TSTP Solution File: SEU406+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU406+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 : Tue Jul 19 12:40:55 EDT 2022
% Result : Theorem 199.34s 199.51s
% Output : CNFRefutation 199.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 7
% Syntax : Number of formulae : 104 ( 39 unt; 0 def)
% Number of atoms : 315 ( 42 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 353 ( 142 ~; 126 |; 71 &)
% ( 10 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 173 ( 13 sgn 70 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t1_latsum_1,conjecture,
! [A,B,C,D] :
~ ( r2_hidden(A,k2_xboole_0(C,D))
& r2_hidden(B,k2_xboole_0(C,D))
& ~ ( r2_hidden(A,k4_xboole_0(C,D))
& r2_hidden(B,k4_xboole_0(C,D)) )
& ~ ( r2_hidden(A,D)
& r2_hidden(B,D) )
& ~ ( r2_hidden(A,k4_xboole_0(C,D))
& r2_hidden(B,D) )
& ~ ( r2_hidden(A,D)
& r2_hidden(B,k4_xboole_0(C,D)) ) ) ).
fof(d2_xboole_0,axiom,
! [A,B,C] :
( C = k2_xboole_0(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> ( r2_hidden(D,A)
| r2_hidden(D,B) ) ) ) ).
fof(t39_xboole_1,axiom,
! [A,B] : k2_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B) ).
fof(subgoal_0,plain,
! [A,B,C,D] :
( ( r2_hidden(A,k2_xboole_0(C,D))
& r2_hidden(B,k2_xboole_0(C,D))
& ~ ( r2_hidden(A,k4_xboole_0(C,D))
& r2_hidden(B,k4_xboole_0(C,D)) )
& ~ ( r2_hidden(A,D)
& r2_hidden(B,D) )
& ~ ( r2_hidden(A,k4_xboole_0(C,D))
& r2_hidden(B,D) ) )
=> r2_hidden(A,D) ),
inference(strip,[],[t1_latsum_1]) ).
fof(subgoal_1,plain,
! [A,B,C,D] :
( ( r2_hidden(A,k2_xboole_0(C,D))
& r2_hidden(B,k2_xboole_0(C,D))
& ~ ( r2_hidden(A,k4_xboole_0(C,D))
& r2_hidden(B,k4_xboole_0(C,D)) )
& ~ ( r2_hidden(A,D)
& r2_hidden(B,D) )
& ~ ( r2_hidden(A,k4_xboole_0(C,D))
& r2_hidden(B,D) )
& r2_hidden(A,D) )
=> r2_hidden(B,k4_xboole_0(C,D)) ),
inference(strip,[],[t1_latsum_1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C,D] :
( ( r2_hidden(A,k2_xboole_0(C,D))
& r2_hidden(B,k2_xboole_0(C,D))
& ~ ( r2_hidden(A,k4_xboole_0(C,D))
& r2_hidden(B,k4_xboole_0(C,D)) )
& ~ ( r2_hidden(A,D)
& r2_hidden(B,D) )
& ~ ( r2_hidden(A,k4_xboole_0(C,D))
& r2_hidden(B,D) ) )
=> r2_hidden(A,D) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B,C] :
( C != k2_xboole_0(A,B)
<=> ? [D] :
( ~ r2_hidden(D,C)
<=> ( r2_hidden(D,A)
| r2_hidden(D,B) ) ) ),
inference(canonicalize,[],[d2_xboole_0]) ).
fof(normalize_0_1,plain,
! [A,B,C] :
( C != k2_xboole_0(A,B)
<=> ? [D] :
( ~ r2_hidden(D,C)
<=> ( r2_hidden(D,A)
| r2_hidden(D,B) ) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B,C,D] :
( ( C != k2_xboole_0(A,B)
| ~ r2_hidden(D,A)
| r2_hidden(D,C) )
& ( C != k2_xboole_0(A,B)
| ~ r2_hidden(D,B)
| r2_hidden(D,C) )
& ( ~ r2_hidden(skolemFOFtoCNF_D(A,B,C),A)
| ~ r2_hidden(skolemFOFtoCNF_D(A,B,C),C)
| C = k2_xboole_0(A,B) )
& ( ~ r2_hidden(skolemFOFtoCNF_D(A,B,C),B)
| ~ r2_hidden(skolemFOFtoCNF_D(A,B,C),C)
| C = k2_xboole_0(A,B) )
& ( C != k2_xboole_0(A,B)
| ~ r2_hidden(D,C)
| r2_hidden(D,A)
| r2_hidden(D,B) )
& ( C = k2_xboole_0(A,B)
| r2_hidden(skolemFOFtoCNF_D(A,B,C),A)
| r2_hidden(skolemFOFtoCNF_D(A,B,C),B)
| r2_hidden(skolemFOFtoCNF_D(A,B,C),C) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B,C,D] :
( C != k2_xboole_0(A,B)
| ~ r2_hidden(D,B)
| r2_hidden(D,C) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [A,B,C,D] :
( ~ r2_hidden(A,D)
& r2_hidden(A,k2_xboole_0(C,D))
& r2_hidden(B,k2_xboole_0(C,D))
& ( ~ r2_hidden(A,D)
| ~ r2_hidden(B,D) )
& ( ~ r2_hidden(A,k4_xboole_0(C,D))
| ~ r2_hidden(B,D) )
& ( ~ r2_hidden(A,k4_xboole_0(C,D))
| ~ r2_hidden(B,k4_xboole_0(C,D)) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( ~ r2_hidden(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D_1)
& r2_hidden(skolemFOFtoCNF_A_2,k2_xboole_0(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1))
& r2_hidden(skolemFOFtoCNF_B_1,k2_xboole_0(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1))
& ( ~ r2_hidden(skolemFOFtoCNF_A_2,k4_xboole_0(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1))
| ~ r2_hidden(skolemFOFtoCNF_B_1,k4_xboole_0(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)) )
& ( ~ r2_hidden(skolemFOFtoCNF_A_2,k4_xboole_0(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1))
| ~ r2_hidden(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1) )
& ( ~ r2_hidden(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D_1)
| ~ r2_hidden(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1) ) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
r2_hidden(skolemFOFtoCNF_A_2,k2_xboole_0(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,C,D] :
( C != k2_xboole_0(A,B)
| ~ r2_hidden(D,C)
| r2_hidden(D,A)
| r2_hidden(D,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_8,plain,
~ r2_hidden(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D_1),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_9,plain,
! [A,B] : k2_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B),
inference(canonicalize,[],[t39_xboole_1]) ).
fof(normalize_0_10,plain,
! [A,B] : k2_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
( ~ r2_hidden(skolemFOFtoCNF_A_2,k4_xboole_0(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1))
| ~ r2_hidden(skolemFOFtoCNF_B_1,k4_xboole_0(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_12,plain,
r2_hidden(skolemFOFtoCNF_B_1,k2_xboole_0(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_13,plain,
( ~ r2_hidden(skolemFOFtoCNF_A_2,k4_xboole_0(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1))
| ~ r2_hidden(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1) ),
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
( C != k2_xboole_0(A,B)
| ~ r2_hidden(D,B)
| r2_hidden(D,C) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( k2_xboole_0(A,B) != k2_xboole_0(A,B)
| ~ r2_hidden(D,B)
| r2_hidden(D,k2_xboole_0(A,B)) ),
inference(subst,[],[refute_0_0:[bind(C,$fot(k2_xboole_0(A,B)))]]) ).
cnf(refute_0_2,plain,
k2_xboole_0(A,B) = k2_xboole_0(A,B),
introduced(tautology,[refl,[$fot(k2_xboole_0(A,B))]]) ).
cnf(refute_0_3,plain,
( ~ r2_hidden(D,B)
| r2_hidden(D,k2_xboole_0(A,B)) ),
inference(resolve,[$cnf( $equal(k2_xboole_0(A,B),k2_xboole_0(A,B)) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
( ~ r2_hidden(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
| r2_hidden(skolemFOFtoCNF_A_2,k2_xboole_0(A,skolemFOFtoCNF_C)) ),
inference(subst,[],[refute_0_3:[bind(B,$fot(skolemFOFtoCNF_C)),bind(D,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_5,plain,
r2_hidden(skolemFOFtoCNF_A_2,k2_xboole_0(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_6,plain,
( C != k2_xboole_0(A,B)
| ~ r2_hidden(D,C)
| r2_hidden(D,A)
| r2_hidden(D,B) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_7,plain,
( k2_xboole_0(A,B) != k2_xboole_0(A,B)
| ~ r2_hidden(D,k2_xboole_0(A,B))
| r2_hidden(D,A)
| r2_hidden(D,B) ),
inference(subst,[],[refute_0_6:[bind(C,$fot(k2_xboole_0(A,B)))]]) ).
cnf(refute_0_8,plain,
( ~ r2_hidden(D,k2_xboole_0(A,B))
| r2_hidden(D,A)
| r2_hidden(D,B) ),
inference(resolve,[$cnf( $equal(k2_xboole_0(A,B),k2_xboole_0(A,B)) )],[refute_0_2,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ r2_hidden(skolemFOFtoCNF_A_2,k2_xboole_0(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1))
| r2_hidden(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
| r2_hidden(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D_1) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_C)),bind(B,$fot(skolemFOFtoCNF_D_1)),bind(D,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_10,plain,
( r2_hidden(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
| r2_hidden(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D_1) ),
inference(resolve,[$cnf( r2_hidden(skolemFOFtoCNF_A_2,k2_xboole_0(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)) )],[refute_0_5,refute_0_9]) ).
cnf(refute_0_11,plain,
~ r2_hidden(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D_1),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_12,plain,
r2_hidden(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
inference(resolve,[$cnf( r2_hidden(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D_1) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
r2_hidden(skolemFOFtoCNF_A_2,k2_xboole_0(A,skolemFOFtoCNF_C)),
inference(resolve,[$cnf( r2_hidden(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) )],[refute_0_12,refute_0_4]) ).
cnf(refute_0_14,plain,
r2_hidden(skolemFOFtoCNF_A_2,k2_xboole_0(X_3578,skolemFOFtoCNF_C)),
inference(subst,[],[refute_0_13:[bind(A,$fot(X_3578))]]) ).
cnf(refute_0_15,plain,
( ~ r2_hidden(X_593,k2_xboole_0(X_591,k4_xboole_0(B,X_591)))
| r2_hidden(X_593,X_591)
| r2_hidden(X_593,k4_xboole_0(B,X_591)) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(X_591)),bind(B,$fot(k4_xboole_0(B,X_591))),bind(D,$fot(X_593))]]) ).
cnf(refute_0_16,plain,
k2_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_17,plain,
k2_xboole_0(X_591,k4_xboole_0(B,X_591)) = k2_xboole_0(X_591,B),
inference(subst,[],[refute_0_16:[bind(A,$fot(X_591))]]) ).
cnf(refute_0_18,plain,
( k2_xboole_0(X_591,k4_xboole_0(B,X_591)) != k2_xboole_0(X_591,B)
| ~ r2_hidden(X_593,k2_xboole_0(X_591,B))
| r2_hidden(X_593,k2_xboole_0(X_591,k4_xboole_0(B,X_591))) ),
introduced(tautology,[equality,[$cnf( ~ r2_hidden(X_593,k2_xboole_0(X_591,k4_xboole_0(B,X_591))) ),[1],$fot(k2_xboole_0(X_591,B))]]) ).
cnf(refute_0_19,plain,
( ~ r2_hidden(X_593,k2_xboole_0(X_591,B))
| r2_hidden(X_593,k2_xboole_0(X_591,k4_xboole_0(B,X_591))) ),
inference(resolve,[$cnf( $equal(k2_xboole_0(X_591,k4_xboole_0(B,X_591)),k2_xboole_0(X_591,B)) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ r2_hidden(X_593,k2_xboole_0(X_591,B))
| r2_hidden(X_593,X_591)
| r2_hidden(X_593,k4_xboole_0(B,X_591)) ),
inference(resolve,[$cnf( r2_hidden(X_593,k2_xboole_0(X_591,k4_xboole_0(B,X_591))) )],[refute_0_19,refute_0_15]) ).
cnf(refute_0_21,plain,
( ~ r2_hidden(skolemFOFtoCNF_A_2,k2_xboole_0(X_3578,skolemFOFtoCNF_C))
| r2_hidden(skolemFOFtoCNF_A_2,X_3578)
| r2_hidden(skolemFOFtoCNF_A_2,k4_xboole_0(skolemFOFtoCNF_C,X_3578)) ),
inference(subst,[],[refute_0_20:[bind(B,$fot(skolemFOFtoCNF_C)),bind(X_591,$fot(X_3578)),bind(X_593,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_22,plain,
( r2_hidden(skolemFOFtoCNF_A_2,X_3578)
| r2_hidden(skolemFOFtoCNF_A_2,k4_xboole_0(skolemFOFtoCNF_C,X_3578)) ),
inference(resolve,[$cnf( r2_hidden(skolemFOFtoCNF_A_2,k2_xboole_0(X_3578,skolemFOFtoCNF_C)) )],[refute_0_14,refute_0_21]) ).
cnf(refute_0_23,plain,
( r2_hidden(skolemFOFtoCNF_A_2,k4_xboole_0(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1))
| r2_hidden(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D_1) ),
inference(subst,[],[refute_0_22:[bind(X_3578,$fot(skolemFOFtoCNF_D_1))]]) ).
cnf(refute_0_24,plain,
( ~ r2_hidden(skolemFOFtoCNF_A_2,k4_xboole_0(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1))
| ~ r2_hidden(skolemFOFtoCNF_B_1,k4_xboole_0(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_25,plain,
( ~ r2_hidden(skolemFOFtoCNF_B_1,k2_xboole_0(X_3581,skolemFOFtoCNF_C))
| r2_hidden(skolemFOFtoCNF_B_1,X_3581)
| r2_hidden(skolemFOFtoCNF_B_1,k4_xboole_0(skolemFOFtoCNF_C,X_3581)) ),
inference(subst,[],[refute_0_20:[bind(B,$fot(skolemFOFtoCNF_C)),bind(X_591,$fot(X_3581)),bind(X_593,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_26,plain,
( ~ r2_hidden(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C)
| r2_hidden(skolemFOFtoCNF_B_1,k2_xboole_0(A,skolemFOFtoCNF_C)) ),
inference(subst,[],[refute_0_3:[bind(B,$fot(skolemFOFtoCNF_C)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_27,plain,
r2_hidden(skolemFOFtoCNF_B_1,k2_xboole_0(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_28,plain,
( ~ r2_hidden(skolemFOFtoCNF_B_1,k2_xboole_0(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1))
| r2_hidden(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C)
| r2_hidden(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_C)),bind(B,$fot(skolemFOFtoCNF_D_1)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_29,plain,
( r2_hidden(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C)
| r2_hidden(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1) ),
inference(resolve,[$cnf( r2_hidden(skolemFOFtoCNF_B_1,k2_xboole_0(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ r2_hidden(skolemFOFtoCNF_A_2,k4_xboole_0(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1))
| ~ r2_hidden(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_31,plain,
( ~ r2_hidden(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)
| r2_hidden(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D_1) ),
inference(resolve,[$cnf( r2_hidden(skolemFOFtoCNF_A_2,k4_xboole_0(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)) )],[refute_0_23,refute_0_30]) ).
cnf(refute_0_32,plain,
~ r2_hidden(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1),
inference(resolve,[$cnf( r2_hidden(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D_1) )],[refute_0_31,refute_0_11]) ).
cnf(refute_0_33,plain,
r2_hidden(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C),
inference(resolve,[$cnf( r2_hidden(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
r2_hidden(skolemFOFtoCNF_B_1,k2_xboole_0(A,skolemFOFtoCNF_C)),
inference(resolve,[$cnf( r2_hidden(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C) )],[refute_0_33,refute_0_26]) ).
cnf(refute_0_35,plain,
r2_hidden(skolemFOFtoCNF_B_1,k2_xboole_0(X_3581,skolemFOFtoCNF_C)),
inference(subst,[],[refute_0_34:[bind(A,$fot(X_3581))]]) ).
cnf(refute_0_36,plain,
( r2_hidden(skolemFOFtoCNF_B_1,X_3581)
| r2_hidden(skolemFOFtoCNF_B_1,k4_xboole_0(skolemFOFtoCNF_C,X_3581)) ),
inference(resolve,[$cnf( r2_hidden(skolemFOFtoCNF_B_1,k2_xboole_0(X_3581,skolemFOFtoCNF_C)) )],[refute_0_35,refute_0_25]) ).
cnf(refute_0_37,plain,
( r2_hidden(skolemFOFtoCNF_B_1,k4_xboole_0(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1))
| r2_hidden(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1) ),
inference(subst,[],[refute_0_36:[bind(X_3581,$fot(skolemFOFtoCNF_D_1))]]) ).
cnf(refute_0_38,plain,
( ~ r2_hidden(skolemFOFtoCNF_A_2,k4_xboole_0(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1))
| r2_hidden(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1) ),
inference(resolve,[$cnf( r2_hidden(skolemFOFtoCNF_B_1,k4_xboole_0(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)) )],[refute_0_37,refute_0_24]) ).
cnf(refute_0_39,plain,
~ r2_hidden(skolemFOFtoCNF_A_2,k4_xboole_0(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)),
inference(resolve,[$cnf( r2_hidden(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1) )],[refute_0_38,refute_0_32]) ).
cnf(refute_0_40,plain,
r2_hidden(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D_1),
inference(resolve,[$cnf( r2_hidden(skolemFOFtoCNF_A_2,k4_xboole_0(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)) )],[refute_0_23,refute_0_39]) ).
cnf(refute_0_41,plain,
$false,
inference(resolve,[$cnf( r2_hidden(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D_1) )],[refute_0_40,refute_0_11]) ).
fof(negate_1_0,plain,
~ ! [A,B,C,D] :
( ( r2_hidden(A,k2_xboole_0(C,D))
& r2_hidden(B,k2_xboole_0(C,D))
& ~ ( r2_hidden(A,k4_xboole_0(C,D))
& r2_hidden(B,k4_xboole_0(C,D)) )
& ~ ( r2_hidden(A,D)
& r2_hidden(B,D) )
& ~ ( r2_hidden(A,k4_xboole_0(C,D))
& r2_hidden(B,D) )
& r2_hidden(A,D) )
=> r2_hidden(B,k4_xboole_0(C,D)) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [A,B,C,D] :
( ~ r2_hidden(B,k4_xboole_0(C,D))
& r2_hidden(A,D)
& r2_hidden(A,k2_xboole_0(C,D))
& r2_hidden(B,k2_xboole_0(C,D))
& ( ~ r2_hidden(A,D)
| ~ r2_hidden(B,D) )
& ( ~ r2_hidden(A,k4_xboole_0(C,D))
| ~ r2_hidden(B,D) )
& ( ~ r2_hidden(A,k4_xboole_0(C,D))
| ~ r2_hidden(B,k4_xboole_0(C,D)) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( ~ r2_hidden(skolemFOFtoCNF_B_2,k4_xboole_0(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2))
& r2_hidden(skolemFOFtoCNF_A_3,k2_xboole_0(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2))
& r2_hidden(skolemFOFtoCNF_A_3,skolemFOFtoCNF_D_2)
& r2_hidden(skolemFOFtoCNF_B_2,k2_xboole_0(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2))
& ( ~ r2_hidden(skolemFOFtoCNF_A_3,k4_xboole_0(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2))
| ~ r2_hidden(skolemFOFtoCNF_B_2,k4_xboole_0(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)) )
& ( ~ r2_hidden(skolemFOFtoCNF_A_3,k4_xboole_0(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2))
| ~ r2_hidden(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_2) )
& ( ~ r2_hidden(skolemFOFtoCNF_A_3,skolemFOFtoCNF_D_2)
| ~ r2_hidden(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_2) ) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
~ r2_hidden(skolemFOFtoCNF_B_2,k4_xboole_0(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [A,B,C] :
( C != k2_xboole_0(A,B)
<=> ? [D] :
( ~ r2_hidden(D,C)
<=> ( r2_hidden(D,A)
| r2_hidden(D,B) ) ) ),
inference(canonicalize,[],[d2_xboole_0]) ).
fof(normalize_1_4,plain,
! [A,B,C] :
( C != k2_xboole_0(A,B)
<=> ? [D] :
( ~ r2_hidden(D,C)
<=> ( r2_hidden(D,A)
| r2_hidden(D,B) ) ) ),
inference(specialize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
! [A,B,C,D] :
( ( C != k2_xboole_0(A,B)
| ~ r2_hidden(D,A)
| r2_hidden(D,C) )
& ( C != k2_xboole_0(A,B)
| ~ r2_hidden(D,B)
| r2_hidden(D,C) )
& ( ~ r2_hidden(skolemFOFtoCNF_D(A,B,C),A)
| ~ r2_hidden(skolemFOFtoCNF_D(A,B,C),C)
| C = k2_xboole_0(A,B) )
& ( ~ r2_hidden(skolemFOFtoCNF_D(A,B,C),B)
| ~ r2_hidden(skolemFOFtoCNF_D(A,B,C),C)
| C = k2_xboole_0(A,B) )
& ( C != k2_xboole_0(A,B)
| ~ r2_hidden(D,C)
| r2_hidden(D,A)
| r2_hidden(D,B) )
& ( C = k2_xboole_0(A,B)
| r2_hidden(skolemFOFtoCNF_D(A,B,C),A)
| r2_hidden(skolemFOFtoCNF_D(A,B,C),B)
| r2_hidden(skolemFOFtoCNF_D(A,B,C),C) ) ),
inference(clausify,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [A,B,C,D] :
( C != k2_xboole_0(A,B)
| ~ r2_hidden(D,B)
| r2_hidden(D,C) ),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
r2_hidden(skolemFOFtoCNF_B_2,k2_xboole_0(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_8,plain,
! [A,B,C,D] :
( C != k2_xboole_0(A,B)
| ~ r2_hidden(D,C)
| r2_hidden(D,A)
| r2_hidden(D,B) ),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_9,plain,
( ~ r2_hidden(skolemFOFtoCNF_A_3,skolemFOFtoCNF_D_2)
| ~ r2_hidden(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_2) ),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_10,plain,
r2_hidden(skolemFOFtoCNF_A_3,skolemFOFtoCNF_D_2),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_11,plain,
~ r2_hidden(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_2),
inference(simplify,[],[normalize_1_9,normalize_1_10]) ).
fof(normalize_1_12,plain,
! [A,B] : k2_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B),
inference(canonicalize,[],[t39_xboole_1]) ).
fof(normalize_1_13,plain,
! [A,B] : k2_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B),
inference(specialize,[],[normalize_1_12]) ).
cnf(refute_1_0,plain,
~ r2_hidden(skolemFOFtoCNF_B_2,k4_xboole_0(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
( C != k2_xboole_0(A,B)
| ~ r2_hidden(D,B)
| r2_hidden(D,C) ),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_2,plain,
( k2_xboole_0(A,B) != k2_xboole_0(A,B)
| ~ r2_hidden(D,B)
| r2_hidden(D,k2_xboole_0(A,B)) ),
inference(subst,[],[refute_1_1:[bind(C,$fot(k2_xboole_0(A,B)))]]) ).
cnf(refute_1_3,plain,
k2_xboole_0(A,B) = k2_xboole_0(A,B),
introduced(tautology,[refl,[$fot(k2_xboole_0(A,B))]]) ).
cnf(refute_1_4,plain,
( ~ r2_hidden(D,B)
| r2_hidden(D,k2_xboole_0(A,B)) ),
inference(resolve,[$cnf( $equal(k2_xboole_0(A,B),k2_xboole_0(A,B)) )],[refute_1_3,refute_1_2]) ).
cnf(refute_1_5,plain,
( ~ r2_hidden(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)
| r2_hidden(skolemFOFtoCNF_B_2,k2_xboole_0(A,skolemFOFtoCNF_C_1)) ),
inference(subst,[],[refute_1_4:[bind(B,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(skolemFOFtoCNF_B_2))]]) ).
cnf(refute_1_6,plain,
r2_hidden(skolemFOFtoCNF_B_2,k2_xboole_0(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_7,plain,
( C != k2_xboole_0(A,B)
| ~ r2_hidden(D,C)
| r2_hidden(D,A)
| r2_hidden(D,B) ),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_8,plain,
( k2_xboole_0(A,B) != k2_xboole_0(A,B)
| ~ r2_hidden(D,k2_xboole_0(A,B))
| r2_hidden(D,A)
| r2_hidden(D,B) ),
inference(subst,[],[refute_1_7:[bind(C,$fot(k2_xboole_0(A,B)))]]) ).
cnf(refute_1_9,plain,
( ~ r2_hidden(D,k2_xboole_0(A,B))
| r2_hidden(D,A)
| r2_hidden(D,B) ),
inference(resolve,[$cnf( $equal(k2_xboole_0(A,B),k2_xboole_0(A,B)) )],[refute_1_3,refute_1_8]) ).
cnf(refute_1_10,plain,
( ~ r2_hidden(skolemFOFtoCNF_B_2,k2_xboole_0(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2))
| r2_hidden(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)
| r2_hidden(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_2) ),
inference(subst,[],[refute_1_9:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_D_2)),bind(D,$fot(skolemFOFtoCNF_B_2))]]) ).
cnf(refute_1_11,plain,
( r2_hidden(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)
| r2_hidden(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_2) ),
inference(resolve,[$cnf( r2_hidden(skolemFOFtoCNF_B_2,k2_xboole_0(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)) )],[refute_1_6,refute_1_10]) ).
cnf(refute_1_12,plain,
~ r2_hidden(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_2),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_13,plain,
r2_hidden(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( r2_hidden(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_2) )],[refute_1_11,refute_1_12]) ).
cnf(refute_1_14,plain,
r2_hidden(skolemFOFtoCNF_B_2,k2_xboole_0(A,skolemFOFtoCNF_C_1)),
inference(resolve,[$cnf( r2_hidden(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1) )],[refute_1_13,refute_1_5]) ).
cnf(refute_1_15,plain,
r2_hidden(skolemFOFtoCNF_B_2,k2_xboole_0(X_5715,skolemFOFtoCNF_C_1)),
inference(subst,[],[refute_1_14:[bind(A,$fot(X_5715))]]) ).
cnf(refute_1_16,plain,
( ~ r2_hidden(X_4456,k2_xboole_0(X_4454,k4_xboole_0(B,X_4454)))
| r2_hidden(X_4456,X_4454)
| r2_hidden(X_4456,k4_xboole_0(B,X_4454)) ),
inference(subst,[],[refute_1_9:[bind(A,$fot(X_4454)),bind(B,$fot(k4_xboole_0(B,X_4454))),bind(D,$fot(X_4456))]]) ).
cnf(refute_1_17,plain,
k2_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B),
inference(canonicalize,[],[normalize_1_13]) ).
cnf(refute_1_18,plain,
k2_xboole_0(X_4454,k4_xboole_0(B,X_4454)) = k2_xboole_0(X_4454,B),
inference(subst,[],[refute_1_17:[bind(A,$fot(X_4454))]]) ).
cnf(refute_1_19,plain,
( k2_xboole_0(X_4454,k4_xboole_0(B,X_4454)) != k2_xboole_0(X_4454,B)
| ~ r2_hidden(X_4456,k2_xboole_0(X_4454,B))
| r2_hidden(X_4456,k2_xboole_0(X_4454,k4_xboole_0(B,X_4454))) ),
introduced(tautology,[equality,[$cnf( ~ r2_hidden(X_4456,k2_xboole_0(X_4454,k4_xboole_0(B,X_4454))) ),[1],$fot(k2_xboole_0(X_4454,B))]]) ).
cnf(refute_1_20,plain,
( ~ r2_hidden(X_4456,k2_xboole_0(X_4454,B))
| r2_hidden(X_4456,k2_xboole_0(X_4454,k4_xboole_0(B,X_4454))) ),
inference(resolve,[$cnf( $equal(k2_xboole_0(X_4454,k4_xboole_0(B,X_4454)),k2_xboole_0(X_4454,B)) )],[refute_1_18,refute_1_19]) ).
cnf(refute_1_21,plain,
( ~ r2_hidden(X_4456,k2_xboole_0(X_4454,B))
| r2_hidden(X_4456,X_4454)
| r2_hidden(X_4456,k4_xboole_0(B,X_4454)) ),
inference(resolve,[$cnf( r2_hidden(X_4456,k2_xboole_0(X_4454,k4_xboole_0(B,X_4454))) )],[refute_1_20,refute_1_16]) ).
cnf(refute_1_22,plain,
( ~ r2_hidden(skolemFOFtoCNF_B_2,k2_xboole_0(X_5715,skolemFOFtoCNF_C_1))
| r2_hidden(skolemFOFtoCNF_B_2,X_5715)
| r2_hidden(skolemFOFtoCNF_B_2,k4_xboole_0(skolemFOFtoCNF_C_1,X_5715)) ),
inference(subst,[],[refute_1_21:[bind(B,$fot(skolemFOFtoCNF_C_1)),bind(X_4454,$fot(X_5715)),bind(X_4456,$fot(skolemFOFtoCNF_B_2))]]) ).
cnf(refute_1_23,plain,
( r2_hidden(skolemFOFtoCNF_B_2,X_5715)
| r2_hidden(skolemFOFtoCNF_B_2,k4_xboole_0(skolemFOFtoCNF_C_1,X_5715)) ),
inference(resolve,[$cnf( r2_hidden(skolemFOFtoCNF_B_2,k2_xboole_0(X_5715,skolemFOFtoCNF_C_1)) )],[refute_1_15,refute_1_22]) ).
cnf(refute_1_24,plain,
( r2_hidden(skolemFOFtoCNF_B_2,k4_xboole_0(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2))
| r2_hidden(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_2) ),
inference(subst,[],[refute_1_23:[bind(X_5715,$fot(skolemFOFtoCNF_D_2))]]) ).
cnf(refute_1_25,plain,
r2_hidden(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_2),
inference(resolve,[$cnf( r2_hidden(skolemFOFtoCNF_B_2,k4_xboole_0(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)) )],[refute_1_24,refute_1_0]) ).
cnf(refute_1_26,plain,
$false,
inference(resolve,[$cnf( r2_hidden(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_2) )],[refute_1_25,refute_1_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU406+1 : TPTP v8.1.0. Released v3.4.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n017.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 : Sun Jun 19 16:08:13 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 199.34/199.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 199.34/199.51
% 199.34/199.51 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 199.34/199.52
%------------------------------------------------------------------------------