TSTP Solution File: GRP012-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP012-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n003.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 10:32:14 EDT 2022
% Result : Unsatisfiable 0.60s 0.84s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 24
% Syntax : Number of clauses : 140 ( 66 unt; 0 nHn; 109 RR)
% Number of literals : 252 ( 94 equ; 114 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 : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 118 ( 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(right_inverse,axiom,
product(X,inverse(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(a_multiply_b_is_c,hypothesis,
product(a,b,c) ).
cnf(inverse_b_multiply_inverse_a_is_d,hypothesis,
product(inverse(b),inverse(a),d) ).
cnf(prove_c_inverse_equals_d,negated_conjecture,
inverse(c) != d ).
cnf(refute_0_0,plain,
product(X_51,X_52,multiply(X_51,X_52)),
inference(subst,[],[total_function1:[bind(X,$fot(X_51)),bind(Y,$fot(X_52))]]) ).
cnf(refute_0_1,plain,
( ~ product(X_51,X_52,X_53)
| ~ product(X_51,X_52,multiply(X_51,X_52))
| X_53 = multiply(X_51,X_52) ),
inference(subst,[],[total_function2:[bind(W,$fot(multiply(X_51,X_52))),bind(X,$fot(X_51)),bind(Y,$fot(X_52)),bind(Z,$fot(X_53))]]) ).
cnf(refute_0_2,plain,
( ~ product(X_51,X_52,X_53)
| X_53 = multiply(X_51,X_52) ),
inference(resolve,[$cnf( product(X_51,X_52,multiply(X_51,X_52)) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ product(inverse(c),identity,d)
| d = multiply(inverse(c),identity) ),
inference(subst,[],[refute_0_2:[bind(X_51,$fot(inverse(c))),bind(X_52,$fot(identity)),bind(X_53,$fot(d))]]) ).
cnf(refute_0_4,plain,
product(X_262,inverse(a),multiply(X_262,inverse(a))),
inference(subst,[],[total_function1:[bind(X,$fot(X_262)),bind(Y,$fot(inverse(a)))]]) ).
cnf(refute_0_5,plain,
( ~ product(X_112,X_113,inverse(b))
| ~ product(X_113,inverse(a),X_110)
| ~ product(inverse(b),inverse(a),d)
| product(X_112,X_110,d) ),
inference(subst,[],[associativity1:[bind(U,$fot(inverse(b))),bind(V,$fot(X_110)),bind(W,$fot(d)),bind(X,$fot(X_112)),bind(Y,$fot(X_113)),bind(Z,$fot(inverse(a)))]]) ).
cnf(refute_0_6,plain,
( ~ product(X_112,X_113,inverse(b))
| ~ product(X_113,inverse(a),X_110)
| product(X_112,X_110,d) ),
inference(resolve,[$cnf( product(inverse(b),inverse(a),d) )],[inverse_b_multiply_inverse_a_is_d,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ product(X_261,X_262,inverse(b))
| ~ product(X_262,inverse(a),multiply(X_262,inverse(a)))
| product(X_261,multiply(X_262,inverse(a)),d) ),
inference(subst,[],[refute_0_6:[bind(X_110,$fot(multiply(X_262,inverse(a)))),bind(X_112,$fot(X_261)),bind(X_113,$fot(X_262))]]) ).
cnf(refute_0_8,plain,
( ~ product(X_261,X_262,inverse(b))
| product(X_261,multiply(X_262,inverse(a)),d) ),
inference(resolve,[$cnf( product(X_262,inverse(a),multiply(X_262,inverse(a))) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ product(inverse(c),a,inverse(b))
| product(inverse(c),multiply(a,inverse(a)),d) ),
inference(subst,[],[refute_0_8:[bind(X_261,$fot(inverse(c))),bind(X_262,$fot(a))]]) ).
cnf(refute_0_10,plain,
product(inverse(c),c,identity),
inference(subst,[],[left_inverse:[bind(X,$fot(c))]]) ).
cnf(refute_0_11,plain,
product(identity,X_111,X_111),
inference(subst,[],[left_identity:[bind(X,$fot(X_111))]]) ).
cnf(refute_0_12,plain,
( ~ product(X_112,X_113,identity)
| ~ product(X_113,X_111,X_110)
| ~ product(identity,X_111,X_111)
| product(X_112,X_110,X_111) ),
inference(subst,[],[associativity1:[bind(U,$fot(identity)),bind(V,$fot(X_110)),bind(W,$fot(X_111)),bind(X,$fot(X_112)),bind(Y,$fot(X_113)),bind(Z,$fot(X_111))]]) ).
cnf(refute_0_13,plain,
( ~ product(X_112,X_113,identity)
| ~ product(X_113,X_111,X_110)
| product(X_112,X_110,X_111) ),
inference(resolve,[$cnf( product(identity,X_111,X_111) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ product(X_112,c,identity)
| ~ product(c,inverse(b),a)
| product(X_112,a,inverse(b)) ),
inference(subst,[],[refute_0_13:[bind(X_110,$fot(a)),bind(X_111,$fot(inverse(b))),bind(X_113,$fot(c))]]) ).
cnf(refute_0_15,plain,
product(inverse(d),d,identity),
inference(subst,[],[left_inverse:[bind(X,$fot(d))]]) ).
cnf(refute_0_16,plain,
( ~ product(inverse(d),identity,c)
| c = multiply(inverse(d),identity) ),
inference(subst,[],[refute_0_2:[bind(X_51,$fot(inverse(d))),bind(X_52,$fot(identity)),bind(X_53,$fot(c))]]) ).
cnf(refute_0_17,plain,
product(d,c,multiply(d,c)),
inference(subst,[],[total_function1:[bind(X,$fot(d)),bind(Y,$fot(c))]]) ).
cnf(refute_0_18,plain,
( ~ product(X_210,c,multiply(multiply(X_210,a),b))
| multiply(multiply(X_210,a),b) = multiply(X_210,c) ),
inference(subst,[],[refute_0_2:[bind(X_51,$fot(X_210)),bind(X_52,$fot(c)),bind(X_53,$fot(multiply(multiply(X_210,a),b)))]]) ).
cnf(refute_0_19,plain,
product(X_209,a,multiply(X_209,a)),
inference(subst,[],[total_function1:[bind(X,$fot(X_209)),bind(Y,$fot(a))]]) ).
cnf(refute_0_20,plain,
product(X_195,b,multiply(X_195,b)),
inference(subst,[],[total_function1:[bind(X,$fot(X_195)),bind(Y,$fot(b))]]) ).
cnf(refute_0_21,plain,
( ~ product(X_109,b,X_111)
| ~ product(X_112,a,X_109)
| ~ product(a,b,c)
| product(X_112,c,X_111) ),
inference(subst,[],[associativity1:[bind(U,$fot(X_109)),bind(V,$fot(c)),bind(W,$fot(X_111)),bind(X,$fot(X_112)),bind(Y,$fot(a)),bind(Z,$fot(b))]]) ).
cnf(refute_0_22,plain,
( ~ product(X_109,b,X_111)
| ~ product(X_112,a,X_109)
| product(X_112,c,X_111) ),
inference(resolve,[$cnf( product(a,b,c) )],[a_multiply_b_is_c,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ product(X_195,b,multiply(X_195,b))
| ~ product(X_197,a,X_195)
| product(X_197,c,multiply(X_195,b)) ),
inference(subst,[],[refute_0_22:[bind(X_109,$fot(X_195)),bind(X_111,$fot(multiply(X_195,b))),bind(X_112,$fot(X_197))]]) ).
cnf(refute_0_24,plain,
( ~ product(X_197,a,X_195)
| product(X_197,c,multiply(X_195,b)) ),
inference(resolve,[$cnf( product(X_195,b,multiply(X_195,b)) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ product(X_209,a,multiply(X_209,a))
| product(X_209,c,multiply(multiply(X_209,a),b)) ),
inference(subst,[],[refute_0_24:[bind(X_195,$fot(multiply(X_209,a))),bind(X_197,$fot(X_209))]]) ).
cnf(refute_0_26,plain,
product(X_209,c,multiply(multiply(X_209,a),b)),
inference(resolve,[$cnf( product(X_209,a,multiply(X_209,a)) )],[refute_0_19,refute_0_25]) ).
cnf(refute_0_27,plain,
product(X_210,c,multiply(multiply(X_210,a),b)),
inference(subst,[],[refute_0_26:[bind(X_209,$fot(X_210))]]) ).
cnf(refute_0_28,plain,
multiply(multiply(X_210,a),b) = multiply(X_210,c),
inference(resolve,[$cnf( product(X_210,c,multiply(multiply(X_210,a),b)) )],[refute_0_27,refute_0_18]) ).
cnf(refute_0_29,plain,
multiply(multiply(d,a),b) = multiply(d,c),
inference(subst,[],[refute_0_28:[bind(X_210,$fot(d))]]) ).
cnf(refute_0_30,plain,
( ~ product(inverse(b),identity,multiply(d,a))
| multiply(d,a) = multiply(inverse(b),identity) ),
inference(subst,[],[refute_0_2:[bind(X_51,$fot(inverse(b))),bind(X_52,$fot(identity)),bind(X_53,$fot(multiply(d,a)))]]) ).
cnf(refute_0_31,plain,
product(d,a,multiply(d,a)),
inference(subst,[],[total_function1:[bind(X,$fot(d)),bind(Y,$fot(a))]]) ).
cnf(refute_0_32,plain,
product(inverse(a),a,identity),
inference(subst,[],[left_inverse:[bind(X,$fot(a))]]) ).
cnf(refute_0_33,plain,
( ~ product(d,X_114,X_111)
| ~ product(inverse(a),X_114,X_110)
| ~ product(inverse(b),inverse(a),d)
| product(inverse(b),X_110,X_111) ),
inference(subst,[],[associativity1:[bind(U,$fot(d)),bind(V,$fot(X_110)),bind(W,$fot(X_111)),bind(X,$fot(inverse(b))),bind(Y,$fot(inverse(a))),bind(Z,$fot(X_114))]]) ).
cnf(refute_0_34,plain,
( ~ product(d,X_114,X_111)
| ~ product(inverse(a),X_114,X_110)
| product(inverse(b),X_110,X_111) ),
inference(resolve,[$cnf( product(inverse(b),inverse(a),d) )],[inverse_b_multiply_inverse_a_is_d,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ product(d,a,X_276)
| ~ product(inverse(a),a,identity)
| product(inverse(b),identity,X_276) ),
inference(subst,[],[refute_0_34:[bind(X_110,$fot(identity)),bind(X_111,$fot(X_276)),bind(X_114,$fot(a))]]) ).
cnf(refute_0_36,plain,
( ~ product(d,a,X_276)
| product(inverse(b),identity,X_276) ),
inference(resolve,[$cnf( product(inverse(a),a,identity) )],[refute_0_32,refute_0_35]) ).
cnf(refute_0_37,plain,
( ~ product(d,a,multiply(d,a))
| product(inverse(b),identity,multiply(d,a)) ),
inference(subst,[],[refute_0_36:[bind(X_276,$fot(multiply(d,a)))]]) ).
cnf(refute_0_38,plain,
product(inverse(b),identity,multiply(d,a)),
inference(resolve,[$cnf( product(d,a,multiply(d,a)) )],[refute_0_31,refute_0_37]) ).
cnf(refute_0_39,plain,
multiply(d,a) = multiply(inverse(b),identity),
inference(resolve,[$cnf( product(inverse(b),identity,multiply(d,a)) )],[refute_0_38,refute_0_30]) ).
cnf(refute_0_40,plain,
product(X_55,multiply(identity,identity),multiply(X_55,multiply(identity,identity))),
inference(subst,[],[total_function1:[bind(X,$fot(X_55)),bind(Y,$fot(multiply(identity,identity)))]]) ).
cnf(refute_0_41,plain,
product(identity,identity,multiply(identity,identity)),
inference(subst,[],[total_function1:[bind(X,$fot(identity)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_42,plain,
product(X_20,identity,X_20),
inference(subst,[],[right_identity:[bind(X,$fot(X_20))]]) ).
cnf(refute_0_43,plain,
( ~ product(X_20,identity,X_20)
| ~ product(identity,identity,X_19)
| product(X_20,X_19,X_20) ),
inference(subst,[],[associativity1:[bind(U,$fot(X_20)),bind(V,$fot(X_19)),bind(W,$fot(X_20)),bind(X,$fot(X_20)),bind(Y,$fot(identity)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_44,plain,
( ~ product(identity,identity,X_19)
| product(X_20,X_19,X_20) ),
inference(resolve,[$cnf( product(X_20,identity,X_20) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
( ~ product(identity,identity,multiply(identity,identity))
| product(X_24,multiply(identity,identity),X_24) ),
inference(subst,[],[refute_0_44:[bind(X_19,$fot(multiply(identity,identity))),bind(X_20,$fot(X_24))]]) ).
cnf(refute_0_46,plain,
product(X_24,multiply(identity,identity),X_24),
inference(resolve,[$cnf( product(identity,identity,multiply(identity,identity)) )],[refute_0_41,refute_0_45]) ).
cnf(refute_0_47,plain,
product(X_50,multiply(identity,identity),X_50),
inference(subst,[],[refute_0_46:[bind(X_24,$fot(X_50))]]) ).
cnf(refute_0_48,plain,
( ~ product(X_50,multiply(identity,identity),X_50)
| ~ product(X_50,multiply(identity,identity),X_53)
| X_53 = X_50 ),
inference(subst,[],[total_function2:[bind(W,$fot(X_50)),bind(X,$fot(X_50)),bind(Y,$fot(multiply(identity,identity))),bind(Z,$fot(X_53))]]) ).
cnf(refute_0_49,plain,
( ~ product(X_50,multiply(identity,identity),X_53)
| X_53 = X_50 ),
inference(resolve,[$cnf( product(X_50,multiply(identity,identity),X_50) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
( ~ product(X_55,multiply(identity,identity),multiply(X_55,multiply(identity,identity)))
| multiply(X_55,multiply(identity,identity)) = X_55 ),
inference(subst,[],[refute_0_49:[bind(X_50,$fot(X_55)),bind(X_53,$fot(multiply(X_55,multiply(identity,identity))))]]) ).
cnf(refute_0_51,plain,
multiply(X_55,multiply(identity,identity)) = X_55,
inference(resolve,[$cnf( product(X_55,multiply(identity,identity),multiply(X_55,multiply(identity,identity))) )],[refute_0_40,refute_0_50]) ).
cnf(refute_0_52,plain,
product(identity,multiply(identity,identity),multiply(identity,identity)),
inference(subst,[],[left_identity:[bind(X,$fot(multiply(identity,identity)))]]) ).
cnf(refute_0_53,plain,
( ~ product(identity,multiply(identity,identity),multiply(identity,identity))
| multiply(identity,identity) = identity ),
inference(subst,[],[refute_0_49:[bind(X_50,$fot(identity)),bind(X_53,$fot(multiply(identity,identity)))]]) ).
cnf(refute_0_54,plain,
multiply(identity,identity) = identity,
inference(resolve,[$cnf( product(identity,multiply(identity,identity),multiply(identity,identity)) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
multiply(X_55,multiply(identity,identity)) = multiply(X_55,multiply(identity,identity)),
introduced(tautology,[refl,[$fot(multiply(X_55,multiply(identity,identity)))]]) ).
cnf(refute_0_56,plain,
( multiply(X_55,multiply(identity,identity)) != multiply(X_55,multiply(identity,identity))
| multiply(identity,identity) != identity
| multiply(X_55,multiply(identity,identity)) = multiply(X_55,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_55,multiply(identity,identity)),multiply(X_55,multiply(identity,identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_57,plain,
( multiply(identity,identity) != identity
| multiply(X_55,multiply(identity,identity)) = multiply(X_55,identity) ),
inference(resolve,[$cnf( $equal(multiply(X_55,multiply(identity,identity)),multiply(X_55,multiply(identity,identity))) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
multiply(X_55,multiply(identity,identity)) = multiply(X_55,identity),
inference(resolve,[$cnf( $equal(multiply(identity,identity),identity) )],[refute_0_54,refute_0_57]) ).
cnf(refute_0_59,plain,
( multiply(X_55,multiply(identity,identity)) != X_55
| multiply(X_55,multiply(identity,identity)) != multiply(X_55,identity)
| multiply(X_55,identity) = X_55 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_55,multiply(identity,identity)),X_55) ),[0],$fot(multiply(X_55,identity))]]) ).
cnf(refute_0_60,plain,
( multiply(X_55,multiply(identity,identity)) != X_55
| multiply(X_55,identity) = X_55 ),
inference(resolve,[$cnf( $equal(multiply(X_55,multiply(identity,identity)),multiply(X_55,identity)) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
multiply(X_55,identity) = X_55,
inference(resolve,[$cnf( $equal(multiply(X_55,multiply(identity,identity)),X_55) )],[refute_0_51,refute_0_60]) ).
cnf(refute_0_62,plain,
multiply(inverse(b),identity) = inverse(b),
inference(subst,[],[refute_0_61:[bind(X_55,$fot(inverse(b)))]]) ).
cnf(refute_0_63,plain,
( multiply(d,a) != multiply(inverse(b),identity)
| multiply(inverse(b),identity) != inverse(b)
| multiply(d,a) = inverse(b) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(d,a),inverse(b)) ),[0],$fot(multiply(inverse(b),identity))]]) ).
cnf(refute_0_64,plain,
( multiply(d,a) != multiply(inverse(b),identity)
| multiply(d,a) = inverse(b) ),
inference(resolve,[$cnf( $equal(multiply(inverse(b),identity),inverse(b)) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
multiply(d,a) = inverse(b),
inference(resolve,[$cnf( $equal(multiply(d,a),multiply(inverse(b),identity)) )],[refute_0_39,refute_0_64]) ).
cnf(refute_0_66,plain,
( multiply(multiply(d,a),b) != multiply(d,c)
| multiply(d,a) != inverse(b)
| multiply(inverse(b),b) = multiply(d,c) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(d,a),b),multiply(d,c)) ),[0,0],$fot(inverse(b))]]) ).
cnf(refute_0_67,plain,
( multiply(multiply(d,a),b) != multiply(d,c)
| multiply(inverse(b),b) = multiply(d,c) ),
inference(resolve,[$cnf( $equal(multiply(d,a),inverse(b)) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
multiply(inverse(b),b) = multiply(d,c),
inference(resolve,[$cnf( $equal(multiply(multiply(d,a),b),multiply(d,c)) )],[refute_0_29,refute_0_67]) ).
cnf(refute_0_69,plain,
product(inverse(X_64),X_64,multiply(inverse(X_64),X_64)),
inference(subst,[],[total_function1:[bind(X,$fot(inverse(X_64))),bind(Y,$fot(X_64))]]) ).
cnf(refute_0_70,plain,
product(inverse(X_52),X_52,identity),
inference(subst,[],[left_inverse:[bind(X,$fot(X_52))]]) ).
cnf(refute_0_71,plain,
( ~ product(inverse(X_52),X_52,X_53)
| ~ product(inverse(X_52),X_52,identity)
| X_53 = identity ),
inference(subst,[],[total_function2:[bind(W,$fot(identity)),bind(X,$fot(inverse(X_52))),bind(Y,$fot(X_52)),bind(Z,$fot(X_53))]]) ).
cnf(refute_0_72,plain,
( ~ product(inverse(X_52),X_52,X_53)
| X_53 = identity ),
inference(resolve,[$cnf( product(inverse(X_52),X_52,identity) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
( ~ product(inverse(X_64),X_64,multiply(inverse(X_64),X_64))
| multiply(inverse(X_64),X_64) = identity ),
inference(subst,[],[refute_0_72:[bind(X_52,$fot(X_64)),bind(X_53,$fot(multiply(inverse(X_64),X_64)))]]) ).
cnf(refute_0_74,plain,
multiply(inverse(X_64),X_64) = identity,
inference(resolve,[$cnf( product(inverse(X_64),X_64,multiply(inverse(X_64),X_64)) )],[refute_0_69,refute_0_73]) ).
cnf(refute_0_75,plain,
multiply(inverse(b),b) = identity,
inference(subst,[],[refute_0_74:[bind(X_64,$fot(b))]]) ).
cnf(refute_0_76,plain,
( multiply(inverse(b),b) != multiply(d,c)
| multiply(inverse(b),b) != identity
| identity = multiply(d,c) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(b),b),multiply(d,c)) ),[0],$fot(identity)]]) ).
cnf(refute_0_77,plain,
( multiply(inverse(b),b) != multiply(d,c)
| identity = multiply(d,c) ),
inference(resolve,[$cnf( $equal(multiply(inverse(b),b),identity) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
identity = multiply(d,c),
inference(resolve,[$cnf( $equal(multiply(inverse(b),b),multiply(d,c)) )],[refute_0_68,refute_0_77]) ).
cnf(refute_0_79,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_80,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_81,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
( identity != multiply(d,c)
| multiply(d,c) = identity ),
inference(subst,[],[refute_0_81:[bind(X0,$fot(identity)),bind(Y0,$fot(multiply(d,c)))]]) ).
cnf(refute_0_83,plain,
multiply(d,c) = identity,
inference(resolve,[$cnf( $equal(identity,multiply(d,c)) )],[refute_0_78,refute_0_82]) ).
cnf(refute_0_84,plain,
( multiply(d,c) != identity
| ~ product(d,c,multiply(d,c))
| product(d,c,identity) ),
introduced(tautology,[equality,[$cnf( product(d,c,multiply(d,c)) ),[2],$fot(identity)]]) ).
cnf(refute_0_85,plain,
( ~ product(d,c,multiply(d,c))
| product(d,c,identity) ),
inference(resolve,[$cnf( $equal(multiply(d,c),identity) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
product(d,c,identity),
inference(resolve,[$cnf( product(d,c,multiply(d,c)) )],[refute_0_17,refute_0_85]) ).
cnf(refute_0_87,plain,
( ~ product(X_405,d,identity)
| ~ product(d,c,identity)
| product(X_405,identity,c) ),
inference(subst,[],[refute_0_13:[bind(X_110,$fot(identity)),bind(X_111,$fot(c)),bind(X_112,$fot(X_405)),bind(X_113,$fot(d))]]) ).
cnf(refute_0_88,plain,
( ~ product(X_405,d,identity)
| product(X_405,identity,c) ),
inference(resolve,[$cnf( product(d,c,identity) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
( ~ product(inverse(d),d,identity)
| product(inverse(d),identity,c) ),
inference(subst,[],[refute_0_88:[bind(X_405,$fot(inverse(d)))]]) ).
cnf(refute_0_90,plain,
product(inverse(d),identity,c),
inference(resolve,[$cnf( product(inverse(d),d,identity) )],[refute_0_15,refute_0_89]) ).
cnf(refute_0_91,plain,
c = multiply(inverse(d),identity),
inference(resolve,[$cnf( product(inverse(d),identity,c) )],[refute_0_90,refute_0_16]) ).
cnf(refute_0_92,plain,
multiply(inverse(d),identity) = inverse(d),
inference(subst,[],[refute_0_61:[bind(X_55,$fot(inverse(d)))]]) ).
cnf(refute_0_93,plain,
( multiply(inverse(d),identity) != inverse(d)
| c != multiply(inverse(d),identity)
| c = inverse(d) ),
introduced(tautology,[equality,[$cnf( $equal(c,multiply(inverse(d),identity)) ),[1],$fot(inverse(d))]]) ).
cnf(refute_0_94,plain,
( c != multiply(inverse(d),identity)
| c = inverse(d) ),
inference(resolve,[$cnf( $equal(multiply(inverse(d),identity),inverse(d)) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
c = inverse(d),
inference(resolve,[$cnf( $equal(c,multiply(inverse(d),identity)) )],[refute_0_91,refute_0_94]) ).
cnf(refute_0_96,plain,
( c != inverse(d)
| inverse(d) = c ),
inference(subst,[],[refute_0_81:[bind(X0,$fot(c)),bind(Y0,$fot(inverse(d)))]]) ).
cnf(refute_0_97,plain,
inverse(d) = c,
inference(resolve,[$cnf( $equal(c,inverse(d)) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
( inverse(d) != c
| ~ product(inverse(d),d,identity)
| product(c,d,identity) ),
introduced(tautology,[equality,[$cnf( product(inverse(d),d,identity) ),[0],$fot(c)]]) ).
cnf(refute_0_99,plain,
( ~ product(inverse(d),d,identity)
| product(c,d,identity) ),
inference(resolve,[$cnf( $equal(inverse(d),c) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
product(c,d,identity),
inference(resolve,[$cnf( product(inverse(d),d,identity) )],[refute_0_15,refute_0_99]) ).
cnf(refute_0_101,plain,
( multiply(d,a) != inverse(b)
| ~ product(d,a,multiply(d,a))
| product(d,a,inverse(b)) ),
introduced(tautology,[equality,[$cnf( product(d,a,multiply(d,a)) ),[2],$fot(inverse(b))]]) ).
cnf(refute_0_102,plain,
( ~ product(d,a,multiply(d,a))
| product(d,a,inverse(b)) ),
inference(resolve,[$cnf( $equal(multiply(d,a),inverse(b)) )],[refute_0_65,refute_0_101]) ).
cnf(refute_0_103,plain,
product(d,a,inverse(b)),
inference(resolve,[$cnf( product(d,a,multiply(d,a)) )],[refute_0_31,refute_0_102]) ).
cnf(refute_0_104,plain,
( ~ product(X_405,d,identity)
| ~ product(d,a,inverse(b))
| product(X_405,inverse(b),a) ),
inference(subst,[],[refute_0_13:[bind(X_110,$fot(inverse(b))),bind(X_111,$fot(a)),bind(X_112,$fot(X_405)),bind(X_113,$fot(d))]]) ).
cnf(refute_0_105,plain,
( ~ product(X_405,d,identity)
| product(X_405,inverse(b),a) ),
inference(resolve,[$cnf( product(d,a,inverse(b)) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
( ~ product(c,d,identity)
| product(c,inverse(b),a) ),
inference(subst,[],[refute_0_105:[bind(X_405,$fot(c))]]) ).
cnf(refute_0_107,plain,
product(c,inverse(b),a),
inference(resolve,[$cnf( product(c,d,identity) )],[refute_0_100,refute_0_106]) ).
cnf(refute_0_108,plain,
( ~ product(X_112,c,identity)
| product(X_112,a,inverse(b)) ),
inference(resolve,[$cnf( product(c,inverse(b),a) )],[refute_0_107,refute_0_14]) ).
cnf(refute_0_109,plain,
( ~ product(inverse(c),c,identity)
| product(inverse(c),a,inverse(b)) ),
inference(subst,[],[refute_0_108:[bind(X_112,$fot(inverse(c)))]]) ).
cnf(refute_0_110,plain,
product(inverse(c),a,inverse(b)),
inference(resolve,[$cnf( product(inverse(c),c,identity) )],[refute_0_10,refute_0_109]) ).
cnf(refute_0_111,plain,
product(inverse(c),multiply(a,inverse(a)),d),
inference(resolve,[$cnf( product(inverse(c),a,inverse(b)) )],[refute_0_110,refute_0_9]) ).
cnf(refute_0_112,plain,
product(X_67,inverse(X_67),multiply(X_67,inverse(X_67))),
inference(subst,[],[total_function1:[bind(X,$fot(X_67)),bind(Y,$fot(inverse(X_67)))]]) ).
cnf(refute_0_113,plain,
product(X_51,inverse(X_51),identity),
inference(subst,[],[right_inverse:[bind(X,$fot(X_51))]]) ).
cnf(refute_0_114,plain,
( ~ product(X_51,inverse(X_51),X_53)
| ~ product(X_51,inverse(X_51),identity)
| X_53 = identity ),
inference(subst,[],[total_function2:[bind(W,$fot(identity)),bind(X,$fot(X_51)),bind(Y,$fot(inverse(X_51))),bind(Z,$fot(X_53))]]) ).
cnf(refute_0_115,plain,
( ~ product(X_51,inverse(X_51),X_53)
| X_53 = identity ),
inference(resolve,[$cnf( product(X_51,inverse(X_51),identity) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
( ~ product(X_67,inverse(X_67),multiply(X_67,inverse(X_67)))
| multiply(X_67,inverse(X_67)) = identity ),
inference(subst,[],[refute_0_115:[bind(X_51,$fot(X_67)),bind(X_53,$fot(multiply(X_67,inverse(X_67))))]]) ).
cnf(refute_0_117,plain,
multiply(X_67,inverse(X_67)) = identity,
inference(resolve,[$cnf( product(X_67,inverse(X_67),multiply(X_67,inverse(X_67))) )],[refute_0_112,refute_0_116]) ).
cnf(refute_0_118,plain,
multiply(a,inverse(a)) = identity,
inference(subst,[],[refute_0_117:[bind(X_67,$fot(a))]]) ).
cnf(refute_0_119,plain,
( multiply(a,inverse(a)) != identity
| ~ product(inverse(c),multiply(a,inverse(a)),d)
| product(inverse(c),identity,d) ),
introduced(tautology,[equality,[$cnf( product(inverse(c),multiply(a,inverse(a)),d) ),[1],$fot(identity)]]) ).
cnf(refute_0_120,plain,
( ~ product(inverse(c),multiply(a,inverse(a)),d)
| product(inverse(c),identity,d) ),
inference(resolve,[$cnf( $equal(multiply(a,inverse(a)),identity) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
product(inverse(c),identity,d),
inference(resolve,[$cnf( product(inverse(c),multiply(a,inverse(a)),d) )],[refute_0_111,refute_0_120]) ).
cnf(refute_0_122,plain,
d = multiply(inverse(c),identity),
inference(resolve,[$cnf( product(inverse(c),identity,d) )],[refute_0_121,refute_0_3]) ).
cnf(refute_0_123,plain,
multiply(inverse(c),identity) = inverse(c),
inference(subst,[],[refute_0_61:[bind(X_55,$fot(inverse(c)))]]) ).
cnf(refute_0_124,plain,
( multiply(inverse(c),identity) != inverse(c)
| d != multiply(inverse(c),identity)
| d = inverse(c) ),
introduced(tautology,[equality,[$cnf( $equal(d,multiply(inverse(c),identity)) ),[1],$fot(inverse(c))]]) ).
cnf(refute_0_125,plain,
( d != multiply(inverse(c),identity)
| d = inverse(c) ),
inference(resolve,[$cnf( $equal(multiply(inverse(c),identity),inverse(c)) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
d = inverse(c),
inference(resolve,[$cnf( $equal(d,multiply(inverse(c),identity)) )],[refute_0_122,refute_0_125]) ).
cnf(refute_0_127,plain,
( d != inverse(c)
| inverse(c) = d ),
inference(subst,[],[refute_0_81:[bind(X0,$fot(d)),bind(Y0,$fot(inverse(c)))]]) ).
cnf(refute_0_128,plain,
d != inverse(c),
inference(resolve,[$cnf( $equal(inverse(c),d) )],[refute_0_127,prove_c_inverse_equals_d]) ).
cnf(refute_0_129,plain,
$false,
inference(resolve,[$cnf( $equal(d,inverse(c)) )],[refute_0_126,refute_0_128]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP012-2 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.36 % DateTime : Tue Jun 14 09:53:10 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.60/0.84 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.60/0.84
% 0.60/0.84 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.60/0.85
%------------------------------------------------------------------------------