TSTP Solution File: GRP029-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP029-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 10:32:33 EDT 2022
% Result : Unsatisfiable 0.20s 0.47s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of clauses : 23 ( 13 unt; 0 nHn; 15 RR)
% Number of literals : 42 ( 0 equ; 21 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 39 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
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(left_identity,axiom,
product(identity,A,A) ).
cnf(left_inverse,axiom,
product(inverse(A),A,identity) ).
cnf(prove_there_is_a_right_identity,negated_conjecture,
~ product(not_right_identity(A),A,not_right_identity(A)) ).
cnf(refute_0_0,plain,
~ product(not_right_identity(identity),identity,not_right_identity(identity)),
inference(subst,[],[prove_there_is_a_right_identity:[bind(A,$fot(identity))]]) ).
cnf(refute_0_1,plain,
product(identity,identity,identity),
inference(subst,[],[left_identity:[bind(A,$fot(identity))]]) ).
cnf(refute_0_2,plain,
( ~ product(X_76,identity,X_75)
| ~ product(identity,identity,identity)
| product(X_75,identity,X_75) ),
inference(subst,[],[associativity2:[bind(U,$fot(X_75)),bind(V,$fot(identity)),bind(W,$fot(X_75)),bind(X,$fot(X_76)),bind(Y,$fot(identity)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_3,plain,
( ~ product(X_76,identity,X_75)
| product(X_75,identity,X_75) ),
inference(resolve,[$cnf( product(identity,identity,identity) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ product(inverse(inverse(X_180)),identity,X_180)
| product(X_180,identity,X_180) ),
inference(subst,[],[refute_0_3:[bind(X_75,$fot(X_180)),bind(X_76,$fot(inverse(inverse(X_180))))]]) ).
cnf(refute_0_5,plain,
product(inverse(inverse(X_178)),inverse(X_178),identity),
inference(subst,[],[left_inverse:[bind(A,$fot(inverse(X_178)))]]) ).
cnf(refute_0_6,plain,
product(inverse(X_173),X_173,identity),
inference(subst,[],[left_inverse:[bind(A,$fot(X_173))]]) ).
cnf(refute_0_7,plain,
product(identity,X_168,X_168),
inference(subst,[],[left_identity:[bind(A,$fot(X_168))]]) ).
cnf(refute_0_8,plain,
( ~ product(X_169,X_170,identity)
| ~ product(X_170,X_168,X_167)
| ~ product(identity,X_168,X_168)
| product(X_169,X_167,X_168) ),
inference(subst,[],[associativity1:[bind(U,$fot(identity)),bind(V,$fot(X_167)),bind(W,$fot(X_168)),bind(X,$fot(X_169)),bind(Y,$fot(X_170)),bind(Z,$fot(X_168))]]) ).
cnf(refute_0_9,plain,
( ~ product(X_169,X_170,identity)
| ~ product(X_170,X_168,X_167)
| product(X_169,X_167,X_168) ),
inference(resolve,[$cnf( product(identity,X_168,X_168) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ product(X_174,inverse(X_173),identity)
| ~ product(inverse(X_173),X_173,identity)
| product(X_174,identity,X_173) ),
inference(subst,[],[refute_0_9:[bind(X_167,$fot(identity)),bind(X_168,$fot(X_173)),bind(X_169,$fot(X_174)),bind(X_170,$fot(inverse(X_173)))]]) ).
cnf(refute_0_11,plain,
( ~ product(X_174,inverse(X_173),identity)
| product(X_174,identity,X_173) ),
inference(resolve,[$cnf( product(inverse(X_173),X_173,identity) )],[refute_0_6,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ product(inverse(inverse(X_178)),inverse(X_178),identity)
| product(inverse(inverse(X_178)),identity,X_178) ),
inference(subst,[],[refute_0_11:[bind(X_173,$fot(X_178)),bind(X_174,$fot(inverse(inverse(X_178))))]]) ).
cnf(refute_0_13,plain,
product(inverse(inverse(X_178)),identity,X_178),
inference(resolve,[$cnf( product(inverse(inverse(X_178)),inverse(X_178),identity) )],[refute_0_5,refute_0_12]) ).
cnf(refute_0_14,plain,
product(inverse(inverse(X_180)),identity,X_180),
inference(subst,[],[refute_0_13:[bind(X_178,$fot(X_180))]]) ).
cnf(refute_0_15,plain,
product(X_180,identity,X_180),
inference(resolve,[$cnf( product(inverse(inverse(X_180)),identity,X_180) )],[refute_0_14,refute_0_4]) ).
cnf(refute_0_16,plain,
product(not_right_identity(identity),identity,not_right_identity(identity)),
inference(subst,[],[refute_0_15:[bind(X_180,$fot(not_right_identity(identity)))]]) ).
cnf(refute_0_17,plain,
$false,
inference(resolve,[$cnf( product(not_right_identity(identity),identity,not_right_identity(identity)) )],[refute_0_16,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP029-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 13:10:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.47 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.47
% 0.20/0.47 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.47
%------------------------------------------------------------------------------