TSTP Solution File: GRP013-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP013-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 10:32:16 EDT 2022
% Result : Unsatisfiable 0.21s 0.45s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 26
% Syntax : Number of clauses : 99 ( 51 unt; 0 nHn; 69 RR)
% Number of literals : 168 ( 105 equ; 71 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 2 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 : 81 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
product(identity,X,X) ).
cnf(right_identity,axiom,
product(X,identity,X) ).
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(associativity2,axiom,
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W)
| product(U,Z,W) ) ).
cnf(squareness,hypothesis,
product(A,A,identity) ).
cnf(a_times_b_is_c,hypothesis,
product(a,b,c) ).
cnf(inverse_a_times_inverse_b_is_d,hypothesis,
product(inverse(a),inverse(b),d) ).
cnf(inverses_have_property,hypothesis,
( ~ product(inverse(A),inverse(B),C)
| product(A,C,B) ) ).
cnf(prove_c_times_d_is_identity,negated_conjecture,
~ product(c,d,identity) ).
cnf(refute_0_0,plain,
product(inverse(a),inverse(b),multiply(inverse(a),inverse(b))),
inference(subst,[],[total_function1:[bind(X,$fot(inverse(a))),bind(Y,$fot(inverse(b)))]]) ).
cnf(refute_0_1,plain,
( ~ product(inverse(a),inverse(b),X_91)
| ~ product(inverse(a),inverse(b),d)
| X_91 = d ),
inference(subst,[],[total_function2:[bind(W,$fot(d)),bind(X,$fot(inverse(a))),bind(Y,$fot(inverse(b))),bind(Z,$fot(X_91))]]) ).
cnf(refute_0_2,plain,
( ~ product(inverse(a),inverse(b),X_91)
| X_91 = d ),
inference(resolve,[$cnf( product(inverse(a),inverse(b),d) )],[inverse_a_times_inverse_b_is_d,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ product(inverse(a),inverse(b),multiply(inverse(a),inverse(b)))
| multiply(inverse(a),inverse(b)) = d ),
inference(subst,[],[refute_0_2:[bind(X_91,$fot(multiply(inverse(a),inverse(b))))]]) ).
cnf(refute_0_4,plain,
multiply(inverse(a),inverse(b)) = d,
inference(resolve,[$cnf( product(inverse(a),inverse(b),multiply(inverse(a),inverse(b))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
product(a,b,multiply(a,b)),
inference(subst,[],[total_function1:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).
cnf(refute_0_6,plain,
( ~ product(a,b,X_91)
| ~ product(a,b,c)
| X_91 = c ),
inference(subst,[],[total_function2:[bind(W,$fot(c)),bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(X_91))]]) ).
cnf(refute_0_7,plain,
( ~ product(a,b,X_91)
| X_91 = c ),
inference(resolve,[$cnf( product(a,b,c) )],[a_times_b_is_c,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ product(a,b,multiply(a,b))
| multiply(a,b) = c ),
inference(subst,[],[refute_0_7:[bind(X_91,$fot(multiply(a,b)))]]) ).
cnf(refute_0_9,plain,
multiply(a,b) = c,
inference(resolve,[$cnf( product(a,b,multiply(a,b)) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
product(inverse(X_7),inverse(X_8),multiply(inverse(X_7),inverse(X_8))),
inference(subst,[],[total_function1:[bind(X,$fot(inverse(X_7))),bind(Y,$fot(inverse(X_8)))]]) ).
cnf(refute_0_11,plain,
( ~ product(inverse(X_7),inverse(X_8),multiply(inverse(X_7),inverse(X_8)))
| product(X_7,multiply(inverse(X_7),inverse(X_8)),X_8) ),
inference(subst,[],[inverses_have_property:[bind(A,$fot(X_7)),bind(B,$fot(X_8)),bind(C,$fot(multiply(inverse(X_7),inverse(X_8))))]]) ).
cnf(refute_0_12,plain,
product(X_7,multiply(inverse(X_7),inverse(X_8)),X_8),
inference(resolve,[$cnf( product(inverse(X_7),inverse(X_8),multiply(inverse(X_7),inverse(X_8))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
product(multiply(identity,identity),multiply(inverse(multiply(identity,identity)),inverse(X_96)),X_96),
inference(subst,[],[refute_0_12:[bind(X_7,$fot(multiply(identity,identity))),bind(X_8,$fot(X_96))]]) ).
cnf(refute_0_14,plain,
product(identity,identity,multiply(identity,identity)),
inference(subst,[],[total_function1:[bind(X,$fot(identity)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_15,plain,
product(identity,X_16,X_16),
inference(subst,[],[left_identity:[bind(X,$fot(X_16))]]) ).
cnf(refute_0_16,plain,
( ~ product(identity,X_16,X_16)
| ~ product(identity,identity,X_14)
| product(X_14,X_16,X_16) ),
inference(subst,[],[associativity2:[bind(U,$fot(X_14)),bind(V,$fot(X_16)),bind(W,$fot(X_16)),bind(X,$fot(identity)),bind(Y,$fot(identity)),bind(Z,$fot(X_16))]]) ).
cnf(refute_0_17,plain,
( ~ product(identity,identity,X_14)
| product(X_14,X_16,X_16) ),
inference(resolve,[$cnf( product(identity,X_16,X_16) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ product(identity,identity,multiply(identity,identity))
| product(multiply(identity,identity),X_23,X_23) ),
inference(subst,[],[refute_0_17:[bind(X_14,$fot(multiply(identity,identity))),bind(X_16,$fot(X_23))]]) ).
cnf(refute_0_19,plain,
product(multiply(identity,identity),X_23,X_23),
inference(resolve,[$cnf( product(identity,identity,multiply(identity,identity)) )],[refute_0_14,refute_0_18]) ).
cnf(refute_0_20,plain,
product(multiply(identity,identity),X_88,X_88),
inference(subst,[],[refute_0_19:[bind(X_23,$fot(X_88))]]) ).
cnf(refute_0_21,plain,
( ~ product(multiply(identity,identity),X_88,X_88)
| ~ product(multiply(identity,identity),X_88,X_91)
| X_91 = X_88 ),
inference(subst,[],[total_function2:[bind(W,$fot(X_88)),bind(X,$fot(multiply(identity,identity))),bind(Y,$fot(X_88)),bind(Z,$fot(X_91))]]) ).
cnf(refute_0_22,plain,
( ~ product(multiply(identity,identity),X_88,X_91)
| X_91 = X_88 ),
inference(resolve,[$cnf( product(multiply(identity,identity),X_88,X_88) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ product(multiply(identity,identity),multiply(inverse(multiply(identity,identity)),inverse(X_96)),X_96)
| X_96 = multiply(inverse(multiply(identity,identity)),inverse(X_96)) ),
inference(subst,[],[refute_0_22:[bind(X_88,$fot(multiply(inverse(multiply(identity,identity)),inverse(X_96)))),bind(X_91,$fot(X_96))]]) ).
cnf(refute_0_24,plain,
X_96 = multiply(inverse(multiply(identity,identity)),inverse(X_96)),
inference(resolve,[$cnf( product(multiply(identity,identity),multiply(inverse(multiply(identity,identity)),inverse(X_96)),X_96) )],[refute_0_13,refute_0_23]) ).
cnf(refute_0_25,plain,
product(multiply(identity,identity),X_95,multiply(multiply(identity,identity),X_95)),
inference(subst,[],[total_function1:[bind(X,$fot(multiply(identity,identity))),bind(Y,$fot(X_95))]]) ).
cnf(refute_0_26,plain,
( ~ product(multiply(identity,identity),X_95,multiply(multiply(identity,identity),X_95))
| multiply(multiply(identity,identity),X_95) = X_95 ),
inference(subst,[],[refute_0_22:[bind(X_88,$fot(X_95)),bind(X_91,$fot(multiply(multiply(identity,identity),X_95)))]]) ).
cnf(refute_0_27,plain,
multiply(multiply(identity,identity),X_95) = X_95,
inference(resolve,[$cnf( product(multiply(identity,identity),X_95,multiply(multiply(identity,identity),X_95)) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
product(multiply(identity,identity),identity,multiply(identity,identity)),
inference(subst,[],[right_identity:[bind(X,$fot(multiply(identity,identity)))]]) ).
cnf(refute_0_29,plain,
( ~ product(multiply(identity,identity),identity,multiply(identity,identity))
| multiply(identity,identity) = identity ),
inference(subst,[],[refute_0_22:[bind(X_88,$fot(identity)),bind(X_91,$fot(multiply(identity,identity)))]]) ).
cnf(refute_0_30,plain,
multiply(identity,identity) = identity,
inference(resolve,[$cnf( product(multiply(identity,identity),identity,multiply(identity,identity)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
multiply(multiply(identity,identity),X_95) = multiply(multiply(identity,identity),X_95),
introduced(tautology,[refl,[$fot(multiply(multiply(identity,identity),X_95))]]) ).
cnf(refute_0_32,plain,
( multiply(multiply(identity,identity),X_95) != multiply(multiply(identity,identity),X_95)
| multiply(identity,identity) != identity
| multiply(multiply(identity,identity),X_95) = multiply(identity,X_95) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(identity,identity),X_95),multiply(multiply(identity,identity),X_95)) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_33,plain,
( multiply(identity,identity) != identity
| multiply(multiply(identity,identity),X_95) = multiply(identity,X_95) ),
inference(resolve,[$cnf( $equal(multiply(multiply(identity,identity),X_95),multiply(multiply(identity,identity),X_95)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
multiply(multiply(identity,identity),X_95) = multiply(identity,X_95),
inference(resolve,[$cnf( $equal(multiply(identity,identity),identity) )],[refute_0_30,refute_0_33]) ).
cnf(refute_0_35,plain,
( multiply(multiply(identity,identity),X_95) != X_95
| multiply(multiply(identity,identity),X_95) != multiply(identity,X_95)
| multiply(identity,X_95) = X_95 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(identity,identity),X_95),X_95) ),[0],$fot(multiply(identity,X_95))]]) ).
cnf(refute_0_36,plain,
( multiply(multiply(identity,identity),X_95) != X_95
| multiply(identity,X_95) = X_95 ),
inference(resolve,[$cnf( $equal(multiply(multiply(identity,identity),X_95),multiply(identity,X_95)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
multiply(identity,X_95) = X_95,
inference(resolve,[$cnf( $equal(multiply(multiply(identity,identity),X_95),X_95) )],[refute_0_27,refute_0_36]) ).
cnf(refute_0_38,plain,
multiply(identity,inverse(X_96)) = inverse(X_96),
inference(subst,[],[refute_0_37:[bind(X_95,$fot(inverse(X_96)))]]) ).
cnf(refute_0_39,plain,
product(inverse(X_7),inverse(inverse(X_7)),identity),
inference(subst,[],[right_inverse:[bind(X,$fot(inverse(X_7)))]]) ).
cnf(refute_0_40,plain,
( ~ product(inverse(X_7),inverse(inverse(X_7)),identity)
| product(X_7,identity,inverse(X_7)) ),
inference(subst,[],[inverses_have_property:[bind(A,$fot(X_7)),bind(B,$fot(inverse(X_7))),bind(C,$fot(identity))]]) ).
cnf(refute_0_41,plain,
product(X_7,identity,inverse(X_7)),
inference(resolve,[$cnf( product(inverse(X_7),inverse(inverse(X_7)),identity) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
product(multiply(identity,identity),identity,inverse(multiply(identity,identity))),
inference(subst,[],[refute_0_41:[bind(X_7,$fot(multiply(identity,identity)))]]) ).
cnf(refute_0_43,plain,
( ~ product(multiply(identity,identity),identity,inverse(multiply(identity,identity)))
| inverse(multiply(identity,identity)) = identity ),
inference(subst,[],[refute_0_22:[bind(X_88,$fot(identity)),bind(X_91,$fot(inverse(multiply(identity,identity))))]]) ).
cnf(refute_0_44,plain,
inverse(multiply(identity,identity)) = identity,
inference(resolve,[$cnf( product(multiply(identity,identity),identity,inverse(multiply(identity,identity))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
multiply(inverse(multiply(identity,identity)),inverse(X_96)) = multiply(inverse(multiply(identity,identity)),inverse(X_96)),
introduced(tautology,[refl,[$fot(multiply(inverse(multiply(identity,identity)),inverse(X_96)))]]) ).
cnf(refute_0_46,plain,
( multiply(inverse(multiply(identity,identity)),inverse(X_96)) != multiply(inverse(multiply(identity,identity)),inverse(X_96))
| inverse(multiply(identity,identity)) != identity
| multiply(inverse(multiply(identity,identity)),inverse(X_96)) = multiply(identity,inverse(X_96)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(identity,identity)),inverse(X_96)),multiply(inverse(multiply(identity,identity)),inverse(X_96))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_47,plain,
( inverse(multiply(identity,identity)) != identity
| multiply(inverse(multiply(identity,identity)),inverse(X_96)) = multiply(identity,inverse(X_96)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(identity,identity)),inverse(X_96)),multiply(inverse(multiply(identity,identity)),inverse(X_96))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
multiply(inverse(multiply(identity,identity)),inverse(X_96)) = multiply(identity,inverse(X_96)),
inference(resolve,[$cnf( $equal(inverse(multiply(identity,identity)),identity) )],[refute_0_44,refute_0_47]) ).
cnf(refute_0_49,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_50,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_51,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_53,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
( multiply(identity,inverse(X_96)) != inverse(X_96)
| multiply(inverse(multiply(identity,identity)),inverse(X_96)) != multiply(identity,inverse(X_96))
| multiply(inverse(multiply(identity,identity)),inverse(X_96)) = inverse(X_96) ),
inference(subst,[],[refute_0_53:[bind(X0,$fot(multiply(inverse(multiply(identity,identity)),inverse(X_96)))),bind(Y0,$fot(multiply(identity,inverse(X_96)))),bind(Z0,$fot(inverse(X_96)))]]) ).
cnf(refute_0_55,plain,
( multiply(identity,inverse(X_96)) != inverse(X_96)
| multiply(inverse(multiply(identity,identity)),inverse(X_96)) = inverse(X_96) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(identity,identity)),inverse(X_96)),multiply(identity,inverse(X_96))) )],[refute_0_48,refute_0_54]) ).
cnf(refute_0_56,plain,
multiply(inverse(multiply(identity,identity)),inverse(X_96)) = inverse(X_96),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(X_96)),inverse(X_96)) )],[refute_0_38,refute_0_55]) ).
cnf(refute_0_57,plain,
( X_96 != multiply(inverse(multiply(identity,identity)),inverse(X_96))
| multiply(inverse(multiply(identity,identity)),inverse(X_96)) != inverse(X_96)
| X_96 = inverse(X_96) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_96,inverse(X_96)) ),[0],$fot(multiply(inverse(multiply(identity,identity)),inverse(X_96)))]]) ).
cnf(refute_0_58,plain,
( X_96 != multiply(inverse(multiply(identity,identity)),inverse(X_96))
| X_96 = inverse(X_96) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(identity,identity)),inverse(X_96)),inverse(X_96)) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
X_96 = inverse(X_96),
inference(resolve,[$cnf( $equal(X_96,multiply(inverse(multiply(identity,identity)),inverse(X_96))) )],[refute_0_24,refute_0_58]) ).
cnf(refute_0_60,plain,
( X_96 != inverse(X_96)
| inverse(X_96) = X_96 ),
inference(subst,[],[refute_0_51:[bind(X0,$fot(X_96)),bind(Y0,$fot(inverse(X_96)))]]) ).
cnf(refute_0_61,plain,
inverse(X_96) = X_96,
inference(resolve,[$cnf( $equal(X_96,inverse(X_96)) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
inverse(b) = b,
inference(subst,[],[refute_0_61:[bind(X_96,$fot(b))]]) ).
cnf(refute_0_63,plain,
multiply(a,inverse(b)) = multiply(a,inverse(b)),
introduced(tautology,[refl,[$fot(multiply(a,inverse(b)))]]) ).
cnf(refute_0_64,plain,
( multiply(a,inverse(b)) != multiply(a,inverse(b))
| inverse(b) != b
| multiply(a,inverse(b)) = multiply(a,b) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(a,inverse(b)),multiply(a,inverse(b))) ),[1,1],$fot(b)]]) ).
cnf(refute_0_65,plain,
( inverse(b) != b
| multiply(a,inverse(b)) = multiply(a,b) ),
inference(resolve,[$cnf( $equal(multiply(a,inverse(b)),multiply(a,inverse(b))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
multiply(a,inverse(b)) = multiply(a,b),
inference(resolve,[$cnf( $equal(inverse(b),b) )],[refute_0_62,refute_0_65]) ).
cnf(refute_0_67,plain,
inverse(a) = a,
inference(subst,[],[refute_0_61:[bind(X_96,$fot(a))]]) ).
cnf(refute_0_68,plain,
multiply(inverse(a),inverse(b)) = multiply(inverse(a),inverse(b)),
introduced(tautology,[refl,[$fot(multiply(inverse(a),inverse(b)))]]) ).
cnf(refute_0_69,plain,
( multiply(inverse(a),inverse(b)) != multiply(inverse(a),inverse(b))
| inverse(a) != a
| multiply(inverse(a),inverse(b)) = multiply(a,inverse(b)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),inverse(b)),multiply(inverse(a),inverse(b))) ),[1,0],$fot(a)]]) ).
cnf(refute_0_70,plain,
( inverse(a) != a
| multiply(inverse(a),inverse(b)) = multiply(a,inverse(b)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),inverse(b)),multiply(inverse(a),inverse(b))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
multiply(inverse(a),inverse(b)) = multiply(a,inverse(b)),
inference(resolve,[$cnf( $equal(inverse(a),a) )],[refute_0_67,refute_0_70]) ).
cnf(refute_0_72,plain,
( multiply(a,inverse(b)) != multiply(a,b)
| multiply(inverse(a),inverse(b)) != multiply(a,inverse(b))
| multiply(inverse(a),inverse(b)) = multiply(a,b) ),
inference(subst,[],[refute_0_53:[bind(X0,$fot(multiply(inverse(a),inverse(b)))),bind(Y0,$fot(multiply(a,inverse(b)))),bind(Z0,$fot(multiply(a,b)))]]) ).
cnf(refute_0_73,plain,
( multiply(a,inverse(b)) != multiply(a,b)
| multiply(inverse(a),inverse(b)) = multiply(a,b) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),inverse(b)),multiply(a,inverse(b))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
multiply(inverse(a),inverse(b)) = multiply(a,b),
inference(resolve,[$cnf( $equal(multiply(a,inverse(b)),multiply(a,b)) )],[refute_0_66,refute_0_73]) ).
cnf(refute_0_75,plain,
( multiply(a,b) != c
| multiply(inverse(a),inverse(b)) != multiply(a,b)
| multiply(inverse(a),inverse(b)) = c ),
inference(subst,[],[refute_0_53:[bind(X0,$fot(multiply(inverse(a),inverse(b)))),bind(Y0,$fot(multiply(a,b))),bind(Z0,$fot(c))]]) ).
cnf(refute_0_76,plain,
( multiply(a,b) != c
| multiply(inverse(a),inverse(b)) = c ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),inverse(b)),multiply(a,b)) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
multiply(inverse(a),inverse(b)) = c,
inference(resolve,[$cnf( $equal(multiply(a,b),c) )],[refute_0_9,refute_0_76]) ).
cnf(refute_0_78,plain,
( multiply(inverse(a),inverse(b)) != c
| multiply(inverse(a),inverse(b)) != d
| c = d ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),inverse(b)),d) ),[0],$fot(c)]]) ).
cnf(refute_0_79,plain,
( multiply(inverse(a),inverse(b)) != d
| c = d ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),inverse(b)),c) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
c = d,
inference(resolve,[$cnf( $equal(multiply(inverse(a),inverse(b)),d) )],[refute_0_4,refute_0_79]) ).
cnf(refute_0_81,plain,
( c != d
| d = c ),
inference(subst,[],[refute_0_51:[bind(X0,$fot(c)),bind(Y0,$fot(d))]]) ).
cnf(refute_0_82,plain,
d = c,
inference(resolve,[$cnf( $equal(c,d) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
( d != c
| ~ product(c,c,identity)
| product(c,d,identity) ),
introduced(tautology,[equality,[$cnf( ~ product(c,d,identity) ),[1],$fot(c)]]) ).
cnf(refute_0_84,plain,
( ~ product(c,c,identity)
| product(c,d,identity) ),
inference(resolve,[$cnf( $equal(d,c) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
~ product(c,c,identity),
inference(resolve,[$cnf( product(c,d,identity) )],[refute_0_84,prove_c_times_d_is_identity]) ).
cnf(refute_0_86,plain,
product(c,c,identity),
inference(subst,[],[squareness:[bind(A,$fot(c))]]) ).
cnf(refute_0_87,plain,
$false,
inference(resolve,[$cnf( product(c,c,identity) )],[refute_0_86,refute_0_85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : GRP013-1 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.36 % Computer : n022.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon Jun 13 11:19:33 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.45 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.45
% 0.21/0.45 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.21/0.46
%------------------------------------------------------------------------------