TSTP Solution File: SET928+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET928+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 03:38:26 EDT 2022
% Result : Theorem 0.13s 0.36s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 97 ( 32 unt; 0 def)
% Number of atoms : 192 ( 79 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 197 ( 102 ~; 60 |; 21 &)
% ( 8 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 135 ( 4 sgn 77 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ).
fof(t55_zfmisc_1,axiom,
! [A,B,C] :
~ ( disjoint(unordered_pair(A,B),C)
& in(A,C) ) ).
fof(t57_zfmisc_1,axiom,
! [A,B,C] :
~ ( ~ in(A,B)
& ~ in(C,B)
& ~ disjoint(unordered_pair(A,C),B) ) ).
fof(t72_zfmisc_1,conjecture,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
<=> ( ~ in(A,C)
& ~ in(B,C) ) ) ).
fof(t83_xboole_1,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ) ).
fof(subgoal_0,plain,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
=> ~ in(A,C) ),
inference(strip,[],[t72_zfmisc_1]) ).
fof(subgoal_1,plain,
! [A,B,C] :
( ( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
& ~ in(A,C) )
=> ~ in(B,C) ),
inference(strip,[],[t72_zfmisc_1]) ).
fof(subgoal_2,plain,
! [A,B,C] :
( ( ~ in(A,C)
& ~ in(B,C) )
=> set_difference(unordered_pair(A,B),C) = unordered_pair(A,B) ),
inference(strip,[],[t72_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
=> ~ in(A,C) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( set_difference(A,B) != A
<=> ~ disjoint(A,B) ),
inference(canonicalize,[],[t83_xboole_1]) ).
fof(normalize_0_1,plain,
! [A,B] :
( set_difference(A,B) != A
<=> ~ disjoint(A,B) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] :
( ( set_difference(A,B) != A
| disjoint(A,B) )
& ( ~ disjoint(A,B)
| set_difference(A,B) = A ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( set_difference(A,B) != A
| disjoint(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [A,B,C] :
( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
& in(A,C) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
& in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,C] :
( ~ disjoint(unordered_pair(A,B),C)
| ~ in(A,C) ),
inference(canonicalize,[],[t55_zfmisc_1]) ).
fof(normalize_0_8,plain,
! [A,B,C] :
( ~ disjoint(unordered_pair(A,B),C)
| ~ in(A,C) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
( set_difference(A,B) != A
| disjoint(A,B) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| disjoint(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))),bind(B,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_2,plain,
set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) ),[0],$fot(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))]]) ).
cnf(refute_0_4,plain,
( unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| disjoint(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_4,refute_0_1]) ).
cnf(refute_0_6,plain,
unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
introduced(tautology,[refl,[$fot(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))]]) ).
cnf(refute_0_7,plain,
disjoint(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C),
inference(resolve,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_6,refute_0_5]) ).
cnf(refute_0_8,plain,
( ~ disjoint(unordered_pair(A,B),C)
| ~ in(A,C) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_9,plain,
( ~ disjoint(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C)
| ~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_10,plain,
~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
inference(resolve,[$cnf( disjoint(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_12,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) )],[refute_0_11,refute_0_10]) ).
fof(negate_1_0,plain,
~ ! [A,B,C] :
( ( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
& ~ in(A,C) )
=> ~ in(B,C) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
! [A,B] :
( set_difference(A,B) != A
<=> ~ disjoint(A,B) ),
inference(canonicalize,[],[t83_xboole_1]) ).
fof(normalize_1_1,plain,
! [A,B] :
( set_difference(A,B) != A
<=> ~ disjoint(A,B) ),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
! [A,B] :
( ( set_difference(A,B) != A
| disjoint(A,B) )
& ( ~ disjoint(A,B)
| set_difference(A,B) = A ) ),
inference(clausify,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [A,B] :
( set_difference(A,B) != A
| disjoint(A,B) ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
? [A,B,C] :
( ~ in(A,C)
& set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
& in(B,C) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_5,plain,
( ~ in(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1)
& set_difference(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1) = unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)
& in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) ),
inference(skolemize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
set_difference(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1) = unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [A,B,C] :
( ~ disjoint(unordered_pair(A,B),C)
| ~ in(A,C) ),
inference(canonicalize,[],[t55_zfmisc_1]) ).
fof(normalize_1_8,plain,
! [A,B,C] :
( ~ disjoint(unordered_pair(A,B),C)
| ~ in(A,C) ),
inference(specialize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(canonicalize,[],[commutativity_k2_tarski]) ).
fof(normalize_1_10,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(specialize,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(conjunct,[],[normalize_1_5]) ).
cnf(refute_1_0,plain,
( set_difference(A,B) != A
| disjoint(A,B) ),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_1,plain,
( set_difference(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1) != unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)
| disjoint(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_1_0:[bind(A,$fot(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1))),bind(B,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_1_2,plain,
set_difference(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1) = unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_3,plain,
( set_difference(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1) != unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)
| unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) != unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)
| set_difference(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1) = unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1),unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)) ),[0],$fot(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1))]]) ).
cnf(refute_1_4,plain,
( unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) != unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)
| set_difference(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1) = unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1),unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)) )],[refute_1_2,refute_1_3]) ).
cnf(refute_1_5,plain,
( unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) != unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)
| disjoint(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1) ),
inference(resolve,[$cnf( $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1),unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)) )],[refute_1_4,refute_1_1]) ).
cnf(refute_1_6,plain,
unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) = unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),
introduced(tautology,[refl,[$fot(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1))]]) ).
cnf(refute_1_7,plain,
disjoint(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)) )],[refute_1_6,refute_1_5]) ).
cnf(refute_1_8,plain,
( ~ disjoint(unordered_pair(A,B),C)
| ~ in(A,C) ),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_9,plain,
( ~ disjoint(unordered_pair(X_25,X_26),X_27)
| ~ in(X_25,X_27) ),
inference(subst,[],[refute_1_8:[bind(A,$fot(X_25)),bind(B,$fot(X_26)),bind(C,$fot(X_27))]]) ).
cnf(refute_1_10,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_11,plain,
unordered_pair(X_26,X_25) = unordered_pair(X_25,X_26),
inference(subst,[],[refute_1_10:[bind(A,$fot(X_26)),bind(B,$fot(X_25))]]) ).
cnf(refute_1_12,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_13,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_14,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_12,refute_1_13]) ).
cnf(refute_1_15,plain,
( unordered_pair(X_26,X_25) != unordered_pair(X_25,X_26)
| unordered_pair(X_25,X_26) = unordered_pair(X_26,X_25) ),
inference(subst,[],[refute_1_14:[bind(X,$fot(unordered_pair(X_26,X_25))),bind(Y,$fot(unordered_pair(X_25,X_26)))]]) ).
cnf(refute_1_16,plain,
unordered_pair(X_25,X_26) = unordered_pair(X_26,X_25),
inference(resolve,[$cnf( $equal(unordered_pair(X_26,X_25),unordered_pair(X_25,X_26)) )],[refute_1_11,refute_1_15]) ).
cnf(refute_1_17,plain,
( unordered_pair(X_25,X_26) != unordered_pair(X_26,X_25)
| ~ disjoint(unordered_pair(X_26,X_25),X_27)
| disjoint(unordered_pair(X_25,X_26),X_27) ),
introduced(tautology,[equality,[$cnf( ~ disjoint(unordered_pair(X_25,X_26),X_27) ),[0],$fot(unordered_pair(X_26,X_25))]]) ).
cnf(refute_1_18,plain,
( ~ disjoint(unordered_pair(X_26,X_25),X_27)
| disjoint(unordered_pair(X_25,X_26),X_27) ),
inference(resolve,[$cnf( $equal(unordered_pair(X_25,X_26),unordered_pair(X_26,X_25)) )],[refute_1_16,refute_1_17]) ).
cnf(refute_1_19,plain,
( ~ disjoint(unordered_pair(X_26,X_25),X_27)
| ~ in(X_25,X_27) ),
inference(resolve,[$cnf( disjoint(unordered_pair(X_25,X_26),X_27) )],[refute_1_18,refute_1_9]) ).
cnf(refute_1_20,plain,
( ~ disjoint(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1)
| ~ in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_1_19:[bind(X_25,$fot(skolemFOFtoCNF_B_1)),bind(X_26,$fot(skolemFOFtoCNF_A_3)),bind(X_27,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_1_21,plain,
~ in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( disjoint(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1) )],[refute_1_7,refute_1_20]) ).
cnf(refute_1_22,plain,
in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_23,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) )],[refute_1_22,refute_1_21]) ).
fof(negate_2_0,plain,
~ ! [A,B,C] :
( ( ~ in(A,C)
& ~ in(B,C) )
=> set_difference(unordered_pair(A,B),C) = unordered_pair(A,B) ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
? [A,B,C] :
( set_difference(unordered_pair(A,B),C) != unordered_pair(A,B)
& ~ in(A,C)
& ~ in(B,C) ),
inference(canonicalize,[],[negate_2_0]) ).
fof(normalize_2_1,plain,
( set_difference(unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_2) != unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2)
& ~ in(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_2)
& ~ in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_2) ),
inference(skolemize,[],[normalize_2_0]) ).
fof(normalize_2_2,plain,
set_difference(unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_2) != unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),
inference(conjunct,[],[normalize_2_1]) ).
fof(normalize_2_3,plain,
! [A,B] :
( set_difference(A,B) != A
<=> ~ disjoint(A,B) ),
inference(canonicalize,[],[t83_xboole_1]) ).
fof(normalize_2_4,plain,
! [A,B] :
( set_difference(A,B) != A
<=> ~ disjoint(A,B) ),
inference(specialize,[],[normalize_2_3]) ).
fof(normalize_2_5,plain,
! [A,B] :
( ( set_difference(A,B) != A
| disjoint(A,B) )
& ( ~ disjoint(A,B)
| set_difference(A,B) = A ) ),
inference(clausify,[],[normalize_2_4]) ).
fof(normalize_2_6,plain,
! [A,B] :
( ~ disjoint(A,B)
| set_difference(A,B) = A ),
inference(conjunct,[],[normalize_2_5]) ).
fof(normalize_2_7,plain,
! [A,B,C] :
( disjoint(unordered_pair(A,C),B)
| in(A,B)
| in(C,B) ),
inference(canonicalize,[],[t57_zfmisc_1]) ).
fof(normalize_2_8,plain,
! [A,B,C] :
( disjoint(unordered_pair(A,C),B)
| in(A,B)
| in(C,B) ),
inference(specialize,[],[normalize_2_7]) ).
fof(normalize_2_9,plain,
~ in(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_2),
inference(conjunct,[],[normalize_2_1]) ).
fof(normalize_2_10,plain,
~ in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_2),
inference(conjunct,[],[normalize_2_1]) ).
cnf(refute_2_0,plain,
set_difference(unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_2) != unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),
inference(canonicalize,[],[normalize_2_2]) ).
cnf(refute_2_1,plain,
( ~ disjoint(A,B)
| set_difference(A,B) = A ),
inference(canonicalize,[],[normalize_2_6]) ).
cnf(refute_2_2,plain,
( ~ disjoint(unordered_pair(X_48,X_50),X_49)
| set_difference(unordered_pair(X_48,X_50),X_49) = unordered_pair(X_48,X_50) ),
inference(subst,[],[refute_2_1:[bind(A,$fot(unordered_pair(X_48,X_50))),bind(B,$fot(X_49))]]) ).
cnf(refute_2_3,plain,
( disjoint(unordered_pair(A,C),B)
| in(A,B)
| in(C,B) ),
inference(canonicalize,[],[normalize_2_8]) ).
cnf(refute_2_4,plain,
( disjoint(unordered_pair(X_48,X_50),X_49)
| in(X_48,X_49)
| in(X_50,X_49) ),
inference(subst,[],[refute_2_3:[bind(A,$fot(X_48)),bind(B,$fot(X_49)),bind(C,$fot(X_50))]]) ).
cnf(refute_2_5,plain,
( set_difference(unordered_pair(X_48,X_50),X_49) = unordered_pair(X_48,X_50)
| in(X_48,X_49)
| in(X_50,X_49) ),
inference(resolve,[$cnf( disjoint(unordered_pair(X_48,X_50),X_49) )],[refute_2_4,refute_2_2]) ).
cnf(refute_2_6,plain,
( set_difference(unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_2) = unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2)
| in(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_2)
| in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_2) ),
inference(subst,[],[refute_2_5:[bind(X_48,$fot(skolemFOFtoCNF_A_4)),bind(X_49,$fot(skolemFOFtoCNF_C_2)),bind(X_50,$fot(skolemFOFtoCNF_B_2))]]) ).
cnf(refute_2_7,plain,
( set_difference(unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_2) != unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2)
| unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2) != unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2)
| set_difference(unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_2) = unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2) ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_2),unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2)) ),[0],$fot(unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2))]]) ).
cnf(refute_2_8,plain,
( unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2) != unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2)
| set_difference(unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_2) = unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2)
| in(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_2)
| in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_2) ),
inference(resolve,[$cnf( $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_2),unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2)) )],[refute_2_6,refute_2_7]) ).
cnf(refute_2_9,plain,
( unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2) != unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2)
| in(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_2)
| in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_2) ),
inference(resolve,[$cnf( $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_2),unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2)) )],[refute_2_8,refute_2_0]) ).
cnf(refute_2_10,plain,
unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2) = unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),
introduced(tautology,[refl,[$fot(unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2))]]) ).
cnf(refute_2_11,plain,
( in(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_2)
| in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_2) ),
inference(resolve,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2)) )],[refute_2_10,refute_2_9]) ).
cnf(refute_2_12,plain,
~ in(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_2),
inference(canonicalize,[],[normalize_2_9]) ).
cnf(refute_2_13,plain,
in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_2),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_2) )],[refute_2_11,refute_2_12]) ).
cnf(refute_2_14,plain,
~ in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_2),
inference(canonicalize,[],[normalize_2_10]) ).
cnf(refute_2_15,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_2) )],[refute_2_13,refute_2_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET928+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n020.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 Jul 10 18:49:13 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36
% 0.13/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.37
%------------------------------------------------------------------------------