TSTP Solution File: SEU186+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU186+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.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 12:39:08 EDT 2022
% Result : Theorem 0.68s 0.83s
% Output : CNFRefutation 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 53 ( 18 unt; 0 def)
% Number of atoms : 114 ( 34 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 108 ( 47 ~; 41 |; 11 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 71 ( 2 sgn 46 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_relat_1,axiom,
! [A] :
( relation(A)
<=> ! [B] :
~ ( in(B,A)
& ! [C,D] : B != ordered_pair(C,D) ) ) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ) ).
fof(t56_relat_1,conjecture,
! [A] :
( relation(A)
=> ( ! [B,C] : ~ in(ordered_pair(B,C),A)
=> A = empty_set ) ) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ) ).
fof(subgoal_0,plain,
! [A] :
( ( relation(A)
& ! [B,C] : ~ in(ordered_pair(B,C),A) )
=> A = empty_set ),
inference(strip,[],[t56_relat_1]) ).
fof(negate_0_0,plain,
~ ! [A] :
( ( relation(A)
& ! [B,C] : ~ in(ordered_pair(B,C),A) )
=> A = empty_set ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A] :
( ~ empty(A)
| A = empty_set ),
inference(canonicalize,[],[t6_boole]) ).
fof(normalize_0_1,plain,
! [A] :
( ~ empty(A)
| A = empty_set ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A] :
? [B] : element(B,A),
inference(canonicalize,[],[existence_m1_subset_1]) ).
fof(normalize_0_3,plain,
! [A] :
? [B] : element(B,A),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A] : element(skolemFOFtoCNF_B_1(A),A),
inference(skolemize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B] :
( ~ element(A,B)
| empty(B)
| in(A,B) ),
inference(canonicalize,[],[t2_subset]) ).
fof(normalize_0_6,plain,
! [A,B] :
( ~ element(A,B)
| empty(B)
| in(A,B) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
? [A] :
( A != empty_set
& relation(A)
& ! [B,C] : ~ in(ordered_pair(B,C),A) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_8,plain,
( skolemFOFtoCNF_A_4 != empty_set
& relation(skolemFOFtoCNF_A_4)
& ! [B,C] : ~ in(ordered_pair(B,C),skolemFOFtoCNF_A_4) ),
inference(skolemize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [B,C] : ~ in(ordered_pair(B,C),skolemFOFtoCNF_A_4),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [B,C] : ~ in(ordered_pair(B,C),skolemFOFtoCNF_A_4),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
relation(skolemFOFtoCNF_A_4),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_12,plain,
! [A] :
( ~ relation(A)
<=> ? [B] :
( in(B,A)
& ! [C,D] : B != ordered_pair(C,D) ) ),
inference(canonicalize,[],[d1_relat_1]) ).
fof(normalize_0_13,plain,
! [A] :
( ~ relation(A)
<=> ? [B] :
( in(B,A)
& ! [C,D] : B != ordered_pair(C,D) ) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A,B,C,D] :
( ( skolemFOFtoCNF_B(A) != ordered_pair(C,D)
| relation(A) )
& ( in(skolemFOFtoCNF_B(A),A)
| relation(A) )
& ( ~ in(B,A)
| ~ relation(A)
| B = ordered_pair(skolemFOFtoCNF_C(B),skolemFOFtoCNF_D(B)) ) ),
inference(clausify,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [A,B] :
( ~ in(B,A)
| ~ relation(A)
| B = ordered_pair(skolemFOFtoCNF_C(B),skolemFOFtoCNF_D(B)) ),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
skolemFOFtoCNF_A_4 != empty_set,
inference(conjunct,[],[normalize_0_8]) ).
cnf(refute_0_0,plain,
( ~ empty(A)
| A = empty_set ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ empty(skolemFOFtoCNF_A_4)
| skolemFOFtoCNF_A_4 = empty_set ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A_4))]]) ).
cnf(refute_0_2,plain,
element(skolemFOFtoCNF_B_1(A),A),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
element(skolemFOFtoCNF_B_1(X_48),X_48),
inference(subst,[],[refute_0_2:[bind(A,$fot(X_48))]]) ).
cnf(refute_0_4,plain,
( ~ element(A,B)
| empty(B)
| in(A,B) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_5,plain,
( ~ element(skolemFOFtoCNF_B_1(X_48),X_48)
| empty(X_48)
| in(skolemFOFtoCNF_B_1(X_48),X_48) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_B_1(X_48))),bind(B,$fot(X_48))]]) ).
cnf(refute_0_6,plain,
( empty(X_48)
| in(skolemFOFtoCNF_B_1(X_48),X_48) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B_1(X_48),X_48) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
( empty(skolemFOFtoCNF_A_4)
| in(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4),skolemFOFtoCNF_A_4) ),
inference(subst,[],[refute_0_6:[bind(X_48,$fot(skolemFOFtoCNF_A_4))]]) ).
cnf(refute_0_8,plain,
~ in(ordered_pair(B,C),skolemFOFtoCNF_A_4),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_9,plain,
~ in(ordered_pair(skolemFOFtoCNF_C(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4)),skolemFOFtoCNF_D(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4))),skolemFOFtoCNF_A_4),
inference(subst,[],[refute_0_8:[bind(B,$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4)))),bind(C,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4))))]]) ).
cnf(refute_0_10,plain,
relation(skolemFOFtoCNF_A_4),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_11,plain,
( empty(X_67)
| in(skolemFOFtoCNF_B_1(X_67),X_67) ),
inference(subst,[],[refute_0_6:[bind(X_48,$fot(X_67))]]) ).
cnf(refute_0_12,plain,
( ~ in(B,A)
| ~ relation(A)
| B = ordered_pair(skolemFOFtoCNF_C(B),skolemFOFtoCNF_D(B)) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_13,plain,
( ~ in(skolemFOFtoCNF_B_1(X_67),X_67)
| ~ relation(X_67)
| skolemFOFtoCNF_B_1(X_67) = ordered_pair(skolemFOFtoCNF_C(skolemFOFtoCNF_B_1(X_67)),skolemFOFtoCNF_D(skolemFOFtoCNF_B_1(X_67))) ),
inference(subst,[],[refute_0_12:[bind(A,$fot(X_67)),bind(B,$fot(skolemFOFtoCNF_B_1(X_67)))]]) ).
cnf(refute_0_14,plain,
( ~ relation(X_67)
| skolemFOFtoCNF_B_1(X_67) = ordered_pair(skolemFOFtoCNF_C(skolemFOFtoCNF_B_1(X_67)),skolemFOFtoCNF_D(skolemFOFtoCNF_B_1(X_67)))
| empty(X_67) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_1(X_67),X_67) )],[refute_0_11,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ relation(skolemFOFtoCNF_A_4)
| skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4) = ordered_pair(skolemFOFtoCNF_C(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4)),skolemFOFtoCNF_D(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4)))
| empty(skolemFOFtoCNF_A_4) ),
inference(subst,[],[refute_0_14:[bind(X_67,$fot(skolemFOFtoCNF_A_4))]]) ).
cnf(refute_0_16,plain,
( skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4) = ordered_pair(skolemFOFtoCNF_C(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4)),skolemFOFtoCNF_D(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4)))
| empty(skolemFOFtoCNF_A_4) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_4) )],[refute_0_10,refute_0_15]) ).
cnf(refute_0_17,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_18,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_19,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4) != ordered_pair(skolemFOFtoCNF_C(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4)),skolemFOFtoCNF_D(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4)))
| ordered_pair(skolemFOFtoCNF_C(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4)),skolemFOFtoCNF_D(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4))) = skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4) ),
inference(subst,[],[refute_0_19:[bind(X,$fot(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4))),bind(Y,$fot(ordered_pair(skolemFOFtoCNF_C(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4)),skolemFOFtoCNF_D(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4)))))]]) ).
cnf(refute_0_21,plain,
( ordered_pair(skolemFOFtoCNF_C(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4)),skolemFOFtoCNF_D(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4))) = skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4)
| empty(skolemFOFtoCNF_A_4) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4),ordered_pair(skolemFOFtoCNF_C(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4)),skolemFOFtoCNF_D(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4)))) )],[refute_0_16,refute_0_20]) ).
cnf(refute_0_22,plain,
( ordered_pair(skolemFOFtoCNF_C(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4)),skolemFOFtoCNF_D(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4))) != skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4)
| ~ in(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4),skolemFOFtoCNF_A_4)
| in(ordered_pair(skolemFOFtoCNF_C(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4)),skolemFOFtoCNF_D(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4))),skolemFOFtoCNF_A_4) ),
introduced(tautology,[equality,[$cnf( ~ in(ordered_pair(skolemFOFtoCNF_C(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4)),skolemFOFtoCNF_D(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4))),skolemFOFtoCNF_A_4) ),[0],$fot(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4))]]) ).
cnf(refute_0_23,plain,
( ~ in(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4),skolemFOFtoCNF_A_4)
| empty(skolemFOFtoCNF_A_4)
| in(ordered_pair(skolemFOFtoCNF_C(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4)),skolemFOFtoCNF_D(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4))),skolemFOFtoCNF_A_4) ),
inference(resolve,[$cnf( $equal(ordered_pair(skolemFOFtoCNF_C(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4)),skolemFOFtoCNF_D(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4))),skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ in(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4),skolemFOFtoCNF_A_4)
| empty(skolemFOFtoCNF_A_4) ),
inference(resolve,[$cnf( in(ordered_pair(skolemFOFtoCNF_C(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4)),skolemFOFtoCNF_D(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4))),skolemFOFtoCNF_A_4) )],[refute_0_23,refute_0_9]) ).
cnf(refute_0_25,plain,
empty(skolemFOFtoCNF_A_4),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_4),skolemFOFtoCNF_A_4) )],[refute_0_7,refute_0_24]) ).
cnf(refute_0_26,plain,
skolemFOFtoCNF_A_4 = empty_set,
inference(resolve,[$cnf( empty(skolemFOFtoCNF_A_4) )],[refute_0_25,refute_0_1]) ).
cnf(refute_0_27,plain,
skolemFOFtoCNF_A_4 != empty_set,
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_28,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_4,empty_set) )],[refute_0_26,refute_0_27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU186+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n010.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 : Sun Jun 19 15:12:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.68/0.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.68/0.83
% 0.68/0.83 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.68/0.83
%------------------------------------------------------------------------------