TSTP Solution File: GRP001-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP001-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n016.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 10:32:07 EDT 2022
% Result : Unsatisfiable 0.21s 0.49s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 41
% Syntax : Number of clauses : 239 ( 106 unt; 0 nHn; 201 RR)
% Number of literals : 432 ( 145 equ; 194 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 189 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
product(identity,X,X) ).
cnf(right_identity,axiom,
product(X,identity,X) ).
cnf(left_inverse,axiom,
product(inverse(X),X,identity) ).
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(associativity1,axiom,
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(U,Z,W)
| product(X,V,W) ) ).
cnf(associativity2,axiom,
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W)
| product(U,Z,W) ) ).
cnf(square_element,hypothesis,
product(X,X,identity) ).
cnf(a_times_b_is_c,negated_conjecture,
product(a,b,c) ).
cnf(prove_b_times_a_is_c,negated_conjecture,
~ product(b,a,c) ).
cnf(refute_0_0,plain,
product(b,X_237,multiply(b,X_237)),
inference(subst,[],[total_function1:[bind(X,$fot(b)),bind(Y,$fot(X_237))]]) ).
cnf(refute_0_1,plain,
product(multiply(X_135,a),b,multiply(multiply(X_135,a),b)),
inference(subst,[],[total_function1:[bind(X,$fot(multiply(X_135,a))),bind(Y,$fot(b))]]) ).
cnf(refute_0_2,plain,
product(X_58,X_59,multiply(X_58,X_59)),
inference(subst,[],[total_function1:[bind(X,$fot(X_58)),bind(Y,$fot(X_59))]]) ).
cnf(refute_0_3,plain,
( ~ product(X_58,X_59,X_60)
| ~ product(X_58,X_59,multiply(X_58,X_59))
| X_60 = multiply(X_58,X_59) ),
inference(subst,[],[total_function2:[bind(W,$fot(multiply(X_58,X_59))),bind(X,$fot(X_58)),bind(Y,$fot(X_59)),bind(Z,$fot(X_60))]]) ).
cnf(refute_0_4,plain,
( ~ product(X_58,X_59,X_60)
| X_60 = multiply(X_58,X_59) ),
inference(resolve,[$cnf( product(X_58,X_59,multiply(X_58,X_59)) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ product(X_134,c,multiply(multiply(X_134,a),b))
| multiply(multiply(X_134,a),b) = multiply(X_134,c) ),
inference(subst,[],[refute_0_4:[bind(X_58,$fot(X_134)),bind(X_59,$fot(c)),bind(X_60,$fot(multiply(multiply(X_134,a),b)))]]) ).
cnf(refute_0_6,plain,
product(X_133,a,multiply(X_133,a)),
inference(subst,[],[total_function1:[bind(X,$fot(X_133)),bind(Y,$fot(a))]]) ).
cnf(refute_0_7,plain,
product(X_120,b,multiply(X_120,b)),
inference(subst,[],[total_function1:[bind(X,$fot(X_120)),bind(Y,$fot(b))]]) ).
cnf(refute_0_8,plain,
( ~ product(X_105,b,X_107)
| ~ product(X_108,a,X_105)
| ~ product(a,b,c)
| product(X_108,c,X_107) ),
inference(subst,[],[associativity1:[bind(U,$fot(X_105)),bind(V,$fot(c)),bind(W,$fot(X_107)),bind(X,$fot(X_108)),bind(Y,$fot(a)),bind(Z,$fot(b))]]) ).
cnf(refute_0_9,plain,
( ~ product(X_105,b,X_107)
| ~ product(X_108,a,X_105)
| product(X_108,c,X_107) ),
inference(resolve,[$cnf( product(a,b,c) )],[a_times_b_is_c,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ product(X_120,b,multiply(X_120,b))
| ~ product(X_122,a,X_120)
| product(X_122,c,multiply(X_120,b)) ),
inference(subst,[],[refute_0_9:[bind(X_105,$fot(X_120)),bind(X_107,$fot(multiply(X_120,b))),bind(X_108,$fot(X_122))]]) ).
cnf(refute_0_11,plain,
( ~ product(X_122,a,X_120)
| product(X_122,c,multiply(X_120,b)) ),
inference(resolve,[$cnf( product(X_120,b,multiply(X_120,b)) )],[refute_0_7,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ product(X_133,a,multiply(X_133,a))
| product(X_133,c,multiply(multiply(X_133,a),b)) ),
inference(subst,[],[refute_0_11:[bind(X_120,$fot(multiply(X_133,a))),bind(X_122,$fot(X_133))]]) ).
cnf(refute_0_13,plain,
product(X_133,c,multiply(multiply(X_133,a),b)),
inference(resolve,[$cnf( product(X_133,a,multiply(X_133,a)) )],[refute_0_6,refute_0_12]) ).
cnf(refute_0_14,plain,
product(X_134,c,multiply(multiply(X_134,a),b)),
inference(subst,[],[refute_0_13:[bind(X_133,$fot(X_134))]]) ).
cnf(refute_0_15,plain,
multiply(multiply(X_134,a),b) = multiply(X_134,c),
inference(resolve,[$cnf( product(X_134,c,multiply(multiply(X_134,a),b)) )],[refute_0_14,refute_0_5]) ).
cnf(refute_0_16,plain,
multiply(multiply(X_135,a),b) = multiply(X_135,c),
inference(subst,[],[refute_0_15:[bind(X_134,$fot(X_135))]]) ).
cnf(refute_0_17,plain,
( multiply(multiply(X_135,a),b) != multiply(X_135,c)
| ~ product(multiply(X_135,a),b,multiply(multiply(X_135,a),b))
| product(multiply(X_135,a),b,multiply(X_135,c)) ),
introduced(tautology,[equality,[$cnf( product(multiply(X_135,a),b,multiply(multiply(X_135,a),b)) ),[2],$fot(multiply(X_135,c))]]) ).
cnf(refute_0_18,plain,
( ~ product(multiply(X_135,a),b,multiply(multiply(X_135,a),b))
| product(multiply(X_135,a),b,multiply(X_135,c)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_135,a),b),multiply(X_135,c)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
product(multiply(X_135,a),b,multiply(X_135,c)),
inference(resolve,[$cnf( product(multiply(X_135,a),b,multiply(multiply(X_135,a),b)) )],[refute_0_1,refute_0_18]) ).
cnf(refute_0_20,plain,
product(multiply(c,a),b,multiply(c,c)),
inference(subst,[],[refute_0_19:[bind(X_135,$fot(c))]]) ).
cnf(refute_0_21,plain,
product(X_68,X_68,multiply(X_68,X_68)),
inference(subst,[],[total_function1:[bind(X,$fot(X_68)),bind(Y,$fot(X_68))]]) ).
cnf(refute_0_22,plain,
product(X_59,X_59,identity),
inference(subst,[],[square_element:[bind(X,$fot(X_59))]]) ).
cnf(refute_0_23,plain,
( ~ product(X_59,X_59,X_60)
| ~ product(X_59,X_59,identity)
| X_60 = identity ),
inference(subst,[],[total_function2:[bind(W,$fot(identity)),bind(X,$fot(X_59)),bind(Y,$fot(X_59)),bind(Z,$fot(X_60))]]) ).
cnf(refute_0_24,plain,
( ~ product(X_59,X_59,X_60)
| X_60 = identity ),
inference(resolve,[$cnf( product(X_59,X_59,identity) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ product(X_68,X_68,multiply(X_68,X_68))
| multiply(X_68,X_68) = identity ),
inference(subst,[],[refute_0_24:[bind(X_59,$fot(X_68)),bind(X_60,$fot(multiply(X_68,X_68)))]]) ).
cnf(refute_0_26,plain,
multiply(X_68,X_68) = identity,
inference(resolve,[$cnf( product(X_68,X_68,multiply(X_68,X_68)) )],[refute_0_21,refute_0_25]) ).
cnf(refute_0_27,plain,
multiply(c,c) = identity,
inference(subst,[],[refute_0_26:[bind(X_68,$fot(c))]]) ).
cnf(refute_0_28,plain,
( multiply(c,c) != identity
| ~ product(multiply(c,a),b,multiply(c,c))
| product(multiply(c,a),b,identity) ),
introduced(tautology,[equality,[$cnf( product(multiply(c,a),b,multiply(c,c)) ),[2],$fot(identity)]]) ).
cnf(refute_0_29,plain,
( ~ product(multiply(c,a),b,multiply(c,c))
| product(multiply(c,a),b,identity) ),
inference(resolve,[$cnf( $equal(multiply(c,c),identity) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
product(multiply(c,a),b,identity),
inference(resolve,[$cnf( product(multiply(c,a),b,multiply(c,c)) )],[refute_0_20,refute_0_29]) ).
cnf(refute_0_31,plain,
product(identity,X_107,X_107),
inference(subst,[],[left_identity:[bind(X,$fot(X_107))]]) ).
cnf(refute_0_32,plain,
( ~ product(X_108,X_109,identity)
| ~ product(X_109,X_107,X_106)
| ~ product(identity,X_107,X_107)
| product(X_108,X_106,X_107) ),
inference(subst,[],[associativity1:[bind(U,$fot(identity)),bind(V,$fot(X_106)),bind(W,$fot(X_107)),bind(X,$fot(X_108)),bind(Y,$fot(X_109)),bind(Z,$fot(X_107))]]) ).
cnf(refute_0_33,plain,
( ~ product(X_108,X_109,identity)
| ~ product(X_109,X_107,X_106)
| product(X_108,X_106,X_107) ),
inference(resolve,[$cnf( product(identity,X_107,X_107) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
( ~ product(multiply(c,a),b,identity)
| ~ product(b,X_193,X_192)
| product(multiply(c,a),X_192,X_193) ),
inference(subst,[],[refute_0_33:[bind(X_106,$fot(X_192)),bind(X_107,$fot(X_193)),bind(X_108,$fot(multiply(c,a))),bind(X_109,$fot(b))]]) ).
cnf(refute_0_35,plain,
( ~ product(b,X_193,X_192)
| product(multiply(c,a),X_192,X_193) ),
inference(resolve,[$cnf( product(multiply(c,a),b,identity) )],[refute_0_30,refute_0_34]) ).
cnf(refute_0_36,plain,
( ~ product(multiply(c,a),identity,b)
| b = multiply(multiply(c,a),identity) ),
inference(subst,[],[refute_0_4:[bind(X_58,$fot(multiply(c,a))),bind(X_59,$fot(identity)),bind(X_60,$fot(b))]]) ).
cnf(refute_0_37,plain,
product(multiply(c,a),multiply(c,a),identity),
inference(subst,[],[square_element:[bind(X,$fot(multiply(c,a)))]]) ).
cnf(refute_0_38,plain,
( ~ product(X_194,multiply(c,a),identity)
| ~ product(multiply(c,a),b,identity)
| product(X_194,identity,b) ),
inference(subst,[],[refute_0_33:[bind(X_106,$fot(identity)),bind(X_107,$fot(b)),bind(X_108,$fot(X_194)),bind(X_109,$fot(multiply(c,a)))]]) ).
cnf(refute_0_39,plain,
( ~ product(X_194,multiply(c,a),identity)
| product(X_194,identity,b) ),
inference(resolve,[$cnf( product(multiply(c,a),b,identity) )],[refute_0_30,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ product(multiply(c,a),multiply(c,a),identity)
| product(multiply(c,a),identity,b) ),
inference(subst,[],[refute_0_39:[bind(X_194,$fot(multiply(c,a)))]]) ).
cnf(refute_0_41,plain,
product(multiply(c,a),identity,b),
inference(resolve,[$cnf( product(multiply(c,a),multiply(c,a),identity) )],[refute_0_37,refute_0_40]) ).
cnf(refute_0_42,plain,
b = multiply(multiply(c,a),identity),
inference(resolve,[$cnf( product(multiply(c,a),identity,b) )],[refute_0_41,refute_0_36]) ).
cnf(refute_0_43,plain,
product(X_64,identity,multiply(X_64,identity)),
inference(subst,[],[total_function1:[bind(X,$fot(X_64)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_44,plain,
product(X_57,identity,X_57),
inference(subst,[],[right_identity:[bind(X,$fot(X_57))]]) ).
cnf(refute_0_45,plain,
( ~ product(X_57,identity,X_57)
| ~ product(X_57,identity,X_60)
| X_60 = X_57 ),
inference(subst,[],[total_function2:[bind(W,$fot(X_57)),bind(X,$fot(X_57)),bind(Y,$fot(identity)),bind(Z,$fot(X_60))]]) ).
cnf(refute_0_46,plain,
( ~ product(X_57,identity,X_60)
| X_60 = X_57 ),
inference(resolve,[$cnf( product(X_57,identity,X_57) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
( ~ product(X_64,identity,multiply(X_64,identity))
| multiply(X_64,identity) = X_64 ),
inference(subst,[],[refute_0_46:[bind(X_57,$fot(X_64)),bind(X_60,$fot(multiply(X_64,identity)))]]) ).
cnf(refute_0_48,plain,
multiply(X_64,identity) = X_64,
inference(resolve,[$cnf( product(X_64,identity,multiply(X_64,identity)) )],[refute_0_43,refute_0_47]) ).
cnf(refute_0_49,plain,
multiply(multiply(c,a),identity) = multiply(c,a),
inference(subst,[],[refute_0_48:[bind(X_64,$fot(multiply(c,a)))]]) ).
cnf(refute_0_50,plain,
( multiply(multiply(c,a),identity) != multiply(c,a)
| b != multiply(multiply(c,a),identity)
| b = multiply(c,a) ),
introduced(tautology,[equality,[$cnf( $equal(b,multiply(multiply(c,a),identity)) ),[1],$fot(multiply(c,a))]]) ).
cnf(refute_0_51,plain,
( b != multiply(multiply(c,a),identity)
| b = multiply(c,a) ),
inference(resolve,[$cnf( $equal(multiply(multiply(c,a),identity),multiply(c,a)) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
b = multiply(c,a),
inference(resolve,[$cnf( $equal(b,multiply(multiply(c,a),identity)) )],[refute_0_42,refute_0_51]) ).
cnf(refute_0_53,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_54,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_55,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
( b != multiply(c,a)
| multiply(c,a) = b ),
inference(subst,[],[refute_0_55:[bind(X0,$fot(b)),bind(Y0,$fot(multiply(c,a)))]]) ).
cnf(refute_0_57,plain,
multiply(c,a) = b,
inference(resolve,[$cnf( $equal(b,multiply(c,a)) )],[refute_0_52,refute_0_56]) ).
cnf(refute_0_58,plain,
( multiply(c,a) != b
| ~ product(multiply(c,a),X_192,X_193)
| product(b,X_192,X_193) ),
introduced(tautology,[equality,[$cnf( product(multiply(c,a),X_192,X_193) ),[0],$fot(b)]]) ).
cnf(refute_0_59,plain,
( ~ product(multiply(c,a),X_192,X_193)
| product(b,X_192,X_193) ),
inference(resolve,[$cnf( $equal(multiply(c,a),b) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
( ~ product(b,X_193,X_192)
| product(b,X_192,X_193) ),
inference(resolve,[$cnf( product(multiply(c,a),X_192,X_193) )],[refute_0_35,refute_0_59]) ).
cnf(refute_0_61,plain,
( ~ product(b,X_237,multiply(b,X_237))
| product(b,multiply(b,X_237),X_237) ),
inference(subst,[],[refute_0_60:[bind(X_192,$fot(multiply(b,X_237))),bind(X_193,$fot(X_237))]]) ).
cnf(refute_0_62,plain,
product(b,multiply(b,X_237),X_237),
inference(resolve,[$cnf( product(b,X_237,multiply(b,X_237)) )],[refute_0_0,refute_0_61]) ).
cnf(refute_0_63,plain,
product(b,multiply(b,c),c),
inference(subst,[],[refute_0_62:[bind(X_237,$fot(c))]]) ).
cnf(refute_0_64,plain,
( ~ product(c,b,multiply(b,c))
| multiply(b,c) = multiply(c,b) ),
inference(subst,[],[refute_0_4:[bind(X_58,$fot(c)),bind(X_59,$fot(b)),bind(X_60,$fot(multiply(b,c)))]]) ).
cnf(refute_0_65,plain,
product(c,multiply(b,c),multiply(c,multiply(b,c))),
inference(subst,[],[total_function1:[bind(X,$fot(c)),bind(Y,$fot(multiply(b,c)))]]) ).
cnf(refute_0_66,plain,
( ~ product(multiply(c,multiply(b,c)),identity,b)
| b = multiply(multiply(c,multiply(b,c)),identity) ),
inference(subst,[],[refute_0_4:[bind(X_58,$fot(multiply(c,multiply(b,c)))),bind(X_59,$fot(identity)),bind(X_60,$fot(b))]]) ).
cnf(refute_0_67,plain,
( multiply(c,a) != b
| ~ product(X_194,b,identity)
| product(X_194,multiply(c,a),identity) ),
introduced(tautology,[equality,[$cnf( ~ product(X_194,multiply(c,a),identity) ),[1],$fot(b)]]) ).
cnf(refute_0_68,plain,
( ~ product(X_194,b,identity)
| product(X_194,multiply(c,a),identity) ),
inference(resolve,[$cnf( $equal(multiply(c,a),b) )],[refute_0_57,refute_0_67]) ).
cnf(refute_0_69,plain,
( ~ product(X_194,b,identity)
| product(X_194,identity,b) ),
inference(resolve,[$cnf( product(X_194,multiply(c,a),identity) )],[refute_0_68,refute_0_39]) ).
cnf(refute_0_70,plain,
( ~ product(multiply(c,multiply(b,c)),b,identity)
| product(multiply(c,multiply(b,c)),identity,b) ),
inference(subst,[],[refute_0_69:[bind(X_194,$fot(multiply(c,multiply(b,c))))]]) ).
cnf(refute_0_71,plain,
product(multiply(c,multiply(b,c)),b,multiply(multiply(c,multiply(b,c)),b)),
inference(subst,[],[total_function1:[bind(X,$fot(multiply(c,multiply(b,c)))),bind(Y,$fot(b))]]) ).
cnf(refute_0_72,plain,
( ~ product(identity,multiply(multiply(c,multiply(b,c)),b),identity)
| identity = multiply(identity,multiply(multiply(c,multiply(b,c)),b)) ),
inference(subst,[],[refute_0_4:[bind(X_58,$fot(identity)),bind(X_59,$fot(multiply(multiply(c,multiply(b,c)),b))),bind(X_60,$fot(identity))]]) ).
cnf(refute_0_73,plain,
product(inverse(X_96),X_96,identity),
inference(subst,[],[left_inverse:[bind(X,$fot(X_96))]]) ).
cnf(refute_0_74,plain,
( ~ product(X_96,X_97,X_96)
| ~ product(inverse(X_96),X_96,identity)
| product(identity,X_97,identity) ),
inference(subst,[],[associativity2:[bind(U,$fot(identity)),bind(V,$fot(X_96)),bind(W,$fot(identity)),bind(X,$fot(inverse(X_96))),bind(Y,$fot(X_96)),bind(Z,$fot(X_97))]]) ).
cnf(refute_0_75,plain,
( ~ product(X_96,X_97,X_96)
| product(identity,X_97,identity) ),
inference(resolve,[$cnf( product(inverse(X_96),X_96,identity) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
( ~ product(c,multiply(multiply(c,multiply(b,c)),b),c)
| product(identity,multiply(multiply(c,multiply(b,c)),b),identity) ),
inference(subst,[],[refute_0_75:[bind(X_96,$fot(c)),bind(X_97,$fot(multiply(multiply(c,multiply(b,c)),b)))]]) ).
cnf(refute_0_77,plain,
product(X_113,b,multiply(X_113,b)),
inference(subst,[],[total_function1:[bind(X,$fot(X_113)),bind(Y,$fot(b))]]) ).
cnf(refute_0_78,plain,
( ~ product(X_108,X_109,a)
| ~ product(X_109,b,X_106)
| ~ product(a,b,c)
| product(X_108,X_106,c) ),
inference(subst,[],[associativity1:[bind(U,$fot(a)),bind(V,$fot(X_106)),bind(W,$fot(c)),bind(X,$fot(X_108)),bind(Y,$fot(X_109)),bind(Z,$fot(b))]]) ).
cnf(refute_0_79,plain,
( ~ product(X_108,X_109,a)
| ~ product(X_109,b,X_106)
| product(X_108,X_106,c) ),
inference(resolve,[$cnf( product(a,b,c) )],[a_times_b_is_c,refute_0_78]) ).
cnf(refute_0_80,plain,
( ~ product(X_112,X_113,a)
| ~ product(X_113,b,multiply(X_113,b))
| product(X_112,multiply(X_113,b),c) ),
inference(subst,[],[refute_0_79:[bind(X_106,$fot(multiply(X_113,b))),bind(X_108,$fot(X_112)),bind(X_109,$fot(X_113))]]) ).
cnf(refute_0_81,plain,
( ~ product(X_112,X_113,a)
| product(X_112,multiply(X_113,b),c) ),
inference(resolve,[$cnf( product(X_113,b,multiply(X_113,b)) )],[refute_0_77,refute_0_80]) ).
cnf(refute_0_82,plain,
( ~ product(c,multiply(c,multiply(b,c)),a)
| product(c,multiply(multiply(c,multiply(b,c)),b),c) ),
inference(subst,[],[refute_0_81:[bind(X_112,$fot(c)),bind(X_113,$fot(multiply(c,multiply(b,c))))]]) ).
cnf(refute_0_83,plain,
product(c,multiply(c,multiply(b,c)),multiply(c,multiply(c,multiply(b,c)))),
inference(subst,[],[total_function1:[bind(X,$fot(c)),bind(Y,$fot(multiply(c,multiply(b,c))))]]) ).
cnf(refute_0_84,plain,
( ~ product(a,identity,multiply(c,multiply(c,multiply(b,c))))
| multiply(c,multiply(c,multiply(b,c))) = multiply(a,identity) ),
inference(subst,[],[refute_0_4:[bind(X_58,$fot(a)),bind(X_59,$fot(identity)),bind(X_60,$fot(multiply(c,multiply(c,multiply(b,c)))))]]) ).
cnf(refute_0_85,plain,
product(c,multiply(c,multiply(multiply(X_185,c),c)),multiply(c,multiply(c,multiply(multiply(X_185,c),c)))),
inference(subst,[],[total_function1:[bind(X,$fot(c)),bind(Y,$fot(multiply(c,multiply(multiply(X_185,c),c))))]]) ).
cnf(refute_0_86,plain,
( ~ product(X_134,c,multiply(multiply(X_134,a),b))
| ~ product(multiply(multiply(X_134,a),b),Z,W)
| ~ product(c,Z,V)
| product(X_134,V,W) ),
inference(subst,[],[associativity1:[bind(U,$fot(multiply(multiply(X_134,a),b))),bind(X,$fot(X_134)),bind(Y,$fot(c))]]) ).
cnf(refute_0_87,plain,
( ~ product(multiply(multiply(X_134,a),b),Z,W)
| ~ product(c,Z,V)
| product(X_134,V,W) ),
inference(resolve,[$cnf( product(X_134,c,multiply(multiply(X_134,a),b)) )],[refute_0_14,refute_0_86]) ).
cnf(refute_0_88,plain,
( multiply(multiply(X_134,a),b) != multiply(X_134,c)
| ~ product(multiply(X_134,c),Z,W)
| product(multiply(multiply(X_134,a),b),Z,W) ),
introduced(tautology,[equality,[$cnf( ~ product(multiply(multiply(X_134,a),b),Z,W) ),[0],$fot(multiply(X_134,c))]]) ).
cnf(refute_0_89,plain,
( ~ product(multiply(X_134,c),Z,W)
| product(multiply(multiply(X_134,a),b),Z,W) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_134,a),b),multiply(X_134,c)) )],[refute_0_15,refute_0_88]) ).
cnf(refute_0_90,plain,
( ~ product(multiply(X_134,c),Z,W)
| ~ product(c,Z,V)
| product(X_134,V,W) ),
inference(resolve,[$cnf( product(multiply(multiply(X_134,a),b),Z,W) )],[refute_0_89,refute_0_87]) ).
cnf(refute_0_91,plain,
( ~ product(multiply(X_134,c),multiply(c,multiply(multiply(X_134,c),c)),identity)
| ~ product(c,multiply(c,multiply(multiply(X_134,c),c)),V)
| product(X_134,V,identity) ),
inference(subst,[],[refute_0_90:[bind(W,$fot(identity)),bind(Z,$fot(multiply(c,multiply(multiply(X_134,c),c))))]]) ).
cnf(refute_0_92,plain,
product(c,multiply(X_162,c),multiply(c,multiply(X_162,c))),
inference(subst,[],[total_function1:[bind(X,$fot(c)),bind(Y,$fot(multiply(X_162,c)))]]) ).
cnf(refute_0_93,plain,
product(multiply(X_158,c),multiply(X_158,c),identity),
inference(subst,[],[square_element:[bind(X,$fot(multiply(X_158,c)))]]) ).
cnf(refute_0_94,plain,
( ~ product(multiply(X_158,c),multiply(X_158,c),identity)
| ~ product(c,multiply(X_158,c),X_155)
| product(X_158,X_155,identity) ),
inference(subst,[],[refute_0_90:[bind(V,$fot(X_155)),bind(W,$fot(identity)),bind(Z,$fot(multiply(X_158,c))),bind(X_134,$fot(X_158))]]) ).
cnf(refute_0_95,plain,
( ~ product(c,multiply(X_158,c),X_155)
| product(X_158,X_155,identity) ),
inference(resolve,[$cnf( product(multiply(X_158,c),multiply(X_158,c),identity) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
( ~ product(c,multiply(X_162,c),multiply(c,multiply(X_162,c)))
| product(X_162,multiply(c,multiply(X_162,c)),identity) ),
inference(subst,[],[refute_0_95:[bind(X_155,$fot(multiply(c,multiply(X_162,c)))),bind(X_158,$fot(X_162))]]) ).
cnf(refute_0_97,plain,
product(X_162,multiply(c,multiply(X_162,c)),identity),
inference(resolve,[$cnf( product(c,multiply(X_162,c),multiply(c,multiply(X_162,c))) )],[refute_0_92,refute_0_96]) ).
cnf(refute_0_98,plain,
product(multiply(X_134,c),multiply(c,multiply(multiply(X_134,c),c)),identity),
inference(subst,[],[refute_0_97:[bind(X_162,$fot(multiply(X_134,c)))]]) ).
cnf(refute_0_99,plain,
( ~ product(c,multiply(c,multiply(multiply(X_134,c),c)),V)
| product(X_134,V,identity) ),
inference(resolve,[$cnf( product(multiply(X_134,c),multiply(c,multiply(multiply(X_134,c),c)),identity) )],[refute_0_98,refute_0_91]) ).
cnf(refute_0_100,plain,
( ~ product(c,multiply(c,multiply(multiply(X_185,c),c)),multiply(c,multiply(c,multiply(multiply(X_185,c),c))))
| product(X_185,multiply(c,multiply(c,multiply(multiply(X_185,c),c))),identity) ),
inference(subst,[],[refute_0_99:[bind(V,$fot(multiply(c,multiply(c,multiply(multiply(X_185,c),c))))),bind(X_134,$fot(X_185))]]) ).
cnf(refute_0_101,plain,
product(X_185,multiply(c,multiply(c,multiply(multiply(X_185,c),c))),identity),
inference(resolve,[$cnf( product(c,multiply(c,multiply(multiply(X_185,c),c)),multiply(c,multiply(c,multiply(multiply(X_185,c),c)))) )],[refute_0_85,refute_0_100]) ).
cnf(refute_0_102,plain,
product(a,multiply(c,multiply(c,multiply(multiply(a,c),c))),identity),
inference(subst,[],[refute_0_101:[bind(X_185,$fot(a))]]) ).
cnf(refute_0_103,plain,
product(inverse(a),multiply(c,multiply(inverse(a),c)),identity),
inference(subst,[],[refute_0_97:[bind(X_162,$fot(inverse(a)))]]) ).
cnf(refute_0_104,plain,
( ~ product(inverse(a),c,b)
| b = multiply(inverse(a),c) ),
inference(subst,[],[refute_0_4:[bind(X_58,$fot(inverse(a))),bind(X_59,$fot(c)),bind(X_60,$fot(b))]]) ).
cnf(refute_0_105,plain,
product(inverse(a),a,identity),
inference(subst,[],[left_inverse:[bind(X,$fot(a))]]) ).
cnf(refute_0_106,plain,
product(identity,b,b),
inference(subst,[],[left_identity:[bind(X,$fot(b))]]) ).
cnf(refute_0_107,plain,
( ~ product(X_122,a,identity)
| ~ product(identity,b,b)
| product(X_122,c,b) ),
inference(subst,[],[refute_0_9:[bind(X_105,$fot(identity)),bind(X_107,$fot(b)),bind(X_108,$fot(X_122))]]) ).
cnf(refute_0_108,plain,
( ~ product(X_122,a,identity)
| product(X_122,c,b) ),
inference(resolve,[$cnf( product(identity,b,b) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
( ~ product(inverse(a),a,identity)
| product(inverse(a),c,b) ),
inference(subst,[],[refute_0_108:[bind(X_122,$fot(inverse(a)))]]) ).
cnf(refute_0_110,plain,
product(inverse(a),c,b),
inference(resolve,[$cnf( product(inverse(a),a,identity) )],[refute_0_105,refute_0_109]) ).
cnf(refute_0_111,plain,
b = multiply(inverse(a),c),
inference(resolve,[$cnf( product(inverse(a),c,b) )],[refute_0_110,refute_0_104]) ).
cnf(refute_0_112,plain,
( b != multiply(inverse(a),c)
| multiply(inverse(a),c) = b ),
inference(subst,[],[refute_0_55:[bind(X0,$fot(b)),bind(Y0,$fot(multiply(inverse(a),c)))]]) ).
cnf(refute_0_113,plain,
multiply(inverse(a),c) = b,
inference(resolve,[$cnf( $equal(b,multiply(inverse(a),c)) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
( multiply(inverse(a),c) != b
| ~ product(inverse(a),multiply(c,multiply(inverse(a),c)),identity)
| product(inverse(a),multiply(c,b),identity) ),
introduced(tautology,[equality,[$cnf( product(inverse(a),multiply(c,multiply(inverse(a),c)),identity) ),[1,1],$fot(b)]]) ).
cnf(refute_0_115,plain,
( ~ product(inverse(a),multiply(c,multiply(inverse(a),c)),identity)
| product(inverse(a),multiply(c,b),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),c),b) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
product(inverse(a),multiply(c,b),identity),
inference(resolve,[$cnf( product(inverse(a),multiply(c,multiply(inverse(a),c)),identity) )],[refute_0_103,refute_0_115]) ).
cnf(refute_0_117,plain,
( ~ product(multiply(c,b),X_193,X_192)
| ~ product(inverse(a),multiply(c,b),identity)
| product(inverse(a),X_192,X_193) ),
inference(subst,[],[refute_0_33:[bind(X_106,$fot(X_192)),bind(X_107,$fot(X_193)),bind(X_108,$fot(inverse(a))),bind(X_109,$fot(multiply(c,b)))]]) ).
cnf(refute_0_118,plain,
( ~ product(multiply(c,b),X_193,X_192)
| product(inverse(a),X_192,X_193) ),
inference(resolve,[$cnf( product(inverse(a),multiply(c,b),identity) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
( ~ product(inverse(a),identity,multiply(c,b))
| multiply(c,b) = multiply(inverse(a),identity) ),
inference(subst,[],[refute_0_4:[bind(X_58,$fot(inverse(a))),bind(X_59,$fot(identity)),bind(X_60,$fot(multiply(c,b)))]]) ).
cnf(refute_0_120,plain,
product(a,multiply(c,multiply(a,c)),identity),
inference(subst,[],[refute_0_97:[bind(X_162,$fot(a))]]) ).
cnf(refute_0_121,plain,
( ~ product(a,c,b)
| b = multiply(a,c) ),
inference(subst,[],[refute_0_4:[bind(X_58,$fot(a)),bind(X_59,$fot(c)),bind(X_60,$fot(b))]]) ).
cnf(refute_0_122,plain,
product(a,a,identity),
inference(subst,[],[square_element:[bind(X,$fot(a))]]) ).
cnf(refute_0_123,plain,
( ~ product(a,a,identity)
| product(a,c,b) ),
inference(subst,[],[refute_0_108:[bind(X_122,$fot(a))]]) ).
cnf(refute_0_124,plain,
product(a,c,b),
inference(resolve,[$cnf( product(a,a,identity) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
b = multiply(a,c),
inference(resolve,[$cnf( product(a,c,b) )],[refute_0_124,refute_0_121]) ).
cnf(refute_0_126,plain,
( b != multiply(a,c)
| multiply(a,c) = b ),
inference(subst,[],[refute_0_55:[bind(X0,$fot(b)),bind(Y0,$fot(multiply(a,c)))]]) ).
cnf(refute_0_127,plain,
multiply(a,c) = b,
inference(resolve,[$cnf( $equal(b,multiply(a,c)) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
( multiply(a,c) != b
| ~ product(a,multiply(c,multiply(a,c)),identity)
| product(a,multiply(c,b),identity) ),
introduced(tautology,[equality,[$cnf( product(a,multiply(c,multiply(a,c)),identity) ),[1,1],$fot(b)]]) ).
cnf(refute_0_129,plain,
( ~ product(a,multiply(c,multiply(a,c)),identity)
| product(a,multiply(c,b),identity) ),
inference(resolve,[$cnf( $equal(multiply(a,c),b) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
product(a,multiply(c,b),identity),
inference(resolve,[$cnf( product(a,multiply(c,multiply(a,c)),identity) )],[refute_0_120,refute_0_129]) ).
cnf(refute_0_131,plain,
( ~ product(X_194,a,identity)
| ~ product(a,multiply(c,b),identity)
| product(X_194,identity,multiply(c,b)) ),
inference(subst,[],[refute_0_33:[bind(X_106,$fot(identity)),bind(X_107,$fot(multiply(c,b))),bind(X_108,$fot(X_194)),bind(X_109,$fot(a))]]) ).
cnf(refute_0_132,plain,
( ~ product(X_194,a,identity)
| product(X_194,identity,multiply(c,b)) ),
inference(resolve,[$cnf( product(a,multiply(c,b),identity) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
( ~ product(inverse(a),a,identity)
| product(inverse(a),identity,multiply(c,b)) ),
inference(subst,[],[refute_0_132:[bind(X_194,$fot(inverse(a)))]]) ).
cnf(refute_0_134,plain,
product(inverse(a),identity,multiply(c,b)),
inference(resolve,[$cnf( product(inverse(a),a,identity) )],[refute_0_105,refute_0_133]) ).
cnf(refute_0_135,plain,
multiply(c,b) = multiply(inverse(a),identity),
inference(resolve,[$cnf( product(inverse(a),identity,multiply(c,b)) )],[refute_0_134,refute_0_119]) ).
cnf(refute_0_136,plain,
multiply(inverse(a),identity) = inverse(a),
inference(subst,[],[refute_0_48:[bind(X_64,$fot(inverse(a)))]]) ).
cnf(refute_0_137,plain,
( multiply(c,b) != multiply(inverse(a),identity)
| multiply(inverse(a),identity) != inverse(a)
| multiply(c,b) = inverse(a) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(c,b),inverse(a)) ),[0],$fot(multiply(inverse(a),identity))]]) ).
cnf(refute_0_138,plain,
( multiply(c,b) != multiply(inverse(a),identity)
| multiply(c,b) = inverse(a) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),identity),inverse(a)) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
multiply(c,b) = inverse(a),
inference(resolve,[$cnf( $equal(multiply(c,b),multiply(inverse(a),identity)) )],[refute_0_135,refute_0_138]) ).
cnf(refute_0_140,plain,
( ~ product(a,identity,inverse(a))
| inverse(a) = multiply(a,identity) ),
inference(subst,[],[refute_0_4:[bind(X_58,$fot(a)),bind(X_59,$fot(identity)),bind(X_60,$fot(inverse(a)))]]) ).
cnf(refute_0_141,plain,
( ~ product(a,a,identity)
| product(a,identity,multiply(c,b)) ),
inference(subst,[],[refute_0_132:[bind(X_194,$fot(a))]]) ).
cnf(refute_0_142,plain,
product(a,identity,multiply(c,b)),
inference(resolve,[$cnf( product(a,a,identity) )],[refute_0_122,refute_0_141]) ).
cnf(refute_0_143,plain,
( multiply(c,b) != inverse(a)
| ~ product(a,identity,multiply(c,b))
| product(a,identity,inverse(a)) ),
introduced(tautology,[equality,[$cnf( product(a,identity,multiply(c,b)) ),[2],$fot(inverse(a))]]) ).
cnf(refute_0_144,plain,
( ~ product(a,identity,multiply(c,b))
| product(a,identity,inverse(a)) ),
inference(resolve,[$cnf( $equal(multiply(c,b),inverse(a)) )],[refute_0_139,refute_0_143]) ).
cnf(refute_0_145,plain,
product(a,identity,inverse(a)),
inference(resolve,[$cnf( product(a,identity,multiply(c,b)) )],[refute_0_142,refute_0_144]) ).
cnf(refute_0_146,plain,
inverse(a) = multiply(a,identity),
inference(resolve,[$cnf( product(a,identity,inverse(a)) )],[refute_0_145,refute_0_140]) ).
cnf(refute_0_147,plain,
multiply(a,identity) = a,
inference(subst,[],[refute_0_48:[bind(X_64,$fot(a))]]) ).
cnf(refute_0_148,plain,
( multiply(a,identity) != a
| inverse(a) != multiply(a,identity)
| inverse(a) = a ),
introduced(tautology,[equality,[$cnf( $equal(inverse(a),multiply(a,identity)) ),[1],$fot(a)]]) ).
cnf(refute_0_149,plain,
( inverse(a) != multiply(a,identity)
| inverse(a) = a ),
inference(resolve,[$cnf( $equal(multiply(a,identity),a) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
inverse(a) = a,
inference(resolve,[$cnf( $equal(inverse(a),multiply(a,identity)) )],[refute_0_146,refute_0_149]) ).
cnf(refute_0_151,plain,
( multiply(c,b) != inverse(a)
| inverse(a) != a
| multiply(c,b) = a ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(c,b),a) ),[0],$fot(inverse(a))]]) ).
cnf(refute_0_152,plain,
( multiply(c,b) != inverse(a)
| multiply(c,b) = a ),
inference(resolve,[$cnf( $equal(inverse(a),a) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
multiply(c,b) = a,
inference(resolve,[$cnf( $equal(multiply(c,b),inverse(a)) )],[refute_0_139,refute_0_152]) ).
cnf(refute_0_154,plain,
( multiply(c,b) != a
| ~ product(a,X_193,X_192)
| product(multiply(c,b),X_193,X_192) ),
introduced(tautology,[equality,[$cnf( ~ product(multiply(c,b),X_193,X_192) ),[0],$fot(a)]]) ).
cnf(refute_0_155,plain,
( ~ product(a,X_193,X_192)
| product(multiply(c,b),X_193,X_192) ),
inference(resolve,[$cnf( $equal(multiply(c,b),a) )],[refute_0_153,refute_0_154]) ).
cnf(refute_0_156,plain,
( ~ product(a,X_193,X_192)
| product(inverse(a),X_192,X_193) ),
inference(resolve,[$cnf( product(multiply(c,b),X_193,X_192) )],[refute_0_155,refute_0_118]) ).
cnf(refute_0_157,plain,
( inverse(a) != a
| ~ product(inverse(a),X_192,X_193)
| product(a,X_192,X_193) ),
introduced(tautology,[equality,[$cnf( product(inverse(a),X_192,X_193) ),[0],$fot(a)]]) ).
cnf(refute_0_158,plain,
( ~ product(inverse(a),X_192,X_193)
| product(a,X_192,X_193) ),
inference(resolve,[$cnf( $equal(inverse(a),a) )],[refute_0_150,refute_0_157]) ).
cnf(refute_0_159,plain,
( ~ product(a,X_193,X_192)
| product(a,X_192,X_193) ),
inference(resolve,[$cnf( product(inverse(a),X_192,X_193) )],[refute_0_156,refute_0_158]) ).
cnf(refute_0_160,plain,
( ~ product(a,multiply(c,multiply(c,multiply(multiply(a,c),c))),identity)
| product(a,identity,multiply(c,multiply(c,multiply(multiply(a,c),c)))) ),
inference(subst,[],[refute_0_159:[bind(X_192,$fot(identity)),bind(X_193,$fot(multiply(c,multiply(c,multiply(multiply(a,c),c)))))]]) ).
cnf(refute_0_161,plain,
product(a,identity,multiply(c,multiply(c,multiply(multiply(a,c),c)))),
inference(resolve,[$cnf( product(a,multiply(c,multiply(c,multiply(multiply(a,c),c))),identity) )],[refute_0_102,refute_0_160]) ).
cnf(refute_0_162,plain,
multiply(multiply(a,c),c) = multiply(multiply(a,c),c),
introduced(tautology,[refl,[$fot(multiply(multiply(a,c),c))]]) ).
cnf(refute_0_163,plain,
( multiply(multiply(a,c),c) != multiply(multiply(a,c),c)
| multiply(a,c) != b
| multiply(multiply(a,c),c) = multiply(b,c) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(a,c),c),multiply(multiply(a,c),c)) ),[1,0],$fot(b)]]) ).
cnf(refute_0_164,plain,
( multiply(a,c) != b
| multiply(multiply(a,c),c) = multiply(b,c) ),
inference(resolve,[$cnf( $equal(multiply(multiply(a,c),c),multiply(multiply(a,c),c)) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
multiply(multiply(a,c),c) = multiply(b,c),
inference(resolve,[$cnf( $equal(multiply(a,c),b) )],[refute_0_127,refute_0_164]) ).
cnf(refute_0_166,plain,
multiply(c,multiply(multiply(a,c),c)) = multiply(c,multiply(multiply(a,c),c)),
introduced(tautology,[refl,[$fot(multiply(c,multiply(multiply(a,c),c)))]]) ).
cnf(refute_0_167,plain,
( multiply(multiply(a,c),c) != multiply(b,c)
| multiply(c,multiply(multiply(a,c),c)) != multiply(c,multiply(multiply(a,c),c))
| multiply(c,multiply(multiply(a,c),c)) = multiply(c,multiply(b,c)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c,multiply(multiply(a,c),c)),multiply(c,multiply(multiply(a,c),c))) ),[1,1],$fot(multiply(b,c))]]) ).
cnf(refute_0_168,plain,
( multiply(multiply(a,c),c) != multiply(b,c)
| multiply(c,multiply(multiply(a,c),c)) = multiply(c,multiply(b,c)) ),
inference(resolve,[$cnf( $equal(multiply(c,multiply(multiply(a,c),c)),multiply(c,multiply(multiply(a,c),c))) )],[refute_0_166,refute_0_167]) ).
cnf(refute_0_169,plain,
multiply(c,multiply(multiply(a,c),c)) = multiply(c,multiply(b,c)),
inference(resolve,[$cnf( $equal(multiply(multiply(a,c),c),multiply(b,c)) )],[refute_0_165,refute_0_168]) ).
cnf(refute_0_170,plain,
multiply(c,multiply(c,multiply(multiply(a,c),c))) = multiply(c,multiply(c,multiply(multiply(a,c),c))),
introduced(tautology,[refl,[$fot(multiply(c,multiply(c,multiply(multiply(a,c),c))))]]) ).
cnf(refute_0_171,plain,
( multiply(c,multiply(multiply(a,c),c)) != multiply(c,multiply(b,c))
| multiply(c,multiply(c,multiply(multiply(a,c),c))) != multiply(c,multiply(c,multiply(multiply(a,c),c)))
| multiply(c,multiply(c,multiply(multiply(a,c),c))) = multiply(c,multiply(c,multiply(b,c))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c,multiply(c,multiply(multiply(a,c),c))),multiply(c,multiply(c,multiply(multiply(a,c),c)))) ),[1,1],$fot(multiply(c,multiply(b,c)))]]) ).
cnf(refute_0_172,plain,
( multiply(c,multiply(multiply(a,c),c)) != multiply(c,multiply(b,c))
| multiply(c,multiply(c,multiply(multiply(a,c),c))) = multiply(c,multiply(c,multiply(b,c))) ),
inference(resolve,[$cnf( $equal(multiply(c,multiply(c,multiply(multiply(a,c),c))),multiply(c,multiply(c,multiply(multiply(a,c),c)))) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
multiply(c,multiply(c,multiply(multiply(a,c),c))) = multiply(c,multiply(c,multiply(b,c))),
inference(resolve,[$cnf( $equal(multiply(c,multiply(multiply(a,c),c)),multiply(c,multiply(b,c))) )],[refute_0_169,refute_0_172]) ).
cnf(refute_0_174,plain,
( multiply(c,multiply(c,multiply(multiply(a,c),c))) != multiply(c,multiply(c,multiply(b,c)))
| ~ product(a,identity,multiply(c,multiply(c,multiply(multiply(a,c),c))))
| product(a,identity,multiply(c,multiply(c,multiply(b,c)))) ),
introduced(tautology,[equality,[$cnf( product(a,identity,multiply(c,multiply(c,multiply(multiply(a,c),c)))) ),[2],$fot(multiply(c,multiply(c,multiply(b,c))))]]) ).
cnf(refute_0_175,plain,
( ~ product(a,identity,multiply(c,multiply(c,multiply(multiply(a,c),c))))
| product(a,identity,multiply(c,multiply(c,multiply(b,c)))) ),
inference(resolve,[$cnf( $equal(multiply(c,multiply(c,multiply(multiply(a,c),c))),multiply(c,multiply(c,multiply(b,c)))) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
product(a,identity,multiply(c,multiply(c,multiply(b,c)))),
inference(resolve,[$cnf( product(a,identity,multiply(c,multiply(c,multiply(multiply(a,c),c)))) )],[refute_0_161,refute_0_175]) ).
cnf(refute_0_177,plain,
multiply(c,multiply(c,multiply(b,c))) = multiply(a,identity),
inference(resolve,[$cnf( product(a,identity,multiply(c,multiply(c,multiply(b,c)))) )],[refute_0_176,refute_0_84]) ).
cnf(refute_0_178,plain,
( multiply(a,identity) != a
| multiply(c,multiply(c,multiply(b,c))) != multiply(a,identity)
| multiply(c,multiply(c,multiply(b,c))) = a ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c,multiply(c,multiply(b,c))),multiply(a,identity)) ),[1],$fot(a)]]) ).
cnf(refute_0_179,plain,
( multiply(c,multiply(c,multiply(b,c))) != multiply(a,identity)
| multiply(c,multiply(c,multiply(b,c))) = a ),
inference(resolve,[$cnf( $equal(multiply(a,identity),a) )],[refute_0_147,refute_0_178]) ).
cnf(refute_0_180,plain,
multiply(c,multiply(c,multiply(b,c))) = a,
inference(resolve,[$cnf( $equal(multiply(c,multiply(c,multiply(b,c))),multiply(a,identity)) )],[refute_0_177,refute_0_179]) ).
cnf(refute_0_181,plain,
( multiply(c,multiply(c,multiply(b,c))) != a
| ~ product(c,multiply(c,multiply(b,c)),multiply(c,multiply(c,multiply(b,c))))
| product(c,multiply(c,multiply(b,c)),a) ),
introduced(tautology,[equality,[$cnf( product(c,multiply(c,multiply(b,c)),multiply(c,multiply(c,multiply(b,c)))) ),[2],$fot(a)]]) ).
cnf(refute_0_182,plain,
( ~ product(c,multiply(c,multiply(b,c)),multiply(c,multiply(c,multiply(b,c))))
| product(c,multiply(c,multiply(b,c)),a) ),
inference(resolve,[$cnf( $equal(multiply(c,multiply(c,multiply(b,c))),a) )],[refute_0_180,refute_0_181]) ).
cnf(refute_0_183,plain,
product(c,multiply(c,multiply(b,c)),a),
inference(resolve,[$cnf( product(c,multiply(c,multiply(b,c)),multiply(c,multiply(c,multiply(b,c)))) )],[refute_0_83,refute_0_182]) ).
cnf(refute_0_184,plain,
product(c,multiply(multiply(c,multiply(b,c)),b),c),
inference(resolve,[$cnf( product(c,multiply(c,multiply(b,c)),a) )],[refute_0_183,refute_0_82]) ).
cnf(refute_0_185,plain,
product(identity,multiply(multiply(c,multiply(b,c)),b),identity),
inference(resolve,[$cnf( product(c,multiply(multiply(c,multiply(b,c)),b),c) )],[refute_0_184,refute_0_76]) ).
cnf(refute_0_186,plain,
identity = multiply(identity,multiply(multiply(c,multiply(b,c)),b)),
inference(resolve,[$cnf( product(identity,multiply(multiply(c,multiply(b,c)),b),identity) )],[refute_0_185,refute_0_72]) ).
cnf(refute_0_187,plain,
product(X_24,X_24,identity),
inference(subst,[],[square_element:[bind(X,$fot(X_24))]]) ).
cnf(refute_0_188,plain,
product(X_20,X_22,multiply(X_20,X_22)),
inference(subst,[],[total_function1:[bind(X,$fot(X_20)),bind(Y,$fot(X_22))]]) ).
cnf(refute_0_189,plain,
( ~ product(X_20,X_22,multiply(X_20,X_22))
| ~ product(X_22,X_22,X_20)
| product(X_22,X_20,multiply(X_20,X_22)) ),
inference(subst,[],[associativity1:[bind(U,$fot(X_20)),bind(V,$fot(X_20)),bind(W,$fot(multiply(X_20,X_22))),bind(X,$fot(X_22)),bind(Y,$fot(X_22)),bind(Z,$fot(X_22))]]) ).
cnf(refute_0_190,plain,
( ~ product(X_22,X_22,X_20)
| product(X_22,X_20,multiply(X_20,X_22)) ),
inference(resolve,[$cnf( product(X_20,X_22,multiply(X_20,X_22)) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
( ~ product(X_24,X_24,identity)
| product(X_24,identity,multiply(identity,X_24)) ),
inference(subst,[],[refute_0_190:[bind(X_20,$fot(identity)),bind(X_22,$fot(X_24))]]) ).
cnf(refute_0_192,plain,
product(X_24,identity,multiply(identity,X_24)),
inference(resolve,[$cnf( product(X_24,X_24,identity) )],[refute_0_187,refute_0_191]) ).
cnf(refute_0_193,plain,
product(X_64,identity,multiply(identity,X_64)),
inference(subst,[],[refute_0_192:[bind(X_24,$fot(X_64))]]) ).
cnf(refute_0_194,plain,
( ~ product(X_64,identity,multiply(identity,X_64))
| multiply(identity,X_64) = X_64 ),
inference(subst,[],[refute_0_46:[bind(X_57,$fot(X_64)),bind(X_60,$fot(multiply(identity,X_64)))]]) ).
cnf(refute_0_195,plain,
multiply(identity,X_64) = X_64,
inference(resolve,[$cnf( product(X_64,identity,multiply(identity,X_64)) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
multiply(identity,multiply(multiply(c,multiply(b,c)),b)) = multiply(multiply(c,multiply(b,c)),b),
inference(subst,[],[refute_0_195:[bind(X_64,$fot(multiply(multiply(c,multiply(b,c)),b)))]]) ).
cnf(refute_0_197,plain,
( multiply(identity,multiply(multiply(c,multiply(b,c)),b)) != multiply(multiply(c,multiply(b,c)),b)
| identity != multiply(identity,multiply(multiply(c,multiply(b,c)),b))
| identity = multiply(multiply(c,multiply(b,c)),b) ),
introduced(tautology,[equality,[$cnf( $equal(identity,multiply(identity,multiply(multiply(c,multiply(b,c)),b))) ),[1],$fot(multiply(multiply(c,multiply(b,c)),b))]]) ).
cnf(refute_0_198,plain,
( identity != multiply(identity,multiply(multiply(c,multiply(b,c)),b))
| identity = multiply(multiply(c,multiply(b,c)),b) ),
inference(resolve,[$cnf( $equal(multiply(identity,multiply(multiply(c,multiply(b,c)),b)),multiply(multiply(c,multiply(b,c)),b)) )],[refute_0_196,refute_0_197]) ).
cnf(refute_0_199,plain,
identity = multiply(multiply(c,multiply(b,c)),b),
inference(resolve,[$cnf( $equal(identity,multiply(identity,multiply(multiply(c,multiply(b,c)),b))) )],[refute_0_186,refute_0_198]) ).
cnf(refute_0_200,plain,
( identity != multiply(multiply(c,multiply(b,c)),b)
| multiply(multiply(c,multiply(b,c)),b) = identity ),
inference(subst,[],[refute_0_55:[bind(X0,$fot(identity)),bind(Y0,$fot(multiply(multiply(c,multiply(b,c)),b)))]]) ).
cnf(refute_0_201,plain,
multiply(multiply(c,multiply(b,c)),b) = identity,
inference(resolve,[$cnf( $equal(identity,multiply(multiply(c,multiply(b,c)),b)) )],[refute_0_199,refute_0_200]) ).
cnf(refute_0_202,plain,
( multiply(multiply(c,multiply(b,c)),b) != identity
| ~ product(multiply(c,multiply(b,c)),b,multiply(multiply(c,multiply(b,c)),b))
| product(multiply(c,multiply(b,c)),b,identity) ),
introduced(tautology,[equality,[$cnf( product(multiply(c,multiply(b,c)),b,multiply(multiply(c,multiply(b,c)),b)) ),[2],$fot(identity)]]) ).
cnf(refute_0_203,plain,
( ~ product(multiply(c,multiply(b,c)),b,multiply(multiply(c,multiply(b,c)),b))
| product(multiply(c,multiply(b,c)),b,identity) ),
inference(resolve,[$cnf( $equal(multiply(multiply(c,multiply(b,c)),b),identity) )],[refute_0_201,refute_0_202]) ).
cnf(refute_0_204,plain,
product(multiply(c,multiply(b,c)),b,identity),
inference(resolve,[$cnf( product(multiply(c,multiply(b,c)),b,multiply(multiply(c,multiply(b,c)),b)) )],[refute_0_71,refute_0_203]) ).
cnf(refute_0_205,plain,
product(multiply(c,multiply(b,c)),identity,b),
inference(resolve,[$cnf( product(multiply(c,multiply(b,c)),b,identity) )],[refute_0_204,refute_0_70]) ).
cnf(refute_0_206,plain,
b = multiply(multiply(c,multiply(b,c)),identity),
inference(resolve,[$cnf( product(multiply(c,multiply(b,c)),identity,b) )],[refute_0_205,refute_0_66]) ).
cnf(refute_0_207,plain,
multiply(multiply(c,multiply(b,c)),identity) = multiply(c,multiply(b,c)),
inference(subst,[],[refute_0_48:[bind(X_64,$fot(multiply(c,multiply(b,c))))]]) ).
cnf(refute_0_208,plain,
( multiply(multiply(c,multiply(b,c)),identity) != multiply(c,multiply(b,c))
| b != multiply(multiply(c,multiply(b,c)),identity)
| b = multiply(c,multiply(b,c)) ),
introduced(tautology,[equality,[$cnf( $equal(b,multiply(multiply(c,multiply(b,c)),identity)) ),[1],$fot(multiply(c,multiply(b,c)))]]) ).
cnf(refute_0_209,plain,
( b != multiply(multiply(c,multiply(b,c)),identity)
| b = multiply(c,multiply(b,c)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(c,multiply(b,c)),identity),multiply(c,multiply(b,c))) )],[refute_0_207,refute_0_208]) ).
cnf(refute_0_210,plain,
b = multiply(c,multiply(b,c)),
inference(resolve,[$cnf( $equal(b,multiply(multiply(c,multiply(b,c)),identity)) )],[refute_0_206,refute_0_209]) ).
cnf(refute_0_211,plain,
( b != multiply(c,multiply(b,c))
| multiply(c,multiply(b,c)) = b ),
inference(subst,[],[refute_0_55:[bind(X0,$fot(b)),bind(Y0,$fot(multiply(c,multiply(b,c))))]]) ).
cnf(refute_0_212,plain,
multiply(c,multiply(b,c)) = b,
inference(resolve,[$cnf( $equal(b,multiply(c,multiply(b,c))) )],[refute_0_210,refute_0_211]) ).
cnf(refute_0_213,plain,
( multiply(c,multiply(b,c)) != b
| ~ product(c,multiply(b,c),multiply(c,multiply(b,c)))
| product(c,multiply(b,c),b) ),
introduced(tautology,[equality,[$cnf( product(c,multiply(b,c),multiply(c,multiply(b,c))) ),[2],$fot(b)]]) ).
cnf(refute_0_214,plain,
( ~ product(c,multiply(b,c),multiply(c,multiply(b,c)))
| product(c,multiply(b,c),b) ),
inference(resolve,[$cnf( $equal(multiply(c,multiply(b,c)),b) )],[refute_0_212,refute_0_213]) ).
cnf(refute_0_215,plain,
product(c,multiply(b,c),b),
inference(resolve,[$cnf( product(c,multiply(b,c),multiply(c,multiply(b,c))) )],[refute_0_65,refute_0_214]) ).
cnf(refute_0_216,plain,
product(X_195,X_195,identity),
inference(subst,[],[square_element:[bind(X,$fot(X_195))]]) ).
cnf(refute_0_217,plain,
( ~ product(X_195,X_193,X_192)
| ~ product(X_195,X_195,identity)
| product(X_195,X_192,X_193) ),
inference(subst,[],[refute_0_33:[bind(X_106,$fot(X_192)),bind(X_107,$fot(X_193)),bind(X_108,$fot(X_195)),bind(X_109,$fot(X_195))]]) ).
cnf(refute_0_218,plain,
( ~ product(X_195,X_193,X_192)
| product(X_195,X_192,X_193) ),
inference(resolve,[$cnf( product(X_195,X_195,identity) )],[refute_0_216,refute_0_217]) ).
cnf(refute_0_219,plain,
( ~ product(c,multiply(b,c),b)
| product(c,b,multiply(b,c)) ),
inference(subst,[],[refute_0_218:[bind(X_192,$fot(b)),bind(X_193,$fot(multiply(b,c))),bind(X_195,$fot(c))]]) ).
cnf(refute_0_220,plain,
product(c,b,multiply(b,c)),
inference(resolve,[$cnf( product(c,multiply(b,c),b) )],[refute_0_215,refute_0_219]) ).
cnf(refute_0_221,plain,
multiply(b,c) = multiply(c,b),
inference(resolve,[$cnf( product(c,b,multiply(b,c)) )],[refute_0_220,refute_0_64]) ).
cnf(refute_0_222,plain,
( multiply(b,c) != multiply(c,b)
| multiply(c,b) != a
| multiply(b,c) = a ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(b,c),a) ),[0],$fot(multiply(c,b))]]) ).
cnf(refute_0_223,plain,
( multiply(b,c) != multiply(c,b)
| multiply(b,c) = a ),
inference(resolve,[$cnf( $equal(multiply(c,b),a) )],[refute_0_153,refute_0_222]) ).
cnf(refute_0_224,plain,
multiply(b,c) = a,
inference(resolve,[$cnf( $equal(multiply(b,c),multiply(c,b)) )],[refute_0_221,refute_0_223]) ).
cnf(refute_0_225,plain,
( multiply(b,c) != a
| ~ product(b,multiply(b,c),c)
| product(b,a,c) ),
introduced(tautology,[equality,[$cnf( product(b,multiply(b,c),c) ),[1],$fot(a)]]) ).
cnf(refute_0_226,plain,
( ~ product(b,multiply(b,c),c)
| product(b,a,c) ),
inference(resolve,[$cnf( $equal(multiply(b,c),a) )],[refute_0_224,refute_0_225]) ).
cnf(refute_0_227,plain,
product(b,a,c),
inference(resolve,[$cnf( product(b,multiply(b,c),c) )],[refute_0_63,refute_0_226]) ).
cnf(refute_0_228,plain,
$false,
inference(resolve,[$cnf( product(b,a,c) )],[refute_0_227,prove_b_times_a_is_c]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP001-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 05:14:30 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.49 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.49
% 0.21/0.49 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.21/0.52
%------------------------------------------------------------------------------