%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN364+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 : Thu Jul 21 09:01:48 EDT 2022
% Result : Theorem 0.12s 0.34s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 1
% Syntax : Number of formulae : 41 ( 10 unt; 0 def)
% Number of atoms : 104 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 98 ( 35 ~; 35 |; 19 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 81 ( 12 sgn 36 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(x2115,conjecture,
( ( ! [X] :
( ? [Y] : big_p(X,Y)
=> ! [Z] : big_p(Z,Z) )
& ! [U] :
? [V] :
( big_p(U,V)
| ( big_m(U)
& big_q(f(U,V)) ) )
& ! [W] :
( big_q(W)
=> ~ big_m(g(W)) ) )
=> ! [U] :
? [V] :
( big_p(g(U),V)
& big_p(U,U) ) ) ).
fof(subgoal_0,plain,
( ( ! [X] :
( ? [Y] : big_p(X,Y)
=> ! [Z] : big_p(Z,Z) )
& ! [U] :
? [V] :
( big_p(U,V)
| ( big_m(U)
& big_q(f(U,V)) ) )
& ! [W] :
( big_q(W)
=> ~ big_m(g(W)) ) )
=> ! [U] :
? [V] :
( big_p(g(U),V)
& big_p(U,U) ) ),
inference(strip,[],[x2115]) ).
fof(negate_0_0,plain,
~ ( ( ! [X] :
( ? [Y] : big_p(X,Y)
=> ! [Z] : big_p(Z,Z) )
& ! [U] :
? [V] :
( big_p(U,V)
| ( big_m(U)
& big_q(f(U,V)) ) )
& ! [W] :
( big_q(W)
=> ~ big_m(g(W)) ) )
=> ! [U] :
? [V] :
( big_p(g(U),V)
& big_p(U,U) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ( ? [U] : ~ big_p(U,U)
| ? [U] :
! [V] : ~ big_p(g(U),V) )
& ( ! [Z] : big_p(Z,Z)
| ! [X,Y] : ~ big_p(X,Y) )
& ! [U] :
( ( big_m(U)
& ? [V] : big_q(f(U,V)) )
| ? [V] : big_p(U,V) )
& ! [W] :
( ~ big_m(g(W))
| ~ big_q(W) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ? [U] : ~ big_p(U,U)
| ? [U] :
! [V] : ~ big_p(g(U),V) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [V] :
( ~ big_p(g(skolemFOFtoCNF_U_1),V)
| ~ big_p(skolemFOFtoCNF_U,skolemFOFtoCNF_U) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [U] :
( ( big_m(U)
& ? [V] : big_q(f(U,V)) )
| ? [V] : big_p(U,V) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_4,plain,
! [U] :
( ( big_m(U)
& ? [V] : big_q(f(U,V)) )
| ? [V] : big_p(U,V) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [U] :
( ( big_m(U)
| big_p(U,skolemFOFtoCNF_V_1(U)) )
& ( big_p(U,skolemFOFtoCNF_V_1(U))
| big_q(f(U,skolemFOFtoCNF_V(U))) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [U] :
( big_p(U,skolemFOFtoCNF_V_1(U))
| big_q(f(U,skolemFOFtoCNF_V(U))) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [W] :
( ~ big_m(g(W))
| ~ big_q(W) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_8,plain,
! [W] :
( ~ big_m(g(W))
| ~ big_q(W) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [U] :
( big_m(U)
| big_p(U,skolemFOFtoCNF_V_1(U)) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_10,plain,
( ! [Z] : big_p(Z,Z)
| ! [X,Y] : ~ big_p(X,Y) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_11,plain,
! [X,Y,Z] :
( ~ big_p(X,Y)
| big_p(Z,Z) ),
inference(clausify,[],[normalize_0_10]) ).
cnf(refute_0_0,plain,
( ~ big_p(g(skolemFOFtoCNF_U_1),V)
| ~ big_p(skolemFOFtoCNF_U,skolemFOFtoCNF_U) ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ big_p(g(skolemFOFtoCNF_U_1),skolemFOFtoCNF_V_1(g(skolemFOFtoCNF_U_1)))
| ~ big_p(skolemFOFtoCNF_U,skolemFOFtoCNF_U) ),
inference(subst,[],[refute_0_0:[bind(V,$fot(skolemFOFtoCNF_V_1(g(skolemFOFtoCNF_U_1))))]]) ).
cnf(refute_0_2,plain,
( big_p(U,skolemFOFtoCNF_V_1(U))
| big_q(f(U,skolemFOFtoCNF_V(U))) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( ~ big_m(g(W))
| ~ big_q(W) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_4,plain,
( big_m(U)
| big_p(U,skolemFOFtoCNF_V_1(U)) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_5,plain,
( big_m(X_4)
| big_p(X_4,skolemFOFtoCNF_V_1(X_4)) ),
inference(subst,[],[refute_0_4:[bind(U,$fot(X_4))]]) ).
cnf(refute_0_6,plain,
( ~ big_p(X,Y)
| big_p(Z,Z) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_7,plain,
( ~ big_p(X_4,skolemFOFtoCNF_V_1(X_4))
| big_p(X_6,X_6) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(X_4)),bind(Y,$fot(skolemFOFtoCNF_V_1(X_4))),bind(Z,$fot(X_6))]]) ).
cnf(refute_0_8,plain,
( big_m(X_4)
| big_p(X_6,X_6) ),
inference(resolve,[$cnf( big_p(X_4,skolemFOFtoCNF_V_1(X_4)) )],[refute_0_5,refute_0_7]) ).
cnf(refute_0_9,plain,
( big_m(X_4)
| big_p(skolemFOFtoCNF_U,skolemFOFtoCNF_U) ),
inference(subst,[],[refute_0_8:[bind(X_6,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_10,plain,
( ~ big_p(g(skolemFOFtoCNF_U_1),g(skolemFOFtoCNF_U_1))
| ~ big_p(skolemFOFtoCNF_U,skolemFOFtoCNF_U) ),
inference(subst,[],[refute_0_0:[bind(V,$fot(g(skolemFOFtoCNF_U_1)))]]) ).
cnf(refute_0_11,plain,
( big_m(X_7)
| big_p(g(skolemFOFtoCNF_U_1),g(skolemFOFtoCNF_U_1)) ),
inference(subst,[],[refute_0_8:[bind(X_4,$fot(X_7)),bind(X_6,$fot(g(skolemFOFtoCNF_U_1)))]]) ).
cnf(refute_0_12,plain,
( ~ big_p(skolemFOFtoCNF_U,skolemFOFtoCNF_U)
| big_m(X_7) ),
inference(resolve,[$cnf( big_p(g(skolemFOFtoCNF_U_1),g(skolemFOFtoCNF_U_1)) )],[refute_0_11,refute_0_10]) ).
cnf(refute_0_13,plain,
( ~ big_p(skolemFOFtoCNF_U,skolemFOFtoCNF_U)
| big_m(X_9) ),
inference(subst,[],[refute_0_12:[bind(X_7,$fot(X_9))]]) ).
cnf(refute_0_14,plain,
( big_m(X_4)
| big_m(X_9) ),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_U,skolemFOFtoCNF_U) )],[refute_0_9,refute_0_13]) ).
cnf(refute_0_15,plain,
big_m(g(W)),
inference(subst,[],[refute_0_14:[bind(X_4,$fot(g(W))),bind(X_9,$fot(g(W)))]]) ).
cnf(refute_0_16,plain,
~ big_q(W),
inference(resolve,[$cnf( big_m(g(W)) )],[refute_0_15,refute_0_3]) ).
cnf(refute_0_17,plain,
~ big_q(f(U,skolemFOFtoCNF_V(U))),
inference(subst,[],[refute_0_16:[bind(W,$fot(f(U,skolemFOFtoCNF_V(U))))]]) ).
cnf(refute_0_18,plain,
big_p(U,skolemFOFtoCNF_V_1(U)),
inference(resolve,[$cnf( big_q(f(U,skolemFOFtoCNF_V(U))) )],[refute_0_2,refute_0_17]) ).
cnf(refute_0_19,plain,
big_p(g(skolemFOFtoCNF_U_1),skolemFOFtoCNF_V_1(g(skolemFOFtoCNF_U_1))),
inference(subst,[],[refute_0_18:[bind(U,$fot(g(skolemFOFtoCNF_U_1)))]]) ).
cnf(refute_0_20,plain,
~ big_p(skolemFOFtoCNF_U,skolemFOFtoCNF_U),
inference(resolve,[$cnf( big_p(g(skolemFOFtoCNF_U_1),skolemFOFtoCNF_V_1(g(skolemFOFtoCNF_U_1))) )],[refute_0_19,refute_0_1]) ).
cnf(refute_0_21,plain,
( ~ big_p(X_12,skolemFOFtoCNF_V_1(X_12))
| big_p(Z,Z) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(X_12)),bind(Y,$fot(skolemFOFtoCNF_V_1(X_12)))]]) ).
cnf(refute_0_22,plain,
big_p(X_12,skolemFOFtoCNF_V_1(X_12)),
inference(subst,[],[refute_0_18:[bind(U,$fot(X_12))]]) ).
cnf(refute_0_23,plain,
big_p(Z,Z),
inference(resolve,[$cnf( big_p(X_12,skolemFOFtoCNF_V_1(X_12)) )],[refute_0_22,refute_0_21]) ).
cnf(refute_0_24,plain,
big_p(skolemFOFtoCNF_U,skolemFOFtoCNF_U),
inference(subst,[],[refute_0_23:[bind(Z,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_25,plain,
$false,
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_U,skolemFOFtoCNF_U) )],[refute_0_24,refute_0_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN364+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n028.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 Jul 12 06:56:59 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34
% 0.12/0.34 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.35
%------------------------------------------------------------------------------