%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COL100-1 : TPTP v8.1.0. Released v2.7.0.
% 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 : Fri Jul 15 00:36:30 EDT 2022
% Result : Unsatisfiable 15.72s 15.90s
% Output : CNFRefutation 15.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of clauses : 36 ( 13 unt; 0 nHn; 35 RR)
% Number of literals : 74 ( 0 equ; 41 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 28 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(r_into_trancl,axiom,
( ~ member(pair(A,B),R)
| member(pair(A,B),trancl(R)) ) ).
cnf(trans_trancl,axiom,
trans(trancl(R)) ).
cnf(transD,axiom,
( ~ trans(R)
| ~ member(pair(A,B),R)
| ~ member(pair(B,C),R)
| member(pair(A,C),R) ) ).
cnf(diamond_strip_lemmaD1,axiom,
( ~ diamond(R)
| ~ member(pair(X,Y),trancl(R))
| ~ member(pair(X,YP),R)
| member(pair(YP,diamond_strip_lemmaD_sk1(X,Y,YP,R)),trancl(R)) ) ).
cnf(diamond_strip_lemmaD2,axiom,
( ~ diamond(R)
| ~ member(pair(X,Y),trancl(R))
| ~ member(pair(X,YP),R)
| member(pair(Y,diamond_strip_lemmaD_sk1(X,Y,YP,R)),R) ) ).
cnf(diamond_trancl_2h1,hypothesis,
diamond(r) ).
cnf(diamond_trancl_2h3,hypothesis,
member(pair(ya,z),r) ).
cnf(diamond_trancl_2h4,hypothesis,
( ~ member(pair(y,YP),trancl(r))
| member(pair(ya,sk1(YP)),trancl(r)) ) ).
cnf(diamond_trancl_2h5,hypothesis,
( ~ member(pair(y,YP),trancl(r))
| member(pair(YP,sk1(YP)),trancl(r)) ) ).
cnf(diamond_trancl_2c1,negated_conjecture,
member(pair(y,yp),trancl(r)) ).
cnf(diamond_trancl_2c2,negated_conjecture,
( ~ member(pair(z,ZA),trancl(r))
| ~ member(pair(yp,ZA),trancl(r)) ) ).
cnf(refute_0_0,plain,
( ~ member(pair(yp,diamond_strip_lemmaD_sk1(ya,sk1(yp),z,r)),trancl(r))
| ~ member(pair(z,diamond_strip_lemmaD_sk1(ya,sk1(yp),z,r)),trancl(r)) ),
inference(subst,[],[diamond_trancl_2c2:[bind(ZA,$fot(diamond_strip_lemmaD_sk1(ya,sk1(yp),z,r)))]]) ).
cnf(refute_0_1,plain,
( ~ member(pair(y,yp),trancl(r))
| member(pair(ya,sk1(yp)),trancl(r)) ),
inference(subst,[],[diamond_trancl_2h4:[bind(YP,$fot(yp))]]) ).
cnf(refute_0_2,plain,
member(pair(ya,sk1(yp)),trancl(r)),
inference(resolve,[$cnf( member(pair(y,yp),trancl(r)) )],[diamond_trancl_2c1,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ diamond(r)
| ~ member(pair(ya,X_523),r)
| ~ member(pair(ya,sk1(yp)),trancl(r))
| member(pair(X_523,diamond_strip_lemmaD_sk1(ya,sk1(yp),X_523,r)),trancl(r)) ),
inference(subst,[],[diamond_strip_lemmaD1:[bind(R,$fot(r)),bind(X,$fot(ya)),bind(Y,$fot(sk1(yp))),bind(YP,$fot(X_523))]]) ).
cnf(refute_0_4,plain,
( ~ diamond(r)
| ~ member(pair(ya,X_523),r)
| member(pair(X_523,diamond_strip_lemmaD_sk1(ya,sk1(yp),X_523,r)),trancl(r)) ),
inference(resolve,[$cnf( member(pair(ya,sk1(yp)),trancl(r)) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ member(pair(ya,X_523),r)
| member(pair(X_523,diamond_strip_lemmaD_sk1(ya,sk1(yp),X_523,r)),trancl(r)) ),
inference(resolve,[$cnf( diamond(r) )],[diamond_trancl_2h1,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ member(pair(ya,z),r)
| member(pair(z,diamond_strip_lemmaD_sk1(ya,sk1(yp),z,r)),trancl(r)) ),
inference(subst,[],[refute_0_5:[bind(X_523,$fot(z))]]) ).
cnf(refute_0_7,plain,
member(pair(z,diamond_strip_lemmaD_sk1(ya,sk1(yp),z,r)),trancl(r)),
inference(resolve,[$cnf( member(pair(ya,z),r) )],[diamond_trancl_2h3,refute_0_6]) ).
cnf(refute_0_8,plain,
~ member(pair(yp,diamond_strip_lemmaD_sk1(ya,sk1(yp),z,r)),trancl(r)),
inference(resolve,[$cnf( member(pair(z,diamond_strip_lemmaD_sk1(ya,sk1(yp),z,r)),trancl(r)) )],[refute_0_7,refute_0_0]) ).
cnf(refute_0_9,plain,
( ~ member(pair(y,yp),trancl(r))
| member(pair(yp,sk1(yp)),trancl(r)) ),
inference(subst,[],[diamond_trancl_2h5:[bind(YP,$fot(yp))]]) ).
cnf(refute_0_10,plain,
member(pair(yp,sk1(yp)),trancl(r)),
inference(resolve,[$cnf( member(pair(y,yp),trancl(r)) )],[diamond_trancl_2c1,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ member(pair(A,sk1(yp)),trancl(r))
| ~ member(pair(sk1(yp),diamond_strip_lemmaD_sk1(ya,sk1(yp),z,r)),trancl(r))
| ~ trans(trancl(r))
| member(pair(A,diamond_strip_lemmaD_sk1(ya,sk1(yp),z,r)),trancl(r)) ),
inference(subst,[],[transD:[bind(B,$fot(sk1(yp))),bind(C,$fot(diamond_strip_lemmaD_sk1(ya,sk1(yp),z,r))),bind(R,$fot(trancl(r)))]]) ).
cnf(refute_0_12,plain,
( ~ member(pair(sk1(yp),diamond_strip_lemmaD_sk1(ya,sk1(yp),z,r)),r)
| member(pair(sk1(yp),diamond_strip_lemmaD_sk1(ya,sk1(yp),z,r)),trancl(r)) ),
inference(subst,[],[r_into_trancl:[bind(A,$fot(sk1(yp))),bind(B,$fot(diamond_strip_lemmaD_sk1(ya,sk1(yp),z,r))),bind(R,$fot(r))]]) ).
cnf(refute_0_13,plain,
( ~ diamond(r)
| ~ member(pair(ya,X_260),r)
| ~ member(pair(ya,sk1(yp)),trancl(r))
| member(pair(sk1(yp),diamond_strip_lemmaD_sk1(ya,sk1(yp),X_260,r)),r) ),
inference(subst,[],[diamond_strip_lemmaD2:[bind(R,$fot(r)),bind(X,$fot(ya)),bind(Y,$fot(sk1(yp))),bind(YP,$fot(X_260))]]) ).
cnf(refute_0_14,plain,
( ~ diamond(r)
| ~ member(pair(ya,X_260),r)
| member(pair(sk1(yp),diamond_strip_lemmaD_sk1(ya,sk1(yp),X_260,r)),r) ),
inference(resolve,[$cnf( member(pair(ya,sk1(yp)),trancl(r)) )],[refute_0_2,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ member(pair(ya,X_260),r)
| member(pair(sk1(yp),diamond_strip_lemmaD_sk1(ya,sk1(yp),X_260,r)),r) ),
inference(resolve,[$cnf( diamond(r) )],[diamond_trancl_2h1,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ member(pair(ya,z),r)
| member(pair(sk1(yp),diamond_strip_lemmaD_sk1(ya,sk1(yp),z,r)),r) ),
inference(subst,[],[refute_0_15:[bind(X_260,$fot(z))]]) ).
cnf(refute_0_17,plain,
member(pair(sk1(yp),diamond_strip_lemmaD_sk1(ya,sk1(yp),z,r)),r),
inference(resolve,[$cnf( member(pair(ya,z),r) )],[diamond_trancl_2h3,refute_0_16]) ).
cnf(refute_0_18,plain,
member(pair(sk1(yp),diamond_strip_lemmaD_sk1(ya,sk1(yp),z,r)),trancl(r)),
inference(resolve,[$cnf( member(pair(sk1(yp),diamond_strip_lemmaD_sk1(ya,sk1(yp),z,r)),r) )],[refute_0_17,refute_0_12]) ).
cnf(refute_0_19,plain,
( ~ member(pair(A,sk1(yp)),trancl(r))
| ~ trans(trancl(r))
| member(pair(A,diamond_strip_lemmaD_sk1(ya,sk1(yp),z,r)),trancl(r)) ),
inference(resolve,[$cnf( member(pair(sk1(yp),diamond_strip_lemmaD_sk1(ya,sk1(yp),z,r)),trancl(r)) )],[refute_0_18,refute_0_11]) ).
cnf(refute_0_20,plain,
trans(trancl(r)),
inference(subst,[],[trans_trancl:[bind(R,$fot(r))]]) ).
cnf(refute_0_21,plain,
( ~ member(pair(A,sk1(yp)),trancl(r))
| member(pair(A,diamond_strip_lemmaD_sk1(ya,sk1(yp),z,r)),trancl(r)) ),
inference(resolve,[$cnf( trans(trancl(r)) )],[refute_0_20,refute_0_19]) ).
cnf(refute_0_22,plain,
( ~ member(pair(yp,sk1(yp)),trancl(r))
| member(pair(yp,diamond_strip_lemmaD_sk1(ya,sk1(yp),z,r)),trancl(r)) ),
inference(subst,[],[refute_0_21:[bind(A,$fot(yp))]]) ).
cnf(refute_0_23,plain,
member(pair(yp,diamond_strip_lemmaD_sk1(ya,sk1(yp),z,r)),trancl(r)),
inference(resolve,[$cnf( member(pair(yp,sk1(yp)),trancl(r)) )],[refute_0_10,refute_0_22]) ).
cnf(refute_0_24,plain,
$false,
inference(resolve,[$cnf( member(pair(yp,diamond_strip_lemmaD_sk1(ya,sk1(yp),z,r)),trancl(r)) )],[refute_0_23,refute_0_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL100-1 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue May 31 06:37:57 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 15.72/15.90 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.72/15.90
% 15.72/15.90 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.72/15.91
%------------------------------------------------------------------------------