TSTP Solution File: NUM001-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM001-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.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 : Mon Jul 18 12:24:01 EDT 2022
% Result : Unsatisfiable 6.75s 6.94s
% Output : CNFRefutation 6.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of clauses : 24 ( 13 unt; 0 nHn; 14 RR)
% Number of literals : 39 ( 0 equ; 16 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(transitivity,axiom,
( ~ equalish(A,B)
| ~ equalish(B,C)
| equalish(A,C) ) ).
cnf(commutativity_of_addition,axiom,
equalish(add(A,B),add(B,A)) ).
cnf(associativity_of_addition,axiom,
equalish(add(A,add(B,C)),add(add(A,B),C)) ).
cnf(prove_equation,negated_conjecture,
~ equalish(add(add(a,b),c),add(a,add(b,c))) ).
cnf(refute_0_0,plain,
( ~ equalish(add(A,B),add(B,A))
| ~ equalish(add(B,A),X_27)
| equalish(add(A,B),X_27) ),
inference(subst,[],[transitivity:[bind(A,$fot(add(A,B))),bind(B,$fot(add(B,A))),bind(C,$fot(X_27))]]) ).
cnf(refute_0_1,plain,
( ~ equalish(add(B,A),X_27)
| equalish(add(A,B),X_27) ),
inference(resolve,[$cnf( equalish(add(A,B),add(B,A)) )],[commutativity_of_addition,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ equalish(add(X_3295,add(X_3296,X_3297)),add(X_3296,add(X_3297,X_3295)))
| equalish(add(add(X_3296,X_3297),X_3295),add(X_3296,add(X_3297,X_3295))) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(add(X_3296,X_3297))),bind(B,$fot(X_3295)),bind(X_27,$fot(add(X_3296,add(X_3297,X_3295))))]]) ).
cnf(refute_0_3,plain,
equalish(add(X_29,add(B,C)),add(add(X_29,B),C)),
inference(subst,[],[associativity_of_addition:[bind(A,$fot(X_29))]]) ).
cnf(refute_0_4,plain,
( ~ equalish(add(X_29,add(B,C)),add(add(X_29,B),C))
| equalish(add(add(B,C),X_29),add(add(X_29,B),C)) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(add(B,C))),bind(B,$fot(X_29)),bind(X_27,$fot(add(add(X_29,B),C)))]]) ).
cnf(refute_0_5,plain,
equalish(add(add(B,C),X_29),add(add(X_29,B),C)),
inference(resolve,[$cnf( equalish(add(X_29,add(B,C)),add(add(X_29,B),C)) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
equalish(add(add(B,X_75),X_29),add(add(X_29,B),X_75)),
inference(subst,[],[refute_0_5:[bind(C,$fot(X_75))]]) ).
cnf(refute_0_7,plain,
( ~ equalish(X_25,add(A,B))
| ~ equalish(add(A,B),add(B,A))
| equalish(X_25,add(B,A)) ),
inference(subst,[],[transitivity:[bind(A,$fot(X_25)),bind(B,$fot(add(A,B))),bind(C,$fot(add(B,A)))]]) ).
cnf(refute_0_8,plain,
( ~ equalish(X_25,add(A,B))
| equalish(X_25,add(B,A)) ),
inference(resolve,[$cnf( equalish(add(A,B),add(B,A)) )],[commutativity_of_addition,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ equalish(add(add(B,X_75),X_29),add(add(X_29,B),X_75))
| equalish(add(add(B,X_75),X_29),add(X_75,add(X_29,B))) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(add(X_29,B))),bind(B,$fot(X_75)),bind(X_25,$fot(add(add(B,X_75),X_29)))]]) ).
cnf(refute_0_10,plain,
equalish(add(add(B,X_75),X_29),add(X_75,add(X_29,B))),
inference(resolve,[$cnf( equalish(add(add(B,X_75),X_29),add(add(X_29,B),X_75)) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
equalish(add(add(X_3243,X_3244),X_3245),add(X_3244,add(X_3245,X_3243))),
inference(subst,[],[refute_0_10:[bind(B,$fot(X_3243)),bind(X_29,$fot(X_3245)),bind(X_75,$fot(X_3244))]]) ).
cnf(refute_0_12,plain,
( ~ equalish(add(A,add(B,C)),add(add(A,B),C))
| ~ equalish(add(add(A,B),C),X_27)
| equalish(add(A,add(B,C)),X_27) ),
inference(subst,[],[transitivity:[bind(A,$fot(add(A,add(B,C)))),bind(B,$fot(add(add(A,B),C))),bind(C,$fot(X_27))]]) ).
cnf(refute_0_13,plain,
( ~ equalish(add(add(A,B),C),X_27)
| equalish(add(A,add(B,C)),X_27) ),
inference(resolve,[$cnf( equalish(add(A,add(B,C)),add(add(A,B),C)) )],[associativity_of_addition,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ equalish(add(add(X_3243,X_3244),X_3245),add(X_3244,add(X_3245,X_3243)))
| equalish(add(X_3243,add(X_3244,X_3245)),add(X_3244,add(X_3245,X_3243))) ),
inference(subst,[],[refute_0_13:[bind(A,$fot(X_3243)),bind(B,$fot(X_3244)),bind(C,$fot(X_3245)),bind(X_27,$fot(add(X_3244,add(X_3245,X_3243))))]]) ).
cnf(refute_0_15,plain,
equalish(add(X_3243,add(X_3244,X_3245)),add(X_3244,add(X_3245,X_3243))),
inference(resolve,[$cnf( equalish(add(add(X_3243,X_3244),X_3245),add(X_3244,add(X_3245,X_3243))) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
equalish(add(X_3295,add(X_3296,X_3297)),add(X_3296,add(X_3297,X_3295))),
inference(subst,[],[refute_0_15:[bind(X_3243,$fot(X_3295)),bind(X_3244,$fot(X_3296)),bind(X_3245,$fot(X_3297))]]) ).
cnf(refute_0_17,plain,
equalish(add(add(X_3296,X_3297),X_3295),add(X_3296,add(X_3297,X_3295))),
inference(resolve,[$cnf( equalish(add(X_3295,add(X_3296,X_3297)),add(X_3296,add(X_3297,X_3295))) )],[refute_0_16,refute_0_2]) ).
cnf(refute_0_18,plain,
equalish(add(add(a,b),c),add(a,add(b,c))),
inference(subst,[],[refute_0_17:[bind(X_3295,$fot(c)),bind(X_3296,$fot(a)),bind(X_3297,$fot(b))]]) ).
cnf(refute_0_19,plain,
$false,
inference(resolve,[$cnf( equalish(add(add(a,b),c),add(a,add(b,c))) )],[refute_0_18,prove_equation]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : NUM001-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n025.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 : Wed Jul 6 03:33:12 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 6.75/6.94 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.75/6.94
% 6.75/6.94 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.75/6.95
%------------------------------------------------------------------------------