TSTP Solution File: SYO607+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYO607+1 : TPTP v8.1.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 18:40:25 EDT 2022
% Result : Theorem 0.12s 0.35s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 2
% Syntax : Number of formulae : 100 ( 26 unt; 0 def)
% Number of atoms : 311 ( 0 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 357 ( 146 ~; 112 |; 89 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-1 aty)
% Number of variables : 229 ( 13 sgn 92 !; 101 ?)
% Comments :
%------------------------------------------------------------------------------
fof(nc6,conjecture,
( ? [A] :
( g_false_only(a,A)
& ? [B] : g_false_only(A,B) )
| ? [A] :
! [B] : g_true_only(A,B)
| ( ? [A] :
( ( g_both(a,A)
| ( ? [B] : g_both(A,B)
& ~ ? [B] : g_false_only(A,B) ) )
& ~ g_true_only(a,A)
& ~ ! [B] : g_true_only(A,B) )
& ~ ? [A] :
( g_false_only(a,A)
& ? [B] : g_false_only(A,B) )
& ? [A] :
( ? [B] : g_both(A,B)
& ~ ? [B] : g_false_only(A,B) )
& ~ ? [A] :
! [B] : g_true_only(A,B) ) ) ).
fof(exhaustion_g,axiom,
! [X_2,X_1] :
( g_true_only(X_2,X_1)
| g_both(X_2,X_1)
| g_false_only(X_2,X_1) ) ).
fof(subgoal_0,plain,
( ( ~ ? [A] :
( g_false_only(a,A)
& ? [B] : g_false_only(A,B) )
& ~ ? [A] :
! [B] : g_true_only(A,B) )
=> ? [A] :
( ( g_both(a,A)
| ( ? [B] : g_both(A,B)
& ~ ? [B] : g_false_only(A,B) ) )
& ~ g_true_only(a,A)
& ~ ! [B] : g_true_only(A,B) ) ),
inference(strip,[],[nc6]) ).
fof(subgoal_1,plain,
( ( ~ ? [A] :
( g_false_only(a,A)
& ? [B] : g_false_only(A,B) )
& ~ ? [A] :
! [B] : g_true_only(A,B)
& ? [A] :
( ( g_both(a,A)
| ( ? [B] : g_both(A,B)
& ~ ? [B] : g_false_only(A,B) ) )
& ~ g_true_only(a,A)
& ~ ! [B] : g_true_only(A,B) ) )
=> ! [A] :
( g_false_only(a,A)
=> ! [B] : ~ g_false_only(A,B) ) ),
inference(strip,[],[nc6]) ).
fof(subgoal_2,plain,
( ( ~ ? [A] :
( g_false_only(a,A)
& ? [B] : g_false_only(A,B) )
& ~ ? [A] :
! [B] : g_true_only(A,B)
& ? [A] :
( ( g_both(a,A)
| ( ? [B] : g_both(A,B)
& ~ ? [B] : g_false_only(A,B) ) )
& ~ g_true_only(a,A)
& ~ ! [B] : g_true_only(A,B) )
& ~ ? [A] :
( g_false_only(a,A)
& ? [B] : g_false_only(A,B) ) )
=> ? [A] :
( ? [B] : g_both(A,B)
& ~ ? [B] : g_false_only(A,B) ) ),
inference(strip,[],[nc6]) ).
fof(subgoal_3,plain,
( ( ~ ? [A] :
( g_false_only(a,A)
& ? [B] : g_false_only(A,B) )
& ~ ? [A] :
! [B] : g_true_only(A,B)
& ? [A] :
( ( g_both(a,A)
| ( ? [B] : g_both(A,B)
& ~ ? [B] : g_false_only(A,B) ) )
& ~ g_true_only(a,A)
& ~ ! [B] : g_true_only(A,B) )
& ~ ? [A] :
( g_false_only(a,A)
& ? [B] : g_false_only(A,B) )
& ? [A] :
( ? [B] : g_both(A,B)
& ~ ? [B] : g_false_only(A,B) ) )
=> ! [A] :
~ ! [B] : g_true_only(A,B) ),
inference(strip,[],[nc6]) ).
fof(negate_0_0,plain,
~ ( ( ~ ? [A] :
( g_false_only(a,A)
& ? [B] : g_false_only(A,B) )
& ~ ? [A] :
! [B] : g_true_only(A,B) )
=> ? [A] :
( ( g_both(a,A)
| ( ? [B] : g_both(A,B)
& ~ ? [B] : g_false_only(A,B) ) )
& ~ g_true_only(a,A)
& ~ ! [B] : g_true_only(A,B) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ! [A] :
( ~ g_false_only(a,A)
| ! [B] : ~ g_false_only(A,B) )
& ! [A] :
( g_true_only(a,A)
| ( ~ g_both(a,A)
& ( ? [B] : g_false_only(A,B)
| ! [B] : ~ g_both(A,B) ) )
| ! [B] : g_true_only(A,B) )
& ! [A] :
? [B] : ~ g_true_only(A,B) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [A] :
? [B] : ~ g_true_only(A,B),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A] :
? [B] : ~ g_true_only(A,B),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A] : ~ g_true_only(A,skolemFOFtoCNF_B_1(A)),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A] :
( g_true_only(a,A)
| ( ~ g_both(a,A)
& ( ? [B] : g_false_only(A,B)
| ! [B] : ~ g_both(A,B) ) )
| ! [B] : g_true_only(A,B) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_5,plain,
! [A] :
( g_true_only(a,A)
| ( ~ g_both(a,A)
& ( ? [B] : g_false_only(A,B)
| ! [B] : ~ g_both(A,B) ) )
| ! [B] : g_true_only(A,B) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B,B0] :
( ( ~ g_both(a,A)
| g_true_only(A,B0)
| g_true_only(a,A) )
& ( ~ g_both(A,B)
| g_false_only(A,skolemFOFtoCNF_B(A))
| g_true_only(A,B0)
| g_true_only(a,A) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B0] :
( ~ g_both(a,A)
| g_true_only(A,B0)
| g_true_only(a,A) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X_1,X_2] :
( g_both(X_2,X_1)
| g_false_only(X_2,X_1)
| g_true_only(X_2,X_1) ),
inference(canonicalize,[],[exhaustion_g]) ).
fof(normalize_0_9,plain,
! [X_1,X_2] :
( g_both(X_2,X_1)
| g_false_only(X_2,X_1)
| g_true_only(X_2,X_1) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A] :
( ~ g_false_only(a,A)
| ! [B] : ~ g_false_only(A,B) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_11,plain,
! [A] :
( ~ g_false_only(a,A)
| ! [B] : ~ g_false_only(A,B) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B] :
( ~ g_false_only(A,B)
| ~ g_false_only(a,A) ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A,B,B0] :
( ~ g_both(A,B)
| g_false_only(A,skolemFOFtoCNF_B(A))
| g_true_only(A,B0)
| g_true_only(a,A) ),
inference(conjunct,[],[normalize_0_6]) ).
cnf(refute_0_0,plain,
~ g_true_only(A,skolemFOFtoCNF_B_1(A)),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
~ g_true_only(skolemFOFtoCNF_B_1(a),skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(a))),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_B_1(a)))]]) ).
cnf(refute_0_2,plain,
( ~ g_both(a,A)
| g_true_only(A,B0)
| g_true_only(a,A) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( ~ g_both(a,skolemFOFtoCNF_B_1(a))
| g_true_only(a,skolemFOFtoCNF_B_1(a))
| g_true_only(skolemFOFtoCNF_B_1(a),B0) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_B_1(a)))]]) ).
cnf(refute_0_4,plain,
~ g_true_only(X_22,skolemFOFtoCNF_B_1(X_22)),
inference(subst,[],[refute_0_0:[bind(A,$fot(X_22))]]) ).
cnf(refute_0_5,plain,
( g_both(X_2,X_1)
| g_false_only(X_2,X_1)
| g_true_only(X_2,X_1) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_6,plain,
( g_both(X_22,skolemFOFtoCNF_B_1(X_22))
| g_false_only(X_22,skolemFOFtoCNF_B_1(X_22))
| g_true_only(X_22,skolemFOFtoCNF_B_1(X_22)) ),
inference(subst,[],[refute_0_5:[bind(X_1,$fot(skolemFOFtoCNF_B_1(X_22))),bind(X_2,$fot(X_22))]]) ).
cnf(refute_0_7,plain,
( g_both(X_22,skolemFOFtoCNF_B_1(X_22))
| g_false_only(X_22,skolemFOFtoCNF_B_1(X_22)) ),
inference(resolve,[$cnf( g_true_only(X_22,skolemFOFtoCNF_B_1(X_22)) )],[refute_0_6,refute_0_4]) ).
cnf(refute_0_8,plain,
( g_both(a,skolemFOFtoCNF_B_1(a))
| g_false_only(a,skolemFOFtoCNF_B_1(a)) ),
inference(subst,[],[refute_0_7:[bind(X_22,$fot(a))]]) ).
cnf(refute_0_9,plain,
( ~ g_false_only(A,B)
| ~ g_false_only(a,A) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_10,plain,
( ~ g_false_only(a,skolemFOFtoCNF_B_1(a))
| ~ g_false_only(skolemFOFtoCNF_B_1(a),skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(a))) ),
inference(subst,[],[refute_0_9:[bind(A,$fot(skolemFOFtoCNF_B_1(a))),bind(B,$fot(skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(a))))]]) ).
cnf(refute_0_11,plain,
( ~ g_false_only(X_23,skolemFOFtoCNF_B_1(X_23))
| ~ g_false_only(a,X_23) ),
inference(subst,[],[refute_0_9:[bind(A,$fot(X_23)),bind(B,$fot(skolemFOFtoCNF_B_1(X_23)))]]) ).
cnf(refute_0_12,plain,
( g_both(X_23,skolemFOFtoCNF_B_1(X_23))
| g_false_only(X_23,skolemFOFtoCNF_B_1(X_23)) ),
inference(subst,[],[refute_0_7:[bind(X_22,$fot(X_23))]]) ).
cnf(refute_0_13,plain,
( ~ g_false_only(a,X_23)
| g_both(X_23,skolemFOFtoCNF_B_1(X_23)) ),
inference(resolve,[$cnf( g_false_only(X_23,skolemFOFtoCNF_B_1(X_23)) )],[refute_0_12,refute_0_11]) ).
cnf(refute_0_14,plain,
( ~ g_false_only(a,skolemFOFtoCNF_B_1(a))
| g_both(skolemFOFtoCNF_B_1(a),skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(a))) ),
inference(subst,[],[refute_0_13:[bind(X_23,$fot(skolemFOFtoCNF_B_1(a)))]]) ).
cnf(refute_0_15,plain,
( g_both(a,skolemFOFtoCNF_B_1(a))
| g_both(skolemFOFtoCNF_B_1(a),skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(a))) ),
inference(resolve,[$cnf( g_false_only(a,skolemFOFtoCNF_B_1(a)) )],[refute_0_8,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ g_both(A,B)
| g_false_only(A,skolemFOFtoCNF_B(A))
| g_true_only(A,B0)
| g_true_only(a,A) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_17,plain,
( ~ g_both(skolemFOFtoCNF_B_1(a),skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(a)))
| g_false_only(skolemFOFtoCNF_B_1(a),skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(a)))
| g_true_only(a,skolemFOFtoCNF_B_1(a))
| g_true_only(skolemFOFtoCNF_B_1(a),X_34) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_B_1(a))),bind(B,$fot(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(a)))),bind(B0,$fot(X_34))]]) ).
cnf(refute_0_18,plain,
( g_both(a,skolemFOFtoCNF_B_1(a))
| g_false_only(skolemFOFtoCNF_B_1(a),skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(a)))
| g_true_only(a,skolemFOFtoCNF_B_1(a))
| g_true_only(skolemFOFtoCNF_B_1(a),X_34) ),
inference(resolve,[$cnf( g_both(skolemFOFtoCNF_B_1(a),skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(a))) )],[refute_0_15,refute_0_17]) ).
cnf(refute_0_19,plain,
~ g_true_only(a,skolemFOFtoCNF_B_1(a)),
inference(subst,[],[refute_0_0:[bind(A,$fot(a))]]) ).
cnf(refute_0_20,plain,
( g_both(a,skolemFOFtoCNF_B_1(a))
| g_false_only(skolemFOFtoCNF_B_1(a),skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(a)))
| g_true_only(skolemFOFtoCNF_B_1(a),X_34) ),
inference(resolve,[$cnf( g_true_only(a,skolemFOFtoCNF_B_1(a)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( g_both(a,skolemFOFtoCNF_B_1(a))
| g_false_only(skolemFOFtoCNF_B_1(a),skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(a)))
| g_true_only(skolemFOFtoCNF_B_1(a),skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(a))) ),
inference(subst,[],[refute_0_20:[bind(X_34,$fot(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(a))))]]) ).
cnf(refute_0_22,plain,
( g_both(a,skolemFOFtoCNF_B_1(a))
| g_false_only(skolemFOFtoCNF_B_1(a),skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(a))) ),
inference(resolve,[$cnf( g_true_only(skolemFOFtoCNF_B_1(a),skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(a))) )],[refute_0_21,refute_0_1]) ).
cnf(refute_0_23,plain,
( ~ g_false_only(a,skolemFOFtoCNF_B_1(a))
| g_both(a,skolemFOFtoCNF_B_1(a)) ),
inference(resolve,[$cnf( g_false_only(skolemFOFtoCNF_B_1(a),skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(a))) )],[refute_0_22,refute_0_10]) ).
cnf(refute_0_24,plain,
g_both(a,skolemFOFtoCNF_B_1(a)),
inference(resolve,[$cnf( g_false_only(a,skolemFOFtoCNF_B_1(a)) )],[refute_0_8,refute_0_23]) ).
cnf(refute_0_25,plain,
( g_true_only(a,skolemFOFtoCNF_B_1(a))
| g_true_only(skolemFOFtoCNF_B_1(a),B0) ),
inference(resolve,[$cnf( g_both(a,skolemFOFtoCNF_B_1(a)) )],[refute_0_24,refute_0_3]) ).
cnf(refute_0_26,plain,
g_true_only(skolemFOFtoCNF_B_1(a),B0),
inference(resolve,[$cnf( g_true_only(a,skolemFOFtoCNF_B_1(a)) )],[refute_0_25,refute_0_19]) ).
cnf(refute_0_27,plain,
g_true_only(skolemFOFtoCNF_B_1(a),skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(a))),
inference(subst,[],[refute_0_26:[bind(B0,$fot(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(a))))]]) ).
cnf(refute_0_28,plain,
$false,
inference(resolve,[$cnf( g_true_only(skolemFOFtoCNF_B_1(a),skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(a))) )],[refute_0_27,refute_0_1]) ).
fof(negate_1_0,plain,
~ ( ( ~ ? [A] :
( g_false_only(a,A)
& ? [B] : g_false_only(A,B) )
& ~ ? [A] :
! [B] : g_true_only(A,B)
& ? [A] :
( ( g_both(a,A)
| ( ? [B] : g_both(A,B)
& ~ ? [B] : g_false_only(A,B) ) )
& ~ g_true_only(a,A)
& ~ ! [B] : g_true_only(A,B) ) )
=> ! [A] :
( g_false_only(a,A)
=> ! [B] : ~ g_false_only(A,B) ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
$false,
inference(canonicalize,[],[negate_1_0]) ).
cnf(refute_1_0,plain,
$false,
inference(canonicalize,[],[normalize_1_0]) ).
fof(negate_2_0,plain,
~ ( ( ~ ? [A] :
( g_false_only(a,A)
& ? [B] : g_false_only(A,B) )
& ~ ? [A] :
! [B] : g_true_only(A,B)
& ? [A] :
( ( g_both(a,A)
| ( ? [B] : g_both(A,B)
& ~ ? [B] : g_false_only(A,B) ) )
& ~ g_true_only(a,A)
& ~ ! [B] : g_true_only(A,B) )
& ~ ? [A] :
( g_false_only(a,A)
& ? [B] : g_false_only(A,B) ) )
=> ? [A] :
( ? [B] : g_both(A,B)
& ~ ? [B] : g_false_only(A,B) ) ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
( ? [A] :
( ~ g_true_only(a,A)
& ( g_both(a,A)
| ( ? [B] : g_both(A,B)
& ! [B] : ~ g_false_only(A,B) ) )
& ? [B] : ~ g_true_only(A,B) )
& ! [A] :
( ~ g_false_only(a,A)
| ! [B] : ~ g_false_only(A,B) )
& ! [A] :
( ? [B] : g_false_only(A,B)
| ! [B] : ~ g_both(A,B) )
& ! [A] :
? [B] : ~ g_true_only(A,B) ),
inference(canonicalize,[],[negate_2_0]) ).
fof(normalize_2_1,plain,
! [A] :
( ~ g_false_only(a,A)
| ! [B] : ~ g_false_only(A,B) ),
inference(conjunct,[],[normalize_2_0]) ).
fof(normalize_2_2,plain,
! [A] :
( ~ g_false_only(a,A)
| ! [B] : ~ g_false_only(A,B) ),
inference(specialize,[],[normalize_2_1]) ).
fof(normalize_2_3,plain,
! [A,B] :
( ~ g_false_only(A,B)
| ~ g_false_only(a,A) ),
inference(clausify,[],[normalize_2_2]) ).
fof(normalize_2_4,plain,
! [A] :
( ? [B] : g_false_only(A,B)
| ! [B] : ~ g_both(A,B) ),
inference(conjunct,[],[normalize_2_0]) ).
fof(normalize_2_5,plain,
! [A] :
( ? [B] : g_false_only(A,B)
| ! [B] : ~ g_both(A,B) ),
inference(specialize,[],[normalize_2_4]) ).
fof(normalize_2_6,plain,
! [A,B] :
( ~ g_both(A,B)
| g_false_only(A,skolemFOFtoCNF_B_4(A)) ),
inference(clausify,[],[normalize_2_5]) ).
fof(normalize_2_7,plain,
? [A] :
( ~ g_true_only(a,A)
& ( g_both(a,A)
| ( ? [B] : g_both(A,B)
& ! [B] : ~ g_false_only(A,B) ) )
& ? [B] : ~ g_true_only(A,B) ),
inference(conjunct,[],[normalize_2_0]) ).
fof(normalize_2_8,plain,
( ~ g_true_only(a,skolemFOFtoCNF_A)
& ( g_both(a,skolemFOFtoCNF_A)
| ( ? [B] : g_both(skolemFOFtoCNF_A,B)
& ! [B] : ~ g_false_only(skolemFOFtoCNF_A,B) ) )
& ? [B] : ~ g_true_only(skolemFOFtoCNF_A,B) ),
inference(skolemize,[],[normalize_2_7]) ).
fof(normalize_2_9,plain,
( g_both(a,skolemFOFtoCNF_A)
| ( ? [B] : g_both(skolemFOFtoCNF_A,B)
& ! [B] : ~ g_false_only(skolemFOFtoCNF_A,B) ) ),
inference(conjunct,[],[normalize_2_8]) ).
fof(normalize_2_10,plain,
! [B] :
( ( ~ g_false_only(skolemFOFtoCNF_A,B)
| g_both(a,skolemFOFtoCNF_A) )
& ( g_both(a,skolemFOFtoCNF_A)
| g_both(skolemFOFtoCNF_A,skolemFOFtoCNF_B_2) ) ),
inference(clausify,[],[normalize_2_9]) ).
fof(normalize_2_11,plain,
! [B] :
( ~ g_false_only(skolemFOFtoCNF_A,B)
| g_both(a,skolemFOFtoCNF_A) ),
inference(conjunct,[],[normalize_2_10]) ).
fof(normalize_2_12,plain,
( g_both(a,skolemFOFtoCNF_A)
| g_both(skolemFOFtoCNF_A,skolemFOFtoCNF_B_2) ),
inference(conjunct,[],[normalize_2_10]) ).
fof(normalize_2_13,plain,
! [A] :
? [B] : ~ g_true_only(A,B),
inference(conjunct,[],[normalize_2_0]) ).
fof(normalize_2_14,plain,
! [A] :
? [B] : ~ g_true_only(A,B),
inference(specialize,[],[normalize_2_13]) ).
fof(normalize_2_15,plain,
! [A] : ~ g_true_only(A,skolemFOFtoCNF_B_5(A)),
inference(skolemize,[],[normalize_2_14]) ).
fof(normalize_2_16,plain,
! [X_1,X_2] :
( g_both(X_2,X_1)
| g_false_only(X_2,X_1)
| g_true_only(X_2,X_1) ),
inference(canonicalize,[],[exhaustion_g]) ).
fof(normalize_2_17,plain,
! [X_1,X_2] :
( g_both(X_2,X_1)
| g_false_only(X_2,X_1)
| g_true_only(X_2,X_1) ),
inference(specialize,[],[normalize_2_16]) ).
cnf(refute_2_0,plain,
( ~ g_false_only(A,B)
| ~ g_false_only(a,A) ),
inference(canonicalize,[],[normalize_2_3]) ).
cnf(refute_2_1,plain,
( ~ g_false_only(a,skolemFOFtoCNF_B_4(a))
| ~ g_false_only(skolemFOFtoCNF_B_4(a),skolemFOFtoCNF_B_4(skolemFOFtoCNF_B_4(a))) ),
inference(subst,[],[refute_2_0:[bind(A,$fot(skolemFOFtoCNF_B_4(a))),bind(B,$fot(skolemFOFtoCNF_B_4(skolemFOFtoCNF_B_4(a))))]]) ).
cnf(refute_2_2,plain,
( ~ g_both(A,B)
| g_false_only(A,skolemFOFtoCNF_B_4(A)) ),
inference(canonicalize,[],[normalize_2_6]) ).
cnf(refute_2_3,plain,
( ~ g_both(skolemFOFtoCNF_B_4(a),skolemFOFtoCNF_B_5(skolemFOFtoCNF_B_4(a)))
| g_false_only(skolemFOFtoCNF_B_4(a),skolemFOFtoCNF_B_4(skolemFOFtoCNF_B_4(a))) ),
inference(subst,[],[refute_2_2:[bind(A,$fot(skolemFOFtoCNF_B_4(a))),bind(B,$fot(skolemFOFtoCNF_B_5(skolemFOFtoCNF_B_4(a))))]]) ).
cnf(refute_2_4,plain,
( ~ g_both(a,skolemFOFtoCNF_A)
| g_false_only(a,skolemFOFtoCNF_B_4(a)) ),
inference(subst,[],[refute_2_2:[bind(A,$fot(a)),bind(B,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_2_5,plain,
( ~ g_false_only(skolemFOFtoCNF_A,B)
| g_both(a,skolemFOFtoCNF_A) ),
inference(canonicalize,[],[normalize_2_11]) ).
cnf(refute_2_6,plain,
( ~ g_false_only(skolemFOFtoCNF_A,skolemFOFtoCNF_B_4(skolemFOFtoCNF_A))
| g_both(a,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_2_5:[bind(B,$fot(skolemFOFtoCNF_B_4(skolemFOFtoCNF_A)))]]) ).
cnf(refute_2_7,plain,
( g_both(a,skolemFOFtoCNF_A)
| g_both(skolemFOFtoCNF_A,skolemFOFtoCNF_B_2) ),
inference(canonicalize,[],[normalize_2_12]) ).
cnf(refute_2_8,plain,
( ~ g_both(skolemFOFtoCNF_A,skolemFOFtoCNF_B_2)
| g_false_only(skolemFOFtoCNF_A,skolemFOFtoCNF_B_4(skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_2_2:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_B_2))]]) ).
cnf(refute_2_9,plain,
( g_both(a,skolemFOFtoCNF_A)
| g_false_only(skolemFOFtoCNF_A,skolemFOFtoCNF_B_4(skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( g_both(skolemFOFtoCNF_A,skolemFOFtoCNF_B_2) )],[refute_2_7,refute_2_8]) ).
cnf(refute_2_10,plain,
g_both(a,skolemFOFtoCNF_A),
inference(resolve,[$cnf( g_false_only(skolemFOFtoCNF_A,skolemFOFtoCNF_B_4(skolemFOFtoCNF_A)) )],[refute_2_9,refute_2_6]) ).
cnf(refute_2_11,plain,
g_false_only(a,skolemFOFtoCNF_B_4(a)),
inference(resolve,[$cnf( g_both(a,skolemFOFtoCNF_A) )],[refute_2_10,refute_2_4]) ).
cnf(refute_2_12,plain,
( ~ g_false_only(X_63,skolemFOFtoCNF_B_5(X_63))
| ~ g_false_only(a,X_63) ),
inference(subst,[],[refute_2_0:[bind(A,$fot(X_63)),bind(B,$fot(skolemFOFtoCNF_B_5(X_63)))]]) ).
cnf(refute_2_13,plain,
~ g_true_only(A,skolemFOFtoCNF_B_5(A)),
inference(canonicalize,[],[normalize_2_15]) ).
cnf(refute_2_14,plain,
~ g_true_only(X_62,skolemFOFtoCNF_B_5(X_62)),
inference(subst,[],[refute_2_13:[bind(A,$fot(X_62))]]) ).
cnf(refute_2_15,plain,
( g_both(X_2,X_1)
| g_false_only(X_2,X_1)
| g_true_only(X_2,X_1) ),
inference(canonicalize,[],[normalize_2_17]) ).
cnf(refute_2_16,plain,
( g_both(X_62,skolemFOFtoCNF_B_5(X_62))
| g_false_only(X_62,skolemFOFtoCNF_B_5(X_62))
| g_true_only(X_62,skolemFOFtoCNF_B_5(X_62)) ),
inference(subst,[],[refute_2_15:[bind(X_1,$fot(skolemFOFtoCNF_B_5(X_62))),bind(X_2,$fot(X_62))]]) ).
cnf(refute_2_17,plain,
( g_both(X_62,skolemFOFtoCNF_B_5(X_62))
| g_false_only(X_62,skolemFOFtoCNF_B_5(X_62)) ),
inference(resolve,[$cnf( g_true_only(X_62,skolemFOFtoCNF_B_5(X_62)) )],[refute_2_16,refute_2_14]) ).
cnf(refute_2_18,plain,
( g_both(X_63,skolemFOFtoCNF_B_5(X_63))
| g_false_only(X_63,skolemFOFtoCNF_B_5(X_63)) ),
inference(subst,[],[refute_2_17:[bind(X_62,$fot(X_63))]]) ).
cnf(refute_2_19,plain,
( ~ g_false_only(a,X_63)
| g_both(X_63,skolemFOFtoCNF_B_5(X_63)) ),
inference(resolve,[$cnf( g_false_only(X_63,skolemFOFtoCNF_B_5(X_63)) )],[refute_2_18,refute_2_12]) ).
cnf(refute_2_20,plain,
( ~ g_false_only(a,skolemFOFtoCNF_B_4(a))
| g_both(skolemFOFtoCNF_B_4(a),skolemFOFtoCNF_B_5(skolemFOFtoCNF_B_4(a))) ),
inference(subst,[],[refute_2_19:[bind(X_63,$fot(skolemFOFtoCNF_B_4(a)))]]) ).
cnf(refute_2_21,plain,
g_both(skolemFOFtoCNF_B_4(a),skolemFOFtoCNF_B_5(skolemFOFtoCNF_B_4(a))),
inference(resolve,[$cnf( g_false_only(a,skolemFOFtoCNF_B_4(a)) )],[refute_2_11,refute_2_20]) ).
cnf(refute_2_22,plain,
g_false_only(skolemFOFtoCNF_B_4(a),skolemFOFtoCNF_B_4(skolemFOFtoCNF_B_4(a))),
inference(resolve,[$cnf( g_both(skolemFOFtoCNF_B_4(a),skolemFOFtoCNF_B_5(skolemFOFtoCNF_B_4(a))) )],[refute_2_21,refute_2_3]) ).
cnf(refute_2_23,plain,
~ g_false_only(a,skolemFOFtoCNF_B_4(a)),
inference(resolve,[$cnf( g_false_only(skolemFOFtoCNF_B_4(a),skolemFOFtoCNF_B_4(skolemFOFtoCNF_B_4(a))) )],[refute_2_22,refute_2_1]) ).
cnf(refute_2_24,plain,
$false,
inference(resolve,[$cnf( g_false_only(a,skolemFOFtoCNF_B_4(a)) )],[refute_2_11,refute_2_23]) ).
fof(negate_3_0,plain,
~ ( ( ~ ? [A] :
( g_false_only(a,A)
& ? [B] : g_false_only(A,B) )
& ~ ? [A] :
! [B] : g_true_only(A,B)
& ? [A] :
( ( g_both(a,A)
| ( ? [B] : g_both(A,B)
& ~ ? [B] : g_false_only(A,B) ) )
& ~ g_true_only(a,A)
& ~ ! [B] : g_true_only(A,B) )
& ~ ? [A] :
( g_false_only(a,A)
& ? [B] : g_false_only(A,B) )
& ? [A] :
( ? [B] : g_both(A,B)
& ~ ? [B] : g_false_only(A,B) ) )
=> ! [A] :
~ ! [B] : g_true_only(A,B) ),
inference(negate,[],[subgoal_3]) ).
fof(normalize_3_0,plain,
$false,
inference(canonicalize,[],[negate_3_0]) ).
cnf(refute_3_0,plain,
$false,
inference(canonicalize,[],[normalize_3_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYO607+1 : TPTP v8.1.0. Released v7.0.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n013.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 : Fri Jul 8 19:52:44 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.35
% 0.12/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.37
%------------------------------------------------------------------------------