TSTP Solution File: GRP012-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP012-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n005.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 0.19s 0.48s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 16
% Syntax : Number of clauses : 74 ( 34 unt; 0 nHn; 62 RR)
% Number of literals : 138 ( 41 equ; 65 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 : 74 ( 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(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_multiply_d_is_identity,negated_conjecture,
~ product(c,d,identity) ).
cnf(refute_0_0,plain,
product(inverse(d),d,identity),
inference(subst,[],[left_inverse:[bind(X,$fot(d))]]) ).
cnf(refute_0_1,plain,
product(X_51,X_52,multiply(X_51,X_52)),
inference(subst,[],[total_function1:[bind(X,$fot(X_51)),bind(Y,$fot(X_52))]]) ).
cnf(refute_0_2,plain,
( ~ product(X_51,X_52,X_53)
| ~ product(X_51,X_52,multiply(X_51,X_52))
| X_53 = multiply(X_51,X_52) ),
inference(subst,[],[total_function2:[bind(W,$fot(multiply(X_51,X_52))),bind(X,$fot(X_51)),bind(Y,$fot(X_52)),bind(Z,$fot(X_53))]]) ).
cnf(refute_0_3,plain,
( ~ product(X_51,X_52,X_53)
| X_53 = multiply(X_51,X_52) ),
inference(resolve,[$cnf( product(X_51,X_52,multiply(X_51,X_52)) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ product(inverse(d),identity,c)
| c = multiply(inverse(d),identity) ),
inference(subst,[],[refute_0_3:[bind(X_51,$fot(inverse(d))),bind(X_52,$fot(identity)),bind(X_53,$fot(c))]]) ).
cnf(refute_0_5,plain,
product(X_111,X_112,multiply(X_111,X_112)),
inference(subst,[],[total_function1:[bind(X,$fot(X_111)),bind(Y,$fot(X_112))]]) ).
cnf(refute_0_6,plain,
product(inverse(X_108),X_108,identity),
inference(subst,[],[left_inverse:[bind(X,$fot(X_108))]]) ).
cnf(refute_0_7,plain,
( ~ product(X_106,X_107,inverse(X_108))
| ~ product(X_107,X_108,X_104)
| ~ product(inverse(X_108),X_108,identity)
| product(X_106,X_104,identity) ),
inference(subst,[],[associativity1:[bind(U,$fot(inverse(X_108))),bind(V,$fot(X_104)),bind(W,$fot(identity)),bind(X,$fot(X_106)),bind(Y,$fot(X_107)),bind(Z,$fot(X_108))]]) ).
cnf(refute_0_8,plain,
( ~ product(X_106,X_107,inverse(X_108))
| ~ product(X_107,X_108,X_104)
| product(X_106,X_104,identity) ),
inference(resolve,[$cnf( product(inverse(X_108),X_108,identity) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ product(X_110,X_111,inverse(X_112))
| ~ product(X_111,X_112,multiply(X_111,X_112))
| product(X_110,multiply(X_111,X_112),identity) ),
inference(subst,[],[refute_0_8:[bind(X_104,$fot(multiply(X_111,X_112))),bind(X_106,$fot(X_110)),bind(X_107,$fot(X_111)),bind(X_108,$fot(X_112))]]) ).
cnf(refute_0_10,plain,
( ~ product(X_110,X_111,inverse(X_112))
| product(X_110,multiply(X_111,X_112),identity) ),
inference(resolve,[$cnf( product(X_111,X_112,multiply(X_111,X_112)) )],[refute_0_5,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ product(d,a,inverse(b))
| product(d,multiply(a,b),identity) ),
inference(subst,[],[refute_0_10:[bind(X_110,$fot(d)),bind(X_111,$fot(a)),bind(X_112,$fot(b))]]) ).
cnf(refute_0_12,plain,
product(d,a,multiply(d,a)),
inference(subst,[],[total_function1:[bind(X,$fot(d)),bind(Y,$fot(a))]]) ).
cnf(refute_0_13,plain,
( ~ product(inverse(b),identity,multiply(d,a))
| multiply(d,a) = multiply(inverse(b),identity) ),
inference(subst,[],[refute_0_3:[bind(X_51,$fot(inverse(b))),bind(X_52,$fot(identity)),bind(X_53,$fot(multiply(d,a)))]]) ).
cnf(refute_0_14,plain,
product(inverse(a),a,identity),
inference(subst,[],[left_inverse:[bind(X,$fot(a))]]) ).
cnf(refute_0_15,plain,
( ~ product(d,X_108,X_105)
| ~ product(inverse(a),X_108,X_104)
| ~ product(inverse(b),inverse(a),d)
| product(inverse(b),X_104,X_105) ),
inference(subst,[],[associativity1:[bind(U,$fot(d)),bind(V,$fot(X_104)),bind(W,$fot(X_105)),bind(X,$fot(inverse(b))),bind(Y,$fot(inverse(a))),bind(Z,$fot(X_108))]]) ).
cnf(refute_0_16,plain,
( ~ product(d,X_108,X_105)
| ~ product(inverse(a),X_108,X_104)
| product(inverse(b),X_104,X_105) ),
inference(resolve,[$cnf( product(inverse(b),inverse(a),d) )],[inverse_b_multiply_inverse_a_is_d,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ product(d,a,X_231)
| ~ product(inverse(a),a,identity)
| product(inverse(b),identity,X_231) ),
inference(subst,[],[refute_0_16:[bind(X_104,$fot(identity)),bind(X_105,$fot(X_231)),bind(X_108,$fot(a))]]) ).
cnf(refute_0_18,plain,
( ~ product(d,a,X_231)
| product(inverse(b),identity,X_231) ),
inference(resolve,[$cnf( product(inverse(a),a,identity) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ product(d,a,multiply(d,a))
| product(inverse(b),identity,multiply(d,a)) ),
inference(subst,[],[refute_0_18:[bind(X_231,$fot(multiply(d,a)))]]) ).
cnf(refute_0_20,plain,
product(inverse(b),identity,multiply(d,a)),
inference(resolve,[$cnf( product(d,a,multiply(d,a)) )],[refute_0_12,refute_0_19]) ).
cnf(refute_0_21,plain,
multiply(d,a) = multiply(inverse(b),identity),
inference(resolve,[$cnf( product(inverse(b),identity,multiply(d,a)) )],[refute_0_20,refute_0_13]) ).
cnf(refute_0_22,plain,
product(X_55,identity,multiply(X_55,identity)),
inference(subst,[],[total_function1:[bind(X,$fot(X_55)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_23,plain,
product(X_50,identity,X_50),
inference(subst,[],[right_identity:[bind(X,$fot(X_50))]]) ).
cnf(refute_0_24,plain,
( ~ product(X_50,identity,X_50)
| ~ product(X_50,identity,X_53)
| X_53 = X_50 ),
inference(subst,[],[total_function2:[bind(W,$fot(X_50)),bind(X,$fot(X_50)),bind(Y,$fot(identity)),bind(Z,$fot(X_53))]]) ).
cnf(refute_0_25,plain,
( ~ product(X_50,identity,X_53)
| X_53 = X_50 ),
inference(resolve,[$cnf( product(X_50,identity,X_50) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ product(X_55,identity,multiply(X_55,identity))
| multiply(X_55,identity) = X_55 ),
inference(subst,[],[refute_0_25:[bind(X_50,$fot(X_55)),bind(X_53,$fot(multiply(X_55,identity)))]]) ).
cnf(refute_0_27,plain,
multiply(X_55,identity) = X_55,
inference(resolve,[$cnf( product(X_55,identity,multiply(X_55,identity)) )],[refute_0_22,refute_0_26]) ).
cnf(refute_0_28,plain,
multiply(inverse(b),identity) = inverse(b),
inference(subst,[],[refute_0_27:[bind(X_55,$fot(inverse(b)))]]) ).
cnf(refute_0_29,plain,
( multiply(d,a) != multiply(inverse(b),identity)
| multiply(inverse(b),identity) != inverse(b)
| multiply(d,a) = inverse(b) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(d,a),inverse(b)) ),[0],$fot(multiply(inverse(b),identity))]]) ).
cnf(refute_0_30,plain,
( multiply(d,a) != multiply(inverse(b),identity)
| multiply(d,a) = inverse(b) ),
inference(resolve,[$cnf( $equal(multiply(inverse(b),identity),inverse(b)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
multiply(d,a) = inverse(b),
inference(resolve,[$cnf( $equal(multiply(d,a),multiply(inverse(b),identity)) )],[refute_0_21,refute_0_30]) ).
cnf(refute_0_32,plain,
( multiply(d,a) != inverse(b)
| ~ product(d,a,multiply(d,a))
| product(d,a,inverse(b)) ),
introduced(tautology,[equality,[$cnf( product(d,a,multiply(d,a)) ),[2],$fot(inverse(b))]]) ).
cnf(refute_0_33,plain,
( ~ product(d,a,multiply(d,a))
| product(d,a,inverse(b)) ),
inference(resolve,[$cnf( $equal(multiply(d,a),inverse(b)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
product(d,a,inverse(b)),
inference(resolve,[$cnf( product(d,a,multiply(d,a)) )],[refute_0_12,refute_0_33]) ).
cnf(refute_0_35,plain,
product(d,multiply(a,b),identity),
inference(resolve,[$cnf( product(d,a,inverse(b)) )],[refute_0_34,refute_0_11]) ).
cnf(refute_0_36,plain,
product(a,b,multiply(a,b)),
inference(subst,[],[total_function1:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).
cnf(refute_0_37,plain,
( ~ product(a,b,X_53)
| ~ product(a,b,c)
| X_53 = c ),
inference(subst,[],[total_function2:[bind(W,$fot(c)),bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(X_53))]]) ).
cnf(refute_0_38,plain,
( ~ product(a,b,X_53)
| X_53 = c ),
inference(resolve,[$cnf( product(a,b,c) )],[a_multiply_b_is_c,refute_0_37]) ).
cnf(refute_0_39,plain,
( ~ product(a,b,multiply(a,b))
| multiply(a,b) = c ),
inference(subst,[],[refute_0_38:[bind(X_53,$fot(multiply(a,b)))]]) ).
cnf(refute_0_40,plain,
multiply(a,b) = c,
inference(resolve,[$cnf( product(a,b,multiply(a,b)) )],[refute_0_36,refute_0_39]) ).
cnf(refute_0_41,plain,
( multiply(a,b) != c
| ~ product(d,multiply(a,b),identity)
| product(d,c,identity) ),
introduced(tautology,[equality,[$cnf( product(d,multiply(a,b),identity) ),[1],$fot(c)]]) ).
cnf(refute_0_42,plain,
( ~ product(d,multiply(a,b),identity)
| product(d,c,identity) ),
inference(resolve,[$cnf( $equal(multiply(a,b),c) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
product(d,c,identity),
inference(resolve,[$cnf( product(d,multiply(a,b),identity) )],[refute_0_35,refute_0_42]) ).
cnf(refute_0_44,plain,
product(identity,X_105,X_105),
inference(subst,[],[left_identity:[bind(X,$fot(X_105))]]) ).
cnf(refute_0_45,plain,
( ~ product(X_106,X_107,identity)
| ~ product(X_107,X_105,X_104)
| ~ product(identity,X_105,X_105)
| product(X_106,X_104,X_105) ),
inference(subst,[],[associativity1:[bind(U,$fot(identity)),bind(V,$fot(X_104)),bind(W,$fot(X_105)),bind(X,$fot(X_106)),bind(Y,$fot(X_107)),bind(Z,$fot(X_105))]]) ).
cnf(refute_0_46,plain,
( ~ product(X_106,X_107,identity)
| ~ product(X_107,X_105,X_104)
| product(X_106,X_104,X_105) ),
inference(resolve,[$cnf( product(identity,X_105,X_105) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
( ~ product(X_269,d,identity)
| ~ product(d,c,identity)
| product(X_269,identity,c) ),
inference(subst,[],[refute_0_46:[bind(X_104,$fot(identity)),bind(X_105,$fot(c)),bind(X_106,$fot(X_269)),bind(X_107,$fot(d))]]) ).
cnf(refute_0_48,plain,
( ~ product(X_269,d,identity)
| product(X_269,identity,c) ),
inference(resolve,[$cnf( product(d,c,identity) )],[refute_0_43,refute_0_47]) ).
cnf(refute_0_49,plain,
( ~ product(inverse(d),d,identity)
| product(inverse(d),identity,c) ),
inference(subst,[],[refute_0_48:[bind(X_269,$fot(inverse(d)))]]) ).
cnf(refute_0_50,plain,
product(inverse(d),identity,c),
inference(resolve,[$cnf( product(inverse(d),d,identity) )],[refute_0_0,refute_0_49]) ).
cnf(refute_0_51,plain,
c = multiply(inverse(d),identity),
inference(resolve,[$cnf( product(inverse(d),identity,c) )],[refute_0_50,refute_0_4]) ).
cnf(refute_0_52,plain,
multiply(inverse(d),identity) = inverse(d),
inference(subst,[],[refute_0_27:[bind(X_55,$fot(inverse(d)))]]) ).
cnf(refute_0_53,plain,
( multiply(inverse(d),identity) != inverse(d)
| c != multiply(inverse(d),identity)
| c = inverse(d) ),
introduced(tautology,[equality,[$cnf( $equal(c,multiply(inverse(d),identity)) ),[1],$fot(inverse(d))]]) ).
cnf(refute_0_54,plain,
( c != multiply(inverse(d),identity)
| c = inverse(d) ),
inference(resolve,[$cnf( $equal(multiply(inverse(d),identity),inverse(d)) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
c = inverse(d),
inference(resolve,[$cnf( $equal(c,multiply(inverse(d),identity)) )],[refute_0_51,refute_0_54]) ).
cnf(refute_0_56,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_57,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_58,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
( c != inverse(d)
| inverse(d) = c ),
inference(subst,[],[refute_0_58:[bind(X0,$fot(c)),bind(Y0,$fot(inverse(d)))]]) ).
cnf(refute_0_60,plain,
inverse(d) = c,
inference(resolve,[$cnf( $equal(c,inverse(d)) )],[refute_0_55,refute_0_59]) ).
cnf(refute_0_61,plain,
( inverse(d) != c
| ~ product(inverse(d),d,identity)
| product(c,d,identity) ),
introduced(tautology,[equality,[$cnf( product(inverse(d),d,identity) ),[0],$fot(c)]]) ).
cnf(refute_0_62,plain,
( ~ product(inverse(d),d,identity)
| product(c,d,identity) ),
inference(resolve,[$cnf( $equal(inverse(d),c) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
product(c,d,identity),
inference(resolve,[$cnf( product(inverse(d),d,identity) )],[refute_0_0,refute_0_62]) ).
cnf(refute_0_64,plain,
$false,
inference(resolve,[$cnf( product(c,d,identity) )],[refute_0_63,prove_c_multiply_d_is_identity]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP012-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n005.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Tue Jun 14 04:19:24 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.48 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.48
% 0.19/0.48 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.48
%------------------------------------------------------------------------------