TSTP Solution File: SEU131+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU131+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 12:38:35 EDT 2022
% Result : Theorem 0.56s 0.77s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 108 ( 25 unt; 0 def)
% Number of atoms : 288 ( 73 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 313 ( 133 ~; 127 |; 28 &)
% ( 19 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 209 ( 16 sgn 90 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ) ).
fof(d4_xboole_0,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& ~ in(D,B) ) ) ) ).
fof(l32_xboole_1,conjecture,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ) ).
fof(t2_tarski,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ) ).
fof(t4_boole,axiom,
! [A] : set_difference(empty_set,A) = empty_set ).
fof(subgoal_0,plain,
! [A,B] :
( set_difference(A,B) = empty_set
=> subset(A,B) ),
inference(strip,[],[l32_xboole_1]) ).
fof(subgoal_1,plain,
! [A,B] :
( subset(A,B)
=> set_difference(A,B) = empty_set ),
inference(strip,[],[l32_xboole_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( set_difference(A,B) = empty_set
=> subset(A,B) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(canonicalize,[],[d3_tarski]) ).
fof(normalize_0_1,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B,C] :
( ( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) )
& ( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) )
& ( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B] :
( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_5,plain,
! [A,B,C] :
( C != set_difference(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
inference(canonicalize,[],[d4_xboole_0]) ).
fof(normalize_0_6,plain,
! [A,B,C] :
( C != set_difference(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,C,D] :
( ( C != set_difference(A,B)
| ~ in(D,B)
| ~ in(D,C) )
& ( C != set_difference(A,B)
| ~ in(D,C)
| in(D,A) )
& ( ~ in(skolemFOFtoCNF_D(A,B,C),B)
| C = set_difference(A,B)
| in(skolemFOFtoCNF_D(A,B,C),C) )
& ( C = set_difference(A,B)
| in(skolemFOFtoCNF_D(A,B,C),A)
| in(skolemFOFtoCNF_D(A,B,C),C) )
& ( C != set_difference(A,B)
| ~ in(D,A)
| in(D,B)
| in(D,C) )
& ( ~ in(skolemFOFtoCNF_D(A,B,C),A)
| ~ in(skolemFOFtoCNF_D(A,B,C),C)
| C = set_difference(A,B)
| in(skolemFOFtoCNF_D(A,B,C),B) ) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B,C,D] :
( C != set_difference(A,B)
| ~ in(D,A)
| in(D,B)
| in(D,C) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
? [A,B] :
( ~ subset(A,B)
& set_difference(A,B) = empty_set ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_10,plain,
( ~ subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
& set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = empty_set ),
inference(skolemize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = empty_set,
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B,C,D] :
( C != set_difference(A,B)
| ~ in(D,B)
| ~ in(D,C) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_13,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(canonicalize,[],[t4_boole]) ).
fof(normalize_0_14,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
~ subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_10]) ).
cnf(refute_0_0,plain,
( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_B)
| subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_2,plain,
( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
( in(skolemFOFtoCNF_C(X_74,B),X_74)
| subset(X_74,B) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(X_74))]]) ).
cnf(refute_0_4,plain,
( C != set_difference(A,B)
| ~ in(D,A)
| in(D,B)
| in(D,C) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( set_difference(A,B) != set_difference(A,B)
| ~ in(D,A)
| in(D,B)
| in(D,set_difference(A,B)) ),
inference(subst,[],[refute_0_4:[bind(C,$fot(set_difference(A,B)))]]) ).
cnf(refute_0_6,plain,
set_difference(A,B) = set_difference(A,B),
introduced(tautology,[refl,[$fot(set_difference(A,B))]]) ).
cnf(refute_0_7,plain,
( ~ in(D,A)
| in(D,B)
| in(D,set_difference(A,B)) ),
inference(resolve,[$cnf( $equal(set_difference(A,B),set_difference(A,B)) )],[refute_0_6,refute_0_5]) ).
cnf(refute_0_8,plain,
( ~ in(skolemFOFtoCNF_C(X_74,B),X_74)
| in(skolemFOFtoCNF_C(X_74,B),X_75)
| in(skolemFOFtoCNF_C(X_74,B),set_difference(X_74,X_75)) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(X_74)),bind(B,$fot(X_75)),bind(D,$fot(skolemFOFtoCNF_C(X_74,B)))]]) ).
cnf(refute_0_9,plain,
( in(skolemFOFtoCNF_C(X_74,B),X_75)
| in(skolemFOFtoCNF_C(X_74,B),set_difference(X_74,X_75))
| subset(X_74,B) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C(X_74,B),X_74) )],[refute_0_3,refute_0_8]) ).
cnf(refute_0_10,plain,
( in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,X_315),set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))
| in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,X_315),skolemFOFtoCNF_B)
| subset(skolemFOFtoCNF_A_2,X_315) ),
inference(subst,[],[refute_0_9:[bind(B,$fot(X_315)),bind(X_74,$fot(skolemFOFtoCNF_A_2)),bind(X_75,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_11,plain,
set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = empty_set,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_12,plain,
( set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != empty_set
| ~ in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,X_315),set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))
| in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,X_315),empty_set) ),
introduced(tautology,[equality,[$cnf( in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,X_315),set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_13,plain,
( ~ in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,X_315),set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))
| in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,X_315),empty_set) ),
inference(resolve,[$cnf( $equal(set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),empty_set) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,X_315),empty_set)
| in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,X_315),skolemFOFtoCNF_B)
| subset(skolemFOFtoCNF_A_2,X_315) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,X_315),set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
( C != set_difference(A,B)
| ~ in(D,B)
| ~ in(D,C) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_16,plain,
( set_difference(A,B) != set_difference(A,B)
| ~ in(D,B)
| ~ in(D,set_difference(A,B)) ),
inference(subst,[],[refute_0_15:[bind(C,$fot(set_difference(A,B)))]]) ).
cnf(refute_0_17,plain,
( ~ in(D,B)
| ~ in(D,set_difference(A,B)) ),
inference(resolve,[$cnf( $equal(set_difference(A,B),set_difference(A,B)) )],[refute_0_6,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ in(X_20,X_19)
| ~ in(X_20,set_difference(empty_set,X_19)) ),
inference(subst,[],[refute_0_17:[bind(A,$fot(empty_set)),bind(B,$fot(X_19)),bind(D,$fot(X_20))]]) ).
cnf(refute_0_19,plain,
set_difference(empty_set,A) = empty_set,
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_20,plain,
set_difference(empty_set,X_19) = empty_set,
inference(subst,[],[refute_0_19:[bind(A,$fot(X_19))]]) ).
cnf(refute_0_21,plain,
( set_difference(empty_set,X_19) != empty_set
| ~ in(X_20,empty_set)
| in(X_20,set_difference(empty_set,X_19)) ),
introduced(tautology,[equality,[$cnf( ~ in(X_20,set_difference(empty_set,X_19)) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_22,plain,
( ~ in(X_20,empty_set)
| in(X_20,set_difference(empty_set,X_19)) ),
inference(resolve,[$cnf( $equal(set_difference(empty_set,X_19),empty_set) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ in(X_20,X_19)
| ~ in(X_20,empty_set) ),
inference(resolve,[$cnf( in(X_20,set_difference(empty_set,X_19)) )],[refute_0_22,refute_0_18]) ).
cnf(refute_0_24,plain,
~ in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,X_315),empty_set),
inference(subst,[],[refute_0_23:[bind(X_19,$fot(empty_set)),bind(X_20,$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,X_315)))]]) ).
cnf(refute_0_25,plain,
( in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,X_315),skolemFOFtoCNF_B)
| subset(skolemFOFtoCNF_A_2,X_315) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,X_315),empty_set) )],[refute_0_14,refute_0_24]) ).
cnf(refute_0_26,plain,
( in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_B)
| subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_25:[bind(X_315,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_27,plain,
subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_B) )],[refute_0_26,refute_0_1]) ).
cnf(refute_0_28,plain,
~ subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_29,plain,
$false,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) )],[refute_0_27,refute_0_28]) ).
fof(negate_1_0,plain,
~ ! [A,B] :
( subset(A,B)
=> set_difference(A,B) = empty_set ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
! [A,B,C] :
( C != set_difference(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
inference(canonicalize,[],[d4_xboole_0]) ).
fof(normalize_1_1,plain,
! [A,B,C] :
( C != set_difference(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
! [A,B,C,D] :
( ( C != set_difference(A,B)
| ~ in(D,B)
| ~ in(D,C) )
& ( C != set_difference(A,B)
| ~ in(D,C)
| in(D,A) )
& ( ~ in(skolemFOFtoCNF_D(A,B,C),B)
| C = set_difference(A,B)
| in(skolemFOFtoCNF_D(A,B,C),C) )
& ( C = set_difference(A,B)
| in(skolemFOFtoCNF_D(A,B,C),A)
| in(skolemFOFtoCNF_D(A,B,C),C) )
& ( C != set_difference(A,B)
| ~ in(D,A)
| in(D,B)
| in(D,C) )
& ( ~ in(skolemFOFtoCNF_D(A,B,C),A)
| ~ in(skolemFOFtoCNF_D(A,B,C),C)
| C = set_difference(A,B)
| in(skolemFOFtoCNF_D(A,B,C),B) ) ),
inference(clausify,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [A,B,C,D] :
( C != set_difference(A,B)
| ~ in(D,C)
| in(D,A) ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
! [A,B,C,D] :
( C != set_difference(A,B)
| ~ in(D,B)
| ~ in(D,C) ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_5,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(canonicalize,[],[t4_boole]) ).
fof(normalize_1_6,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(specialize,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [A,B] :
( A = B
| ? [C] :
( ~ in(C,A)
<=> in(C,B) ) ),
inference(canonicalize,[],[t2_tarski]) ).
fof(normalize_1_8,plain,
! [A,B] :
( A = B
| ? [C] :
( ~ in(C,A)
<=> in(C,B) ) ),
inference(specialize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [A,B] :
( ( ~ in(skolemFOFtoCNF_C_1(A,B),A)
| ~ in(skolemFOFtoCNF_C_1(A,B),B)
| A = B )
& ( A = B
| in(skolemFOFtoCNF_C_1(A,B),A)
| in(skolemFOFtoCNF_C_1(A,B),B) ) ),
inference(clausify,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
! [A,B] :
( A = B
| in(skolemFOFtoCNF_C_1(A,B),A)
| in(skolemFOFtoCNF_C_1(A,B),B) ),
inference(conjunct,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
? [A,B] :
( set_difference(A,B) != empty_set
& subset(A,B) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_12,plain,
( set_difference(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) != empty_set
& subset(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) ),
inference(skolemize,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
subset(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_1_12]) ).
fof(normalize_1_14,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(canonicalize,[],[d3_tarski]) ).
fof(normalize_1_15,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(specialize,[],[normalize_1_14]) ).
fof(normalize_1_16,plain,
! [A,B,C] :
( ( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) )
& ( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) )
& ( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ) ),
inference(clausify,[],[normalize_1_15]) ).
fof(normalize_1_17,plain,
! [A,B,C] :
( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ),
inference(conjunct,[],[normalize_1_16]) ).
fof(normalize_1_18,plain,
set_difference(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) != empty_set,
inference(conjunct,[],[normalize_1_12]) ).
cnf(refute_1_0,plain,
( C != set_difference(A,B)
| ~ in(D,C)
| in(D,A) ),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_1,plain,
( set_difference(A,B) != set_difference(A,B)
| ~ in(D,set_difference(A,B))
| in(D,A) ),
inference(subst,[],[refute_1_0:[bind(C,$fot(set_difference(A,B)))]]) ).
cnf(refute_1_2,plain,
set_difference(A,B) = set_difference(A,B),
introduced(tautology,[refl,[$fot(set_difference(A,B))]]) ).
cnf(refute_1_3,plain,
( ~ in(D,set_difference(A,B))
| in(D,A) ),
inference(resolve,[$cnf( $equal(set_difference(A,B),set_difference(A,B)) )],[refute_1_2,refute_1_1]) ).
cnf(refute_1_4,plain,
( ~ in(skolemFOFtoCNF_C_1(set_difference(A,B),empty_set),set_difference(A,B))
| in(skolemFOFtoCNF_C_1(set_difference(A,B),empty_set),A) ),
inference(subst,[],[refute_1_3:[bind(D,$fot(skolemFOFtoCNF_C_1(set_difference(A,B),empty_set)))]]) ).
cnf(refute_1_5,plain,
( C != set_difference(A,B)
| ~ in(D,B)
| ~ in(D,C) ),
inference(canonicalize,[],[normalize_1_4]) ).
cnf(refute_1_6,plain,
( set_difference(A,B) != set_difference(A,B)
| ~ in(D,B)
| ~ in(D,set_difference(A,B)) ),
inference(subst,[],[refute_1_5:[bind(C,$fot(set_difference(A,B)))]]) ).
cnf(refute_1_7,plain,
( ~ in(D,B)
| ~ in(D,set_difference(A,B)) ),
inference(resolve,[$cnf( $equal(set_difference(A,B),set_difference(A,B)) )],[refute_1_2,refute_1_6]) ).
cnf(refute_1_8,plain,
( ~ in(X_347,X_346)
| ~ in(X_347,set_difference(empty_set,X_346)) ),
inference(subst,[],[refute_1_7:[bind(A,$fot(empty_set)),bind(B,$fot(X_346)),bind(D,$fot(X_347))]]) ).
cnf(refute_1_9,plain,
set_difference(empty_set,A) = empty_set,
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_10,plain,
set_difference(empty_set,X_346) = empty_set,
inference(subst,[],[refute_1_9:[bind(A,$fot(X_346))]]) ).
cnf(refute_1_11,plain,
( set_difference(empty_set,X_346) != empty_set
| ~ in(X_347,empty_set)
| in(X_347,set_difference(empty_set,X_346)) ),
introduced(tautology,[equality,[$cnf( ~ in(X_347,set_difference(empty_set,X_346)) ),[1],$fot(empty_set)]]) ).
cnf(refute_1_12,plain,
( ~ in(X_347,empty_set)
| in(X_347,set_difference(empty_set,X_346)) ),
inference(resolve,[$cnf( $equal(set_difference(empty_set,X_346),empty_set) )],[refute_1_10,refute_1_11]) ).
cnf(refute_1_13,plain,
( ~ in(X_347,X_346)
| ~ in(X_347,empty_set) ),
inference(resolve,[$cnf( in(X_347,set_difference(empty_set,X_346)) )],[refute_1_12,refute_1_8]) ).
cnf(refute_1_14,plain,
~ in(skolemFOFtoCNF_C_1(X_354,empty_set),empty_set),
inference(subst,[],[refute_1_13:[bind(X_346,$fot(empty_set)),bind(X_347,$fot(skolemFOFtoCNF_C_1(X_354,empty_set)))]]) ).
cnf(refute_1_15,plain,
( A = B
| in(skolemFOFtoCNF_C_1(A,B),A)
| in(skolemFOFtoCNF_C_1(A,B),B) ),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_16,plain,
( X_354 = empty_set
| in(skolemFOFtoCNF_C_1(X_354,empty_set),X_354)
| in(skolemFOFtoCNF_C_1(X_354,empty_set),empty_set) ),
inference(subst,[],[refute_1_15:[bind(A,$fot(X_354)),bind(B,$fot(empty_set))]]) ).
cnf(refute_1_17,plain,
( X_354 = empty_set
| in(skolemFOFtoCNF_C_1(X_354,empty_set),X_354) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(X_354,empty_set),empty_set) )],[refute_1_16,refute_1_14]) ).
cnf(refute_1_18,plain,
( set_difference(A,B) = empty_set
| in(skolemFOFtoCNF_C_1(set_difference(A,B),empty_set),set_difference(A,B)) ),
inference(subst,[],[refute_1_17:[bind(X_354,$fot(set_difference(A,B)))]]) ).
cnf(refute_1_19,plain,
( set_difference(A,B) = empty_set
| in(skolemFOFtoCNF_C_1(set_difference(A,B),empty_set),A) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(set_difference(A,B),empty_set),set_difference(A,B)) )],[refute_1_18,refute_1_4]) ).
cnf(refute_1_20,plain,
( set_difference(skolemFOFtoCNF_A_3,B) = empty_set
| in(skolemFOFtoCNF_C_1(set_difference(skolemFOFtoCNF_A_3,B),empty_set),skolemFOFtoCNF_A_3) ),
inference(subst,[],[refute_1_19:[bind(A,$fot(skolemFOFtoCNF_A_3))]]) ).
cnf(refute_1_21,plain,
subset(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_1_13]) ).
cnf(refute_1_22,plain,
( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ),
inference(canonicalize,[],[normalize_1_17]) ).
cnf(refute_1_23,plain,
( ~ in(X_381,skolemFOFtoCNF_A_3)
| ~ subset(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)
| in(X_381,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_1_22:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(X_381))]]) ).
cnf(refute_1_24,plain,
( ~ in(X_381,skolemFOFtoCNF_A_3)
| in(X_381,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) )],[refute_1_21,refute_1_23]) ).
cnf(refute_1_25,plain,
( ~ in(skolemFOFtoCNF_C_1(set_difference(skolemFOFtoCNF_A_3,B),empty_set),skolemFOFtoCNF_A_3)
| in(skolemFOFtoCNF_C_1(set_difference(skolemFOFtoCNF_A_3,B),empty_set),skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_1_24:[bind(X_381,$fot(skolemFOFtoCNF_C_1(set_difference(skolemFOFtoCNF_A_3,B),empty_set)))]]) ).
cnf(refute_1_26,plain,
( set_difference(skolemFOFtoCNF_A_3,B) = empty_set
| in(skolemFOFtoCNF_C_1(set_difference(skolemFOFtoCNF_A_3,B),empty_set),skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(set_difference(skolemFOFtoCNF_A_3,B),empty_set),skolemFOFtoCNF_A_3) )],[refute_1_20,refute_1_25]) ).
cnf(refute_1_27,plain,
( set_difference(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) = empty_set
| in(skolemFOFtoCNF_C_1(set_difference(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),empty_set),skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_1_26:[bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_1_28,plain,
( ~ in(skolemFOFtoCNF_C_1(set_difference(A,B),empty_set),B)
| ~ in(skolemFOFtoCNF_C_1(set_difference(A,B),empty_set),set_difference(A,B)) ),
inference(subst,[],[refute_1_7:[bind(D,$fot(skolemFOFtoCNF_C_1(set_difference(A,B),empty_set)))]]) ).
cnf(refute_1_29,plain,
( ~ in(skolemFOFtoCNF_C_1(set_difference(A,B),empty_set),B)
| set_difference(A,B) = empty_set ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(set_difference(A,B),empty_set),set_difference(A,B)) )],[refute_1_18,refute_1_28]) ).
cnf(refute_1_30,plain,
( ~ in(skolemFOFtoCNF_C_1(set_difference(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),empty_set),skolemFOFtoCNF_B_1)
| set_difference(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) = empty_set ),
inference(subst,[],[refute_1_29:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_1_31,plain,
set_difference(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) = empty_set,
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(set_difference(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),empty_set),skolemFOFtoCNF_B_1) )],[refute_1_27,refute_1_30]) ).
cnf(refute_1_32,plain,
set_difference(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) != empty_set,
inference(canonicalize,[],[normalize_1_18]) ).
cnf(refute_1_33,plain,
$false,
inference(resolve,[$cnf( $equal(set_difference(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),empty_set) )],[refute_1_31,refute_1_32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU131+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n022.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 07:10:46 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.56/0.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.56/0.77
% 0.56/0.77 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.56/0.78
%------------------------------------------------------------------------------