%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP009-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 10:32:13 EDT 2022
% Result : Unsatisfiable 0.19s 0.50s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 21
% Syntax : Number of clauses : 104 ( 51 unt; 0 nHn; 74 RR)
% Number of literals : 187 ( 71 equ; 85 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 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 : 110 ( 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(a_is_an_inverse_of_b,hypothesis,
product(a,b,identity) ).
cnf(c_is_an_inverse_of_b,hypothesis,
product(c,b,identity) ).
cnf(prove_a_equals_c,negated_conjecture,
a != c ).
cnf(refute_0_0,plain,
product(X_50,X_51,multiply(X_50,X_51)),
inference(subst,[],[total_function1:[bind(X,$fot(X_50)),bind(Y,$fot(X_51))]]) ).
cnf(refute_0_1,plain,
( ~ product(X_50,X_51,X_52)
| ~ product(X_50,X_51,multiply(X_50,X_51))
| X_52 = multiply(X_50,X_51) ),
inference(subst,[],[total_function2:[bind(W,$fot(multiply(X_50,X_51))),bind(X,$fot(X_50)),bind(Y,$fot(X_51)),bind(Z,$fot(X_52))]]) ).
cnf(refute_0_2,plain,
( ~ product(X_50,X_51,X_52)
| X_52 = multiply(X_50,X_51) ),
inference(resolve,[$cnf( product(X_50,X_51,multiply(X_50,X_51)) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ product(a,identity,c)
| c = multiply(a,identity) ),
inference(subst,[],[refute_0_2:[bind(X_50,$fot(a)),bind(X_51,$fot(identity)),bind(X_52,$fot(c))]]) ).
cnf(refute_0_4,plain,
product(multiply(X_202,a),b,multiply(multiply(X_202,a),b)),
inference(subst,[],[total_function1:[bind(X,$fot(multiply(X_202,a))),bind(Y,$fot(b))]]) ).
cnf(refute_0_5,plain,
( ~ product(X_201,identity,multiply(multiply(X_201,a),b))
| multiply(multiply(X_201,a),b) = multiply(X_201,identity) ),
inference(subst,[],[refute_0_2:[bind(X_50,$fot(X_201)),bind(X_51,$fot(identity)),bind(X_52,$fot(multiply(multiply(X_201,a),b)))]]) ).
cnf(refute_0_6,plain,
product(X_200,a,multiply(X_200,a)),
inference(subst,[],[total_function1:[bind(X,$fot(X_200)),bind(Y,$fot(a))]]) ).
cnf(refute_0_7,plain,
product(X_192,b,multiply(X_192,b)),
inference(subst,[],[total_function1:[bind(X,$fot(X_192)),bind(Y,$fot(b))]]) ).
cnf(refute_0_8,plain,
( ~ product(X_105,b,X_107)
| ~ product(X_108,a,X_105)
| ~ product(a,b,identity)
| product(X_108,identity,X_107) ),
inference(subst,[],[associativity1:[bind(U,$fot(X_105)),bind(V,$fot(identity)),bind(W,$fot(X_107)),bind(X,$fot(X_108)),bind(Y,$fot(a)),bind(Z,$fot(b))]]) ).
cnf(refute_0_9,plain,
( ~ product(X_105,b,X_107)
| ~ product(X_108,a,X_105)
| product(X_108,identity,X_107) ),
inference(resolve,[$cnf( product(a,b,identity) )],[a_is_an_inverse_of_b,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ product(X_192,b,multiply(X_192,b))
| ~ product(X_194,a,X_192)
| product(X_194,identity,multiply(X_192,b)) ),
inference(subst,[],[refute_0_9:[bind(X_105,$fot(X_192)),bind(X_107,$fot(multiply(X_192,b))),bind(X_108,$fot(X_194))]]) ).
cnf(refute_0_11,plain,
( ~ product(X_194,a,X_192)
| product(X_194,identity,multiply(X_192,b)) ),
inference(resolve,[$cnf( product(X_192,b,multiply(X_192,b)) )],[refute_0_7,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ product(X_200,a,multiply(X_200,a))
| product(X_200,identity,multiply(multiply(X_200,a),b)) ),
inference(subst,[],[refute_0_11:[bind(X_192,$fot(multiply(X_200,a))),bind(X_194,$fot(X_200))]]) ).
cnf(refute_0_13,plain,
product(X_200,identity,multiply(multiply(X_200,a),b)),
inference(resolve,[$cnf( product(X_200,a,multiply(X_200,a)) )],[refute_0_6,refute_0_12]) ).
cnf(refute_0_14,plain,
product(X_201,identity,multiply(multiply(X_201,a),b)),
inference(subst,[],[refute_0_13:[bind(X_200,$fot(X_201))]]) ).
cnf(refute_0_15,plain,
multiply(multiply(X_201,a),b) = multiply(X_201,identity),
inference(resolve,[$cnf( product(X_201,identity,multiply(multiply(X_201,a),b)) )],[refute_0_14,refute_0_5]) ).
cnf(refute_0_16,plain,
product(X_70,identity,multiply(X_70,identity)),
inference(subst,[],[total_function1:[bind(X,$fot(X_70)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_17,plain,
product(X_49,identity,X_49),
inference(subst,[],[right_identity:[bind(X,$fot(X_49))]]) ).
cnf(refute_0_18,plain,
( ~ product(X_49,identity,X_49)
| ~ product(X_49,identity,X_52)
| X_52 = X_49 ),
inference(subst,[],[total_function2:[bind(W,$fot(X_49)),bind(X,$fot(X_49)),bind(Y,$fot(identity)),bind(Z,$fot(X_52))]]) ).
cnf(refute_0_19,plain,
( ~ product(X_49,identity,X_52)
| X_52 = X_49 ),
inference(resolve,[$cnf( product(X_49,identity,X_49) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ product(X_70,identity,multiply(X_70,identity))
| multiply(X_70,identity) = X_70 ),
inference(subst,[],[refute_0_19:[bind(X_49,$fot(X_70)),bind(X_52,$fot(multiply(X_70,identity)))]]) ).
cnf(refute_0_21,plain,
multiply(X_70,identity) = X_70,
inference(resolve,[$cnf( product(X_70,identity,multiply(X_70,identity)) )],[refute_0_16,refute_0_20]) ).
cnf(refute_0_22,plain,
multiply(X_201,identity) = X_201,
inference(subst,[],[refute_0_21:[bind(X_70,$fot(X_201))]]) ).
cnf(refute_0_23,plain,
( multiply(X_201,identity) != X_201
| multiply(multiply(X_201,a),b) != multiply(X_201,identity)
| multiply(multiply(X_201,a),b) = X_201 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_201,a),b),multiply(X_201,identity)) ),[1],$fot(X_201)]]) ).
cnf(refute_0_24,plain,
( multiply(multiply(X_201,a),b) != multiply(X_201,identity)
| multiply(multiply(X_201,a),b) = X_201 ),
inference(resolve,[$cnf( $equal(multiply(X_201,identity),X_201) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
multiply(multiply(X_201,a),b) = X_201,
inference(resolve,[$cnf( $equal(multiply(multiply(X_201,a),b),multiply(X_201,identity)) )],[refute_0_15,refute_0_24]) ).
cnf(refute_0_26,plain,
multiply(multiply(X_202,a),b) = X_202,
inference(subst,[],[refute_0_25:[bind(X_201,$fot(X_202))]]) ).
cnf(refute_0_27,plain,
( multiply(multiply(X_202,a),b) != X_202
| ~ product(multiply(X_202,a),b,multiply(multiply(X_202,a),b))
| product(multiply(X_202,a),b,X_202) ),
introduced(tautology,[equality,[$cnf( product(multiply(X_202,a),b,multiply(multiply(X_202,a),b)) ),[2],$fot(X_202)]]) ).
cnf(refute_0_28,plain,
( ~ product(multiply(X_202,a),b,multiply(multiply(X_202,a),b))
| product(multiply(X_202,a),b,X_202) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_202,a),b),X_202) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
product(multiply(X_202,a),b,X_202),
inference(resolve,[$cnf( product(multiply(X_202,a),b,multiply(multiply(X_202,a),b)) )],[refute_0_4,refute_0_28]) ).
cnf(refute_0_30,plain,
product(multiply(identity,a),b,identity),
inference(subst,[],[refute_0_29:[bind(X_202,$fot(identity))]]) ).
cnf(refute_0_31,plain,
product(inverse(c),c,identity),
inference(subst,[],[left_inverse:[bind(X,$fot(c))]]) ).
cnf(refute_0_32,plain,
( ~ product(inverse(c),identity,b)
| b = multiply(inverse(c),identity) ),
inference(subst,[],[refute_0_2:[bind(X_50,$fot(inverse(c))),bind(X_51,$fot(identity)),bind(X_52,$fot(b))]]) ).
cnf(refute_0_33,plain,
product(identity,b,b),
inference(subst,[],[left_identity:[bind(X,$fot(b))]]) ).
cnf(refute_0_34,plain,
( ~ product(X_105,b,X_107)
| ~ product(X_108,c,X_105)
| ~ product(c,b,identity)
| product(X_108,identity,X_107) ),
inference(subst,[],[associativity1:[bind(U,$fot(X_105)),bind(V,$fot(identity)),bind(W,$fot(X_107)),bind(X,$fot(X_108)),bind(Y,$fot(c)),bind(Z,$fot(b))]]) ).
cnf(refute_0_35,plain,
( ~ product(X_105,b,X_107)
| ~ product(X_108,c,X_105)
| product(X_108,identity,X_107) ),
inference(resolve,[$cnf( product(c,b,identity) )],[c_is_an_inverse_of_b,refute_0_34]) ).
cnf(refute_0_36,plain,
( ~ product(X_140,c,identity)
| ~ product(identity,b,b)
| product(X_140,identity,b) ),
inference(subst,[],[refute_0_35:[bind(X_105,$fot(identity)),bind(X_107,$fot(b)),bind(X_108,$fot(X_140))]]) ).
cnf(refute_0_37,plain,
( ~ product(X_140,c,identity)
| product(X_140,identity,b) ),
inference(resolve,[$cnf( product(identity,b,b) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
( ~ product(inverse(c),c,identity)
| product(inverse(c),identity,b) ),
inference(subst,[],[refute_0_37:[bind(X_140,$fot(inverse(c)))]]) ).
cnf(refute_0_39,plain,
product(inverse(c),identity,b),
inference(resolve,[$cnf( product(inverse(c),c,identity) )],[refute_0_31,refute_0_38]) ).
cnf(refute_0_40,plain,
b = multiply(inverse(c),identity),
inference(resolve,[$cnf( product(inverse(c),identity,b) )],[refute_0_39,refute_0_32]) ).
cnf(refute_0_41,plain,
multiply(inverse(c),identity) = inverse(c),
inference(subst,[],[refute_0_21:[bind(X_70,$fot(inverse(c)))]]) ).
cnf(refute_0_42,plain,
( multiply(inverse(c),identity) != inverse(c)
| b != multiply(inverse(c),identity)
| b = inverse(c) ),
introduced(tautology,[equality,[$cnf( $equal(b,multiply(inverse(c),identity)) ),[1],$fot(inverse(c))]]) ).
cnf(refute_0_43,plain,
( b != multiply(inverse(c),identity)
| b = inverse(c) ),
inference(resolve,[$cnf( $equal(multiply(inverse(c),identity),inverse(c)) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
b = inverse(c),
inference(resolve,[$cnf( $equal(b,multiply(inverse(c),identity)) )],[refute_0_40,refute_0_43]) ).
cnf(refute_0_45,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_46,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_47,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
( b != inverse(c)
| inverse(c) = b ),
inference(subst,[],[refute_0_47:[bind(X0,$fot(b)),bind(Y0,$fot(inverse(c)))]]) ).
cnf(refute_0_49,plain,
inverse(c) = b,
inference(resolve,[$cnf( $equal(b,inverse(c)) )],[refute_0_44,refute_0_48]) ).
cnf(refute_0_50,plain,
( inverse(c) != b
| ~ product(inverse(c),c,identity)
| product(b,c,identity) ),
introduced(tautology,[equality,[$cnf( product(inverse(c),c,identity) ),[0],$fot(b)]]) ).
cnf(refute_0_51,plain,
( ~ product(inverse(c),c,identity)
| product(b,c,identity) ),
inference(resolve,[$cnf( $equal(inverse(c),b) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
product(b,c,identity),
inference(resolve,[$cnf( product(inverse(c),c,identity) )],[refute_0_31,refute_0_51]) ).
cnf(refute_0_53,plain,
product(identity,X_107,X_107),
inference(subst,[],[left_identity:[bind(X,$fot(X_107))]]) ).
cnf(refute_0_54,plain,
( ~ product(X_108,X_109,identity)
| ~ product(X_109,X_107,X_106)
| ~ product(identity,X_107,X_107)
| product(X_108,X_106,X_107) ),
inference(subst,[],[associativity1:[bind(U,$fot(identity)),bind(V,$fot(X_106)),bind(W,$fot(X_107)),bind(X,$fot(X_108)),bind(Y,$fot(X_109)),bind(Z,$fot(X_107))]]) ).
cnf(refute_0_55,plain,
( ~ product(X_108,X_109,identity)
| ~ product(X_109,X_107,X_106)
| product(X_108,X_106,X_107) ),
inference(resolve,[$cnf( product(identity,X_107,X_107) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
( ~ product(X_328,b,identity)
| ~ product(b,c,identity)
| product(X_328,identity,c) ),
inference(subst,[],[refute_0_55:[bind(X_106,$fot(identity)),bind(X_107,$fot(c)),bind(X_108,$fot(X_328)),bind(X_109,$fot(b))]]) ).
cnf(refute_0_57,plain,
( ~ product(X_328,b,identity)
| product(X_328,identity,c) ),
inference(resolve,[$cnf( product(b,c,identity) )],[refute_0_52,refute_0_56]) ).
cnf(refute_0_58,plain,
( ~ product(multiply(identity,a),b,identity)
| product(multiply(identity,a),identity,c) ),
inference(subst,[],[refute_0_57:[bind(X_328,$fot(multiply(identity,a)))]]) ).
cnf(refute_0_59,plain,
product(multiply(identity,a),identity,c),
inference(resolve,[$cnf( product(multiply(identity,a),b,identity) )],[refute_0_30,refute_0_58]) ).
cnf(refute_0_60,plain,
product(multiply(identity,identity),X_55,multiply(multiply(identity,identity),X_55)),
inference(subst,[],[total_function1:[bind(X,$fot(multiply(identity,identity))),bind(Y,$fot(X_55))]]) ).
cnf(refute_0_61,plain,
product(identity,X_10,X_10),
inference(subst,[],[left_identity:[bind(X,$fot(X_10))]]) ).
cnf(refute_0_62,plain,
product(X_7,X_7,multiply(X_7,X_7)),
inference(subst,[],[total_function1:[bind(X,$fot(X_7)),bind(Y,$fot(X_7))]]) ).
cnf(refute_0_63,plain,
( ~ product(X_7,X_7,multiply(X_7,X_7))
| ~ product(X_7,X_8,X_8)
| product(multiply(X_7,X_7),X_8,X_8) ),
inference(subst,[],[associativity2:[bind(U,$fot(multiply(X_7,X_7))),bind(V,$fot(X_8)),bind(W,$fot(X_8)),bind(X,$fot(X_7)),bind(Y,$fot(X_7)),bind(Z,$fot(X_8))]]) ).
cnf(refute_0_64,plain,
( ~ product(X_7,X_8,X_8)
| product(multiply(X_7,X_7),X_8,X_8) ),
inference(resolve,[$cnf( product(X_7,X_7,multiply(X_7,X_7)) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
( ~ product(identity,X_10,X_10)
| product(multiply(identity,identity),X_10,X_10) ),
inference(subst,[],[refute_0_64:[bind(X_7,$fot(identity)),bind(X_8,$fot(X_10))]]) ).
cnf(refute_0_66,plain,
product(multiply(identity,identity),X_10,X_10),
inference(resolve,[$cnf( product(identity,X_10,X_10) )],[refute_0_61,refute_0_65]) ).
cnf(refute_0_67,plain,
product(multiply(identity,identity),X_49,X_49),
inference(subst,[],[refute_0_66:[bind(X_10,$fot(X_49))]]) ).
cnf(refute_0_68,plain,
( ~ product(multiply(identity,identity),X_49,X_49)
| ~ product(multiply(identity,identity),X_49,X_52)
| X_52 = X_49 ),
inference(subst,[],[total_function2:[bind(W,$fot(X_49)),bind(X,$fot(multiply(identity,identity))),bind(Y,$fot(X_49)),bind(Z,$fot(X_52))]]) ).
cnf(refute_0_69,plain,
( ~ product(multiply(identity,identity),X_49,X_52)
| X_52 = X_49 ),
inference(resolve,[$cnf( product(multiply(identity,identity),X_49,X_49) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
( ~ product(multiply(identity,identity),X_55,multiply(multiply(identity,identity),X_55))
| multiply(multiply(identity,identity),X_55) = X_55 ),
inference(subst,[],[refute_0_69:[bind(X_49,$fot(X_55)),bind(X_52,$fot(multiply(multiply(identity,identity),X_55)))]]) ).
cnf(refute_0_71,plain,
multiply(multiply(identity,identity),X_55) = X_55,
inference(resolve,[$cnf( product(multiply(identity,identity),X_55,multiply(multiply(identity,identity),X_55)) )],[refute_0_60,refute_0_70]) ).
cnf(refute_0_72,plain,
product(multiply(identity,identity),identity,multiply(identity,identity)),
inference(subst,[],[right_identity:[bind(X,$fot(multiply(identity,identity)))]]) ).
cnf(refute_0_73,plain,
( ~ product(multiply(identity,identity),identity,multiply(identity,identity))
| multiply(identity,identity) = identity ),
inference(subst,[],[refute_0_69:[bind(X_49,$fot(identity)),bind(X_52,$fot(multiply(identity,identity)))]]) ).
cnf(refute_0_74,plain,
multiply(identity,identity) = identity,
inference(resolve,[$cnf( product(multiply(identity,identity),identity,multiply(identity,identity)) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
multiply(multiply(identity,identity),X_55) = multiply(multiply(identity,identity),X_55),
introduced(tautology,[refl,[$fot(multiply(multiply(identity,identity),X_55))]]) ).
cnf(refute_0_76,plain,
( multiply(multiply(identity,identity),X_55) != multiply(multiply(identity,identity),X_55)
| multiply(identity,identity) != identity
| multiply(multiply(identity,identity),X_55) = multiply(identity,X_55) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(identity,identity),X_55),multiply(multiply(identity,identity),X_55)) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_77,plain,
( multiply(identity,identity) != identity
| multiply(multiply(identity,identity),X_55) = multiply(identity,X_55) ),
inference(resolve,[$cnf( $equal(multiply(multiply(identity,identity),X_55),multiply(multiply(identity,identity),X_55)) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
multiply(multiply(identity,identity),X_55) = multiply(identity,X_55),
inference(resolve,[$cnf( $equal(multiply(identity,identity),identity) )],[refute_0_74,refute_0_77]) ).
cnf(refute_0_79,plain,
( multiply(multiply(identity,identity),X_55) != X_55
| multiply(multiply(identity,identity),X_55) != multiply(identity,X_55)
| multiply(identity,X_55) = X_55 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(identity,identity),X_55),X_55) ),[0],$fot(multiply(identity,X_55))]]) ).
cnf(refute_0_80,plain,
( multiply(multiply(identity,identity),X_55) != X_55
| multiply(identity,X_55) = X_55 ),
inference(resolve,[$cnf( $equal(multiply(multiply(identity,identity),X_55),multiply(identity,X_55)) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
multiply(identity,X_55) = X_55,
inference(resolve,[$cnf( $equal(multiply(multiply(identity,identity),X_55),X_55) )],[refute_0_71,refute_0_80]) ).
cnf(refute_0_82,plain,
multiply(identity,a) = a,
inference(subst,[],[refute_0_81:[bind(X_55,$fot(a))]]) ).
cnf(refute_0_83,plain,
( multiply(identity,a) != a
| ~ product(multiply(identity,a),identity,c)
| product(a,identity,c) ),
introduced(tautology,[equality,[$cnf( product(multiply(identity,a),identity,c) ),[0],$fot(a)]]) ).
cnf(refute_0_84,plain,
( ~ product(multiply(identity,a),identity,c)
| product(a,identity,c) ),
inference(resolve,[$cnf( $equal(multiply(identity,a),a) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
product(a,identity,c),
inference(resolve,[$cnf( product(multiply(identity,a),identity,c) )],[refute_0_59,refute_0_84]) ).
cnf(refute_0_86,plain,
c = multiply(a,identity),
inference(resolve,[$cnf( product(a,identity,c) )],[refute_0_85,refute_0_3]) ).
cnf(refute_0_87,plain,
multiply(a,identity) = a,
inference(subst,[],[refute_0_21:[bind(X_70,$fot(a))]]) ).
cnf(refute_0_88,plain,
( multiply(a,identity) != a
| c != multiply(a,identity)
| c = a ),
introduced(tautology,[equality,[$cnf( $equal(c,multiply(a,identity)) ),[1],$fot(a)]]) ).
cnf(refute_0_89,plain,
( c != multiply(a,identity)
| c = a ),
inference(resolve,[$cnf( $equal(multiply(a,identity),a) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
c = a,
inference(resolve,[$cnf( $equal(c,multiply(a,identity)) )],[refute_0_86,refute_0_89]) ).
cnf(refute_0_91,plain,
( c != a
| a = c ),
inference(subst,[],[refute_0_47:[bind(X0,$fot(c)),bind(Y0,$fot(a))]]) ).
cnf(refute_0_92,plain,
c != a,
inference(resolve,[$cnf( $equal(a,c) )],[refute_0_91,prove_a_equals_c]) ).
cnf(refute_0_93,plain,
$false,
inference(resolve,[$cnf( $equal(c,a) )],[refute_0_90,refute_0_92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP009-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n026.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 Jun 13 21:40:21 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.50 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.50
% 0.19/0.50 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.51
%------------------------------------------------------------------------------