55),X_57,add(add(X_57,X_55),X_57)),
inference(subst,[],[closure_of_addition:[bind(X,$fot(add(X_57,X_55))),bind(Y,$fot(X_57))]]) ).
cnf(refute_0_12,plain,
sum(X_31,add(X_31,X_33),X_33),
inference(subst,[],[absorbtion1:[bind(A,$fot(X_31)),bind(B,$fot(X_33))]]) ).
cnf(refute_0_13,plain,
( ~ sum(X_31,add(X_31,X_33),X_33)
| sum(add(X_31,X_33),X_31,X_33) ),
inference(subst,[],[commutativity_of_addition:[bind(X,$fot(X_31)),bind(Y,$fot(add(X_31,X_33))),bind(Z,$fot(X_33))]]) ).
cnf(refute_0_14,plain,
sum(add(X_31,X_33),X_31,X_33),
inference(resolve,[$cnf( sum(X_31,add(X_31,X_33),X_33) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
sum(add(X_41,X_38),X_41,X_38),
inference(subst,[],[refute_0_14:[bind(X_31,$fot(X_41)),bind(X_33,$fot(X_38))]]) ).
cnf(refute_0_16,plain,
( ~ sum(add(X_41,X_38),X_41,X_38)
| ~ sum(add(X_41,X_38),X_41,X_39)
| X_38 = X_39 ),
inference(subst,[],[addition_is_well_defined:[bind(U,$fot(X_38)),bind(V,$fot(X_39)),bind(X,$fot(add(X_41,X_38))),bind(Y,$fot(X_41))]]) ).
cnf(refute_0_17,plain,
( ~ sum(add(X_41,X_38),X_41,X_39)
| X_38 = X_39 ),
inference(resolve,[$cnf( sum(add(X_41,X_38),X_41,X_38) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ sum(add(X_57,X_55),X_57,add(add(X_57,X_55),X_57))
| X_55 = add(add(X_57,X_55),X_57) ),
inference(subst,[],[refute_0_17:[bind(X_38,$fot(X_55)),bind(X_39,$fot(add(add(X_57,X_55),X_57))),bind(X_41,$fot(X_57))]]) ).
cnf(refute_0_19,plain,
X_55 = add(add(X_57,X_55),X_57),
inference(resolve,[$cnf( sum(add(X_57,X_55),X_57,add(add(X_57,X_55),X_57)) )],[refute_0_11,refute_0_18]) ).
cnf(refute_0_20,plain,
X_55 = add(add(add(X_55,X_58),X_55),add(X_55,X_58)),
inference(subst,[],[refute_0_19:[bind(X_57,$fot(add(X_55,X_58)))]]) ).
cnf(refute_0_21,plain,
X_58 = add(add(X_55,X_58),X_55),
inference(subst,[],[refute_0_19:[bind(X_55,$fot(X_58)),bind(X_57,$fot(X_55))]]) ).
cnf(refute_0_22,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_23,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_24,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( X_58 != add(add(X_55,X_58),X_55)
| add(add(X_55,X_58),X_55) = X_58 ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(X_58)),bind(Y0,$fot(add(add(X_55,X_58),X_55)))]]) ).
cnf(refute_0_26,plain,
add(add(X_55,X_58),X_55) = X_58,
inference(resolve,[$cnf( $equal(X_58,add(add(X_55,X_58),X_55)) )],[refute_0_21,refute_0_25]) ).
cnf(refute_0_27,plain,
( X_55 != add(add(add(X_55,X_58),X_55),add(X_55,X_58))
| add(add(X_55,X_58),X_55) != X_58
| X_55 = add(X_58,add(X_55,X_58)) ),
introduced(tautology,[equality,[$cnf( $equal(X_55,add(add(add(X_55,X_58),X_55),add(X_55,X_58))) ),[1,0],$fot(X_58)]]) ).
cnf(refute_0_28,plain,
( X_55 != add(add(add(X_55,X_58),X_55),add(X_55,X_58))
| X_55 = add(X_58,add(X_55,X_58)) ),
inference(resolve,[$cnf( $equal(add(add(X_55,X_58),X_55),X_58) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
X_55 = add(X_58,add(X_55,X_58)),
inference(resolve,[$cnf( $equal(X_55,add(add(add(X_55,X_58),X_55),add(X_55,X_58))) )],[refute_0_20,refute_0_28]) ).
cnf(refute_0_30,plain,
X_55 = add(X_74,add(X_55,X_74)),
inference(subst,[],[refute_0_29:[bind(X_58,$fot(X_74))]]) ).
cnf(refute_0_31,plain,
( X_55 != add(X_74,add(X_55,X_74))
| add(X_74,add(X_55,X_74)) = X_55 ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(X_55)),bind(Y0,$fot(add(X_74,add(X_55,X_74))))]]) ).
cnf(refute_0_32,plain,
add(X_74,add(X_55,X_74)) = X_55,
inference(resolve,[$cnf( $equal(X_55,add(X_74,add(X_55,X_74))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
( add(X_74,add(X_55,X_74)) != X_55
| ~ sum(X_74,X_55,X_73)
| sum(X_74,add(X_74,add(X_55,X_74)),X_73) ),
introduced(tautology,[equality,[$cnf( ~ sum(X_74,add(X_74,add(X_55,X_74)),X_73) ),[1],$fot(X_55)]]) ).
cnf(refute_0_34,plain,
( ~ sum(X_74,X_55,X_73)
| sum(X_74,add(X_74,add(X_55,X_74)),X_73) ),
inference(resolve,[$cnf( $equal(add(X_74,add(X_55,X_74)),X_55) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ sum(X_74,X_55,X_73)
| add(X_55,X_74) = X_73 ),
inference(resolve,[$cnf( sum(X_74,add(X_74,add(X_55,X_74)),X_73) )],[refute_0_34,refute_0_10]) ).
cnf(refute_0_36,plain,
( ~ sum(multiply(additive_identity,X_171),multiply(additive_identity,X_171),multiply(additive_identity,X_171))
| add(multiply(additive_identity,X_171),multiply(additive_identity,X_171)) = multiply(additive_identity,X_171) ),
inference(subst,[],[refute_0_35:[bind(X_55,$fot(multiply(additive_identity,X_171))),bind(X_73,$fot(multiply(additive_identity,X_171))),bind(X_74,$fot(multiply(additive_identity,X_171)))]]) ).
cnf(refute_0_37,plain,
product(additive_identity,multiply(additive_identity,B),multiply(additive_identity,B)),
inference(subst,[],[clause43:[bind(A,$fot(additive_identity))]]) ).
cnf(refute_0_38,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(subst,[],[additive_identity1:[bind(X,$fot(additive_identity))]]) ).
cnf(refute_0_39,plain,
( ~ product(additive_identity,X_166,X_165)
| ~ sum(additive_identity,additive_identity,additive_identity)
| sum(X_165,X_165,X_165) ),
inference(subst,[],[distributivity3:[bind(V1,$fot(X_165)),bind(V2,$fot(X_165)),bind(V3,$fot(additive_identity)),bind(V4,$fot(X_165)),bind(X,$fot(X_166)),bind(Y,$fot(additive_identity)),bind(Z,$fot(additive_identity))]]) ).
cnf(refute_0_40,plain,
( ~ product(additive_identity,X_166,X_165)
| sum(X_165,X_165,X_165) ),
inference(resolve,[$cnf( sum(additive_identity,additive_identity,additive_identity) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( ~ product(additive_identity,multiply(additive_identity,B),multiply(additive_identity,B))
| sum(multiply(additive_identity,B),multiply(additive_identity,B),multiply(additive_identity,B)) ),
inference(subst,[],[refute_0_40:[bind(X_165,$fot(multiply(additive_identity,B))),bind(X_166,$fot(multiply(additive_identity,B)))]]) ).
cnf(refute_0_42,plain,
sum(multiply(additive_identity,B),multiply(additive_identity,B),multiply(additive_identity,B)),
inference(resolve,[$cnf( product(additive_identity,multiply(additive_identity,B),multiply(additive_identity,B)) )],[refute_0_37,refute_0_41]) ).
cnf(refute_0_43,plain,
sum(multiply(additive_identity,X_171),multiply(additive_identity,X_171),multiply(additive_identity,X_171)),
inference(subst,[],[refute_0_42:[bind(B,$fot(X_171))]]) ).
cnf(refute_0_44,plain,
add(multiply(additive_identity,X_171),multiply(additive_identity,X_171)) = multiply(additive_identity,X_171),
inference(resolve,[$cnf( sum(multiply(additive_identity,X_171),multiply(additive_identity,X_171),multiply(additive_identity,X_171)) )],[refute_0_43,refute_0_36]) ).
cnf(refute_0_45,plain,
add(multiply(additive_identity,X_171),multiply(additive_identity,X_171)) = additive_identity,
inference(subst,[],[clause34:[bind(A,$fot(multiply(additive_identity,X_171)))]]) ).
cnf(refute_0_46,plain,
( add(multiply(additive_identity,X_171),multiply(additive_identity,X_171)) != multiply(additive_identity,X_171)
| add(multiply(additive_identity,X_171),multiply(additive_identity,X_171)) != additive_identity
| additive_identity = multiply(additive_identity,X_171) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,X_171),multiply(additive_identity,X_171)),multiply(additive_identity,X_171)) ),[0],$fot(additive_identity)]]) ).
cnf(refute_0_47,plain,
( add(multiply(additive_identity,X_171),multiply(additive_identity,X_171)) != multiply(additive_identity,X_171)
| additive_identity = multiply(additive_identity,X_171) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_171),multiply(additive_identity,X_171)),additive_identity) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
additive_identity = multiply(additive_identity,X_171),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_171),multiply(additive_identity,X_171)),multiply(additive_identity,X_171)) )],[refute_0_44,refute_0_47]) ).
cnf(refute_0_49,plain,
additive_identity = multiply(additive_identity,b),
inference(subst,[],[refute_0_48:[bind(X_171,$fot(b))]]) ).
cnf(refute_0_50,plain,
( additive_identity != multiply(additive_identity,b)
| multiply(additive_identity,b) = additive_identity ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(additive_identity)),bind(Y0,$fot(multiply(additive_identity,b)))]]) ).
cnf(refute_0_51,plain,
multiply(additive_identity,b) = additive_identity,
inference(resolve,[$cnf( $equal(additive_identity,multiply(additive_identity,b)) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
( multiply(additive_identity,b) != additive_identity
| ~ product(a,b,multiply(additive_identity,b))
| product(a,b,additive_identity) ),
introduced(tautology,[equality,[$cnf( product(a,b,multiply(additive_identity,b)) ),[2],$fot(additive_identity)]]) ).
cnf(refute_0_53,plain,
( ~ product(a,b,multiply(additive_identity,b))
| product(a,b,additive_identity) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,b),additive_identity) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
product(a,b,additive_identity),
inference(resolve,[$cnf( product(a,b,multiply(additive_identity,b)) )],[refute_0_6,refute_0_53]) ).
cnf(refute_0_55,plain,
( ~ product(a,b,X_195)
| ~ product(a,b,additive_identity)
| additive_identity = X_195 ),
inference(subst,[],[multiplication_is_well_defined:[bind(U,$fot(additive_identity)),bind(V,$fot(X_195)),bind(X,$fot(a)),bind(Y,$fot(b))]]) ).
cnf(refute_0_56,plain,
( ~ product(a,b,X_195)
| additive_identity = X_195 ),
inference(resolve,[$cnf( product(a,b,additive_identity) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
( ~ product(a,b,multiply(a,b))
| additive_identity = multiply(a,b) ),
inference(subst,[],[refute_0_56:[bind(X_195,$fot(multiply(a,b)))]]) ).
cnf(refute_0_58,plain,
additive_identity = multiply(a,b),
inference(resolve,[$cnf( product(a,b,multiply(a,b)) )],[refute_0_0,refute_0_57]) ).
cnf(refute_0_59,plain,
( multiply(a,b) != c
| additive_identity != multiply(a,b)
| additive_identity = c ),
introduced(tautology,[equality,[$cnf( $equal(additive_identity,multiply(a,b)) ),[1],$fot(c)]]) ).
cnf(refute_0_60,plain,
( additive_identity != multiply(a,b)
| additive_identity = c ),
inference(resolve,[$cnf( $equal(multiply(a,b),c) )],[clause36,refute_0_59]) ).
cnf(refute_0_61,plain,
additive_identity = c,
inference(resolve,[$cnf( $equal(additive_identity,multiply(a,b)) )],[refute_0_58,refute_0_60]) ).
cnf(refute_0_62,plain,
( additive_identity != c
| c = additive_identity ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(additive_identity)),bind(Y0,$fot(c))]]) ).
cnf(refute_0_63,plain,
c = additive_identity,
inference(resolve,[$cnf( $equal(additive_identity,c) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
( additive_identity != d
| c != additive_identity
| c = d ),
introduced(tautology,[equality,[$cnf( $equal(c,additive_identity) ),[1],$fot(d)]]) ).
cnf(refute_0_65,plain,
( additive_identity != d
| c = d ),
inference(resolve,[$cnf( $equal(c,additive_identity) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
( additive_identity != multiply(additive_identity,X_171)
| multiply(additive_identity,X_171) = additive_identity ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(additive_identity)),bind(Y0,$fot(multiply(additive_identity,X_171)))]]) ).
cnf(refute_0_67,plain,
multiply(additive_identity,X_171) = additive_identity,
inference(resolve,[$cnf( $equal(additive_identity,multiply(additive_identity,X_171)) )],[refute_0_48,refute_0_66]) ).
cnf(refute_0_68,plain,
multiply(additive_identity,a) = additive_identity,
inference(subst,[],[refute_0_67:[bind(X_171,$fot(a))]]) ).
cnf(refute_0_69,plain,
product(a,multiply(b,X_24),multiply(X_24,X_24)),
inference(subst,[],[clause44:[bind(A,$fot(X_24)),bind(B,$fot(X_24))]]) ).
cnf(refute_0_70,plain,
multiply(X_24,X_24) = X_24,
inference(subst,[],[clause35:[bind(A,$fot(X_24))]]) ).
cnf(refute_0_71,plain,
( multiply(X_24,X_24) != X_24
| ~ product(a,multiply(b,X_24),multiply(X_24,X_24))
| product(a,multiply(b,X_24),X_24) ),
introduced(tautology,[equality,[$cnf( product(a,multiply(b,X_24),multiply(X_24,X_24)) ),[2],$fot(X_24)]]) ).
cnf(refute_0_72,plain,
( ~ product(a,multiply(b,X_24),multiply(X_24,X_24))
| product(a,multiply(b,X_24),X_24) ),
inference(resolve,[$cnf( $equal(multiply(X_24,X_24),X_24) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
product(a,multiply(b,X_24),X_24),
inference(resolve,[$cnf( product(a,multiply(b,X_24),multiply(X_24,X_24)) )],[refute_0_69,refute_0_72]) ).
cnf(refute_0_74,plain,
product(a,multiply(b,b),b),
inference(subst,[],[refute_0_73:[bind(X_24,$fot(b))]]) ).
cnf(refute_0_75,plain,
( multiply(b,b) != b
| ~ product(a,multiply(b,b),b)
| product(a,b,b) ),
introduced(tautology,[equality,[$cnf( product(a,multiply(b,b),b) ),[1],$fot(b)]]) ).
cnf(refute_0_76,plain,
( ~ product(a,multiply(b,b),b)
| product(a,b,b) ),
inference(resolve,[$cnf( $equal(multiply(b,b),b) )],[refute_0_2,refute_0_75]) ).
cnf(refute_0_77,plain,
product(a,b,b),
inference(resolve,[$cnf( product(a,multiply(b,b),b) )],[refute_0_74,refute_0_76]) ).
cnf(refute_0_78,plain,
( ~ product(a,b,b)
| additive_identity = b ),
inference(subst,[],[refute_0_56:[bind(X_195,$fot(b))]]) ).
cnf(refute_0_79,plain,
additive_identity = b,
inference(resolve,[$cnf( product(a,b,b) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
( additive_identity != b
| b = additive_identity ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(additive_identity)),bind(Y0,$fot(b))]]) ).
cnf(refute_0_81,plain,
b = additive_identity,
inference(resolve,[$cnf( $equal(additive_identity,b) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
multiply(b,a) = multiply(b,a),
introduced(tautology,[refl,[$fot(multiply(b,a))]]) ).
cnf(refute_0_83,plain,
( multiply(b,a) != multiply(b,a)
| b != additive_identity
| multiply(b,a) = multiply(additive_identity,a) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(b,a),multiply(b,a)) ),[1,0],$fot(additive_identity)]]) ).
cnf(refute_0_84,plain,
( b != additive_identity
| multiply(b,a) = multiply(additive_identity,a) ),
inference(resolve,[$cnf( $equal(multiply(b,a),multiply(b,a)) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
multiply(b,a) = multiply(additive_identity,a),
inference(resolve,[$cnf( $equal(b,additive_identity) )],[refute_0_81,refute_0_84]) ).
cnf(refute_0_86,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_87,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_24,refute_0_86]) ).
cnf(refute_0_88,plain,
( multiply(additive_identity,a) != additive_identity
| multiply(b,a) != multiply(additive_identity,a)
| multiply(b,a) = additive_identity ),
inference(subst,[],[refute_0_87:[bind(X0,$fot(multiply(b,a))),bind(Y0,$fot(multiply(additive_identity,a))),bind(Z0,$fot(additive_identity))]]) ).
cnf(refute_0_89,plain,
( multiply(additive_identity,a) != additive_identity
| multiply(b,a) = additive_identity ),
inference(resolve,[$cnf( $equal(multiply(b,a),multiply(additive_identity,a)) )],[refute_0_85,refute_0_88]) ).
cnf(refute_0_90,plain,
multiply(b,a) = additive_identity,
inference(resolve,[$cnf( $equal(multiply(additive_identity,a),additive_identity) )],[refute_0_68,refute_0_89]) ).
cnf(refute_0_91,plain,
( multiply(b,a) != additive_identity
| multiply(b,a) != d
| additive_identity = d ),
introduced(tautology,[equality,[$cnf( $equal(multiply(b,a),d) ),[0],$fot(additive_identity)]]) ).
cnf(refute_0_92,plain,
( multiply(b,a) != d
| additive_identity = d ),
inference(resolve,[$cnf( $equal(multiply(b,a),additive_identity) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
additive_identity = d,
inference(resolve,[$cnf( $equal(multiply(b,a),d) )],[clause37,refute_0_92]) ).
cnf(refute_0_94,plain,
( additive_identity != d
| d = additive_identity ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(additive_identity)),bind(Y0,$fot(d))]]) ).
cnf(refute_0_95,plain,
d = additive_identity,
inference(resolve,[$cnf( $equal(additive_identity,d) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
( additive_identity != additive_identity
| d != additive_identity
| additive_identity = d ),
introduced(tautology,[equality,[$cnf( ~ $equal(additive_identity,d) ),[1],$fot(additive_identity)]]) ).
cnf(refute_0_97,plain,
( additive_identity != additive_identity
| additive_identity = d ),
inference(resolve,[$cnf( $equal(d,additive_identity) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
( additive_identity != additive_identity
| c = d ),
inference(resolve,[$cnf( $equal(additive_identity,d) )],[refute_0_97,refute_0_65]) ).
cnf(refute_0_99,plain,
additive_identity != additive_identity,
inference(resolve,[$cnf( $equal(c,d) )],[refute_0_98,prove_c_equals_d]) ).
cnf(refute_0_100,plain,
additive_identity = additive_identity,
introduced(tautology,[refl,[$fot(additive_identity)]]) ).
cnf(refute_0_101,plain,
$false,
inference(resolve,[$cnf( $equal(additive_identity,additive_identity) )],[refute_0_100,refute_0_99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : RNG039-1 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n027.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 11:27:46 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.44 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44
% 0.18/0.44 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.45
%------------------------------------------------------------------------------